From Gödel to God

FREQUENTLY ASKED QUESTIONS ABOUT THE PROOF

1. Question: Why does the proof claim that a Theory of Everything is impossible? Aren’t scientists close to finding a Grand Unified Theory (GUT)?

Answer -  A GUT is an attempt to unify three forces of physics (the electromagnetic, weak and strong forces).  A GUT is a subset of a TOE, which is, as its name suggests, a theory of literally everything, including the force of gravity which is not addressed by a GUT. Scientists already have unified electromagnetic and weak forces and while a GUT may or may not be possible, its achievement does not suggest the near or even possible achievement of a TOE.

2. Question: Which God does the proof establish? Allah, Yahweh, Zeus, Shiva?

Answer -  The proof shows that a greatest being possible is necessary for an explanation of our Universe. Unmasking who that being is within a particular religious framework is not addressed in the proof. However, the proof actually rubbishes many of those "gods". Gods that are part of the created world or are themselves the Universe (of which the created world is intricately connected) or are beholden to the created world (gods of thunder and the seas and the sun, etc.) are not the God of this proof. It is a mistake to think that dismissing "gods" is the same as dismissing "God". The God that the Abrahamic religions worship, a God that is omniscient, omnipotent, omnipresent, a God that creates all and stands outside of, and is infinitely greater than all, is the God of this proof. The ancient Hebrews vehemently denied gods OF nature but they didn't make the mistake of dismissing the God who created nature. To them, both worshipping such gods and denying the One True God were equally foolish.

​However, this does not mean that the Abrahamic religions worship the same God, though the answer to this question is very much dependent on the perspective of the person being asked. A Jew would deny that Christians and Muslims worship his God. A Muslim is likely to say that all three do worship the same God but only the Muslim does so correctly. While the Christian would affirm that Jews worship his God (albeit incompletely) but Muslims do not. Why the discrepancy if they all have the same ontological starting point? A common response to this is that Christian’s Trinitarian views are a violation of the absolute simplicity assumption (i.e. God as a perfect singularity that nothing can be added to) of monotheism. However, this is a misunderstanding. Christians do not believe in separate gods but one God of three persons. Regardless, Trinitarianism is a dividing issue from the Christian's perspective between his God and the God of Islam (who repeatedly says in the Qur'an that he is not a Trinity - or has any other "partners", more precisely). Additionally, the Christian God and the God of Islam diverge in their root identity. The Trinitarian God of Christianity has a root identity in the monotheistic Hebrew's YHWH. In fact, Christianity was first held as the belief of a small group of Jesus' Jewish disciples. Islam's Allah, on the other hand, emerged from Arabic polytheism. "Allah" which literally means "the God" (the "al" and god "ilah") in Arabic (Malcolm Clarke - "Islam For Dummies", LOC 980), was probably held to be the supreme God (either (i) derived separately or (ii) from the Meccan's Hubal, the moon god or al-'Uzza) among a pantheon of gods in Muhammed's Quraysh tribe. Allah's etymological root (i.e. "the God") should not be confused with its root identity, as a god within polytheism. The polytheistic beginning of Allah is evidenced by the Satanic verses, espousing polytheism, later stripped from the Qur'anic revelations. So, the Christian God and Allah diverge on both views about the Trinity and in their root identities. Just because two things can be etymologically equated does not mean that they are equivalent in all things.

3. Question: Why is God alone equated to the "greatest"? Couldn't we have many "greatest"; for example, many consider Muhammad Ali as the "greatest", or the Beatles or Elvis or Pele?

Answer - Greatest is necessarily singular. St. Anselm, in the 11th century, first presented the ontological argument with the rationale that if anything greater could be conceived, then it was not the greatest. Similarly, in the proof, "greatest" refers to the greatest possible, not greatest in known-existence or experience. By this definition, greatest belongs to God alone.

