The Quranic Verses about Math and Is It Discovered or Invented?

May 6, 2024Zia H Shah

Epigraph:

هُوَ الَّذِي جَعَلَ الشَّمْسَ ضِيَاءً وَالْقَمَرَ نُورًا وَقَدَّرَهُ مَنَازِلَ لِتَعْلَمُوا عَدَدَ السِّنِينَ وَالْحِسَابَ ۚ مَا خَلَقَ اللَّهُ ذَٰلِكَ إِلَّا بِالْحَقِّ ۚ يُفَصِّلُ الْآيَاتِ لِقَوْمٍ يَعْلَمُونَ

إِنَّ فِي اخْتِلَافِ اللَّيْلِ وَالنَّهَارِ وَمَا خَلَقَ اللَّهُ فِي السَّمَاوَاتِ وَالْأَرْضِ لَآيَاتٍ لِّقَوْمٍ يَتَّقُونَ

Allah it is Who made the sun radiate a brilliant light and the moon reflect a luster, and ordained for it stages, that you might know the number of years, reckoning of time and mathematics. Allah has not created this but in truth. He details the Signs for a people who have knowledge. Indeed, in the alternation of night and day, and in all that Allah has created in the heavens and the earth there are Signs for a God-fearing people. (Al Quran 10:5-6)

وَجَعَلْنَا اللَّيْلَ وَالنَّهَارَ آيَتَيْنِ ۖ فَمَحَوْنَا آيَةَ اللَّيْلِ وَجَعَلْنَا آيَةَ النَّهَارِ مُبْصِرَةً لِّتَبْتَغُوا فَضْلًا مِّن رَّبِّكُمْ وَلِتَعْلَمُوا عَدَدَ السِّنِينَ وَالْحِسَابَ ۚ وَكُلَّ شَيْءٍ فَصَّلْنَاهُ تَفْصِيلًا

And We have made the night and the day two Signs, and the Sign of night We have made dark, and the Sign of day We have made sight giving, that you may seek bounty from your Lord, and that you may know the computation of years, reckoning of time and mathematics. And everything We have explained with a detailed explanation. (Al Quran 17:12)

Indispensability Arguments in the Philosophy of Mathematics

Source: Stanford Encyclopedia of Philosophy

First published Mon Dec 21, 1998; substantive revision Mon Mar 6, 2023

One of the most intriguing features of mathematics is its applicability to empirical science. Every branch of science draws upon large and often diverse portions of mathematics, from the use of Hilbert spaces in quantum mechanics to the use of differential geometry in general relativity. It’s not just the physical sciences that avail themselves of the services of mathematics either. Biology, for instance, makes extensive use of difference equations and statistics. The roles mathematics plays in these theories is also varied. Not only does mathematics help with empirical predictions, it allows elegant and economical statement of many theories. Indeed, so important is the language of mathematics to science, that it is hard to imagine how theories such as quantum mechanics and general relativity could even be stated without employing a substantial amount of mathematics.

From the rather remarkable but seemingly uncontroversial fact that mathematics is indispensable to science, some philosophers have drawn serious metaphysical conclusions. In particular, Quine (1976; 1980a; 1980b; 1981a; 1981c) and Putnam (1979a; 1979b) have argued that the indispensability of mathematics to empirical science gives us good reason to believe in the existence of mathematical entities. According to this line of argument, reference to (or quantification over) mathematical entities such as sets, numbers, functions and such is indispensable to our best scientific theories, and so we ought to be committed to the existence of these mathematical entities. To do otherwise is to be guilty of what Putnam has called “intellectual dishonesty” (Putnam 1979b, p. 347). Moreover, mathematical entities are seen to be on an epistemic par with the other theoretical entities of science, since belief in the existence of the former is justified by the same evidence that confirms the theory as a whole (and hence belief in the latter). This argument is known as the Quine-Putnam indispensability argument for mathematical realism. There are other indispensability arguments, but this one is by far the most influential, and so in what follows, we’ll mostly focus on it.

In general, an indispensability argument is an argument that purports to establish the truth of some claim based on the indispensability of the claim in question for certain purposes (to be specified by the particular argument). For example, if explanation is specified as the purpose, then we have an explanatory indispensability argument. Thus we see that inference to the best explanation is a special case of an indispensability argument. See the introduction of Field (1989, pp. 14–20) for a nice discussion of indispensability arguments and inference to the best explanation. See also Maddy (1992) and Resnik (1995a) for variations on the Quine-Putnam version of the argument. We should add that although the version of the argument presented here is generally attributed to Quine and Putnam, it differs in a number of ways from the arguments advanced by either Quine or Putnam.^[1]

1. Spelling Out the Quine-Putnam Indispensability Argument

The Quine-Putnam indispensability argument has attracted a great deal of attention, in part because many see it as the best argument for mathematical realism (or platonism). Thus anti-realists about mathematical entities (or nominalists) need to identify where the Quine-Putnam argument goes wrong. Many platonists, on the other hand, rely very heavily on this argument to justify their belief in mathematical entities. The argument places nominalists who wish to be realist about other theoretical entities of science (quarks, electrons, black holes and such) in a particularly difficult position. For typically they accept something quite like the Quine-Putnam argument^[2]) as justification for realism about quarks and black holes. (This is what Quine (1980b, p. 45) calls holding a “double standard” with regard to ontology.)

For future reference, we’ll state the Quine-Putnam indispensability argument in the following explicit form:

(P1) We ought to have ontological commitment to all and only the entities that are indispensable to our best scientific theories.

(P2) Mathematical entities are indispensable to our best scientific theories.

(C) We ought to have ontological commitment to mathematical entities.

Thus formulated, the argument is valid. This forces the focus onto the two premises. In particular, a couple of important questions naturally arise. The first concerns how we are to understand the claim that mathematics is indispensable. We address this in the next section. The second question concerns the first premise. It is nowhere near as self-evident as the second and it clearly needs some defense. We’ll discuss its defense in the following section. We’ll then present some of the more important objections to the argument, before considering the Quine-Putnam argument’s role in the larger scheme of things — where it stands in relation to other influential arguments for and against mathematical realism.

2. What is it to be Indispensable?

The question of how we should understand ‘indispensability’ in the present context is crucial to the Quine-Putnam argument, and yet it has received surprisingly little attention. Quine actually speaks in terms of the entities quantified over in the canonical form of our best scientific theories rather than indispensability. Still, the debate continues in terms of indispensability, so we would be well served to clarify this term.

The first thing to note is that ‘dispensability’ is not the same as ‘eliminability’. If this were not so, every entity would be dispensable (due to a theorem of Craig).^[3] What we require for an entity to be ‘dispensable’ is for it to be eliminable and that the theory resulting from the entity’s elimination be an attractive theory. (Perhaps, even stronger, we require that the resulting theory be more attractive than the original.) We will need to spell out what counts as an attractive theory but for this we can appeal to the standard desiderata for good scientific theories: empirical success; unificatory power; simplicity; explanatory power; fertility and so on. Of course there will be debate over what desiderata are appropriate and over their relative weightings, but such issues need to be addressed and resolved independently of issues of indispensability. (See Burgess (1983) and Colyvan (1999) for more on these issues.)

These issues naturally prompt the question of how much mathematics is indispensable (and hence how much mathematics carries ontological commitment). It seems that the indispensability argument only justifies belief in enough mathematics to serve the needs of science. Thus we find Putnam speaking of “the set theoretic ‘needs’ of physics” (Putnam 1979b, p. 346) and Quine claiming that the higher reaches of set theory are “mathematical recreation … without ontological rights” (Quine 1986, p. 400) since they do not find physical applications. One could take a less restrictive line and claim that the higher reaches of set theory, although without physical applications, do carry ontological commitment by virtue of the fact that they have applications in other parts of mathematics. So long as the chain of applications eventually “bottoms out” in physical science, we could rightfully claim that the whole chain carries ontological commitment. Quine himself justifies some transfinite set theory along these lines (Quine 1984, p. 788), but he sees no reason to go beyond the constructible sets (Quine 1986, p. 400). His reasons for this restriction, however, have little to do with the indispensability argument and so supporters of this argument need not side with Quine on this issue.

3. Naturalism and Holism

Although both premises of the Quine-Putnam indispensability argument have been questioned, it’s the first premise that is most obviously in need of support. This support comes from the doctrines of naturalism and holism.

Following Quine, naturalism is usually taken to be the philosophical doctrine that there is no first philosophy and that the philosophical enterprise is continuous with the scientific enterprise (Quine 1981b). By this Quine means that philosophy is neither prior to nor privileged over science. What is more, science, thus construed (i.e. with philosophy as a continuous part) is taken to be the complete story of the world. This doctrine arises out of a deep respect for scientific methodology and an acknowledgment of the undeniable success of this methodology as a way of answering fundamental questions about all nature of things. As Quine suggests, its source lies in “unregenerate realism, the robust state of mind of the natural scientist who has never felt any qualms beyond the negotiable uncertainties internal to science” (Quine 1981b, p. 72). For the metaphysician this means looking to our best scientific theories to determine what exists, or, perhaps more accurately, what we ought to believe to exist. In short, naturalism rules out unscientific ways of determining what exists. For example, naturalism rules out believing in the transmigration of souls for mystical reasons. Naturalism would not, however, rule out the transmigration of souls if our best scientific theories were to require the truth of this doctrine.^[4]

Naturalism, then, gives us a reason for believing in the entities in our best scientific theories and no other entities. Depending on exactly how you conceive of naturalism, it may or may not tell you whether to believe in all the entities of your best scientific theories. We take it that naturalism does give us some reason to believe in all such entities, but that this is defeasible. This is where holism comes to the fore: in particular, confirmational holism.

Confirmational holism is the view that theories are confirmed or disconfirmed as wholes (Quine 1980b, p. 41). So, if a theory is confirmed by empirical findings, the whole theory is confirmed. In particular, whatever mathematics is made use of in the theory is also confirmed (Quine 1976, pp. 120–122). Furthermore, it is the same evidence that is appealed to in justifying belief in the mathematical components of the theory that is appealed to in justifying the empirical portion of the theory (if indeed the empirical can be separated from the mathematical at all). Naturalism and holism taken together then justify P1. Roughly, naturalism gives us the “only” and holism gives us the “all” in P1.

It is worth noting that in Quine’s writings there are at least two holist themes. The first is the confirmational holism discussed above (often called the Quine-Duhem thesis). The other is semantic holism which is the view that the unit of meaning is not the single sentence, but systems of sentences (and in some extreme cases the whole of language). This latter holism is closely related to Quine’s well-known denial of the analytic-synthetic distinction (Quine 1980b) and his equally famous indeterminacy of translation thesis (Quine 1960). Although for Quine, semantic holism and confirmational holism are closely related, there is good reason to distinguish them, since the former is generally thought to be highly controversial while the latter is considered relatively uncontroversial.

Why this is important to the present debate is that Quine explicitly invokes the controversial semantic holism in support of the indispensability argument (Quine 1980b, pp. 45–46). Most commentators, however, are of the view that only confirmational holism is required to make the indispensability argument fly (see, for example, Colyvan (1998a); Field (1989, pp. 14–20); Hellman (1999); Resnik (1995a; 1997); Maddy (1992)) and my presentation here follows that accepted wisdom. It should be kept in mind, however, that while the argument, thus construed, is Quinean in flavor it is not, strictly speaking, Quine’s argument.

4. Objections

There have been many objections to the indispensability argument, including Charles Parsons’ (1980) concern that the obviousness of basic mathematical statements is left unaccounted for by the Quinean picture and Philip Kitcher’s (1984, pp. 104–105) worry that the indispensability argument doesn’t explain why mathematics is indispensable to science. The objections that have received the most attention, however, are those due to Hartry Field, Penelope Maddy and Elliott Sober. In particular, Field’s nominalisation program has dominated recent discussions of the ontology of mathematics.

Field (2016) presents a case for denying the second premise of the Quine-Putnam argument. That is, he suggests that despite appearances mathematics is not indispensable to science. There are two parts to Field’s project. The first is to argue that mathematical theories don’t have to be true to be useful in applications, they need merely to be conservative. (This is, roughly, that if a mathematical theory is added to a nominalist scientific theory, no nominalist consequences follow that wouldn’t follow from the nominalist scientific theory alone.) This explains why mathematics can be used in science but it does not explain why it is used. The latter is due to the fact that mathematics makes calculation and statement of various theories much simpler. Thus, for Field, the utility of mathematics is merely pragmatic — mathematics is not indispensable after all.

