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A Case Against Omniscience:
Infinite Regress

3. Reply to Objections to
Infinite Regress of Reasons

In this section, I consider objections to my Argument from Infinite Regress of Reasons. Below is a complete list of objections considered. For other pertinent replies to infinite regress arguments, see my responses to objections to my second argument, the Argument from Infinite Regress of Knowing.

Book cover: Democracy and Its Crisis by A. C. Grayling

Objection 1: You have assumed that X/God is omniscient and then concluded that X/God is not omniscient. You have contradicted yourself.

Reply: In laying out my premises, nowhere do I assume that X is omniscient. All of my premises (1) to (9) are conditional statements only. They say what is the case if X is omniscient. Then, in the Analysis and Conclusion section, I explore the implications of assuming that X is omniscient and conclude that either way one attempts to short circuit the infinite loop of justifications leads to a contradiction. This form of argument from assuming the contrary of the conclusion to demonstrating a contradiction is a standard reductio ad absurdum.

Objection 2: Your argument assumes that God reasons sequentially, one truth at a time.

Reply: There is an arguable case to be made for thinking that a knower who knows that they know a truth is engaged in a temporal process of first knowing and then evaluating their reasons for knowing that they know. However, my argument can do without that supposition while remaining sound. How? When I refer in §2 to the 'sequence of justifications' that 'repeat without end', this 'sequence' can be just as easily understood as not existing in time.

An example of such an atemporal sequence is the set of natural numbers. Each number in the series of natural numbers is defined as the successor of the previous number. A feature that this set shares with the series of epistemic justifications featured in my argument is that it contains an infinite number of members. In both cases, atemporality is not an impediment to the sequencing. Similarly, just as there is no final number in the series of natural numbers, there is no final justification in the series of justifications afforded by a posited omniscient knower. And with no final justification, there is no perfect knowledge of all things known.

Giving up temporality for God, though, comes at a cost for the classical theist. If God does not exist in time, then all of the historical events attributed to the divine being in the holy texts could not have happened (e.g., world's creation, Noah's flood, handing down the Decalogue). Nor can hoped-for future divine actions eventuate (e.g., answering prayers, forgiving sins, judging actions on Judgment Day). Secondly, if God does not exist in time, God cannot know the fact that I am writing this reply now. If God does not know that basic fact, he can't be omniscient. (For more on the problem of indexicals such as 'now', see Grim [1983, 1985, 2013].

Objection 3: All of your premises assuming God's knowledge is propositional are false. God's knowledge is 'knowledge by identity' where the knower is identical with its object. At the limit, the distinction between knower and known vanishes. What is known by an omniscient being is not knowledge in our usual sense of 'justified true belief'.

Reply: My argument does not assume that God's knowledge is propositional. It refers throughout to what is known as 'truths'. Notwithstanding, what of the claim that there is no distinction between the knower and what is known? Aurobindo gives an example of this type of 'knowledge by identity' as when we experience an 'uprush of wrath' in which 'we lose sight of the thinker and become the thought and the thinking' [1940: 544]. If all of God's knowledge were of this kind, then it strains comprehension to see how God can knows truths that are expressed in abstract language, such as '2+2=4' and 'All bachelors are unmarried'. It becomes even more incomprehensible to think that God is identical with negative conceptual truths, such as 'It is false that 2+2=5' and 'It is a lie that all bachelors are married'. If it be admitted that God is not identical with these kinds of truths (and therefore does not 'know' them), then there are many things that God does not know that we mere mortals know as a matter of course. In that case, God is not omniscient.

Secondly, if God's knowledge was of this immediate kind, then his omniscience conflicts with his moral perfection. Consider, for example, what it's like to be angry and to torture an innocent child for sheer pleasure. If God knows what it's like to be angry, he literally is the anger. If God knows what it's like to torture an innocent child for sheer pleasure, then he literally is the torturing of an innocent child for sheer pleasure. Knowledge of this kind also conflicts potentially with his immutability. If God knows there are floods now in Pakistan, then he changes his state when the floods subside.

Objection 4: In your argument you assume wrongly that for a knower to know a truth, it must be capable of epistemically justifying the truth.

Reply: This may be true of conscious beings with low cognitive ability, such as very young children and non-human sentient creatures. In a sense, we can say that a very young child and a giraffe 'know' that there is a tree in front of them simply on the basis that they are awake and looking towards the tree with their vision systems functioning correctly; that is, on the basis that they are standing in the right casual relation to the tree seen. In such a case, we do not require the very young child and the giraffe to give a verbalized reason for knowing that there is a tree before them. My argument, however, references knowers who believe themselves omniscient. Having that kind of belief requires a cognitive capacity that understands the concepts, at the least, of 'truth', 'know', 'reason' and 'justification'.

