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Elsewhere, in light of the idea that understanding is not a species of knowledge but an epistemic genus parallel to knowledge, and then in terms of an understanding logic, I asked whether knowledge of analytic truth might be framed as uS → kS, i.e. some S is analytic if understanding it is sufficient in order to knowing it. The thesis that all existential S are synthetic could then be framed as something like ~(u∃S → k∃S).

The Wikipedia article on the ontological argument says of Aquinas' position on this subject:

He suggested that people cannot know the nature of God and, therefore, cannot conceive of God in the way Anselm proposed. The ontological argument would be meaningful only to someone who understands the essence of God completely.

However, Aquinas also said that God is subsistent being itself. Now Ayn Rand (in)famously axiomatized the assertion, "Existence exists." So, firstly: is, "Existence exists," analytic or synthetic (if "true" at all)? But more importantly: is it possible, in understanding existence itself, to then know whether certain things do or do not, as such, exist? As if they were "encoded" into the sheer form of existence, then. Then we might say, not that existence is analytic of God, but that God is analytic of existence (insofar as the creation/uncreation function would be a fundamental existential type).

In other words, does Aquinas implicitly advance his own ontological argument, notwithstanding his claim to disavow such an argument scheme?

EDIT: As a historical aside, consider that according to Ayn Rand, all truths are analytic because the analytic-synthetic distinction is a delusion (and unlike Quine, she does not seem to rule in favor of universally synthetic truth). Ergo, Rand's essential philosophical thesis, and an unusual one at that (not to recommend it!), is that existence truths are also analytic, and indeed, "Existence exists," would be analytically true. Modulo a reliance on principles for resolving contradictions, this thesis becomes the idea that resolving contradictions is the crux of our knowledge of what exists.

In other words, in Rand's system, foundationalism and coherentism effectively collapse into each other.

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  • (Re-post, due to error). One thing which occurred to me upon reading your (bolded) question was: Do you need to differentiate between that which exists in the form of perception/imagination vs that which exists independently of perception/imagination? Or does your question encompass that which exists both independently of & dependent upon mind? Dec 4, 2021 at 13:16
  • Assuming "existence" means existence in reality, the answer of the author of the analytic/synthetic distinction, almost universally accepted today, is no, positive existence claims are never analytic. It makes no difference whether one moves from a concept to its existence or from existence to "encoded" concepts. In the end, "not the least bit gets added to the thing when I posit in addition that this thing is. For otherwise what would exist would not be the same as what I had thought in my concept".
    – Conifold
    Dec 4, 2021 at 13:37
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    @Futilitarian, I admit I don't have a deep opinion about how existential quantification "works" in these terms. Sometimes it seems to me that existence is a property, after all, but I usually just accept Kant's thesis that modal descriptors are not otherwise substantive descriptors. At any rate, in the latter case, I take "exists" as shorthand for something like "is given outside of mere imagination." Dec 4, 2021 at 14:56
  • @Conifold, it is true that mainstream philosophy disavows analytic existence claims. It seems to me, though, that there is a community dedicated to analytic existence claims, viz. mainstream set theorists. Either per Gödel they say that large cardinal axioms "unfold" the iterative conception of sets, despite these axioms being existence claims; or they are plenitudinous Platonists who think that pure consistency establishes set-theoretic existence. Either way, on either the containment or contradiction models of analytic propositions, set theorists seem opposed to philosophers, here. Dec 4, 2021 at 22:19
  • IIRC one prominent set theorist even outright said something like, "If it is possible, it exists!" regarding which systems of large cardinals exist. (I remember the quote being the epigraph of an essay but I don't remember the exact essay...) Dec 4, 2021 at 22:20

2 Answers 2

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A start on answering your question could begin with "existence exists". I think you are misunderstanding this claim. This slogan from Rand was not a claim about existence in general, but instead a shorthand assertion of direct realism. IE that we can directly and reliably apprehend the world around us and know that what we perceive is real.

Rand is therefore making a claim about a different leg of the three recognized methods of gaining knowledge -- direct (intuitive) apprehension, analytic reasoning, and synthetic inference. Science has fairly effectively refuted direct realism, and your project is on the analytic leg, so this is probably not the best quote to start your project from.

A useful way to answer your questions about analytic knowledge is to try to drive down to what is needed for the analytic method of knowledge to be successful. There are a variety of conditions:

  • There must be one and only one true logic
  • We must be able to apprehend this one true logic and know intuitively that it IS the one true logic
  • The applications of that one true logic must be clear and unambiguously valid or invalid, such that we all can depend on it for knowledge.
  • the terms that one true logic operates on must be clear and unambiguous (if the terms are not clear, the outcome of logic processes cannot be clear)
  • Using all of the above, you will then need to show that existence is logically necessary, IE both provide a proof that some state is necessary, plus a proof that logic can be causal of reality.

The current majority views of philosophy are that every one of those preconditions are suspect.

The current consensus among logicians is that logic is pluralistic: https://www.cambridge.org/core/journals/think/article/abs/guide-to-logical-pluralism-for-nonlogicians/EDFDFA1C9EB65DB71848DABD6B12D877

Logical pluralism was arrived at, because of non-classical logics that give different but valid answers from classical logic. Which leaves us with no clearly perceived "one true logic".

What one can actually demonstrate using logic, even when one has disputants who all share the same concept of "one true logic" is often in dispute, bringing the third point into question.

Key definitions you will need, appear to be intractably fuzzy. Let us take your premise of getting from "understanding" to "knowledge", as an example. BOTH understanding and knowledge are terms with fuzzy definitions, and much dispute about their content. Analyticity is impossible with fuzzy terms.

And our universe, and the laws in it, appear to be intrinsically contingent. https://www.pnas.org/content/93/25/14256 And a contingent thing CANNOT be necessary.