The second part of Field’s program is to demonstrate that our best scientific theories can be suitably nominalised. That is, he attempts to show that we could do without quantification over mathematical entities and that what we would be left with would be reasonably attractive theories. To this end he is content to nominalise a large fragment of Newtonian gravitational theory. Although this is a far cry from showing that all our current best scientific theories can be nominalised, it is certainly not trivial. The hope is that once one sees how the elimination of reference to mathematical entities can be achieved for a typical physical theory, it will seem plausible that the project could be completed for the rest of science.^[5]

There has been a great deal of debate over the likelihood of the success of Field’s program but few have doubted its significance. Recently, however, Penelope Maddy, has pointed out that if P1 is false, Field’s project may turn out to be irrelevant to the realism/anti-realism debate in mathematics.

Maddy presents some serious objections to the first premise of the indispensability argument (Maddy 1992; 1995; 1997). In particular, she suggests that we ought not have ontological commitment to all the entities indispensable to our best scientific theories. Her objections draw attention to problems of reconciling naturalism with confirmational holism. In particular, she points out how a holistic view of scientific theories has problems explaining the legitimacy of certain aspects of scientific and mathematical practices. Practices which, presumably, ought to be legitimate given the high regard for scientific practice that naturalism recommends. It is important to appreciate that her objections, for the most part, are concerned with methodological consequences of accepting the Quinean doctrines of naturalism and holism — the doctrines used to support the first premise. The first premise is thus called into question by undermining its support.

Maddy’s first objection to the indispensability argument is that the actual attitudes of working scientists towards the components of well-confirmed theories vary from belief, through tolerance, to outright rejection (Maddy 1992, p. 280). The point is that naturalism counsels us to respect the methods of working scientists, and yet holism is apparently telling us that working scientists ought not have such differential support to the entities in their theories. Maddy suggests that we should side with naturalism and not holism here. Thus we should endorse the attitudes of working scientists who apparently do not believe in all the entities posited by our best theories. We should thus reject P1.

The next problem follows from the first. Once one rejects the picture of scientific theories as homogeneous units, the question arises whether the mathematical portions of theories fall within the true elements of the confirmed theories or within the idealized elements. Maddy suggests the latter. Her reason for this is that scientists themselves do not seem to take the indispensable application of a mathematical theory to be an indication of the truth of the mathematics in question. For example, the false assumption that water is infinitely deep is often invoked in the analysis of water waves, or the assumption that matter is continuous is commonly made in fluid dynamics (Maddy 1992, pp. 281–282). Such cases indicate that scientists will invoke whatever mathematics is required to get the job done, without regard to the truth of the mathematical theory in question (Maddy 1995, p. 255). Again it seems that confirmational holism is in conflict with actual scientific practice, and hence with naturalism. And again Maddy sides with naturalism. (See also Parsons (1983) for some related worries about Quinean holism.) The point here is that if naturalism counsels us to side with the attitudes of working scientists on such matters, then it seems that we ought not take the indispensability of some mathematical theory in a physical application as an indication of the truth of the mathematical theory. Furthermore, since we have no reason to believe that the mathematical theory in question is true, we have no reason to believe that the entities posited by the (mathematical) theory are real. So once again we ought to reject P1.

Maddy’s third objection is that it is hard to make sense of what working mathematicians are doing when they try to settle independent questions. These are questions, that are independent of the standard axioms of set theory — the ZFC axioms.^[6] In order to settle some of these questions, new axiom candidates have been proposed to supplement ZFC, and arguments have been advanced in support of these candidates. The problem is that the arguments advanced seem to have nothing to do with applications in physical science: they are typically intra-mathematical arguments. According to indispensability theory, however, the new axioms should be assessed on how well they cohere with our current best scientific theories. That is, set theorists should be assessing the new axiom candidates with one eye on the latest developments in physics. Given that set theorists do not do this, confirmational holism again seems to be advocating a revision of standard mathematical practice, and this too, claims Maddy, is at odds with naturalism (Maddy 1992, pp. 286–289).

Although Maddy does not formulate this objection in a way that directly conflicts with P1 it certainly illustrates a tension between naturalism and confirmational holism.^[7] And since both these are required to support P1, the objection indirectly casts doubt on P1. Maddy, however, endorses naturalism and so takes the objection to demonstrate that confirmational holism is false. We’ll leave the discussion of the impact the rejection of confirmational holism would have on the indispensability argument until after we outline Sober’s objection, because Sober arrives at much the same conclusion.

Elliott Sober’s objection is closely related to Maddy’s second and third objections. Sober (1993) takes issue with the claim that mathematical theories share the empirical support accrued by our best scientific theories. In essence, he argues that mathematical theories are not being tested in the same way as the clearly empirical theories of science. He points out that hypotheses are confirmed relative to competing hypotheses. Thus if mathematics is confirmed along with our best empirical hypotheses (as indispensability theory claims), there must be mathematics-free competitors. But Sober points out that all scientific theories employ a common mathematical core. Thus, since there are no competing hypotheses, it is a mistake to think that mathematics receives confirmational support from empirical evidence in the way other scientific hypotheses do.

This in itself does not constitute an objection to P1 of the indispensability argument, as Sober is quick to point out (Sober 1993, p. 53), although it does constitute an objection to Quine’s overall view that mathematics is part of empirical science. As with Maddy’s third objection, it gives us some cause to reject confirmational holism. The impact of these objections on P1 depends on how crucial you think confirmational holism is to that premise. Certainly much of the intuitive appeal of P1 is eroded if confirmational holism is rejected. In any case, to subscribe to the conclusion of the indispensability argument in the face of Sober’s or Maddy’s objections is to hold the position that it’s permissible at least to have ontological commitment to entities that receive no empirical support. This, if not outright untenable, is certainly not in the spirit of the original Quine-Putnam argument.

5. Explanatory Versions of the Argument

The arguments against holism from Maddy and Sober resulted in a reevaluation of the indispensability argument. If, contra Quine, scientists do not accept all the entities of our best scientific theories, where does this leave us? We need criteria for when to treat posits realistically. Here is where the debate over the indispensability argument took an interesting turn. Scientific realists, at least, accept those posits of our best scientific theories that contribute to scientific explanations. According to this line of thought, we ought to believe in electrons, say, not because they are indispensable to our best scientific theories but because they are indispensable in a very specific way: they are explanatorily indispensable. If mathematics could be shown to contribute to scientific explanations in this way, mathematical realism would again be on par with scientific realism. Indeed, this is the focus of most of the contemporary discussion on the indispensability argument. The central question is: does mathematics contribute to scientific explanations and if so, does it do it in the right kind of way.

One example of how mathematics might be thought to be explanatory is found in the periodic cicada case (Yoshimura 1997 and Baker 2005). North American Magicicadas are found to have life cycles of 13 or 17 years. It is proposed by some biologists that there is an evolutionary advantage in having such prime-numbered life cycles. Prime-numbered life cycles mean that the Magicicadas avoid competition, potential predators, and hybridisation. The idea is quite simple: because prime numbers have no non-trivial factors, there are very few other life cycles that can be synchronised with a prime-numbered life cycle. The Magicicadas thus have an effective avoidance strategy that, under certain conditions, will be selected for. While the explanation being advanced involves biology (e.g. evolutionary theory, theories of competition and predation), a crucial part of the explanation comes from number theory, namely, the fundamental fact about prime numbers. Baker (2005) argues that this is a genuinely mathematical explanation of a biological fact. There are other examples of alleged mathematical explanations in the literature but this remains the most widely discussed and is something of a poster child for mathematical explanation.

Questions about this case focus on whether the mathematics is really contributing to the explanation (or whether it is merely standing in for the biological facts and it is these that really do the explaining), whether the alleged explanation is an explanation at all, and whether the mathematics in question is involved in the explanation in the right kind of way. Finally, it is worth mentioning that although the recent interest in mathematical explanation arose out of debates over the indispensability argument, the status of mathematical explanations in the empirical sciences has also attracted interest in its own right. Moreover, such explanations (sometimes called “extra-mathematical explanations”) lead one very naturally to think about explanations of mathematical facts by appeal to further mathematical facts (sometimes called “intra-mathematical explanation”). These two kinds of mathematical explanation are related, of course. If, for example, some theorem of mathematics has its explanation rest in an explanatory proof, then any applications of that theorem in the empirical realm would give rise to a prima facie case that the full explanation of the empirical phenomenon in question involves the intra-mathematical explanation of the theorem. For these and other reasons, both kinds of mathematical explanation have attracted a great deal of interest from philosophers of mathematics and philosophers of science in recent years.

6. Conclusion

It is not clear how damaging the above criticisms are to the indispensability argument and whether the explanatory version of the argument survives. Indeed, the debate is very much alive, with many recent articles devoted to the topic. (See bibliography notes below.) Closely related to this debate is the question of whether there are any other decent arguments for platonism. If, as some believe, the indispensability argument is the only argument for platonism worthy of consideration, then if it fails, platonism in the philosophy of mathematics seems bankrupt. Of relevance then is the status of other arguments for and against mathematical realism. In any case, it is worth noting that the indispensability argument is one of a small number of arguments that have dominated discussions of the ontology of mathematics. It is therefore important that this argument not be viewed in isolation.

The two most important arguments against mathematical realism are the epistemological problem for platonism — how do we come by knowledge of causally inert mathematical entities? (Benacerraf 1983b) — and the indeterminacy problem for the reduction of numbers to sets — if numbers are sets, which sets are they (Benacerraf 1983a)? Apart from the indispensability argument, the other major argument for mathematical realism appeals to a desire for a uniform semantics for all discourse: mathematical and non-mathematical alike (Benacerraf 1983b). Mathematical realism, of course, meets this challenge easily, since it explains the truth of mathematical statements in exactly the same way as in other domains.^[8] It is not so clear, however, how nominalism can provide a uniform semantics.

Finally, it is worth stressing that even if the indispensability argument is the only good argument for platonism, the failure of this argument does not necessarily authorize nominalism, for the latter too may be without support. It does seem fair to say, however, that if the objections to the indispensability argument are sustained then one of the most important arguments for platonism is undermined. This would leave platonism on rather shaky ground.

Bibliography

Although the indispensability argument is to be found in many places in Quine’s writings (including 1976; 1980a; 1980b; 1981a; 1981c), the locus classicus is Putnam’s short monograph Philosophy of Logic (included as a chapter of the second edition of the third volume of his collected papers (Putnam, 1979b)). See also Putnam (1979a) and the introduction of Field (1989), which has an excellent outline of the argument. Colyvan (2001) presents a sustained defence of the argument.

See Chihara (1973), and Field (1989; 2016) for attacks on the second premise and Colyvan (1999; 2001), Lyon and Colyvan (2008), Maddy (1990), Malament (1982), Resnik (1985), Shapiro (1983) and Urquhart (1990) for criticisms of Field’s program. See the preface to the second edition of Field 2016 for a good retrospective on these debates. For a fairly comprehensive look at nominalist strategies in the philosophy of mathematics (including an excellent discussion of Field’s program), see Burgess and Rosen (1997), while Feferman (1993) questions the amount of mathematics required for empirical science. See Azzouni (1997; 2004; 2012), Balaguer (1996b; 1998), Bueno (2012), Leng (2002; 2010; 2012), Liggins (2012), Maddy (1992; 1995; 1997), Melia (2000; 2002), Peressini (1997), Pincock (2004), Sober (1993), Vineberg (1996) and Yablo (1998; 2005; 2012) for attacks on the first premise. Baker (2001; 2005; 2012), Bangu (2012), Colyvan (1998a; 2001; 2002; 2007; 2010; 2012), Hellman (1999) and Resnik (1995a; 1997) reply to some of these objections.

For variants of the Quinean indispensability argument see Maddy (1992) and Resnik (1995a).