4. Question: Why must everything have an explanation?

Answer - That everything has an explanation follows from the Principle of Sufficient Reason (PSR) and is defensible on the grounds: (i) we tend to find explanations when we look for them or else we can conceive of reasons for the lack of evidence, and (ii) the world makes sense only if PSR is true or else we would frequently observe events for which no explanation is conceivable, i.e. rationality (and science) would be impossible. As Alexander Pruss points out, denying PSR entails radical skepticism about perception and there is no good reason why its denial should be true. 

5. Question: Torkel Franzén and others have cautioned against extra-mathematical usage of the Incompleteness Theorem, how does the proof not violate this?

Answer - Two things need to be said in this regard. Firstly, the proof establishes that God is the ultimate explanation of the Universe because of the progression to an infinite or greatest formal system. So the conclusion is mathematically grounded. But secondly, and perhaps more importantly, many critics (including eminent scientists) are hamstrung by their own ideological biases (remember, not all statements by scientists are scientific statements). What these critics forget is that Gödel himself sought to develop the Theorems because of his desire to demonstrate the correctness of his platonic philosophical viewpoint (an extra-mathematical usage). So the pearls clutching reaction of secular-minded mathematicians and physicists who deride such extra-mathematical conclusions is quite hilarious as they are not doing so because of the correctness of restraint but because they are very much asserting their own non-mathematical ideology (See question below).

6. Question: Why should one not be skeptical of Gödel's belief that higher formal systems could be extended into infinity, and thus, logically deriving that mathematics emanates from a true, infinite, eternal 'realm'?

Answer - According to Rebecca Goldstein, what Gödel aimed at through his Theorem was solving a philosophical problem via a mathematical result. Gödel was a Platonist. He believed that there are abstract objects that exist outside of space and time and he saw his Theorem as proof of that. Skeptics deny this conclusion. To understand why they do and why they are wrong to do so, consider Goldbach's conjecture. Goldbach's conjecture says that every even integer greater than two could be expressed as the sum of two prime numbers. No proof of this conjecture has ever been discovered but neither has there been any falsification. Bivalence demands that it is either true or false and since it hasn't been falsified, one is perfectly in the right to hold it as being true (this is consistent with the hypothetico-deductive scientific model). Skeptics argue that while it hasn't been falsified, it can be viewed as both true and not true. But this is a clear violation of logical bivalence. Something cannot be both true and false at the same time. Bringing the discussion back to Gödel, the fact that it hasn't been falsified that formal systems could be infinitely extended would naturally suggest that Gödel is right about Platonism (at least the infinite aspect of it). In fact, Gödel's Incompleteness Theorems do establish the inexhaustibility of mathematics in formal systems. Only by holding the illogical position that things can be both true and false at the same time can one avoid acceptance of this.

7. Question: Aren't Gödel's Incompleteness Theorems simply a demonstration that our mathematical language is incapable of demonstrating all mathematical truth?

Answer - No, Gödel arithmeticized all meta-mathematical expressions and thus showed that regardless of the structure of our formal systems, mathematics is *essentially* incomplete.

​8. Question: Gödel's theorems dealt only with provability and not truth, so how can they be used to say anything true about God's existence?

Answer - There is a misconception here. Gödel did show that provability and truth are separable in mathematical systems; however, his second incompleteness theorem demonstrates that mathematics is essentially incomplete because there will always remain at least one true axiom that is not provable within the system, regardless if that system is extened into the transfinite..

9. Question: While Gödel Incompleteness Theorems may vindicate some Platonic views, can't one be a Platonist and still doubt the existence of God?

Answer - One can do whatever one likes but let's examine these particular circumstances. There are 3 responses to Platonism: (1) realism - accepting that a third realm (or something like it) actually exists apart from our material world, (2) nominalism - refusing to accept Platonism and continuing to believe that the material world is all that there is, or (3) conceptualism - accepting that there are infinite forms/abstracts (universals ('redness', 'triangularity', etc.), numbers (arithmetic axioms/mathematical truths) and propositions ("2+2 = 4", "Snow is white", etc.) but that they only exist in the mind.

