GUENON’S INFINITY: SOME MORE CLARIFICATIONS

Cantus Laud did me a favour and responded to my post on the “ Guenonian proof “. Let me say here that I appreciate it. It was clear and straight to the point, something I like in Cantus’ writing. I also like that he took my advice and rearranged the arguments in a more coherent form. I will have to learn how to do that sooner or later. That said, he thinks the argument fails. Not that he isn’t a Theist, he just isn’t a “Classical Theist”, if I could use that term; meaning He does not subscribe to the “classical” theistic philosophies (Aristotelian, Platonist, etc) that have a particular view of God’s being (Divine Simplicity, Aseity, Infinity, etc.). Before I address his response, I want to show his rearrangement of the Guenonian argument:

1. If the infinite exists, then it is that which has no limits. [ASSUMPTION (see notes)]
2. The infinite can be conceived in the mind. [ASSUMPTION]
3. Whatever can be conceived in the mind exists in the mind, [ASSUMPTION]
4. The infinite exists in the mind [2, 3, UNIVERSAL-ELIMINATION]
5. The infinite can either exist only in the mind or in reality outside the mind. [4, WEDGE-INTRODUCTION]
6. The infinite exists [4, EXISTENTIAL-INTRODUCTION]
7. The infinite is that which has no limits [1,6 ARROW-ELIMINATION]
8. The infinite does not have limited existence [7, SIMPLIFICATION (see notes)]
9. If the infinite does not have limited existence, then the infinite does not exist only in the mind. [ASSUMPTION]
10. The infinite does not exist only in the mind. [8, 9, ARROW-ELIMINATION]
11. The infinite exists in reality outside the mind. [5, 10, WEDGE-ELIMINATION]
12. The infinite exists in reality outside the mind and the infinite does not have limited existence. [8,11, AMPERSAND-INTRODUCTION]
13. If the infinite exists in reality outside the mind and the infinite does not have limited existence, then the infinite is not the universe [ASSUMPTION]
14. The infinite is not the universe [12, 13, ARROW-ELIMINATION]
15. If there is more than one thing that is infinite, then the things that are infinite exclude one another. [ASSUMPTION]
16. If the things that are infinite exclude one another, then the things that are infinite are limited. [ASSUMPTION]
17. There is more than one thing is infinite [ASSUMPTION (to be discharged)]
18. The things that are infinite exclude one another. [15, 17, ARROW-ELIMINATION]
19. The things that are infinite are limited. [16, 18, ARROW-ELIMINATION]
20. It is not the case that there is more than one thing that is infinite. [7, 19, REDUCTIO AD ABSURDUM (17 is discharged)]
21. There is either some greater quality than the infinite or the infinite is the quality that is the greatest of all qualities. [ASSUMPTION]
22. If something is greater than the infinite, then the infinite is limited. [ASSUMPTION]
23. It is not the case that there is something greater than the infinite. [7, 22, MODUS TOLLENDO TOLLENS]
24. The infinite is the quality that is the greatest of all qualities. [21, 23, WEDGE-ELIMINATION]
25. If a quality is the greatest of all qualities, then the quality that is the greatest of all qualities is instantiated. [ASSUMPTION]
26. A quality is the greatest of all qualities. [24, EXISTENTIAL-INTRODUCTION]
27. The quality that is the greatest of all qualities is instantiated. [25, 26, ARROW-ELIMINATION]
28. The infinite is instantiated. [24, 27, IDENTITY-ELIMINATION]
29. If the infinite is not the universe & if it is not the case that there is more than one thing that is infinite & if the infinite is the greatest of all qualities & if the infinite is instantiated, then God exists [ASSUMPTION]
30. The infinite is not the universe, it is not the case that there is more than one thing that is infinite, the infinite is the greatest of all qualities, and the infinite is instantiated. [n.b. skipping steps. Do AMPERSAND-INTRODUCTION on 14 and 20, then the result on 24, then again on 28]
31. God exists [29, 30, ARROW-ELIMINATION]

It is safe to say I mostly agree with the way he arranged the argument. I only have a slight quibble with the way 1 was put, but we’ll address that later in the post. The first problem he has with the argument is:

First, here’s the ambiguity. A word can sometimes refer to the concept of the thing it refers to or otherwise the thing it refers to itself. If “whatever can be conceived in the mind” in premise 3 refers to my concept of the infinite then 3 is true. The concept of whatever I can conceive in the mind of course exists in the mind. My concept of a kettle exists in my mind even if actual kettles do not. On this story either 7 is an invalid inference or 1 is false. If “the infinite” in 1 is disambiguated as a straight referring term then 7 is invalid as the antecedent of 1 is not satisfied by 3. 3 infects 4 with its disambiguation (as 4 is derived from 2 and 3) and then 4 in turn infects 6. So, when 7 uses 6 with 1 the referent of “the infinite” in 6 is the concept and therefore does not match the referent of “the infinite” in 1 (which is the actual thing referred to). If “the infinite” in 1 also means concept-of-the-infinite then this would satisfy the antecedent. The problem is that 1 would be just false as our concept of the infinite has limits; one of which is that it is contained inside our minds. Another is that it is just a concept and is whatever a concept is (Abbreviated definitions? Informational indicators? There is no consensus among philosophers or psychologists on this one).

It is from here I realized our disagreement begins and ends in the disagreement between what I will label the “Platonist” and “Non-Platonist” understandings of reality (Now called P and NP respectively); Cantus is represented in the latter while I am represented in the former. Keep in mind that these terms refer not just to their relationship to the thoughts of the ancient Plato, but to a particular “tendency” or “agreement” between philosophers old and new, east and west; “Plato” being possibly the most famous of them.

Let me begin my response to this by saying that I concur that there is no agreement between philosophers and psychologists as to what a “concept” is, although I have to say this lack of consensus is very modern, as the west has been more or less “Platonic” for a long time, and barring minor details, many, if not most, classical philosophies had a pretty good idea of what a “concept” is. It seems to me that there was much greater consensus then than now. I also think that such a Platonic definition of “concept” cannot be reached by psychologists, precisely because of the metaphysical nature of such a definition.

This disagreement between P and NP is in very much seen in the wording of Cantus’ objections. In the above quote Cantus views the mind as a “container” of sorts (of course not a “literal” container), where there are “thoughts” and “concepts”, which are discrete “objects” on their own, bearing what seems like an accidental relationship with whatever is “outside” the mind, the “outside” in question being what some might call the “real world”. It is from this that Cantus can (rightly) say that if “the infinite” is a straight referring term (that is if there is an “actual infinite” in the mind), then the definition in 1 (If the infinite exists, then it is that which has no limits) is not satisfied by the 3 (whatever can be conceived by the mind exists in the mind) because the mind is limited, while the infinite is not supposed to be.

But, that is not what I mean by either “conceived” or “exists in the mind”. If I saw the world in the way Cantus seems to be assuming, then he would have me dead to rights. However, I see the world quite differently. Rather than a container, P sees the mind as a “mirror” or a “lens”, depending on whether you want to stress the mind’s passive “substance” or active “essence” [1]. The mind, for P, is a tool of the “intellect”, an intermediary between the impersonal (or supra-personal) irreducible subject “I” and the object “it”. Following the metaphor of the “mirror”, the mind only “conceives” an “image” of what already is. It “reflects” reality rather than “containing” it, except in a derived sense, where a reflection “contains” an image of something real and independent of it. This “reflection” goes both ways. Just as an object in the reality we are used to can, through its appearance, impress upon our minds, so to can “objects” not from our “physical” world impress upon it from the “intellect”. These “conceptions” come from the “ideas” and are synonymous with what is “possible”, in that what is impossible in the absolute sense (or in the sense of impossible in any “possible” world) is strictly unimaginable and absurd. We cannot imagine or “conceive” it, because if we could, then that means it can be actual in some world with which it is “compossible” (to use Leibnitz’s language), making it “possible” in the widest definition of the world. What this means is that, following this metaphor to its end, that there is nothing “conceivable” that isn’t “real” in some sense, and that doesn’t “exist” in some sense.