There has been a great deal of recent literature on the explanatory version of the indispensability argument. Early presentations of such an argument can be found in Colyvan (1998b; 2002), and most explicitly in Baker (2005), although this work was anticipated by Steiner (1978a; 1978b) on mathematical explanation and Smart on geometric explanation (1990). Some of the key articles on the explanatory version of the argument include Baker (2005; 2009; 2012; 2017; 2021), Bangu (2008; 2013), Baron (2014), Batterman (2010), Bueno and French (2012), Colyvan (2002; 2010; 2012; 2018), Lyon (2012), Rizza (2011), Saatsi (2011; 2016) and Yablo (2012).

Arising out of this debate over the role of mathematical explanation in indispensability arguments, has been a renewed interest in mathematical explanation for its own sake. This includes work on reconciling mathematical explanations in science with other forms of scientific explanation as well as investigating explanation within mathematics itself. Some of this work includes: Baron (2016), Baron et al. (2017; 2020), Colyvan et al. (2018), Lange (2017), Mancosu (2008), and Pincock (2011).

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–––, 2001, The Indispensability of Mathematics, New York: Oxford University Press.
–––, 2002, “Mathematics and Aesthetic Considerations in Science”, Mind, 111(441): 69–74.
–––, 2007, “Mathematical Recreation Versus Mathematical Knowledge”, in M. Leng, A. Paseau, and M. Potter (eds.), Mathematical Knowledge, Oxford: Oxford University Press, pp. 109–122.
–––, 2010, “There is No Easy Road to Nominalism”, Mind, 119(474): 285–306.
–––, 2012, “Road Work Ahead: Heavy Machinery on the Easy Road”, Mind, 121(484): 1031–1046.
–––, 2018, “The Ins and Outs of Mathematical Explanation”, Mathematical Intelligencer, 40(4): 26–9.
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Feferman, S., 1993, “Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics”, Proceedings of the Philosophy of Science Association, 2: 442–455.
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Liggins, D., 2012, “Weaseling and the Content of Science”, Mind, 121(484): 997–1005.
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–––, 1992, “Indispensability and Practice”, Journal of Philosophy, 89(6): 275–289.
–––, 1995, “Naturalism and Ontology”, Philosophia Mathematica, 3(3): 248–270.
–––, 1997, Naturalism in Mathematics, Oxford: Clarendon Press.
–––, 1998, “How to be a Naturalist about Mathematics”, in H.G. Dales and G. Oliveri (eds.), Truth in Mathematics, Oxford: Clarendon, pp. 161–180.
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Acknowledgments

The author would like to thank Hilary Putnam, Helen Regan, Angela Rosier and Edward Zalta for comments on earlier versions of this entry.

What are abstract objects and do they make God necessary?

May 5, 2024May 5, 2024Zia H Shah

Epigraph:

بَدِيعُ السَّمَاوَاتِ وَالْأَرْضِ ۖ وَإِذَا قَضَىٰ أَمْرًا فَإِنَّمَا يَقُولُ لَهُ كُن فَيَكُونُ

He is the Originator of the heavens and the earth, and when He decrees something, He says only, ‘Be,’ and it is. (Al Quran 2:117)

Have they been created from nothing, or are they their own creators? Have they created the heavens and the earth? In truth they put no faith in anything. (Al Quran 52:35-36)

This article is not written by AI or a robot but by Zia H Shah MD

In this article I have borrowed extensively from Encyclopedia Britannica and Stanford Encyclopedia of Philosophy.

Different numbers, which are infinite and all the mathematical formulas and equations are among abstract objects.

One doesn’t go far in the study of what there is without encountering the view that every entity falls into one of two categories: concrete or abstract. The distinction is supposed to be of fundamental significance for metaphysics (especially for ontology), epistemology, and the philosophy of the formal sciences (especially for the philosophy of mathematics); it is also relevant for analysis in the philosophy of language, the philosophy of mind, and the philosophy of the empirical sciences.

The abstract/concrete distinction has a curious status in contemporary philosophy. It is widely agreed that the ontological distinction is of fundamental importance, but as yet, there is no standard account of how it should be drawn. There is a consensus about how to classify certain paradigm cases. For example, it is usually acknowledged that numbers and the other objects of pure mathematics, like pure sets, are abstract (if they exist), whereas rocks, trees, and human beings are concrete. In everyday language, it is common to use expressions that refer to concrete entities as well as those that apparently refer to abstractions such as democracy, happiness, motherhood, etc. Moreover, formulations of mathematical theories seem to appeal directly to abstract entities, and the use of mathematical expressions in the empirical sciences seems indispensable to the formulation of our best empirical theories (see Quine 1948; Putnam 1971; and the entry on indispensability arguments in the philosophy of mathematics). Finally, apparent reference to abstract entities such as sets, properties, concepts, propositions, types, and possible worlds, among others, is ubiquitous in different areas of philosophy.

Though there is a pervasive appeal to abstract objects, philosophers have nevertheless wondered whether they exist. The alternatives are: platonism, which endorses their existence, and nominalism, which denies the existence of abstract objects across the board. (See the entries on nominalism in metaphysics and platonism in metaphysics.) But the question of how to draw the distinction between abstract and concrete objects is an open one: it is not clear how one should characterize these two categories nor is there a definite list of items that fall under one or the other category (assuming neither is empty).

The first challenge, then, is to articulate the distinction, either by defining the terms explicitly or by embedding them in a theory that makes their connections to other important categories more explicit. In the absence of such an account, the philosophical significance of the contrast remains uncertain, for the attempt to classify things as abstract or concrete by appeal to intuition is often problematic. Is it clear that scientific theories (e.g., the general theory of relativity), works of fiction (e.g., Dante’s Inferno), fictional characters (e.g., Bilbo Baggins) or conventional entities (e.g., the International Monetary Fund or the Spanish Constitution of 1978) are abstract?

It should be stressed that there may not be one single “correct” way of explaining the abstract/concrete distinction. Any plausible account will classify the paradigm cases in the standard way or give reasons for proceeding otherwise, and any interesting account will draw a clear and philosophically significant line in the domain of objects. Yet there may be many equally interesting ways of accomplishing these two goals, and if we find ourselves with two or more accounts that do the job rather well, there may be no point in asking which corresponds to the real abstract/concrete distinction. This illustrates a general point: when technical terminology is introduced in philosophy by means of examples, but without explicit definition or theoretical elaboration, the resulting vocabulary is often vague or indeterminate in reference. In such cases, it usually is pointless to seek a single correct account. A philosopher may find herself asking questions like, ‘What is idealism?’ or ‘What is a substance?’ and treating these questions as difficult questions about the underlying nature of a certain determinate philosophical category. A better approach may be to recognize that in many cases of this sort, we simply have not made up our minds about how the term is to be understood, and that what we seek is not a precise account of what this term already means, but rather a proposal for how it might fruitfully be used for philosophical analysis. Anyone who believes that something in the vicinity of the abstract/concrete distinction matters for philosophy would be well advised to approach the project of explaining the distinction with this in mind.

Let us read again the most important line above:

Though there is a pervasive appeal to abstract objects, philosophers have nevertheless wondered whether they exist. The alternatives are: platonism, which endorses their existence, and nominalism, which denies the existence of abstract objects across the board.

How are the academic philosophers divided on this issue of Platonism versus nominalism. Let us go to a recent poll of the Western philosophers, who on a different question were noted to be 75% atheists:

Abstract objects: Platonism 39.3%; nominalism 37.7%; other 23.0%.

For the sake of simplicity let us assume that half the top academic philosophers believe that abstract objects necessarily exist and half of them believe in nominalism and say they do not exist. When it comes to mathematicians, we know from other polls that 3/4th of them are Platonists.[1]

The whole of the poll and all the 30 questions can be reviewed in the following PDF file. Perhaps, each question is a goldmine for our future philosophical and theological discussions:

What-do-philosophers-believe-1-1-1 Download

According to Encyclopedia Britannica:

A complete explanation of mathematical Platonism should begin with what is meant by an abstract object. Among contemporary Platonists, the most common view is that the defining trait of an abstract object is nonspatiotemporality. That is, abstract objects are not located anywhere in the physical universe, and they are also entirely nonmental, and yet they have always existed and they will always exist. This understanding does not preclude having mental ideas of abstract objects; according to Platonists, one can. For example, one can have a mental idea of the number 4. However, having a mental idea of the number 4 does not imply that the number 4 is just a mental idea. After all, people have ideas of the Moon, but it does not follow from that fact that the Moon is just an idea, because the Moon and people’s ideas of the Moon are distinct things. Thus, when Platonists say that the number 4 is an abstract object, they mean to say that it is a real and objective thing that, like the Moon, exists independently of people and their thinking but, unlike the Moon, is nonphysical.

I beg to differ here a little. If nothing exists at all, no universe, no humans, no consciousness, no God, a total blank, the abstract objects cannot exist:

Nothing comes out of absolute nothing: ex nihilo nihil fit!

This is examined in further details in a separate article: The best proof against atheism is to imagine what they profess: What if nothing exists, no God a total blank!

Again according to Encyclopedia Britannica:

Abstract objects are also, according to Platonists, unchanging and entirely noncausal. Because abstract objects are not extended in space and not made of physical matter, it follows that they cannot enter into cause-and-effect relationships with other objects.

Platonists also assert that mathematical theorems provide true descriptions of such objects. What does this claim amount to? Consider the positive integers (1, 2, 3,…). According to Platonists, the theory of arithmetic indicates what this sequence of abstract objects is like. Since ancient times, mathematicians have discovered all sorts of interesting facts about this sequence. For instance, the Greek mathematician Euclid proved more than 2,000 years ago that there are infinitely many prime numbers among the positive integers. Thus, according to Platonists, the sequence of positive integers is an object of study, just as the solar system is an object of study for astronomers.

On the one hand, it is impossible to deny the existence of mathematical abstract objects and on the other hand to imagine them freely unless guided by certain ideology without any consciousness, be it divine, human or extraterrestrial. Remember, half the philosophers believe in Platonism and half in nominalism and three fourth of mathematicians believe in Platonism. If we believe in mathematical heaven then the religious heaven is not too far: How Could Most Mathematicians Believe in Heaven, But Not in God?

If we believe in nominalism and mathematics and laws of nature do not exist, then how can we have a universe that we live in: The best proof against atheism is to imagine what they profess: What if nothing exists, no God a total blank!

Platonism or nominalism the necessity of God is inescapable: Video: Is God Necessary or Who Made God?

References

https://themuslimtimes.info/2024/02/28/most-mathematicians-believe-in-heaven-but-not-in-god/

The Problem of Free Will: Is There a Problem?

May 3, 2024Zia H Shah

Epigraph:

Allah burdens not any soul beyond its capacity. It shall have the reward it earns, and it shall get the punishment it incurs. Our Lord, do not punish us, if we forget or fall into error; and our Lord, lay not on us a responsibility as You did lay upon those before us. Our Lord, burden us not with what we have not the strength to bear; and efface our sins, and grant us forgiveness and have mercy on us; You are our Master; so help us against the disbelieving people. (Al Quran 2:286)

Presented and collected by Zia H Shah MD

Before you watch the 13 minute above video, please consider reading the paragraphs till the PDF file below.

The Western philosophers have debated free will for two centuries. If free will does not exist then all religions are wrong as no one has a responsibility and as such is not accountable. In Islam after Monotheism the second most important belief is about Afterlife. So, as a Muslim theologian, it is very much my responsibility to examine and defend free will. In other words discussions about free will are at the very core of defense for theism against the current academic culture of atheism in the modern Western universities.

Before, one can fully understand the above 13 minute video, one has to understand three terms:

Determinism
Compatibilism
Libertarianism
Indeterminism

Determinism, in philosophy and science, the thesis that all events in the universe, including human decisions and actions, are causally inevitable. Determinism entails that, in a situation in which a person makes a certain decision or performs a certain action, it is impossible that he or she could have made any other decision or performed any other action. In other words, it is never true that people could have decided or acted otherwise than they actually did. This is called hard determinism. Determinism in this sense is usually understood to be incompatible with free will, or the supposed power or capacity of humans to make decisions or perform actions independently of any prior event or state of the universe. Philosophers and scientists who deny the existence of free will on this basis are known as “hard” determinists.