Realism is the only viable alternative because: (1) the 'one over many' argument - 'triangularity', 'redness' and 'humaness' are not reducable to any particular triangle, red thing or human being; (2) the argument from geometry - the perfect of lines, angles and shapes exist apart from our minds; (3) the argument from mathematics in general - mathematical truths are necessary and unalterable (and infinite!); (4) the argument from nature - the truth or falsity of some propositions cannot be identified with anything either material or mental (even contingent ones like 'Caesar was assassinated on the Ides of March' would remain true even if the entire world and every human mind went out of existence tomorrow); (5) the argument from science - science is in the business of discovering objective, mind-independent facts; (6) the vicious regress problem - a stop sign and firetruck 'resemble' each other because they are both red and one cannot simply assert that there is nothing independently common (though the both do indeed resemble each other) as a brute fact because this simply regresses the argument to why this is a brute fact; (7) the 'words are universals too' problem - words are mutually intelligible because they express commonly understood universals, without that being true, they won't resemble each other or be able to communicate things to different minds who then won't have a clue to what the words relate to; (8) the argument from the objectivity of concepts and knowledge - similarly, concepts such as 'dog' or 'red' convey similar meaning in each mind entertaining it; and (9) the argument from the possibility of communication - communication is possible, implying that universals, numbers and propositions are mind independent. The statement, "snow is white" is communicable between you and me.

The fact that the Platonic realism is soundly vindicated by the above may not in fact directly lead to belief in God, but what does so in our proof is that an infinite and powerful source of mathematical truth is a natural progression from the Incompleteness Theorems.

10. Question: Does Platonic reasoning lead to the existence of God?

Answer - The proof does not conclude on Platonic reasoning. That is, it does not say that God must exist simply because of mathematical realism. What the proof does conclude is that God must exist because axiomatic mathematics exists with infinite explanatory power. This is along the lines of an Anslem’s ontology. However, Platonic reasoning does itself lead to a conclusion of the existence of God. To see this, consider the three alternative ways of looking at the realism of abstract objects: Platonic Realism, Aristotelian Realism and Scholastic Realism. Only Scholastic Realism necessitates the existence of God but it is defensible as the correct view on the matter. Feser in ‘Five Proofs” explains as follows.

Platonic Realism holds that abstract objects exist in a “third realm” that is neither material nor mental. They in essence, possess an aseity independent of God. One problem of Platonic reasoning is that Platonic forms appear to be casually inert. And if they have no effect, no casual capabilities, how can we know about them or refer to them as explanations? Another objection to Platonic Realism is the “Third Man argument”. A Platonic Form under this realism is both a universal (instantiated over many) and a particular (individual in its own right). But as a particular, there should be a Form it participates in and so we would have to posit a Super-Form…and so, we have an infinite regress. Another problem is that some universals may inherently contain contradictions; such as, the universal, animality, which if instantiated over both humans and animals would contradictorily entail both rationality and non-rationality. Therefore, how does animality exist as a universal in Platonic realism? Yet another problem with Platonic realism is that trees aren’t really trees and humans aren’t really humans. Trees and humans merely imperfectly instantiate treeness and humanness. If that appears absurd, it’s probably because it is.

Aristotelian Realism denies that universals exist in a “third realm”. Aristotelian realists emphasize that abstract objects are essentially tied to the mind. For example, there is animality in Socrates but it is inseparably from his rationality and specifically, his humanness. And there is animality in a dog too, but it is inseparable from its non-rationality and doggyness. So, though animality, triangularity, redness, humanness and doggyness can exist as abstract objects, they do not exist as mind-independent reality. Oderberg in ‘Real Essentialism’ writes on Aristotelian Realism, “…we do not encounter squareness in the abstract because squareness is something that we abstract, from square things. In short, nothing abstract exists without abstraction. And abstraction is an intellectual process by which we recognize what is literally shared by a multiplicity of particular things.” So far, all this seems reasonable but how would the Aristotelian realist deal with propositions, mathematical objects, necessities and possibilities? Suppose that no material world or human mind ever existed (surely a possibility), it is still possible that the material world and human minds could come into existence, but what would ground that possibility? As there is no material world to instantiate the natures or essences of it, nor human minds to even abstract those natures and essences, where is the grounding for the possibility? What about “pure possibilities” like unicorns, centaurs and mermaids? It is at least possible for these things to exist and note, their unicornity, centaurness and mermaidness are universals which neither require neither instantiations nor human mind abstractions, since their possibilities were present even before human minds ever entertained the idea of them. These pure possibilities are problematic for Aristotelian Realism. Consider also, that there are propositions that are true whether or not the material world or any human mind existed. For example, the proposition “there is no material world nor any human minds in existence” would be true if the material world and human minds all went out of existence tomorrow, and would have been true if neither had come into existence in the first place. So too are the necessary truths of mathematics and logic. Grounding such necessity is Scholastic Realism.