Book cover: Dialogues Concerning Natural Religion by David Hume

For such a knower, if a belief in a truth cannot be justified, it is mere belief, whim or opinion and not knowledge. The dominant theories of knowledge proposed by philosophers distinguish between such mere belief, whim and opinion on the one hand and genuine knowledge on the other using some criteria of epistemic justification. Without such reasonable grounds for believing, what warrant does any knower capable of abstract conceptual thought have for claiming knowledge and not simply for evincing some subjective feeling of conviction? For a knower who believes they are omniscient and is in fact omniscient, they must have a watertight reason for knowing they are omniscient. Otherwise, all they have is an ungrounded belief, whim or opinion.

What will follow if we excuse the need for epistemic justification for a belief that one is omniscient? Well-known philosopher of religion, Alvin Plantinga [2000: 109], suggests just such an excuse when he writes:

Not even God himself, necessarily omniscient as he is, can give a noncircular argument for the reliability of his ways of forming beliefs. God himself is trapped inside the circle of his own ideas.

Here we have a solipsist God, on Plantinga's own admission 'trapped inside' his own thinking. This supposed God can't know then that his means of knowing is reliable, other than via his own internal reasoning.[2] This God is in no more an epistemically robust position than those psychotic patients occupying mental facilities who sincerely think they are God. (For a study of such cases, see, for example, Moralis [2008: 260] and Rudalevičienė et al [2008].)

The upshot here is that if we do not require an omniscient knower to have a justifiable reason for believing itself omniscient before we accept their claim to omniscience, we will be lumbered with a large surplus of omniscient beings. We will end up with one omniscient knower for every delusional person who believes that they are God.

Objection 5: If an infinite regress of justifications were required for knowledge, no one would know anything. If knowledge of any truth required a justificatory reason that is itself distinct from the truth known and that also must be known, we would all end up with the vicious regress you point out. Your presumption that every instance of knowledge must have an independent foundation is self-defeating, leading to universal skepticism.

Reply: Firstly, if the requirement for independent justification for each instance of knowledge leads to universal skepticism, then that is not a reason in itself to dismiss my argument. Perhaps the notion that we know anything and the notion that omniscience can be instantiated must both be discarded.

Secondly, my argument does not presume any particular theory of justification. For example, a coherentist or fallibilist theory of knowledge is consistent with the premises of my argument. On this account, the epistemic demands on a perfect knower are different to the demands on a fallible human knower. Unlike a perfect knower, we human knowers must be content in providing a stop point in our series of justifications for reasons of practicality. Our termination point is context dependent and occurs where the point of stopping incurs a minimal risk of a very unfortunate outcome. This is the case in ordinary discourse, in scientific reasoning and reasoning in logic, mathematics, geometry, etc. The price we humans pay is fallibility for all of our knowledge claims. An omniscient knower, on the other hand, having perfect knowledge of all truths, is not so encumbered by contextual limitations. As a perfect knower, an omniscient knower necessarily knows much, much more that we fallible knowers. That's how, on a coherentist or fallibilist account of justification, it's possible for we mere mortals to possess knowledge without leading to an infinite regress of justifications.

Objection 6: It is possible that an omniscient knower does not use discursive/inferential reasoning. In classical theism, the very need to reason discursively/inferentially, that is, in terms of distinct truths linked together into arguments, is a feature of embodied intellects only and not of God.

Reply: It appears that the notion that a knower can know every truth non-discursively/non-inferentially appears incoherent. Understanding any formal logical rule of inference requires reasoning discursively. Otherwise, the rule of inference escapes the knower's understanding. Take any disjunction of the form: 'P OR Q' and the additional premise: 'NOT P'. For any knower to know that 'P OR Q' and 'NOT P' entails 'Q' requires applying the rule of inference known as 'Disjunctive Syllogism' to the two premises to entail the conclusion. Without applying this discursive rule of inference, any knower, including an omniscient knower, does not know the truth of the theorem:

'P OR Q' and 'NOT P' entails 'Q'

For a knower to know what 'entailment' is, they must apprehend and understand that entailment is a discursive process. To claim otherwise is akin to claiming that a knower can know the meaning of 'red' without ever having the experience of redness. Even understanding the meaning of the logical operators ('AND', 'OR', etc.) requires discursive thinking. Each logical operator is defined by the iterative assignment of possible truth values (as set out in the logical operator's truth table). If a knower doesn't know the truth value of 'P AND Q' for each iterative assignment of truth values to P and Q, then they haven't understood 'P AND Q'.