In contrast, the so-called “soft” determinists, also called compatibilists, believe that determinism and free will are compatible after all. In most cases, soft determinists attempt to achieve this reconciliation by subtly revising or weakening the commonsense notion of free will. Contemporary soft determinists have included the English philosopher G.E. Moore (1873–1958), who held that acting freely means only that one would have acted otherwise had one decided to do so (even if, in fact, one could not have decided to do so), and the American philosopher Harry Frankfurt, who argued that acting freely amounts to identifying with or approving of one’s own desires (even if those desires are such that one cannot help but act on them).

In the following survey, in the PDF file below, a large majority of the philosophers are compatibilist (59.1%) or believe in soft determinism and in so doing weaken the notion of free will or complete responsibility, a subtle denial of accountability and Afterlife.

Libertarianism is a position defending and leaning towards freewill for theological or philosophical reasons. So, I am a libertarian and so is Peter Van Inwagen in the above video, even though for different reasons. The first recorded use of the term libertarianism was in 1789 by William Belsham in a discussion of free will and in opposition to necessitarian or determinist views.^[7][8] Metaphysical libertarianism is one philosophical viewpoint under that of incompatibilism. Libertarianism holds onto a concept of free will that requires the agent to be able to take more than one possible course of action under a given set of circumstances.

Accounts of libertarianism subdivide into non-physical theories and physical or naturalistic theories. Non-physical theories hold that the events in the brain that lead to the performance of actions do not have an entirely physical explanation, and consequently the world is not closed under physics. Such interactionist dualists believe that some non-physical mind, will, or soul overrides physical causality.

Explanations of libertarianism that do not involve dispensing with physicalism require physical indeterminism, such as probabilistic subatomic particle behavior—a theory unknown to many of the early writers on free will. Physical determinism, under the assumption of physicalism, implies there is only one possible future and is therefore not compatible with libertarian free will. Some libertarian explanations involve invoking panpsychism, the theory that a quality of mind is associated with all particles, and pervades the entire universe, in both animate and inanimate entities. Other approaches do not require free will to be a fundamental constituent of the universe; ordinary randomness is appealed to as supplying the “elbow room” believed to be necessary by libertarians.

The extreme alternative to determinism is indeterminism, the view that at least some events have no deterministic cause but occur randomly, or by chance. Indeterminism is supported to some extent by research in quantum mechanics, which suggests that some events at the quantum level are in principle unpredictable (and therefore random). The indeterminists may or may not be libertarian.

Now, a few words about Peter Van Inwagen.

Peter van Inwagen (/væn ɪnˈwɑːɡən/; born September 21, 1942) is an American analytic philosopher and the John Cardinal O’Hara Professor of Philosophy at the University of Notre Dame. He is also a research professor of philosophy at Duke University each spring.^[2] He previously taught at Syracuse University, earning his PhD from the University of Rochester in 1969^[3] under the direction of Richard Taylor.^[4] Van Inwagen is one of the leading figures in contemporary metaphysics, philosophy of religion, and philosophy of action. He was the president of the Society of Christian Philosophers from 2010 to 2013.^[5]

Peter Van Inwagen presents three premises, in his above 13 minute video, in his main argument that free will is in fact incompatible with determinism, that moral responsibility is incompatible with determinism, and that (since we have moral responsibility) determinism is false. Hence, he concludes, we have free will, and he is a libertarian and among a minority of 13.7% in the survey below:

What-do-philosophers-believe-1-1 Download

Having understood the current debates about free will, one is now ready to launch a deeper study of theology and philosophy and better tackle the atheistic tendencies of the modern academic philosophers. In the above poll only 15% of academic philosophers are theists.

…

Could Free Will and Consciousness be a Defeater for Atheism and Physicalism

Epigraph “Watch your thoughts, they become your words; watch your words, they become your actions; watch your actions, they become your habits; watch your habits, they become your character; watch […]

Analyzing Free Will with Robert Lawrence Kuhn

Written and collected by Zia H Shah MD In this video, episode number 910, Kuhn and the first interviewee start off with false dilemma of determinism and indeterminism. Indeterminism is […]

Rewiring the Brain to Treat OCD and Its Impact on Free Will

Rewiring the Brain to Treat OCD Source: Discovery magazine A groundbreaking therapy, relying on mindfulness meditation to treat obsessive compulsive disorder, suggests even adult brains have neuroplasticity By Steve Volk Dec […]

Gathering Philosophers and Scientists Who Believe in Free Will

Epigraph: And if your Lord had enforced His will, surely, all who are on the earth would have believed together. Wilt you, then, force men to become believers? (Al Quran 10:99) … […]

If there is freewill, so is Providence: Refuting the best of atheism through the latest science

Epigraph: And He (Allah) gave you all that you wanted of Him; and if you try to count the favors of Allah, you will not be able to number them. Indeed, man […]

The best proof against atheism is to imagine what they profess: What if nothing exists, no God a total blank!

April 27, 2024April 27, 2024Zia H Shah

Epigraph:

بَدِيعُ السَّمَاوَاتِ وَالْأَرْضِ ۖ وَإِذَا قَضَىٰ أَمْرًا فَإِنَّمَا يَقُولُ لَهُ كُن فَيَكُونُ

He is the Originator of the heavens and the earth, and when He decrees something, He says only, ‘Be,’ and it is. (Al Quran 2:117)

Have they been created from nothing, or are they their own creators? Have they created the heavens and the earth? In truth they put no faith in anything. (Al Quran 52:35-36)

Written and collected by Zia H Shah MD

Imagine a world where there are no material things, no universe, now imagine yourself in deep anesthesia a feeling of nothing, you do not exist and no other consciousness exists, no humans, no God, no angels, no Satan, nothing at all!

My main suggestion to the open minded readers is to read on and in the words of Sir Francis Bacon, “Read not to contradict … but to weigh and consider.”

Now, go to minute 2.30 of the above video, What is Nothing by Closer to Truth and locate a 15 seconds comment of the Nobel Laureate Steven Weinberg, who shared his 1979 Nobel Prize in physics with Dr. Abdus Salam and Sheldon Glashow. He clearly states and I may be paraphrasing a little that even if we find a theory of everything, some mathematical explanation, we will still not know where mathematics came from.

With his statement it is also easy to explain the position of the majority of the mathematicians that mathematics is discovered and not invented by humanity. What we discover would exist in the mind of the eternal creator, who created our universe with truth, justice and mathematics: Allah created the universe or the multiverse through mathematics بِالْحَقِّ.

A precise and open discussion about nothing, I believe, brings us to the conclusion that God is necessary. An eternal creator of our universe is necessary.

We merely have to imagine nothing precisely, no materials, no space, no time, nothing abstract like numbers or logic, then we arrive at the truth painlessly. If you do reach the end of the above video, the moderator Robert Lawrence Kuhn describes 9 levels of nothing and to me the total blank is his highest level nine of nothing. We cannot get our universe from the highest blank: nothing comes out of nothing. By imagining nothing in all its essence, ultimately leads us to our creator, and He had told us about Himself in that light in the verses of the Quran quoted as epigraph.

QED

Additional reading and viewing

Video: Is God Necessary or Who Made God?

How Could Most Mathematicians Believe in Heaven, But Not in God?

Videos and A Book: Why is There Anything At All?

What Would Happen If Everyone Truly Believed Everything Is One?

April 11, 2024Zia H Shah

Epigraph — The Crown verse of the Quran:

Allah — there is no God but He, the Living, the Self-Subsisting and All-Sustaining. Slumber seizes Him not, nor sleep. To Him belongs whatsoever is in the heavens and whatsoever is in the earth. Who is he that will intercede with Him except by His permission? He knows what is before them and what is behind them; and they encompass nothing of His knowledge except what He pleases. His knowledge extends over the heavens and the earth; and the care of them burdens Him not; and He is the High, the Great. (Al Quran 2:255)

Research suggests a belief in oneness has broad implications for psychological functioning and compassion for those outside of our immediate circle.

Scientific American

By Scott Barry Kaufman

We experience ourselves, our thoughts and feelings as something separate from the rest. A kind of optical delusion of consciousness.” — Albert Einstein

“In our quest for happiness and the avoidance of suffering, we are all fundamentally the same, and therefore equal. Despite the characteristics that differentiate us – race, language, religion, gender, wealth and many others – we are all equal in terms of our basic humanity.” — Dalai Lama (on twitter)

The belief that everything in the universe is part of the same fundamental whole exists throughout many cultures and philosophical, religious, spiritual, and scientific traditions, as captured by the phrase ‘all that is.’ The Nobel winner Erwin Schrodinger once observed that quantum physics is compatible with the notion that there is indeed a basic oneness of the universe. Therefore, despite it seeming as though the world is full of many divisions, many people throughout the course of human history and even today truly believe that individual things are part of some fundamental entity.

Despite the prevalence of this belief, there has been a lack of a well validated measure in psychology that captures this belief. While certain measures of spirituality do exist, the belief in oneness questions are typically combined with other questions that assess other aspects of spirituality, such as meaning, purpose, sacredness, or having a relationship with God. What happens when we secularize the belief in oneness?

In a s eries of studies, Kate Diebels and Mark Leary set out to find out. In their first study, they found that only 20.3% of participants had thought about the oneness of all things “often” or “many times”, while 25.9% of people “seldom” thought about the oneness of all things, and 12.5% of people “never” had thought about it.

The researchers also created a 6-item “Belief in Oneness Scale” consisting of the following items:

Beyond surface appearances, everything is fundamentally one.

Although many seemingly separate things exist, they all are part of the same whole.

At the most basic level of reality, everything is one.

The separation among individual things is an illusion; in reality everything is one.

Everything is composed of the same basic substance, whether one thinks of it as spirit, consciousness, quantum processes, or whatever.

The same basic essence permeates everything that exists.

Those who scored higher on this scale were much more likely to have an identity that extends beyond the individual to encompass wider aspects of humankind, life, nature, and even the cosmos. In fact, a belief in oneness was more strongly related to feeling connected with distant people and aspects of the natural world than with people with whom one is close! Also, while a belief in oneness was related to actual experiences of oneness (“mystical experiences”), there was no relationship between a belief in oneness and feeling closer to God during a spiritual experience.

In their second study, the researchers looked at values and self-views that might be related to the belief in oneness. They found that a belief in oneness was related to values indicating a universal concern for the welfare of other people, as well as greater compassion for other people. A belief in oneness was also associated with feeling connected to others through a recognition of our common humanity, common problems, and common imperfections. At the same time, there was no relationship between a belief in oneness and the degree to which people endorsed self-focused values such as hedonism, self-direction, security, or achievement. This means that people can have a belief in oneness and still have a great deal of self-care, healthy boundaries, and self-direction in life.

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Allah created the universe or the multiverse through mathematics بِالْحَقِّ

April 10, 2024April 15, 2024Zia H Shah

Written and collected by Zia H Shah MD, as a chapter of upcoming book: The Quran and the Biological Evolution

Galileo Galilei famously said, “Mathematics is the language in which God has written the universe.” Quantum mechanics is the theory that mathematically describes the behavior of the atoms and the subatomic particles and Einstein’s theory of general and spcial relativity provide the same at macroscopic level. In more recent pursuits, in the string theory physicists and mathematicians are seeking an equation that will harmonize the macroscopic and subatomic understanding and in so doing, they perhaps want to read the mind of God.

The expression Al Haqq الْحَقُّ appears more than 260 times in the Quran with different accents. It means the truth. Sometimes it is used in more specific meanings, for example it is one of the attributes of Allah mentioned in the Quran. It is often used for the prophet Muhammad, may peace be on him and also for the Quran. If we add a ‘B’ before it, then it means with or through truth or for a purpose, the Arabic then becomes بِالْحَقِّ. There are almost a dozen verses in the Quran stating that Allah created the universe بِالْحَقِّ. This has been generally translated as with good reason, truth, justice, wisdom, due authority or for a specific and a genuine purpose, but, a more apt translation in our age of physics and science can be ‘with mathematics.’ If nothing else the reader could consider it as a leap of faith on my part.