Scholastic Realism is Aristotelian in spirit but gives as least a nod to Platonic Realism. Like Aristotelian realism, Scholastic realism affirms that universals exist only either in the things that instantiate them, or in intellects which entertain them. It agrees that there is no Platonic “third realm” independent both of the material world and of all intellects. However, the Scholastic realist agrees with the Platonist that there must be some realm distinct both from the material world and from human and other finite intellects. In particular—and endorsing a thesis famously associated with Saint Augustine—it holds that universals, propositions, mathematical and logical truths, and necessities and possibilities exist in an infinite, eternal, divine intellect. If some form of realism must be true, then, but Platonic realism and Aristotelian realism are in various ways inadequate, then the only remaining version, Scholastic realism, must be correct. And since Scholastic realism entails that there is an infinite divine intellect, then there really must be such an intellect. In other words, God exists. This is the basic thrust of what is sometimes called the “argument from eternal truths” for the existence of God, historically associated with Augustinian philosophy and defended also by thinkers like G. W. Leibniz.

11. Question: Aren't Gödel's Theorems just dressed up Liar's paradox?

Answer - Gödel's Theorems are not a paradox as truth and provability were shown to be two different things. A paradox occurs when something true cannot possibly be so (or vice versa) while Gödel's Theorems demonstrate that there are true statements which cannot be proved. Quite evidently then, building a proof of God as the ultimate explanation of the Universe around Gödel's Theorems is not the same thing as building around the Liar's paradox.

12. Question: Don't Gödel's Theorems commit the same fallacious reasoning as the Richard Paradox?

Answer - No, Gödel's Theorems are crucially dissimilar. In Gödel's Theorems, the indeterminate theorem only mirrors (by coincidence) the meta-mathematical statement associated to it, while in the Richard Paradox, the number n is directly representative of a specific meta-mathematical expression. Therefore, in Gödel's Theorems, there isn't any ambiguity between statements within the formal system and statements about the formal system, unlike in the Richard Paradox.

13. Question: By Gödel numbering, Platonic Forms are violated, therefore, how can it be used as a justification for Platonic realism?

Answer - Criticism that Gödel numbering violates Platonic Forms is a misunderstanding of numbers as Platonic Forms. Real numbers CAN be Platonic Forms but integers are themselves abstractions depending on the formal system used. Integers can thus be encoded and axiomated (themselves Platonic Properties).

14. Question: Why was Wittgenstein mistaken in his claim that Gödel was wrong because meta-mathematics is based on tautological axioms so it must be complete and consistent?

Answer - Gödel doesn't disagree. BECAUSE meta-mathematics is complete and consistent, it justifies Platonism.

15. Question: While the proof may be logically valid and sound, does that mean it conveys truth on objective reality?

Answer -  Logic can't tell us what is objectively true or false. It does, however, tell us what is true or false relative to other statements we already know to be true or false. It is important to supplement the logical conclusions of this proof with an examination of the evidence for God (see the Faith in Jesus section and be sure to check out its references). At the very least, you can’t keep denying the mere possibility of the existence of God.