What I'm pointing out here is that it's a mistake to presume that the need to reason discursively/inferentially is a feature only of embodied intellects. Reasoning discursively is a necessary requirement for knowing what logical entailment is whatever the metaphysical nature of the knower.

What I said above about understanding logical inference applies also to mathematical knowledge. From the 1800s, work in the axiomatization of mathematics has laid bare the understanding of mathematical objects as the iterative application of a small number of rules to a minimal set of axioms. These axiomatizations reveal how each number generated is the result of the application of the 'successor' function.[3] So, again, a knower cannot know what a number is unless they recognize the recursive application of the rule that generates them. In mathematics, the application of a small number of rules of inference generates an infinite number of natural numbers. Likewise, using the rules of logical inference generates an infinite number of theorems in logic.[4]

Even understanding the word 'non-recursive' itself requires recursive reasoning. Understanding the word requires applying the rule: whenever you see the prefix 'non-' added to the beginning of an English word, understand the meaning of the composite word to be the denial of whatever follows the prefix.

Book cover: Summa Theologica by Thomas Aquinas

A classical theist may concede all of the above, admitting that an omniscient knower must understand fully the necessary recursive and discursive elements of mathematics and logic. However, they may say, an omniscient God does not understand the truths of mathematics and logic successively, one thing at a time. God understands all at once, they may say. In his Summa Theologica, Aquinas likens God's non-discursive understanding to the way we limited humans understand some discursions all at once. As Aquinas puts it:

For many things, which we understand in succession if each is considered in itself, we understand simultaneously if we see them in some one thing; if, for instance, we understand the parts in the whole, or see different things in a mirror.

[ST 1.14.7]

I concur that we sometimes get a flash of insight into understanding a proof or theorem at an intuitive level. I recall a number of times when studying logic and working through a proof using the truth table method line by line. Some time afterwards, the proof just 'clicked' with me. However, that intuitive insight I had did not replace my line-by-line reasoning. Nor did it legitimate my line-by-line understanding. Without that line-by-line analysis, that insight of mine can no more count as genuine knowledge as the 'insight' of the pseudo-scientist who proclaims boldly that Einstein's four-dimensional space-time model is fundamentally mistaken. That moment of insight is the reward that comes after many, many hours working discursively through the proofs. That moment of insight is not a short-cut alternative to reasoned, discursive analysis, but is grounded in it. If there is an omniscient knower, its in-an-instant 'grasp' of a whole similarly counts as knowledge only if grounded in a prior proper analysis of the parts of the proof.

Objection 7: Your argument completely misses the mark because God's perfect knowledge is incomparable to our limited human knowledge.

Reply: This objection varies somewhat according to which aspect of 'knowing' the theist is claiming does not apply to God and that I have assumed applies in my argument. Whatever the particular claim, this genre of objection attempts to avoid consideration of the steps in my argument altogether. On this objection, God's knowledge is somehow special. The examples of this asserted exceptionalism I will treat here are:

God's knowledge does not consist of beliefs.

God's knowledge does not require justification.

God's knowledge does not require a good reason to believe.

This claim is usually made in conjunction with some metaphysical claim about God that appears to ground the exception. Depending on the particular theist who is objecting, God is 'the ground of being', 'is being', 'is truth', 'is knowledge', 'is the ground of knowledge', 'is everything', 'is necessary', 'is maximally great', 'is eternal', 'is infinite', 'is immaterial' or 'is omnipotent'.

Now, my argument makes no statement about the truth or otherwise of any of these attributions of God. Theists disagree among themselves about which metaphysical attributes apply to God necessarily and about how each impacts logically on other claimed attributes. Leaving that aside for the classical theists to dispute over, my argument focuses on one claim and one claim only: that God is omniscient. If it is impossible for God to know all things, then all 'God' claims of the classical sort fail.

My response to the claim of exceptionalism about God's knowledge is that these classical theists have co-opted the term 'knowledge' for use in a highly idiosyncratic fashion. This usage is so divorced from common usage that it bears little to no resemblance both to the ordinary and philosophically accepted meaning of 'knowledge'.

One method we use to test the semantically essential necessary aspects of the meaning of a word is by using counterposition. Imagine a person in a usual conversational setting saying any of the following:

'I know I am taller than my sister, but I don't believe it.'