Now let us examine all the occurrences of بِالْحَقِّ as it regards to creation. The first of these verses that I want to examine is:

وَمَا خَلَقْنَا السَّمَاوَاتِ وَالْأَرْضَ وَمَا بَيْنَهُمَا إِلَّا بِالْحَقِّ

“We have created the heavens and the earth and all that is between the two in accordance with the perfect truth, wisdom and mathematics.” (Al Quran 15:85)

This verse implies that the laws of nature are inviolable and that indeed was the underpinning that set the study of nature and the scientific revolution into motion. This is what humanity has been discovering in the last few centuries, in the field of physics, starting with Copernicus, Newton, Einstein, Heisenberg, Bohr and 1979 Nobel laureate in physics Abdus Salam.

The discoveries of physics are always accompanied by mathematical proofs. No wonder majority of the mathematicians believe mathematics to have an independent reality and believe it to be discovered by humanity, rather than invented to explain reality of the universe.

Many mathematicians agree that the universe is governed by a singular order that is defined using mathematical principles. Consequently, even if the universe ceased to exist, all mathematical principles would still be true. Therefore, like other aspects of human nature, mathematics is part of human discovery. Furthermore, there are several mathematical principles that are yet to be discovered. When these principles are discovered, they will then assist us in building models that will give us predictive power and understanding of the physical phenomena we seek to understand. Therefore, math is a natural concept that is to be discovered and used by humanity. This argument is common among lovers of mathematics.

For example, Jim Holt, who is an American journalist, popular-science author, and essayist, wrote for the New York Times in 2008:

“A physicist, a biologist and a mathematician walk into a bar. Bartender says, ‘Any of you believe in God?’ Which of the three is most likely to say yes? Answer: the mathematician. Mathematicians believe in God at a rate two and a half times that of biologists, a survey of members of the National Academy of Sciences a decade ago revealed. Admittedly, this rate is not very high in absolute terms. Only 14.6 percent of the mathematicians embraced the God hypothesis (versus 5.5 percent of the biologists).

“But here is something you probably didn’t know. Most mathematicians believe in heaven. Not a heaven with angels, but one populated by the abstract objects they devote themselves to studying: perfect spheres, infinite numbers, the square root of minus one and the like. Moreover, they believe they commune with this realm of timeless entities through a sort of extrasensory perception. Mathematicians who buy into this fantasy are called “Platonists,” since their mathematical heaven resembles the realm of the Good and the True described in Plato’s “Republic.” Some years ago, while giving a lecture to an international audience of elite mathematicians in Berkeley, I asked how many of them were Platonists. About three-quarters raised their hands. So you might say that mathematicians are no strangers to belief in the unseen.”[i]

Another viable explanation of the existence of mathematics is that it is merely part of the human creation. According to Jim Holt in the above quote this will be a quarter of the top mathematicians. The argument about math being part of the intricate web of nature could be easily refuted by the view that human beings invented mathematics as a tool that could aid in the description of the physical world. Therefore, mathematics is only popular among human beings because it suits their needs when they are exploring the world.

It is also true that some mathematical concepts have been changed and altered for them to be palatable to human beings. If the universe ceased to exist, there would be no need for mathematics and it would not exist. Mathematics has been made possible by geography, astronomy, and physics among other areas of universal studies. Mathematics exists solely to satisfy the needs of studying and understanding the universe but it is not part of these studies. Therefore, mathematics is not something that is discovered but it is a human creation.

The assumption in the above paragraph that if the universe ceased to exist, there would be no need for mathematics and it would not exist is true only in an atheistic paradigm. If we focus on cosmology and how universe came to be then we know mathematics existed not in the consciousness of humanity, but in the mind of the All Knowing Creator. Just by assuming the possibility of an Eternal God the whole understanding takes a different shift. Mathematics then moves again from the category of invented to discovered.

Let us now examine all the verses that talk about Allah creating the universe with a purpose through mathematics. For the first few verses I will quote part of the Arabic to show that these all use the Arabic expression بِالْحَقِّ with a ‘B.” As stated before the traditional translations have translated this word with words like wisdom, truth and purpose. I have added mathematics given the development of physics and mathematics in the last few centuries:

قَوْلُهُ الْحَقُّ وَيَوْمَ يَقُولُ كُن فَيَكُونُ وَهُوَ الَّذِي خَلَقَ السَّمَاوَاتِ وَالْأَرْضَ بِالْحَقِّ

“And He it is Who created the heavens and the earth in accordance with the requirements of wisdom and mathematics; and the day He says, ‘Be!’, it will be. His word is the truth.” (6:73)

مَا خَلَقَ اللَّهُ ذَٰلِكَ إِلَّا بِالْحَقِّ

“He it is Who made the sun radiate a brilliant light and the moon reflect a lustre, and ordained for it stages, that you might know the number of years and the reckoning of time. Allah has not created this but in truth with mathematics. He details the Signs for a people who have knowledge.” (10:5)

أَنَّ اللَّهَ خَلَقَ السَّمَاوَاتِ وَالْأَرْضَ بِالْحَقِّ

“Do you not see that Allah created the heavens and the earth in accordance with the requirements of wisdom and mathematics? If He please, He can do away with you, and bring a new creation.” (14:19)

خَلَقَ السَّمَاوَاتِ وَالْأَرْضَ بِالْحَقِّ

“He has created the heavens and the earth in accordance with the requirements of wisdom and mathematics. Exalted is He above all that they associate with Him.” (16:3)

To justify my interpretation of the word Al Haqq as not only truth but also mathematics, let me quote two other verses of the Quran:

“He it is Who made the sun radiate a brilliant light and the moon reflect a luster, and ordained for it stages, that you might know the number of years and the calculation of time الْحِسَابَ. Allah has not created this but in truth بِالْحَقِّ. He details the Signs for a people who have knowledge.” (10:5)

The word الْحِسَابَ above has been translated as calculation of time but also means mathematics.

Allah describes the lunar motion as a source of calendar and mathematics and links it with his creation through بِالْحَقِّ mathematics. The field of mathematics and algebra were initially consolidated through study of astronomy by the early Muslim mathematicians, the most notable was Muhammad ibn Musa al-Khwarizmi from whose book we get the word algebra.

The second verse clearly linking creation with mathematics is:

“And We have made the night and the day two Signs, and the Sign of night We have made dark, and the Sign of day We have made sight giving, that you may seek bounty from your Lord, and that you may know the computation of years and the science of reckoning الْحِسَابَ. And everything We have explained with a detailed explanation.” (17:12)

Again, this verse is dealing with the creation of day and night or sun, moon and stars and the word used is الْحِسَابَ also meaning mathematics.

Going back to our main theme of the article. In the verse below Allah not only confirms the theme of بِالْحَقِّ mathematics that we are discussing here but calls such a study of cosmology a miracle and a Sign:

“Allah created the heavens and the earth in accordance with the requirements of wisdom and mathematics. In that surely is a Sign for the believers.” (29:44)

The biggest miracle that humanity has discovered in cosmology is the fine tuning of the universe to make it hospitable for life, consciousness and humanity, in the last few decades. In other words our universe is biophilic. This is topic of numerous articles, videos and books and is not examined here. The discussion of biophilic character not only covers our universe but also delves into the possibility of multiverse. I am merely adding a few references from the Muslim Times here.[ii] [iii] [iv]

Allah says that atheistic views arise hand in hand with the denial of accountability or Afterlife:

“Do they not reflect in their own minds? Allah has not created the heavens and the earth and all that is between the two but in accordance with the requirements of wisdom and and mathematics for a fixed term. But many among men believe not in the meeting of their Lord.” (30:8)

Allah predicts that our solar system will not last forever:

“He created the heavens and the earth in accordance with the requirements of wisdom and mathematics. He makes the night to cover the day, and He makes the day to cover the night; and He has pressed the sun and the moon into service; each pursues its course until an appointed time. Hearken, it is He alone Who is the Mighty, the Great Forgiver.” (39:5)

In the Quran, God’s creativity in our universe is intimately linked to the promise of accountability and Afterlife:

“And Allah has created the heavens and the earth with truth and mathematics and that every soul may be requited for that which it earns; and they shall not be wronged.” (45:22)

Allah not only talks about the earth and the heavens but also mentions what is between the two, like meteors and interstellar cloud or gas as in:

“We have not created the heavens and the earth, and all that is between them, but with truth, and for an appointed term; but those who disbelieve turn away from that of which they have been warned.” (46:3)

The lawfulness and mathematics is not only a part of the creation of the inanimate universe but also life and creation of humanity itself:

“We created them not but with the requirements of truth, justice and mathematics, but most of them understand not.” (44:39) And: “He created the heavens and the earth with truth and mathematics, and He shaped you and made your shapes beautiful, and to Him is the ultimate return.” (64:3)

Bertrand Russell the famous mathematician and philosopher from UK, wrote in Study of Mathematics:

“Mathematics, rightly viewed, possesses not only truth, but supreme beauty, a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.”

Eugene Paul Wigner (November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles.

He wrote an article which has been very popular among the physicists and the mathematicians for more than half a century now, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” It was published in 1960 in Communication in Pure and Applied Mathematics. In it, Wigner observes that a theoretical physics’ mathematical structure often points the way to further advances in that theory and to empirical predictions. Mathematical theories often have predictive power in describing nature.

He concluded with the following paragraph:

“Let me end on a more cheerful note. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.”

The holy Quran also stresses the converse of Al Haqq or the truth as well, it is Al Batil. In the following verses Allah says that He did not create the universe through Al Batil, randomly or chaotically as if it was magical and not coherent:

“And to Allah belongs the kingdom of the heavens and the earth; and Allah has power over all things. In the creation of the heavens and the earth and in the alternation of the night and the day there are indeed Signs for men of understanding; Those who remember Allah while standing, sitting, and lying on their sides, and ponder over the creation of the heavens and the earth: “Our Lord, You have not created this in vain without the truth (Al Batil).” (Al Quran 3:189-191)

To me popping a statue of mud out of no where and magically changing it into a live and kicking human of flesh and bones, calling him Adam and then using one of his ribs, right or left to make a wife for him will not be Al Haqq, wisdom, truth or mathematics rather it will be Al Batil. Allah is indeed All-Powerful, according to the Quran, but He is also All-Wise and Al Haqq.

What do you think? What does the Quran say about the origin of humans? This leads us to the next chapter about the role of water in all life forms on our planet earth, especially humanity.

[i]https://www.nytimes.com/2008/01/13/books/review/Holt-t.html#kbh :~:text=Only%2014.6%20percent%20of%20the,Most%20mathematicians%20believe%20in%20heaven

[ii] https://themuslimtimes.info/2024/04/04/what-do-fine-tuning-and-the-multiverse-say-about-god/

[iii] https://themuslimtimes.info/category/biophylic/

[iv] https://themuslimtimes.info/2021/11/21/ten-raised-to-five-hundred-reasons-for-our-gracious-god-5/

What do “fine-tuning” and the “multiverse” say about God?

April 4, 2024April 5, 2024Zia H Shah

Epigraph:

We will show them Our Signs in the universe and also among their own selves, until it becomes manifest to them that the Quran is the truth. (Al Quran 41:53)

He is the Mighty, the Forgiving; Who created the seven heavens, one above the other. You will not see any flaw in what the Lord of Mercy creates. Look again! Can you see any flaw? Look again! And again! Your sight will turn back to you, weak and defeated. (Al Quran 67:2-4)

Source: BioLogos

Some Christians argue that fine-tuning is proof of God’s existence, while some atheists argue that the multiverse replaces God. Is either side right?

Scientists of all worldviews agree that the physical constants of our universe and the conditions of the early universe are exquisitely fine-tuned for life. Multiple theories in physics predict that our universe may be one of very many, an idea known as the multiverse. Some Christians argue that fine-tuning is proof of God’s existence, while some atheists argue that the multiverse replaces God. Neither conclusion can be reached on the basis of science alone, because the existence of God is not a scientific question. Yet our fruitful cosmos resonates with the Christian understanding of God as the creator of a world fit for life. When viewed through the eyes of faith, we see a personal God crafting an abundant, complex universe that includes our life-giving home, the Earth. Even if multiverse theories eventually explain scientifically how our universe began, the multiverse itself would still be God’s creation. Scientific explanations cannot replace God but rather increase our wonder and praise of the Creator God.

Fine-tuning refers to the surprising precision of nature’s physical constants and the early conditions of the universe. To explain how a habitable planet like Earth could even exist, these fundamental constants have to be set to just the right values (like tuning a dial to find just the right radio station). If the universe had physical constants with even slightly different values, the universe simply could not support life: it would expand too quickly, or never form carbon atoms, or never make complex molecules like DNA.