This sense of “real” is exactly why P believes in the existence of a “realm of forms/ideas”, Schuon himself equating “ideas/forms” with the “possible”:

The notion of possibility gives rise a priori to two interpretations, the first “horizontal” and the second “vertical”, analogically speaking: on the one hand we say “that is possible, therefore it can be done”; on the other hand we say, “that has been done, or that exists, therefore it was possible”. In the first case, the possible is what may either be or not be, and is thus opposed to the necessary, which must be; in the second case, the possible is what can and must be, and is therefore causal and produces something which is necessary since it exists. In the latter sense, the notion of the possible corresponds to a retrospective observation, possibility being then an underlying potency which is directed at a necessity of manifestation; in the other sense, the notion is prospective and opens out onto the uncertain. On the one hand, it is possible to pick fruit, therefore I can do so in principle, but it may be that I cannot do so in fact; on the other hand, I have picked fruit, therefore it was possible for me; or again, a particular fruit exists, therefore it corresponds to a possibility within earthly existence. Starting from the more or less empirical distinction between the “possible” and the “real”, one may say, in this respect, that what manifests itself is “real” and that what can either manifest itself or not is merely “possible”; but in another respect, which abolishes this distinction, it is the possible which is the real, manifestation being accidental or illusory; in this case, the possible is identified with a Platonic archetype, therefore with a concrete element in the divine Order and not with a human uncertainty. In other words, instead of limiting ourselves to distinguishing between the “possible” and the “real”, which without being false is nonetheless insufficient, we ought, on the one hand, to distinguish between the contingently possible and the necessary and, on the other hand, between the principially possible and the actual; the necessary is more than the possible if this last term is taken to mean the indefinite expanse of modal and temporal contingencies, but the possible as principial potency is eminently more real than the actual or the manifested. It goes without saying that cosmic, therefore manifested and non-principial, necessities are by definition contingent to some degree, and conversely that realized contingencies are relatively necessary. [2]

In this way of seeing things, “conception” is not a “trick” or “power” of the mind to “create” or “conceive” something ex nihilo, whether or not it conforms to reality, but the mind’s ability to hold in itself something of the real, a “reflection”, by which it is “united” to what it reflects, and to what it reflects to. We still use the word “reflection” to refer to deep thought, and it is the “I” that we are “reflecting” to. Who this transpersonal “I” is should be apparent to anyone who knows Neo-platonic and “Vedantic” thought. Therefore, to say something “exists” in the mind does not mean it is limited to the mind as such. The form my original argument is put may obscure this, and I take responsibility for that, although I did say I dislike syllogisms. What I mean by “exists in the mind alone” is that a concept may not correspond to something in what we may call “physically manifested reality”, or more correctly “our world”, since it is possible that there are “physical worlds” beyond our own (some would call it an “alternate universe”, and I do believe there are, for reasons related to, but beyond the scope of this post). The idea itself exists in the “realm of forms”, which is not the mind, but what Plotinus called the “Intellect”, an explanation of which is also beyond the scope of this post, but is well explained by Gerson [3]. The infinite may be manifested in (or to) the mind, but if assumption 1 holds true, it cannot just be manifest in the mind. It cannot also remain confined to the world of ideas, or any “world” and realm in particular, but all realms and all worlds. In fact this definition should lead one to the conclusion that the “location” of the infinite is not confined to any realm whatsoever, that of forms or otherwise. You cannot “conceive” of the infinite the way you conceive of a kettle, or “faux-heat” (to use two of Cantus’ examples). Speaking of “faux-heat”, Cantus uses this to explain why he thinks the Platonic view cannot save the argument:

The problem is with concepts with necessarily non-existent referents. I have the ability to sit down and imagine that heat is not mean molecular motion. However, heat necessarily mean molecular motion. We may call my concept of heat that is not mean molecular motion “faux-heat”. My concept of faux-heat cannot be the result of faux-heat manifesting itself in my mind in some way as faux-heat is necessarily impossible.