16. Question: How can one argue from a metaphysical demonstration to the real existence of a perfect or necessary being?

Answer - Anselm of Canterbury put forward an early ontological argument that moves God from a necessary being in imagination to a necessary being in reality. This is quite different from what is being done in this proof; God is a necessary being of our mathematical reality and so is a necessary being in our physical (or derived from mathematical operations in our material world) reality. In this current proof, one isn't asked to imagine anything. The positivism espoused is incontrovertible. Deflections to Kant's "Critique of Pure Reason" and Russell's teapot are sadly misguided (besides, the burden of proof has undoubtedly been met).

17. Question: Philosophers and scientists have tried for centuries to prove and disprove God, why is this proof anything other than another failed attempt?

Answer -  This is a red herring question as it does not attempt to even remotely examine the validity and soundness of the proof. As to the assertion that all other proofs of God have failed, many would disagree (See (i) Feser, Edward. 2017. "Five Proofs of the Existence of God". Ignatius Press: San Francisco; and (ii) Walls, Jerry L. and Trent Dougherty (Editors). 2018. "The Platinga Project: Two Dozen (or so) Arguments for God". Oxford University Press: New York, for just a sample of some convincing arguments).

18. Question: Just because mathematical incompleteness is true, does that mean that a TOE is impossible?

Answer -  Yes. That is precisely what it means. You can’t have a TOE of everything and have an incomplete part when it comes to arithmetic! One can of course come up with countless philosophical and otherwise explanations of why and how we've come to be here but they should not be mistaken with physics' grail of a TOE.

19. Question: Why does the proof show that God is the ultimate explanation of the Universe and not the cause of the Universe?

Answer -  It is impossible to prove causality. One can never rule out every single hypothesized cause as the “true” cause. For example, “if I jump up, I fall back to earth because gravity caused me to do so” could never be proved since I can’t rule out that the true cause of me falling back to earth isn’t in fact the sneezing of a little green man on a planet called Qudorian 400 million light years away. However, gravity is well able to predict my falling back to earth and hasn’t been falsified as a wholly satisfactory explanation so I’m in the right to accept it as the leading explanation. Similarly, I can’t rule out countless other hypothesized unfalsifiable causes of our universe but we can falsify a finite, internal explanation because of Gödel’s Incompleteness Theorem which also leads us (logical bivalence will be pleased) to an infinite, external explanation.

Nevertheless, while the proof does not relate to causation but rather explanation, I will remove some further causation concerns. The first is the asserted possibility of uncaused events, the second is self-causation and the third is a misguided epistemological conclusion from causation. 

Uncaused entities: Quantum mechanics is often used as the refutation to the necessity of causation. The nondeterministic character of quantum systems is offered to show incompatibility with the principles of causality. Additionally, Bell inequalities are cited as proof that there are correlations without causal explanation and quantum field theories show that particles can come into and go out of existence at apparent random. On the first point, a counter-objection is that from an Aristotelian point of view, it is a mistake to suppose in the first place that causality entails determinism. For a cause to be sufficient to explain its effect, it is not necessary that it causes it in a deterministic way. Secondly, as a counter-objection to the Bell inequalities criticism, several can be offered: (1) denying that causal influences never travel faster than light, (2) allowing for either backward causation or an absolute reference frame, and (3) positing a law to the effect that the correlations in question take place. Finally, as to the objection that particles can come into or go out of existence at random in a quantum vacuum, in addition to what has already been stated, Alexander Pruss suggests that one might propose a hidden variable theory, or, alternatively, propose that the system described by the laws of quantum field theory is what causes the events in question (unreasonably, we are asked to ignore the whole quantum vacuum and natural laws for this criticism to have force), albeit indeterministically. (See Feser, Edward. 2017. "Five Proofs of the Existence of God". Ignatius Press: San Francisco).