The multiverse is the idea that our universe is one of possibly infinitely many universes. Out of the many possible universes that may exist, each with different strengths of forces and properties of particles, our universe is one of very few which is capable of hosting life as we know it. How do people respond to fine-tuning and the multiverse? What do they imply for our understanding of God?

Fine-tuning refers to “just right” properties

Our universe has several properties that are set to precise values, and slight changes to those values would prevent life as we know it. Here are three examples.

1. The strength of gravity

When the Big Bang occurred billions of years ago, the matter in the universe was uniformly distributed. There were no stars, planets or galaxies—just particles floating about in the dark void of space. As the universe expanded outwards from the Big Bang, gravity pulled ever-so-gently on the matter, gathering it into clumps that eventually became stars and galaxies. But gravity had to have just the right force—if it was a bit stronger, it would have pulled all the atoms together into one big ball. The Big Bang—and our prospects—would have ended quickly in a Big Crunch. And if gravity was a bit weaker, the expanding universe would have distributed the atoms so widely that they would never have been gathered into stars and galaxies.

The strength of gravity has to be exactly right for stars to form. But what do we mean by “exactly”? Well, it turns out that if we change gravity by even a tiny fraction of a percent—enough so that you would be, say, one billionth of a gram heavier or lighter—the universe becomes so different that there are no stars, galaxies, or planets. And with no planets, there would be no life. Change the value slightly, and the universe moves along a very different path. And remarkably, every one of these different paths leads to a universe without life in it. Our universe is friendly to life, but only because the past 13.8 billion years have unfolded in a particular way that led to a habitable planet with liquid water and rich chemistry.

2. The formation of carbon

Carbon is the element upon which all known life is based. Carbon atoms form in the cores of stars by fusion reactions. In these reactions, three helium atoms collide and fuse together to make a carbon atom. However, in order for that fusion reaction to work, the energy levels must match up in just the right way, or the three helium atoms would bounce off of each other before they could fuse.

To create this unusual match-up of energies, two physical forces (the strong and electromagnetic forces) must cooperate in just the right way. The slightest change to either the strong or electromagnetic forces would alter the energy levels, resulting in greatly reduced production of carbon. The values are tuned so that carbon is produced efficiently, leading to abundant amounts of an element we need for life.

3. The stability of DNA

Every atom has a nucleus of protons and neutrons and a cloud of electrons swirling around it. When an atom binds with another atom to make a molecule, the charged protons and electrons interact to hold them together. The mass of a proton is nearly 2,000 times the mass of the electron (1,836.15267389 times, to be precise). But if this ratio changed by only a small amount, the stability of many common chemicals would be compromised. In the end, this would prevent the formation of many molecules, including DNA, the building blocks of life. As theologian and scientist Alister McGrath has pointed out,¹

[The entire biological] evolutionary process depends upon the unusual chemistry of carbon, which allows it to bond to itself, as well as other elements, creating highly complex molecules that are stable over prevailing terrestrial temperatures, and are capable of conveying genetic information (especially DNA).

These are just a few examples.

Evidence for fine-tuning is recognized by physicists and astronomers of all religions and worldviews, and has been for decades. As agnostic Steven Weinberg, a Nobel Laureate in Physics, wrote,

…how surprising it is that the laws of nature and the initial conditions of the universe should allow for the existence of beings who could observe it. Life as we know it would be impossible if any one of several physical quantities had slightly different values.

Implications of fine-tuning

Some agnostics and atheists see fine-tuning simply as a lucky accident. For some, this is a nonchalant shrugging of the shoulders; fine-tuning “is what it is” without any further implications. Some make a more specific argument: because humans exist, the laws of nature clearly must be the ones compatible with life, otherwise, we simply wouldn’t be here to notice the fact. (This is called the “anthropic principle;” see this good introduction by leading Christian physicist John Polkinghorne.) To argue against this line of reasoning, philosopher John Leslie makes the analogy of surviving an execution at a firing squad completely unharmed,² summarized here by astronomer and BioLogos President Deborah Haarsma:

Of course the survivor would look for an explanation for why such an unlikely event occurred! In the same way, most people are curious to figure out why the universe is the way it is, both scientifically and theologically. As astronomer Fred Hoyle wrote, “A common sense interpretation of the facts suggests that a super-intellect has monkeyed with physics, as well as with chemistry and biology.” Physicist Freeman Dyson wrote, “The more I examine the universe, and the details of its architecture, the more evidence I find that the Universe in some sense must have known we were coming.”³

In recent years, several theories for a multiverse have been put forth. In a multiverse model, there are many other universes in addition to our own. Each of these universes has different properties and different values of the basic constants of physics, such that some of these universes would have gravity set just right to form stars, but many universes would not. Only a few universes would be suitable for life, and of course we would be living in one of those (because we couldn’t survive in the others). If the number of these universes is extremely large, it would be less surprising that one of them would happen to provide the specific conditions for life. Would a multiverse explain away fine-tuning and point away from God?

Science of the multiverse

The term “multiverse” is actually used for several different scientific models, not just one. The different multiverse models arise out of theoretical physics and cosmology and the leading ones have a rich mathematical basis. One version of the multiverse arises from string theory. String theory is the best theory developed so far to unify the four fundamental forces of physics, by picturing each particle as a tiny vibrating string operating in 11-dimensional space. String theory was not invented to explain fine-tuning or multiple universes; the multiverse prediction arose out of the math of the theory. String theory hasn’t been confirmed experimentally yet; testing it will be challenging and requires large, high energy experiments like the Large Hadron Collider and more.

Another version of the multiverse arises from inflation theory, which was developed to answer questions about the properties of the universe, such as its nearly uniform temperature and the imbalance of matter and antimatter. In inflation, the universe expands at an incredibly rapid rate in its first moments (by a factor of 10²⁶in about 10^-33seconds). In those moments, tiny fluctuations in the early universe expand nearly to the size of galaxies, leading to the structures we see in the universe today. Inflation made specific predictions for properties of the Cosmic Microwave Background, the heat radiation leftover from the early universe, and those predictions have been fully confirmed: inflation theory has been thoroughly tested and confirmed. Intriguingly, most versions of inflation theory also predict a multiverse. New universes form by a phase transition, analogous to a pot of water just beginning to boil, leading to many “bubbles,” each bubble a universe with different properties.

Perhaps the biggest question for the multiverse is, “Is this science?” It is highly improbable that we could ever do any measurements of another universe; it is inaccessible to us. Cosmologists themselves debate whether the multiverse is in the realm of science. Some argue that using the multiverse as an explanation would weaken the very nature of scientific reasoning, since it cannot be tested directly. Others argue that a physical theory (like inflation) can be confirmed if some of its predictions are confirmed (as they have with the Cosmic Microwave Background) even if not all predictions can be tested.

Scientists also have found that, even if the multiverse models are right, the multiverse would not eliminate fine-tuning. For example, in order to produce such an enormous inflationary rate of expansion, inflation theories require certain parameters to take on particularly precise values. While inflation explains some properties in our universe that previously appeared fine-tuned, the fine-tuning is not eliminated—it is pushed a step back into the origin of the multiverse itself.

Whether universe or multiverse, God is the Creator

When some atheists argue that the multiverse weakens the case for God’s existence, they overstep what science itself can claim. The multiverse models are fascinating and address scientific questions in this universe, but at a scientific level the predictions for other universes are virtually impossible to verify. But even if a multiverse model were well-established on a scientific level, it would not and could not replace God. No scientific theory can. From the perspective of biblical faith, science merely investigates the physical world that God created and sustains.

The physicists who are investigating the multiverse include Christians who ponder the multiverse as God’s creation. The multiverse raises theological questions that need consideration (see for example physicist Robert Mann’s discussion). And yet, as physicist Gerald Cleaver writes, if multiverse theories are shown to be correct, it would be “the next step in understanding the beauty, splendor, complexity, and vastness of God’s creation.”

Reference

Additional reading and viewing

Ten Raised to Five Hundred Reasons for Our Gracious God

…

Physics at the Theological Frontiers: What is said about Christianity here would apply to Judaism and Islam also

Robert B Mann – Professor of Physics Download

Why Intelligent Design Movement is Not only Bad Science, But Also Bad Theology

March 27, 2024March 27, 2024Zia H Shah

Epigraph:

لَّا تُدْرِكُهُ الْأَبْصَارُ وَهُوَ يُدْرِكُ الْأَبْصَارَ ۖ وَهُوَ اللَّطِيفُ الْخَبِيرُ

Eyes cannot reach God but He reaches the human consciousness. And He is the Incomprehensible, the All-Aware. (Al Quran 6:103)

هُوَ الْأَوَّلُ وَالْآخِرُ وَالظَّاهِرُ وَالْبَاطِنُ ۖ وَهُوَ بِكُلِّ شَيْءٍ عَلِيمٌ

He is the First and the Last, and the Manifest and the Hidden, and He knows all things full well. (Al Quran 57:3)

Written and collected by Zia H Shah MD, Chief Editor of the Muslim Times

Why is Intelligent Design Movement (ID) bad science? I will leave that discussion mostly to the contemporary scientists. They have said enough in defense of modern science. I will start off with introducing ID, its scientific lack of merit and then describe two broad categories of reasons why it is bad theology.

ID is a pseudoscientific argument for the existence of God, presented by its proponents as “an evidence-based scientific theory about life’s origins”.^{[1][2][3][4][5]} Proponents claim that “certain features of the universe and of living things are best explained by an intelligent cause, not an undirected process such as natural selection.”^[6] ID is a form of creationism that lacks empirical support and offers no testable or tenable hypotheses, and is therefore not science.^[7][8][9] The leading proponents of ID are associated with the Discovery Institute, a Christian, politically conservative think tank based in the United States.^{[n 1]}

If my articles are boring to you, it may be that you need to read more of them, as was suggested by John Cage, an American musician, “If something is boring after two minutes, try it for four. If still boring, then eight. Then sixteen. Then thirty-two. Eventually one discovers that it is not boring at all.”

Although the phrase intelligent design had featured previously in theological discussions of the argument from design,^[10] its first publication in its present use as an alternative term for creationism was in Of Pandas and People,^[11]^[12] a 1989 creationist textbook intended for high school biology classes. The term was substituted into drafts of the book, directly replacing references to creation science and creationism, after the 1987 Supreme Court‘s Edwards v. Aguillard decision barred the teaching of creation science in public schools on constitutional grounds.^[13] From the mid-1990s, the intelligent design movement (IDM), supported by the Discovery Institute,^[14] advocated inclusion of intelligent design in public school biology curricula.^[7] This led to the 2005 Kitzmiller v. Dover Area School District trial, which found that intelligent design was not science, that it “cannot uncouple itself from its creationist, and thus religious, antecedents”, and that the public school district’s promotion of it therefore violated the Establishment Clause of the First Amendment to the United States Constitution.^[15]

ID presents two main arguments against evolutionary explanations: irreducible complexity and specified complexity, asserting that certain biological and informational features of living things are too complex to be the result of natural selection. Detailed scientific examination has rebutted several examples for which evolutionary explanations are claimed to be impossible.

It is important for me at this stage to introduce two terms methodological naturalism and metaphysical naturalism.

One should consider the latter as equivalent to atheism. So, as a devout Muslim, who believes in transcendent Unitarian God of the Abrahamic faiths, I cannot accept metaphysical naturalism, but I fully believe and endorse methodological naturalism. In fact I often use it not only to deny pseudoscience but also bad theology. It is my main weapon against bad theology.

So what are these terms that distinguish me from ID on the one hand and from the atheist scientists on the other?

In philosophy, naturalism is the idea that only natural laws and forces (as opposed to supernatural ones) operate in the universe.^[1] In its primary sense^[2] it is also known as ontological naturalism, metaphysical naturalism, pure naturalism, philosophical naturalism and antisupernaturalism. “Ontological” refers to ontology, the philosophical study of what exists. Philosophers often treat naturalism as equivalent to materialism.