On the wider point of “non-existent referents”, see the previous paragraph, where I talk about what I mean by “exists in the mind”. Concerning the example, the problem I find with it is that “meaning” is a loaded term, and unless you’re a hard core philosophical materialist (Cantus is a materialist, but not a materialist monist), a phenomenon can “mean” several things at once. The Sun is a star. The Sun is also a fusion powered ball of gas and dust. The former is not strictly reducible to the latter, as there are many meanings of the word “star”, such as a ruling angel, or a bright object in sky (which may or may not be a fusion powered gas ball). “Heat” can mean the reproductive “state” of a biological organism, and such a definition is certainly not compatible with the idea that heat necessarily means molecular motion, that is, if “necessarily” here means that “Heat” must mean only “molecular motion”. Even if we want to get more specific and limit “Heat” to mean the phenomena that the concept of “molecular motion” describes on a molecular level, the term “Heat” does not necessarily mean molecular motion, precisely because on the scale of humans we do not “experience” it as such. Heat can also mean the “energy” latent in a material, and we don’t have to conceive of, or discover “molecular motion” in order for that definition to be valid in its own sphere. When computing phenomena, we often represent them in terms other than their molecular or atomic realities. We don’t model “molecular motion” but things like latent heat, heat capacity, and so on. These work because they are adequate, and certainly correspond to the reality of the phenomenon up to a certain point. So yes, I can imagine heat as other than molecular motion, we all do it.

This leads me to the last objection:

At this point some Platonists invoke God to pick up the slack. God can step in to provide the ontological foundations necessarily for the Platonist view of concept-acquisition to run. Maybe this is so. Making this move in the current context would be question-begging. The theory of concepts the argument relies on cannot presuppose the existence of God as the argument is purportedly an argument for the existence of God.

Now, I will recall Cantus to my original post. I said that the argument was inevitably flawed, in that it doesn’t prove God directly, but that God “proves” the argument. This is indeed “Question begging” in that I presume God exists in order for the argument to work, but then I ask, what is the alternative when dealing with ultimate reality? This is where my problem with Cantus’ rearrangement of Assumption 1 comes in. The very “idea” of the infinite is, in the last analysis, not subject to probability. It necessarily exists, and necessarily exists in all worlds, otherwise it would not even be possible to “think” it. Coming back to my statement three paragraphs ago, we do not “think” of the infinite like just any concept. Perhaps he missed that in the original post, where I quoted Cutsinger explaining what it means to “think” in the context of the infinite. It is not a “concept” even in the sense of residing in the Platonic “realm of ideas”. It is what makes that realm, and all others, possible in the first place. It is, in Guenon’s words, “All-Possibility” [1,4]; that which makes possibilities and forms what they are. We presuppose it in every act of thinking, because we know there are an indefinite and innumerable multitude of possibilities, whether actual in the sense of manifesting in our world, or in any other world, including the “higher” and far more “expansive” platonic world of ideas. The infinite is their very “background”; that with which they are “contrasted”; an “omnipresent light”, which is not reducible to “space” or “time” of any kind. What the argument does is make us aware of that “background” that is impossible to know in the same way we know other things. The platonic “theory of concepts”, as Cantus puts it, on which this argument is based actually does presuppose the God it aims to argue for. What the argument does is take the logic of its own theory of concepts to its root. It aims to answer the question:

If the mind is the “mirror”, from whence comes the “light”; the “ideas”, the “appearances”, or somewhere else?

This is what leads Platonists to use the Sun as a symbol of God, who is infinite being, and who “illuminates” all beings, whom are “mirrors” in different ways. This includes the “ideas”, which, united as the “intellect”, “reflect” to the mind, which “reflects” both to the world and back to the ideas themselves, and all the way back to God, the source and end of this “light”. Hence, God is symbolized as both centre-source and circumference-end, beyond which there is nothing. Christ is described as the “light of the world”, who is to “enter” our reflective “heart-intellect” for a reason.

[1] Guenon, R. (2004). The Multiple States of the Being. Sophia Perennis.

[2] Schuon, F. (2013). From the Divine to the Human: A New Translation with Selected Letters (Writings of Frithjof Schuon). World Wisdom.

[3] Gerson, L. P. (1999). Plotinus (The Arguments of the Philosophers).

[4] Guenon, R. (2004). The Metaphysical Principles of the Infinitesimal Calculus (Collected Works of Rene Guenon) (Vol. 1). Sophia Perennis.

Originally published at http://theosymmetry.wordpress.com on August 13, 2020.