1 Introduction

Bertrand Russell, in discussing Kant’s critique of Leibniz’s ontological argument, famously remarked, “The argument does not, to a modern mind, seem very convincing, but it is easier to feel convinced that it must be fallacious than it is to find out precisely where the fallacy lies” (1967, 586). In this paper, I answer Russell’s question regarding Anselm’s argument in Proslogion (P), 2:¹ The fallacy of Anselm’s argument lies in the assumption that there is such thing as existence in the mind if one understands the referential formula to God—“something beyond which a greater nothing can be thought” (henceforth, formula) and that understanding of God as existing in the mind leads to our understanding God as also existing in reality. By examining the text of P2 and Wittgenstein’s later writings, I show that presumed existence in the mind presupposes mentalism, a view that meaning resides in the mind and that language gets its meaning from the mental metaphysical realm (Baker and Hacker 2005, 17–18; Gunnell 2020, 3). Mentalism is the belief that linguistic rules are self-referential because they already contain all the steps in their application. The mentalism method is common in ostensive refereeing to one’s inward sensation (i.e., “I am in pain”), in which case language does not add anything to one’s own understanding of the sensation. Wittgenstein dismissed mentalism as a myth, as a philosophical and logical ideal he postulated in his earlier philosophy.

Anselm’s argument in P2 is based on the assumption, with roots in Augustine, that all meaning and use of our language depend on purely mental understanding. This understanding is so fundamental that without it, ordinary language would have no meaning. If one can understand the meaning of the formula given ostensibly, then God so understood resides in the mind of the one who hears and thinks the formula. The rest of the argument evolves from the crucial role of mental existence. However, if the assumption is possible only within a mentalist framework and if mentalism proved wrong, then this argument’s conclusion is also flawed.

To my knowledge, neither the defenders nor the critics of this argument have considered its mentalist assumption. Contemporary criticisms of Anselm’s argument highlight logical inconsistencies, particularly regarding the standards of relative developments in formal logic. Millican argued that the argument in P2 has a formal fallacy and is logically contradictory. Anselm’s reference to God fails to instantiate existence because the clause is “logically shallow” (2004, 451). However, if we carefully read the forms that the formula takes in P2 (grouped here from A to H), we will notice that Anselm does not initiate God’s existence, only that we cannot think or understand God as existing in the mind alone. This, as I argue, makes his argument not ontological but epistemological.²

King (1984) and Viger (2002) pointed out that the reference to God as “something beyond which a greater nothing can be thought” succumbs to primitive set-theoretical paradoxes. However, their criticisms would be valid only if we think of Anselm’s formula as not much different from Gaunilo’s description of God as “a maximally great being” (maius omnibus esse) in Pro insipiente (G) (1, S1), which would not make God a transcendental being above every existing thing but part of the chain of beings as the greatest of them all. To that mistake, Anselm objected to the strongest terms in three places in his Reply (R) (1, S24–S28; 4, S8–S9; 5, S12–S17).

There is also a continuous debate on how many arguments one can read from P2–4 and in R, as well as the nature of the argument(s). Some have argued that Anselm’s argument for the existence of God either extends through P2–4 (Campbell 2022, chap. 3) or that there is more than one argument: one in P2 and another in his R (Smith 2014) or that P2 provides a modal argument from necessity (Leftow 2022, chap. 1). Some have argued that the argument is not ontological because it does not treat existence as perfection (Anscombe 2011; Logan 2009) or that it was not set to prove God’s existence but that the divine attributes in Monologion (M) necessarily belong to God (Southern 1990, 128).

One of the most common criticisms of Anselm’s argument is that it has a fallacy of affirming the antecedent, that he invokes God in the main act of proving its existence (Lewis 1970). However, the text is open to multiple readings and interpretations (Millican 2018). As I will show, one way to avoid the charge of question-begging is to read the argument in P2 not as ontological but as epistemological. The goal is not to prove God’s existence but to emphasize our ability to know God as “something beyond which a greater nothing can be thought” and understand that it must exist also in reality.

Finally, there is considerable disagreement on nature of the formula “something beyond which a greater nothing can be thought:” is it a definition, a description of God, or an ostension? Logan (2009, 18) and Tapp and Siegwart (2022) claimed that Anselm never intended to define but only provided a description. Engelland believes that even description does not do justice to the Anselmian formula unless we understand the description in Kripke’s sense of “a reference-fixing description” (2023, 381). The formula in P2 is neither a definition nor a description because the formula is what we think of God without listing divine attributes or indicating his essence. Instead, the Anselmian formula is an ostension with the correctness criterion being understanding the formula itself. The argument is just the beginning of understanding from a correct understanding of the formula to expanding one’s understanding of God’s existence in reality.