For example, philosopher Paul Kurtz argues that nature is best accounted for by reference to material principles. These principles include mass, energy, and other physical and chemical properties accepted by the scientific community. Further, this sense of naturalism holds that spirits, deities, and ghosts are not real and that there is no “purpose” in nature. This stronger formulation of naturalism is commonly referred to as metaphysical naturalism.^[3] On the other hand, the more moderate view that naturalism should be assumed in one’s working methods as the current paradigm, without any further consideration of whether naturalism is true in the robust metaphysical sense, is called methodological naturalism.^[4]

The term “methodological naturalism” is much more recent, though. According to Ronald Numbers, it was coined in 1983 by Paul de Vries, a Wheaton College philosopher. De Vries distinguished between what he called “methodological naturalism”, a disciplinary method that says nothing about God’s existence, and “metaphysical naturalism”, which “denies the existence of a transcendent God”.^[23] The term “methodological naturalism” had been used in 1937 by Edgar S. Brightman in an article in The Philosophical Review as a contrast to “naturalism” in general, but there the idea was not really developed to its more recent distinctions.^[24]

ID seeks to challenge the methodological naturalism inherent in modern science,^[2][16] though proponents concede that they have yet to produce a scientific theory.^[17] As a positive argument against evolution, ID proposes an analogy between natural systems and human artifacts, a version of the theological argument from design for the existence of God.^{[1][n 2]} ID proponents then conclude by analogy that the complex features, as defined by ID, are evidence of design.^{[18][n 3]} Critics of ID find a false dichotomy in the premise that evidence against evolution constitutes evidence for design.^[19][20]

Before we go any further, let me suggest to the open minded readers, to read on and in the words of Sir Francis Bacon, “Read not to contradict … but to weigh and consider.”

Now, moving to the second part of my article as to why ID is bad theology. It is bad theology for they often present God of the gaps. Which means inserting God in gaps of knowledge that are not yet understood by science but over time we begin to have better understanding of these domains. Secondly, they violate a principal tribute of the Unitarian God of the Abrahamic faiths, namely that He is Al Baatin الْبَاطِنُ or the Hidden as documented in the verses quoted as epigraph of this article.

The transcendent God of Abrahamic faiths is beyond time, space and matter and we cannot find his fingerprint or hand in a scientific paradigm.

The mistakes of ID are very evident in the biography of one of its pioneers William Dembski, otherwise a very knowledgeable scholar and his work I can use in Monotheistic metaphysics. Please note my emphasis in metaphysics not in science or physics.

Dembski (born July 18, 1960) is an American mathematician, philosopher and theologian. He was a proponent of intelligent design (ID) pseudoscience,^[1] specifically the concept of specified complexity, and was a senior fellow of the Discovery Institute‘s Center for Science and Culture (CSC).^[2] On September 23, 2016, he officially retired from intelligent design, resigning all his “formal associations with the ID community, including [his] Discovery Institute fellowship of 20 years.” ^[3] A February 2021 interview in the CSC’s blog Evolution News announced “his return to the intelligent design arena.” ^[4]

In 2012, he taught as the Phillip E. Johnson Research Professor of Science and Culture at the Southern Evangelical Seminary in Matthews, North Carolina near Charlotte.^[5]

Dembski has written books about intelligent design, including The Design Inference (1998), Intelligent Design: The Bridge Between Science & Theology (1999), The Design Revolution (2004), The End of Christianity (2009), and Intelligent Design Uncensored (2010). The second and revised edition of his first book has appeared in 2023. All his books can be useful for the Abrahamic or the Muslim metaphysics.

Why is he a bad scientist and a bad theologian, while qualifying in my opinion as a very good metaphysician and philosopher?

Dembski objects to the presence of the theory of evolution in a variety of disciplines, presenting intelligent design as an alternative to reductionist materialism that gives a sense of purpose that the unguided evolutionary process lacks^[85] and the ultimate significance of ID is its success in undermining materialism and naturalism.^[32] Dembski has also stated that ID has little chance as a serious scientific theory as long as methodological naturalism is the basis for science.^[86] Although intelligent design proponents (including Dembski) have made little apparent effort to publish peer-reviewed scientific research to support their hypotheses, in recent years they have made vigorous efforts to promote the teaching of intelligent design in schools.^[87] Dembski is a strong supporter of this drive as a means of making young people more receptive to intelligent design, and said he wants “to see intelligent design flourish as a scientific research program” among a “new generation of scholars” willing to consider the theory and textbooks that include it.^[88]

In December 2007, Dembski told Focus on the Family that “The Designer of intelligent design is, ultimately, the Christian God.”^[90]

So, if he is going to be an apologist for the Triune God of Christianity then every thing I have written against the dogma of Christianity, resurrection, vicarious atonement is a demonstration of his bad theology. Nevertheless, I am an apologist for God of Judaism, Unitarian Christianity and Islam and for Afterlife. I present my arguments as theology, philosophy or metaphysics and never as science and in that domain I would borrow from his scholarship.

I am a firm believer in a quote attributed to the 16th century Christian martyr Michael Servetus:

Dembski is also presenting bad theology because he probably considers miracles as violation of the natural law and I do not. He believes that he can catch the fingerprint or hand of God in the workings of our universe, while I believe in the Most Subtle and the Hidden الْبَاطِنُ God of the Quran, whom eyes cannot reach. But, He chooses to reach human consciousness, when He wills, through veils.

Dembski also knows bad religion or bad theology when he sees it. He once took his family to a meeting conducted by Todd Bentley, a faith healer, in hopes of receiving a “miraculous healing” for his son, who is autistic.^[100][101] In an article for the Baptist Press he recalled disappointment with the nature of the meeting and with the prevention of his son and other attendees from joining those in wheelchairs who were selected to receive prayer. He then concluded, “Minimal time was given to healing, though plenty was devoted to assaulting our senses with blaring insipid music and even to Bentley promoting and selling his own products (books and CDs).” He wrote that he did not regret the trip and called it an “education,” which showed “how easily religion can be abused, in this case to exploit our family.”^[101]

Shall we say that he has not woken up to the limitations of some of the dogma of Christianity? Let me, very respectfully, suggest additional reading materials:

Video About Historical Adam: Is it a Landmine for the Christian Dogma?

Video: William Lane Craig in Quest of the Historical Adam and My Muslim Perspective

Charles Darwin: An Epiphany for the Muslims, A Catastrophe for the Christians

If the Atheists and the Christians Debate, Islam Wins!

BBC Documentary: Did Jesus Die On the Cross?

How Even a Single Profound and True Revelation Defeats Materialism or Physicalism

March 19, 2024May 3, 2024Zia H Shah

Written and collected by Zia H Shah MD, Chief Editor of the Muslim Times

If God exists strict materialism or physicalism is not true.

What is a true dream? If the content of a dream cannot be explained by the conscious or subconscious mind of the recipient and it carries specific, new and useful information then it suggests a Transcendent source. A source that can communicate with the recipient during his or her sleep.

In philosophy, naturalism is the idea that only natural laws and forces (as opposed to supernatural ones) operate in the universe.^[1] In its primary sense^[2] it is also known as ontological naturalism, metaphysical naturalism, pure naturalism, philosophical naturalism and antisupernaturalism. “Ontological” refers to ontology, the philosophical study of what exists. Philosophers often treat naturalism as equivalent to materialism.

On the other hand, the more moderate view that naturalism should be assumed in one’s working methods as the current paradigm, without any further consideration of whether naturalism is true in the robust metaphysical sense, is called methodological naturalism.^[4]

I believe in methodological naturalism as I aspire to be a scientist, but not in ontological or metaphysical naturalism, as I believe in God and Afterlife. A single true revelation will defeat ontological naturalism, because it suggests a Transcendent source, for the new information in the dream.

Four-Horsemen of the Apocalypse in the *Book of Revelation* in the Bible

I don’t specifically believe in Four-Horsemen of the Apocalypse specifically. But, I found the picture as a suitable representation for revelation in general.

If a Jew or Christian feels sure of a single Biblical verse and is able to demonstrate that it does not have a human explanation then materialism or physicalism is defeated. Likewise, if a Muslim like me knows of a single Quranic verse that rises above human explanation it becomes a defeater for materialism or physicalism. Even a true dream of a scientists, a poet, a musician, which gives him or her any new information that cannot be derived from the subconscious mind of the recipient defeats materialism or physicalism. Three articles are linked at the end of this article.

Below is a recent survey of academic philosophers on 30 different questions including, atheism, naturalism and mind:

What-do-philosophers-believe-1 Download

In the above survey 72% of the academic philosophers are atheist, 50% are naturalists and 57% regard mind to be also physical.

Now, I quote from the magazine Nature, about demographics of belief in God or Afterlife among the leading scientists:

The question of religious belief among US scientists has been debated since early in the century. Our latest survey finds that, among the top natural scientists, disbelief is greater than ever — almost total.

Research on this topic began with the eminent US psychologist James H. Leuba and his landmark survey of 1914. He found that 58% of 1,000 randomly selected US scientists expressed disbelief or doubt in the existence of God, and that this figure rose to near 70% among the 400 “greater” scientists within his sample¹. Leuba repeated his survey in somewhat different form 20 years later, and found that these percentages had increased to 67 and 85, respectively².

In 1996, we repeated Leuba’s 1914 survey and reported our results in Nature³. We found little change from 1914 for American scientists generally, with 60.7% expressing disbelief or doubt. This year, we closely imitated the second phase of Leuba’s 1914 survey to gauge belief among “greater” scientists, and find the rate of belief lower than ever — a mere 7% of respondents.

Leuba attributed the higher level of disbelief and doubt among “greater” scientists to their “superior knowledge, understanding, and experience”². Similarly, Oxford University scientist Peter Atkins commented on our 1996 survey, “You clearly can be a scientist and have religious beliefs. But I don’t think you can be a real scientist in the deepest sense of the word because they are such alien categories of knowledge.”⁴ Such comments led us to repeat the second phase of Leuba’s study for an up-to-date comparison of the religious beliefs of “greater” and “lesser” scientists.

Our chosen group of “greater” scientists were members of the National Academy of Sciences (NAS). Our survey found near universal rejection of the transcendent by NAS natural scientists. Disbelief in God and immortality among NAS biological scientists was 65.2% and 69.0%, respectively, and among NAS physical scientists it was 79.0% and 76.3%. Most of the rest were agnostics on both issues, with few believers. We found the highest percentage of belief among NAS mathematicians (14.3% in God, 15.0% in immortality). Biological scientists had the lowest rate of belief (5.5% in God, 7.1% in immortality), with physicists and astronomers slightly higher (7.5% in God, 7.5% in immortality). Overall comparison figures for the 1914, 1933 and 1998 surveys appear in Table 1.

The whole of the article in Nature is available in PDF version:

Leading scientists still reject God Download

In this debate very early on Michael Egnor asks David Papineau as to what is the physical cause of Big Bang and does not get a straight forward answer. Around minute 46 he asks Papineau for a cogent explanation of quantum physics in the materialistic framework? Does Quantum physics and / or extra dimensions of string theory provide for materialism to be false ontologically?

I do believe in methodological naturalism and that I believe is perfectly in keeping with the Quranic theology, given the following two very well known verses:

Eyes cannot reach Him but He reaches the eyes. And He is the Incomprehensible, the All-Aware. (Al Quran 6:103)

His is the kingdom of the heavens and the earth; He gives life and He causes death; and He has power over all things. He is the First and the Last, and the Manifest and the Hidden, and He knows all things full well. (Al Quran 57:2-3)

God being the Hidden implies that he operates through laws of nature and we cannot see Him or His providence directly.

Now, I will share articles to suggest that sometimes scientists, mathematicians and others have received very convincing revelations from the All Knowing:

Al Aleem: The Bestower of true dreams

Revealing Dreams of Scientists

Movie: Ramanujan: A Prophet of Mathematics Born in a Hindu Family

Periodic Table in Chemistry was Revealed in a Dream

Why is the Quran a Sign or a Miracle, According to Itself?

The Quran: Allah has bound the sun and the moon into service, each running its course for an appointed term

The Quran and the Breathtaking Universe: Is This God Speaking or Muhammad?

The Quran and the Expanding Universe: Is This God Speaking or Muhammad?

The Quran and Creation Ex Nihilo: Is This God Speaking or Muhammad?