Self-causation: Self-causation is contentious because something would have to precede its own self to cause itself: a paradox. However, when applied to God who by definition is timeless (or rather, outside of time), this may not be as controversial as it first appears. Indeed, Descartes' Meditations of First Philosophy argues on such grounds. God is regarded as self-caused rather than uncaused, i.e. positive aseity. It is not as self-evident to apply positive aseity to the universe. But couldn't the universe be infinite and cause itself without the need for God? Let's assume it could, there are scientific and philosophical hurdles that render this criticism either erroneous or innocuous. If the universe (here described with infinitely present space-time) it infinite in its existence, then how does one even get to today? Time would stretch back infinitely and forward infinitely. Time becomes meaningless and so, even the present moment is unattainable. Another problem arises from confusing causation with a dependency relation. C.S. Lewis famously applied the two books on a desk illustration that could be illuminating here. Suppose we have two books on a desk, one book on top of the other. It will be correct to say that the bottom book is supporting the top book. That is, the top book owes its position in spacetime to the bottom book. Now, even if we assume that these books were always in such relation, that is, that the bottom book in no way caused the top book to be in its spacetime position, it remains nevertheless true that the bottom book is supporting the top book. So, even if we were to dismiss God as the casual factor for the universe, it is still illogical to conclude that the universe is not dependent on God or that God doesn't exist. However, suffice it to say, an infinite space-time universe doesn't fit with the current scientific understanding of our universe; our universe is finite. It has a limited amount of energy, there are even scientific detections of a beginning. Besides, a false equivalency would be have to be drawn between infinite existence and infinite explanatory power to trouble the proof. The finitary/non-finitary existence of the universe has no bearing on the need for an infinite explanatory power for there to arithmetical completeness. However, this is just one way to think of an infinite universe. The preceding is thinking of our space-time universe as always existing. There's another way to think about this: our universe could have come into existence billions of years ago (in harmony with the Big Bang Theory) but it's only part of an infinite regress and progression of existence and non-existence of universes and even just one of an infinite number of universes! An infinite multiverse! Wild stuff, to be sure! But even a hypothesized infinite multiverse universe cannot overcome the proof. This is easy to understand by the principle of proportionate causality (PPC). Essentially, PPC means that something cannot be in an effect which is not in its cause in some form. As (Feser, Edward. 2017. "Five Proofs of the Existence of God". Ignatius Press: San Francisco) explains, "Suppose for example, that I give you $20. The effect...is your having the $20, and I am the cause of this effect. But the only way I can cause that effect is if I have $20 to give you in the first place. Now there are several ways in which I might have it....When I have a $20 bill [or two $10 or four $5, etc.]...and I cause you to have it, what was in the effect was in the cause "formally"...When I don't have the $20 bill ready to hand [over] but I do have at least $20 credit in my bank account, you might say that what was in the effect was in that case in the cause "virtually"... And when I get...the power to manufacture $20 bills, you might say...that I had the $20 "eminently". When it is said, then, that what is in an effect must in some way be in its cause, what is meant is that it must be in the cause at least "virtually" or "eminently" even if not "formally"." So for an infinite multiverse to have caused our universe with the effect of mathematical incompletion means that an infinite multiverse universe must itself have (at least) the potential for mathematical incompletion of the sort we see, requiring an infinite explanatory power. We are back to square one and the argument remains intact! Another popular way to think of an infinite universe is that the universe has always gone through a series of big bangs and big crunches, over and over. This just pushes the materialist's need for an explanation for mathematical incompleteness out of our current big bang cycle but does nothing to ultimately explain. Besides, in our current big bang, the leading hypotheses favor either a continuation of expansion or an eventual finely balanced stasis, not a big crunch. The only solution for an explanation of our universe (or infinite multiverse) with mathematical incompletion remains God! Now, there is one further possible refinement to the infinite multiverse theory one may use to make God superfluous: what if an infinite multiverse had an infinite number and variety of foundational natural laws in the universes, wouldn't that render God unnecessary? Different laws of physics actually occured in the first fractions of the first second (plank time) after the big bang, the transition to our current physics is known as phase transition. But, physics is downstream from mathematics and its changes don't affect mathematical incompleteness. Regardless, multiverse reasoning is a curious case of trying to avoid the lion's claws by jumping into his mouth. In an infinite multiverse such described, God logically WILL exist. Gödel proved this with his Ontological Argument (a separate argument from what we're discussing but worth looking up). This is because as the philosopher Alvin Plantinga notes, "if every possible universe exists, then there must be a universe in which God exists, since his existence is logically possible. It then follows that since God is omnipotent and omnipresent he must exist in every universe; hence there is only one universe (added: given this shared feature), this universe, of which he is the Creator and upholder!". In each case: a single finite universe, a single infinite universe, an infinite multiverse with constant laws, a repeated series of big bangs and big crunches, or an infinite multiverse with infinitely variable laws, God must logically exist.