In Section 2, I will closely examine the text of P2, focusing on various uses of the formula referring to God. In Section 3, I examine Anselm’s texts where he deals with existence in understanding. Section 4 examines the notion of ostension in Augustine and Wittgenstein, with Augustine being an important source of ostension for both Anselm and Wittgenstein. In Section 5, I present Wittgenstein’s challenge to mentalism and ostension; I prove that Anselm’s epistemological argument is based on a shallow metaphysical assumption that meaning comes from and resides in the mind.

This article analyses specific notions of existence in understanding, providing insights from the perspective of the contemporary philosophy of language and epistemology inspired by Wittgenstein’s later writings, especially his Philosophical Investigations (PI) (2003) and On Certainty (OC) (1970). Some may argue that any critique of Anselm from a Wittgensteinian perspective of language and meaning is unfair, given the time difference of over 800 years and advances in philosophy of which Anselm was unaware. Others will correctly point out that Wittgenstein never even mentioned Anselm or his argument. Another objection could be that by undermining existence in understanding, one also undermines one of the fundamental assumptions of Christian Neoplatonism, to which Anselm adhered.³

However, Anselm makes important claims in P2 that extend beyond the topic of the philosophy of religion or his adherence to Augustinian Neoplatonism. His notion of existence in intellect, with a self-referential criterion of correctness, has had direct and indirect influences throughout the history of philosophy. Therefore, despite the obvious limitations of this study, it offers important evaluations of Anselm’s claims about the philosophy of language and epistemology, making this study a relevant contribution to ongoing debates.

2 The Argument in P2

P2 is a short passage comprised of 13 sentences. These sentences can be grouped into five steps: introduction (S1), the existence of God in intellect (S2–S5,S8), the painter metaphor (S6–S7), the reductio argument (S9–S12) and the conclusion (S13). Sentence 1 draws on the last three sentences from P1, a text that sets the theological context for the whole work. The author seeks to understand what he believes only “to some extent” while his main goal is to invoke faith so he can understand. It is not only faith that searches understanding; it is also understanding that seeks faith:

I do not intent, Lord, to pierce your loftiness, for by no means can it compare with my understanding (intellectum);⁴ however, I desire to some extent understand (intelligere) your truth, which I believe and love with my heart. I do not look for understanding so that I believe, but I believe so that I can understand. For I also believe this, that “unless I believe, I will not understand.” (P1, S76–S78)

The first sentence in P2 is an introduction to the argument naturally following from the quoted P1:

{Step 1}: [S1] Therefore, Lord, you give understanding (intellectum) to faith; give me that I may understand (intelligam) as much as you know how to give because you are as we believe [to be], and this is what we believe. (P2, S1)

The second step serves as the condition on which everything that follows depends—anyone with enough linguistic understanding can and should accept that God at least exists in the mind alone:

{Step 2.1}: [S2] Moreover, indeed, we believe that you are [A] something beyond which nothing greater could be thought. [S3] May there be no such nature, since “The fool said in his heart: there is no God?” [S4] However, the same fool himself, when he hears this very thing that I say: [B] “something beyond which a greater nothing can be thought,” understands what he hears and understands that it is in his understanding, even if he does not understand that it exists. [S5] For it is not the same to have a thing in understanding and to understand that a thing exists. (P2, S2–S5)

At this step, Anselm gives two different formulas to God. In P2 we find seven of them.⁵ If we look carefully at the original text, not a single formula is used more than once. Differences in formulas reflect an ascending understanding of the reader as one proceeds with the argument. Formulas are not synonymous but constitute progression, an epistemic crescendo, from a fundamental understanding in S2 to an epistemically necessary statement in S13.

This progression is shown in Table 1. All that is needed to start the argument is to acknowledge the possibility of the existence of “something beyond which nothing greater could be (possit) thought.” Then Anselm states that what the fool denies is “something beyond which a greater nothing can be (potest) thought.”

Notice two differences in B versus A. The first is in stressing over “nihil,” which denotes “maius” in A and “maius” over “nihil” in B. This accentuating of “greater” over “nothing” in B speaks of the greatness of God transcending every being. However, what he says in A is merely that there is nothing like God. This way, B stands to A as claiming more about God.

The second is the difference in verbal forms of “cogitari possit” in A (subjunctive of possum, such as in “may he able [to]”) from “cogitari potest” in B (indicative of possum, such as in “he can”). The best translation of possit is “could be” and of potest is “can be.” In both English and Latin, “can” is stronger than “could.” “God could be thought” conveys possibility, while “God can be thought” is an assertive affirmation. In S4–S5, “God can be thought” refers not just to the thought of God but to God’s existence in intellect because of thinking of God even when denying God’s existence.