All of these inferences apply to human thinking. One COULD postulate that a God's thinking is fundamentally different, rather than just being human-like, to a larger scale. But then one would need to spell out a NECESSARY Judaification for a God to think radically differently from humans, in ways that would make your argument work.

Your project may not be impossible, but it has a lot of tasks that need to be addressed before it can be considered plausible.

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  • I appreciate the bullet points you list, and (oddly?) one of my responses to their theme, in the essay I'm writing, is something called methodological pluralism. Some of your remarks do not engage with the premises of my argument (e.g. "Analyticity is impossible with fuzzy terms," only applies to uses of the word 'analyticity' more in line with the explicit tradition than my use apparently is) but more importantly, the OP really is more about Aquinas than anything else, even (especially!) Ayn Rand. There is a set-theoretic question at stake for me too, but for now that is an aside. Feb 1 at 11:42
  • As far as referencing Rand at all, it was long ago recommended to me that when writing essays, you want to start out with something that will both engage your audience and then lead into the rest of your essay. Rand seems likelier to "engage" the average outsider audience member than Aquinas. On top of that, though, my "avowed enemy" in philosophy, Cornelius van Til, claimed that the created-uncreated dichotomy was a metaphysical primitive in the academic-philosophy sense, and does after all seem to be a concept of existence itself. So to roundabout-reply to that man, though he is dead... Feb 1 at 11:45
  • @KristianBerry - I saw that you wanted to get eventually to God>>Necessary Existence. Aquinas was very much in the Analytic leg of knowledge, and asserted my last bullet point. But I don't think we can very usefully discuss his own arguments, because the prior ones I listed which tend to make the analytic leg invalid in the minds of most philosophers, were developed after he wrote. To recreate his conclusions, modern thinkers have a huge project, of overturning a massive set of uncertainties we have since established. Or living with them, and making analyticity work anyway.
    – Dcleve
    Feb 1 at 15:40
  • To some extent I'm sometimes a "fan" of Rawls' statements in AToJ about replacement conceptions. Rather than make my essay (or at least some crucial section of it) depend on whether validates a classical or semiclassical analytic-synthetic distinction, I point towards a distinction identifiable in other terms, but clearly (particular cases can be distinctly constructed), and then say something to the effect that we 'might as well' call this the analytic-synthetic distinction, since it does what that was 'supposed' to do, maybe. Feb 1 at 21:55
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I do not have an answer to your main question, but I think you misunderstand Rand's argument on this matter, so I'll try to clean that part up, and hopefully this will help your analysis. You say (correctly) that Rand rejects the analytic-synthetic dichotomy, but then you go on to attribute to her positions which are rooted in that dichotomy --- i.e., that truths are "analytic", etc. That is a contradictory position you put, and I am not aware of Rand having ever characterised her philosophy in the ways you attribute to her. (For example, I notice that you provide no reference for the assertion that Rand asserted all truths to be "analytic"; if she actually said this, can you show where?)

Since Rand rejected the validity of the analytic-synthetic dichotomy, quite naturally, she didn't then try to fit her philosophy into that dichotomy. Attempts to try to mash her philosophy into these other categories are not really all that helpful, since they gloss over different underlying premises (e.g., in what a concept is).

On this point, it might help to understand the reason that Rand rejected the analytic-synthetic dichotomy. As explained in detail by Piekoff (see e.g., here), this dichotomy is rooted in an epistemological theory that treats concepts as consisting of certain essential aspects of existents (which form part of the definition of the concept), but excluding non-essential aspects of those existents. This means that some aspects of the referent existents are included in the concept and some are not, which leads to the analytic-synthetic split. Contrarily, the Objectivist theory of concepts says that a concept refers to all of its referent existents, and thereby includes all the properties of those existents. An example used in this discussion is the concept of a "bachelor", defined as an "unmarried adult male". Under the Objectivist epistemology, this concept would refer to all actual unmarried adult males, with all their attendant properties. In the A-S system, a statement like "bachelors cannot fly by flapping their arms" is considered a synthetic truth, since the concept is considered to be equivalent to its definition, and the means of locomotion is not an essential part of the concept of a "bachelor". However, in the Objectivist system it is the existents that form the concept (and the definition merely circumscribes which existents are included). In this latter system there is no split between essential/inessential properties, so a statement like "bachelors cannot fly by flapping their arms" is just true --- not an analytic truth or synthetic truth, just a truth.

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  • If the definition of analytic knowledge is "knowledge grounded in applying the laws of identity and noncontradiction," which is the definition going back to Kant, then Rand's theory of knowledge is thoroughly analytical as such, regardless of her refusal to use the relevant words. It's like saying that Aquinas equated analytic and self-evident knowledge; true, though he didn't use the precise description "analytic" (or some Latin cognate). Jan 4 at 15:53
  • Again, your initial question heavily misrepresents Rand (and you seem to walk this back somewhat in the present comment). Re the definition of analytic knowledge (as described by Kant), that is not how knowledge is formed within Rand's theory. Indeed, Objectivist epistemology heavily stresses observation of the world as the means of obtaining knowledge (including knowledge of the axioms of the theory).
    – Ben
    Jan 4 at 21:27
  • You seem to be conflating a rejection of apriority with a rejection of analyticity, and this does go back to Kant (though inconsistently, i.e. 'officially' he says there is no analytic aposteriority, but he then goes on to describe things as analytic and a posteriori together at times). At any rate, I am not deeply invested in defending (or critiquing) Ayn Rand, so a perfect interpretation of her philosophy is not something I aim at or look for. As if there were in her case such a perfect interpretation possible, when it seems doubtfully possible respecting many others. Jan 8 at 1:21

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