Finally, epistemological objections to causation that go toward a skepticism that we can never know are a red herring to the demonstration of wholly reasonable explanation. As in the case of this proof, a valid and sound metaphysical demonstration of God as a necessary explanation of our universe has been put forth, in order to truly refute it, one must demonstrate that the premises are incorrect or that the conclusion does not naturally flow, arguments to epistemological moderation are pathetically ineffective dismissals. 

​​20. Question: Doesn't this proof just prove that God is an impersonal set of infinite and eternal laws?

Answer - Don't commit a category mistake and confuse a physical law (or a mechanism of explanation) with personal agency. The proof show that our physical laws require an infinite, eternal God, not that the physical laws are God. See mathematical ontology.

21. Question: Is the proof an Argument from Eternal Truths?

Answer - Yes, but it is a specific case involving mathematical axioms. A good format for the argument from eternal truths is given by Lorraine Juliano Keller in "Two Dozen (or so) Arguments for God: The Plantinga Project". It can be summarized as: (1) Propositions represent, essentially. [premise], (2) Only agents represent fundamentally. [premise], (3) So, propositions depend for their existence on agents. [from 1, 2], (4) There are propositions that no finite agent entertains (transcendent propositions). [choice argument], (5) The representation of transcendent propositions is independent of the representation of finite agents. [from 4], (6) So, transcendent propositions cannot depend on finite agents. [from 3, 5], (7) In this website's proof, the argument is made that the complete and consistent mathematical axiomatic set represent essentially only because there exists an infinite agent who represents fundamentally. Gödel appeared to share this conviction, "Gödel was a Platonist about logic and mathematics...He held that the science of logic and mathematics are concerned with abstract, acausal, non-spatial concepts, and with objects that are unchanging and timeless or "eternals". He argued for an eternal, timeless, and fixed objective mathematical and logical reality, in part on the basis of his incompleteness theorems." Tieszen, R. 2017, "Simply Gödel", pg. 111, Simply Charly: New York.

​22. Question: How do we know that the mathematics behind dark matter and energy, accounting for at least 95% of the universe, does not lead to a conclusion of inconsistency in mathematical systems?

​Answer - This is not a falsifiable hypothesis and it is an appeal to ignorance. What we do know is that the mathematics of the visible universe is characterized by consistency and therefore, incompleteness.

23. Question: While inconsistency in mathematical axions aren't observed in our universe at present, couldn't it be possible that inconsistency was a feature of the early universe or that axioms may be different (therefore inconsistent) in other universes?

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Answer - There are falsification issues with this hypothesis, making it non-scientific. Additionally, only an argument from silence fallacy would lead to a conclusion that inconsistency is a feature of our mathematical axioms. 

24. Question: Why should I trust a philosophical argument? I only trust science.

Answer - This is a position called scientism and it is pitiably self-refuting. The assertion that science is the source of all knowledge is itself a philosophical assertion. Science proceeds on premises that the universe is rationally constructed so that it can be studied, that we can indeed have true knowledge and that our senses are capable of securing that knowledge. None of these assumptions are scientifically derived but are philosophical arguments. Thus, scientism acknowledges philosophy as capable of generating truth and therefore, it's self-defeating. 

25. Question: How could God exist alongside evolution or be good and there be evil in the world or be good and send people to hell?

Answer - These are red herring arguments. However, they are addressed here.

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