'I know that water is made up of oxygen and hydrogen, but I have no justification for saying that.'

'I know that Paris is the capital of France, but I have no good reason to believe it.'

Our first question to such a speaker is whether they are using the term 'believe'/'justification'/'good reason' in scare quotes; quoting someone else's use of that term (use–mention distinction). If they say 'no', that they are using the term in its usual sense and that they are genuine in their assertion, then we are right to think that they misunderstand the meaning of the word and have not mastered its use in conversation. We are right to think that they are not a competent user as yet of that term. This demonstrates that for sentences such as, 'I know trees are plants', there is an inextricable semantic link between the term 'know' on the one hand and 'believe', 'justification' and 'good reason' on the other. To divorce these semantic connections is to misconstrue seriously the meaning of the word 'know'.

Book cover: The Miracle of Theism by J. L. Mackie

Not only are these theists' use of the term 'know' when they apply it to God a corruption of ordinary usage, this mischaracterization is also not supported by the dominant theories of knowledge. I refer readers to Ichikawa and Steup's [2018] most up-to-date and authoritative review of the work in this field. Their review articulates how the most current theories in epistemology continue to maintain (from the time of Plato) that to know that something is true is to, at the least, 'believe' it true, be 'justified' or have a 'good reason' or a 'sufficient reason' to believe it true, or stand in the appropriate epistemic relation to what is known. All of this is standard fare in the field of epistemology.

I also refer readers to the definitions of 'know' given by the most authoritative dictionaries (e.g., Cambridge, Merriam-Webster, Collins). These define 'know' as a cognitive process in which a mind apprehends a fact or truth.

So, when the premises of my argument describe an omniscient knower 'believing' a truth on the basis of a 'justificatory reason', then my use of the term 'know' faithfully represents the essential semantic aspects of the word. On the other hand, classical theists who reject one or more of these necessary aspects of 'knowing' are using the word in a way that is supported neither by common usage nor by expert analysis by professional epistemologists.

The classical theist may respond here that their usage is a defining characteristic of classical theism and that if I am to criticize classical theism, I need to do it on their terms. My response is that I and other critics are not obligated to go along with the classical theists 'bait and switch' here. My advice to classical theists who wish to hang on to their claim that God holds some kind of special epistemic relationship with truths is that they use specially formulated terms specific to their purpose (e.g., use 'omnibient' in place of 'omniscient' and 'krow' in place of 'know'). In that way, the public, lay religious and other interested parties will not be misled into thinking that classical theists mean that God is really 'omniscient' and 'all-knowing'.

Objection 8: Your argument is not really an argument against the existence of God. At best, it's an argument against God having the attribute of omniscience.

Reply: I agree that my argument is not an argument against the existence of every kind of conceived God. My argument is particularly focused on the classical conception of God as a perfect being. However, perfection in attributes has been seen as a necessary requirement for divinity by key religious thinkers through the ages, from Anselm to Aquinas to Descartes to most modern-day theologians of all stripes. Secondly, if God is not thought of as perfect in all his attributes, then it becomes more difficult to regard such a God as worshipworthy.

Footnotes

  1. [2] It may be thought that since Plantinga's God is 'necessarily omniscient', that this will allow God to escape from his solipsist world. It does not. On one reading of 'necessarily omniscient', God is necessarily omniscient in the same way that bachelors are necessarily unmarried and male. Such necessity is simply in virtue of the meanings of the words 'God' and 'bachelor'. This kind of logical/semantic necessity does not guarantee that God or bachelors, in fact, exist. On the other hand, the Scholastics, taking a leaf from Aristotle's book, thought that each kind of being possessed its own 'essential' or 'necessary' attributes. However, even if we grant this sense of a 'necessary' attribute, it does not help the classical theist. Any being can only possess an attribute necessarily if that being, in fact, exists. If the being does not exist, there are no necessary attributes for it to possess. And my argument gives us reason to believe, in the case of God, that it is impossible for such a being to exist.
  2. [3] In Peano's systematization, for example, each successive natural number results from the application of the 'successor' function S. So, the number 1 is defined as the successor of 0 or S(0), 2 is defined as the successor of the successor of 0 or S(S(0)), and so on for all of the natural numbers. In this way, the successive application of the single S function generates the infinite number of natural numbers.
  3. [4] For example, the Addition rule generates 'AAB'; 'AABC'; 'AABCD' and so on and so on to a theorem with infinitely many elements.

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