Michael Heller: Templeton Award-winner 2008, Denies Intelligent Design Movement

March 11, 2024March 11, 2024Zia H Shah

Epigraph

وَهُوَ الَّذِي خَلَقَ السَّمَاوَاتِ وَالْأَرْضَ بِالْحَقِّ ۖ وَيَوْمَ يَقُولُ كُن فَيَكُونُ ۚ قَوْلُهُ الْحَقُّ ۚ وَلَهُ الْمُلْكُ يَوْمَ يُنفَخُ فِي الصُّورِ ۚ عَالِمُ الْغَيْبِ وَالشَّهَادَةِ ۚ وَهُوَ الْحَكِيمُ الْخَبِيرُ

It is He who created the heavens and the earth for a true purpose. On the Day when He says, ‘Be,’ it will be: His word is the truth. All control on the Day the Trumpet is blown belongs to Him. He knows the seen and the unseen: He is the All Wise, the All Aware. (Al Quran 6:73)

Also see 3:59, 16:40, 36:82 and 2:117 regarding the Divine fiat Be! and it is. يَقُولُ كُن فَيَكُونُ

He says about Intelligent Design:

Adherents of the so-called intelligent design ideology commit a grave theological error. They claim that scientific theories, that ascribe the great role to chance and random events in the evolutionary processes, should be replaced, or supplemented, by theories acknowledging the thread of intelligent design in the universe. Such views are theologically erroneous. They implicitly revive the old manicheistic error postulating the existence of two forces acting against each other: God and an inert matter; in this case, chance and intelligent design. There is no opposition here. Within the all-comprising Mind of God what we call chance and random events is well composed into the symphony of creation.

His whole presentation is very important to avoid presenting God of the gaps and for the best correlation between religion and science.

His Press Release at the time of Award

Source of his full message: Templeton Website

The 17^th-century German mathematician and philosopher, Gottfried Wilhelm Leibniz, is my philosophical hero. I am proud (but not quite happy) that I share with this great philosopher at least one feature. He was a master in spreading, not to say dissipating, his genius into too many fields of interest. If he had a greater ability to concentrate on fewer problems, he would have become not only a precursor but also a real creator of several momentous scientific achievements. But in such a case, the history of philosophy would be poorer by one of its greatest thinkers. This is not to say that in my case the history of philosophy would lose anything. This is only to stress the fact that I am interested in too many things.

Amongst my numerous fascinations, two have most imposed themselves and proven more time resistant than others: science and religion. I am also too ambitious. I always wanted to do the most important things, and what can be more important than science and religion? Science gives us Knowledge, and religion gives us Meaning. Both are prerequisites of the decent existence. The paradox is that these two great values seem often to be in conflict. I am frequently asked how I could reconcile them with each other. When such a question is posed by a scientist or a philosopher, I invariably wonder how educated people could be so blind not to see that science does nothing else but explores God’s creation. To see what I mean, let us go to Leibniz.

In one of his essays, entitled Dialogus, in the margin we find a short sentence written by Leibniz’s hand. It reads: “When God calculates and thinks things through, the world is made.” Everybody has some experience in dealing with numbers, and everybody, at least sometimes, experiences a feeling of necessity involved in the process of calculating. We can easily be led astray when thinking about everyday matters or pondering all pros and cons when facing an important decision, but when we have to add or multiply even big numbers everything goes almost mechanically. This is a routine work, and if we are cautious enough there is no doubt as far as the final result is concerned. However, the true mathematical thinking begins when one has to solve a real problem, that is to say, to identify a mathematical structure that would match the conditions of the problem, to understand principles of its functioning, to grasp connections with other mathematical structures, and to deduce the consequences implied by the logic of the problem. Such manipulations of structures are always immersed into various calculations since calculations form a natural language of mathematical structures.

It is more or less such an image that we should associate with Leibniz’s metaphor of calculating God. Things thought through by God should be identified with mathematical structures interpreted as structures of the world. Since for God to plan is the same as to implement the plan, when “God calculates and thinks things through,” the world is created.

We have mastered a lot of calculation techniques. We are able to think things through in our human way. Can we imitate God in His creating activity?

In 1915 Albert Einstein wrote down his famous equations of gravitational field. The road leading to them was painful and laborious – a combination of deep thinking and tedious work of doing calculations. From the beginning Einstein saw an inadequacy of time-honored Newton’s theory of gravity: it did not fit into a spatio-temporal pattern of special relativity, a synthesis of classical mechanics and Maxwell’s electrodynamical theory. He was hunting for some empirical clues that would narrow the field of possibilities. He found some in the question: Why is inertial mass equal to gravitational mass in spite of the fact that, in Newton’s theory, they are completely independent concepts? He tried to implement his ideas into a mathematical model. Several attempts failed. At a certain stage, he understood that he could not go further without studying tensorial calculus and Riemannian geometry. It is the matter distribution that generates space-time geometry, and the space-time geometry that determines motions of matter. How to express this illuminating idea in the form of mathematical equations? When finally, after many weeks of exhausting work, the equations emerged before his astonished eyes, the new world has been created.

In the beginning, only three, numerically small, empirical effects corroborated Einstein’s new theory. But the world, newly created by Einstein, has soon become an independent reality. Yet in his early work, the field equations suggested to Einstein the existence of solutions describing an expanding universe. He discarded them by modifying his original equations, but in less than two decades it turned out that the equations were wiser than Einstein himself: measurements of galactic spectra have revealed that, indeed, the universe is expanding. In the subsequent period, lasting until now, theoretical physicists and mathematicians have found a host of new solutions to Einstein’s equations and interpreted them as representing gravitational waves, cosmic strings, neutron stars, stationary and rotating black holes, gravitational lensing, dark matter and dark energy, late stages of life of massive stars, and various aspects of cosmic evolution. In Einstein’s time nobody would have even suspected the existence of such objects and processes, but all of them have been found by astronomers in the real universe.

Perhaps now we better understand Leibniz’s idea of God creating the universe by thinking mathematical structures through. We should only free the above sketched image of creating physical theories from all human constraints and limitations, and take into account a theological truth that for God to intend is to obtain the result, and to obtain the result is to instantiate it. Einstein was not far from Leibniz’s idea when he was saying that the only goal of science is to decode the Mind of God present in the structure of the universe.

And what about chancy or random events? Do they destroy mathematical harmony of the universe, and introduce into it elements of chaos and disorder? Is chance a rival force of God’s creative Mind, a sort of manicheistic principle fighting against goals of creation? But what is chance? It is an event of low probability which happens in spite of the fact that it is of low probability. If one wants to determine whether an event is of low or high probability, one must use the calculus of probability, and the calculus of probability is a mathematical theory as good as any other mathematical theory. Chance and random processes are elements of the mathematical blueprint of the universe in the same way as other aspects of the world architecture.

Mathematical structures that are parts of the composition determining the functioning of the universe are called laws of physics. It is a very subtle composition indeed. Like in any masterly symphony, elements of chance and necessity are interwoven with each other and together span the structure of the whole. Elements of necessity determine the pattern of possibilities and dynamical paths of becoming, but they leave enough room for chancy events to make this becoming rich and individual.

Adherents of the so-called intelligent design ideology commit a grave theological error. They claim that scientific theories, that ascribe the great role to chance and random events in the evolutionary processes, should be replaced, or supplemented, by theories acknowledging the thread of intelligent design in the universe. Such views are theologically erroneous. They implicitly revive the old manicheistic error postulating the existence of two forces acting against each other: God and an inert matter; in this case, chance and intelligent design. There is no opposition here. Within the all-comprising Mind of God what we call chance and random events is well composed into the symphony of creation.

When contemplating the universe, the question imposes itself: Does the universe need to have a cause? It is clear that causal explanations are a vital part of the scientific method. Various processes in the universe can be displayed as a succession of states in such a way that the preceding state is a cause of the succeeding one. If we look deeper at such processes, we see that there is always a dynamical law prescribing how one state should generate another state. But dynamical laws are expressed in the form of mathematical equations, and if we ask about the cause of the universe we should ask about a cause of mathematical laws. By doing so we are back in the Great Blueprint of God’s thinking the universe. The question on ultimate causality is translated into another of Leibniz’s questions: “Why is there something rather than nothing?” (from his Principles of Nature and Grace). When asking this question, we are not asking about a cause like all other causes. We are asking about the root of all possible causes.

When thinking about science as deciphering the Mind of God, we should not forget that science is also a collective product of human brains, and the human brain is itself the most complex and sophisticated product of the universe. It is in the human brain that the world’s structure has reached its focal point – the ability to reflect upon itself. Science is but a collective effort of the Human Mind to read the Mind of God from question marks out of which we and the world around us seem to be made. To place ourselves in this double entanglement is to experience that we are a part of the Great Mystery. Another name for this Mystery is the Humble Approach to reality – the motto of all John Templeton Foundation activities. The true humility does not consist in pretending that we are feeble and insignificant, but in the audacious acknowledgement that we are an essential part of the Greatest Mystery of all – of the entanglement of the Human Mind with the Mind of God.

Templeton Prize
300 Conshohocken State Rd., Suite 500
West Conshohocken, Pennsylvania 19428, USA

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Epigraph:

Suggested additional posts: Allah created the universe or the multiverse through mathematics بِالْحَقِّ and What are abstract objects and do they make God necessary?

Indispensability Arguments in the Philosophy of Mathematics

Source: Stanford Encyclopedia of Philosophy

1. Spelling Out the Quine-Putnam Indispensability Argument

2. What is it to be Indispensable?

3. Naturalism and Holism

4. Objections

5. Explanatory Versions of the Argument

6. Conclusion

Bibliography

Academic Tools

Other Internet Resources

Related Entries

Acknowledgments

Epigraph:

بَدِيعُ السَّمَاوَاتِ وَالْأَرْضِ ۖ وَإِذَا قَضَىٰ أَمْرًا فَإِنَّمَا يَقُولُ لَهُ كُن فَيَكُونُ

This article is not written by AI or a robot but by Zia H Shah MD

References

Epigraph:

Presented and collected by Zia H Shah MD

Epigraph:

بَدِيعُ السَّمَاوَاتِ وَالْأَرْضِ ۖ وَإِذَا قَضَىٰ أَمْرًا فَإِنَّمَا يَقُولُ لَهُ كُن فَيَكُونُ

Written and collected by Zia H Shah MD

Epigraph — The Crown verse of the Quran:

Research suggests a belief in oneness has broad implications for psychological functioning and compassion for those outside of our immediate circle.

Written and collected by Zia H Shah MD, as a chapter of upcoming book: The Quran and the Biological Evolution

وَمَا خَلَقْنَا السَّمَاوَاتِ وَالْأَرْضَ وَمَا بَيْنَهُمَا إِلَّا بِالْحَقِّ

قَوْلُهُ الْحَقُّ وَيَوْمَ يَقُولُ كُن فَيَكُونُ وَهُوَ الَّذِي خَلَقَ السَّمَاوَاتِ وَالْأَرْضَ بِالْحَقِّ

مَا خَلَقَ اللَّهُ ذَٰلِكَ إِلَّا بِالْحَقِّ

أَنَّ اللَّهَ خَلَقَ السَّمَاوَاتِ وَالْأَرْضَ بِالْحَقِّ

خَلَقَ السَّمَاوَاتِ وَالْأَرْضَ بِالْحَقِّ

Some Christians argue that fine-tuning is proof of God’s existence, while some atheists argue that the multiverse replaces God. Is either side right?

Fine-tuning refers to “just right” properties

1. The strength of gravity

2. The formation of carbon

3. The stability of DNA

Implications of fine-tuning

Science of the multiverse

Whether universe or multiverse, God is the Creator

Additional reading and viewing

Epigraph:

لَّا تُدْرِكُهُ الْأَبْصَارُ وَهُوَ يُدْرِكُ الْأَبْصَارَ ۖ وَهُوَ اللَّطِيفُ الْخَبِيرُ

هُوَ الْأَوَّلُ وَالْآخِرُ وَالظَّاهِرُ وَالْبَاطِنُ ۖ وَهُوَ بِكُلِّ شَيْءٍ عَلِيمٌ

Written and collected by Zia H Shah MD, Chief Editor of the Muslim Times

Written and collected by Zia H Shah MD, Chief Editor of the Muslim Times

Epigraph

His Press Release at the time of Award

Source of his full message: Templeton Website