This is what Anselm achieves by S5 and what is further strengthened by the painting metaphor in Step 3. In S6–S7, God exists in the intellect of anyone who thinks of God as “something beyond which a greater nothing can be thought” (B):

{Step 3}: [S6] When a painter thinks in advance of what he is going to paint, he indeed has it in his understanding, although he does not yet understand it as existent what he has not yet painted. [S7] However, when he has already painted, he has it in his understanding and understands that it exists what he has already painted. (P2, S6–S7)

The metaphor underlines the idea of existence in understanding even if the object of thought exists in reality or only in the understanding of the thinker. As we will see, Anselm discusses a similar example in M10. Understanding that something exists in reality is greater than understanding in the mind alone, just as existence in reality is greater than that in the mind alone. However, as I will show in the next section, without mental existence, one cannot reach an understanding of the thing that exists in an extramental reality. Naming objects, signifying them in language, the ability itself derives from this primary ability of the intellect to discern.

The metaphor comes as the first of the two degressions from the main argument in P2, the second being his reductio argument. Here, the metaphor serves merely to strengthen Anselm’s points raised in Steps 1 and 2 that basic linguistic understanding is enough to claim existence in intellect, the former resulting from the latter. Gaunilo overemphasizes the metaphor in G3, S2–S5 and Anselm downplays it in R8, S2.

In S8, after digression of the painter’s metaphor, Anselm returns to the same idea of existence in the mind alone in relation to the fool’s rudimentary linguistic understanding:

{Step 2.2}: [S8] Therefore, even the fool is convinced that in understanding there is at least [C] something beyond which nothing greater can be thought because he understands this when he hears it, and whatever is understood is in the intellect. (P2, S8)

Formula C in S8 has the same verb’s stronger form as in B, “potest,” but otherwise, it is the same wording as in A. Now, with a stronger form of the verb and since existence in understanding with the help of the metaphor considered to be proved in S4–S5, a reader can take a further step in understanding.

Step 4 presents a reductio argument stating the impossibility that something greater can exist in understanding rather than in reality. In S9, we read that the existence of God in the intellect alone goes against Formula D and implicitly for earlier Formulas A–C. Notice also that S9 serves as an introduction to the argument-within-the-argument, the reductio, and S12 as its conclusion:

{Step 4}: [S9] Furthermore, [D] that beyond which a greater unable be thought cannot be in understanding alone. [S10] For if it is only in understanding, it can be conceived also in reality, which is greater. [S11] If, therefore, [E] that beyond which a greater cannot be thought is solely within understanding, ​​the very thing [F] that which itself greater cannot be thought is [G] [that] which a greater can be thought. [S12] However, this surely cannot be the case. (P2, S9–S12)

Formulas D–F change the noun “something” (aliquid) into the determinative pronoun “that” (id). Engelland thinks this change from noun to pronoun refers to God as a person and not as a mere thought (2023). This does not seem to be the case. First, the reductio argument attempts to imagine something impossible—existence in the intellect alone is greater than in reality. Formula G is such a contradiction and is not a reference to God. Notice also that in G, Anselm provides the least definite pronoun about God, “which” (quo). Second, the final Formula H in S13 returns to the impersonal noun “something.” This “something” is enough for Anselm in his demonstration that we must think of God existing in reality as “something beyond which a greater not able to be thought” (H). The pronoun “id” in the reductio argument serves as a thought experiment to speak of a contradictory deity greater in understanding than in reality. Once the reductio argument fulfilled its purpose, the text returns to “something” in S13 as before.

Anscombe translated S10 as “For if is only in the intellect, what is greater can be thought to be in reality as well” (2011, 40). In this way, Anselm’s argument is immune to Kant’s critiques of ontological arguments in Descartes and Leibniz that by proving existence in understanding, one must conclude existence in reality, since existence is an essential property of being. As Campbell (2022, 142), Engelland (2023, 389) and Rogers (2024, 380) showed, in this respect, “greater” means metaphysically speaking better in that good and being convert into each other. To have existence in reality and understanding is better; hence, it is greater than in understanding alone.

That stress on greatness in existence in reality in S10 can also explain the difference between D (in S9) and E (in S11). Formulas D and E have a similar construction as formulas A and B, except that D uses “nequit” while E uses “non potest,” the latter being a stronger form than the former to convey a similar tactic of comparison we saw between A and B in S2–S4. By the time we reach E in S11, we have a greater understanding of existence in reality than with D in S9 and significantly greater than A and B. The Formula F in S11 has a powerful accentuation on “that itself” (id ipsum) combined with the absurdity that F equals G. Anselm puts both F and G together to stress the evident contradiction between them. In M3, S3 Anselm will show again the contradiction between two formulas: that “id ipsum quo maius cogitari neguit” (that itself beyond which a greater cannot be thought) is not the same as “id quo maius cogitari nequit” (that beyond which a greater cannot be thought).

Finally, S13 serves as a logical conclusion of the argument in which Anselm returns to the noun “aliquid:”

{Step 5}: “[S13] There is, therefore, without a doubt [H] something beyond which a greater not able to be thought, both in the understanding and in reality. (P2, 13)

The wording in H, “non valet,” is the strongest formula’s modifying term we have seen so far. Compare it with “could” (possit) in A, “can” (potest) in B, C, E and G, and “unable” (nequit) in D. English “unable” and “not able” share the same meaning and cannot properly render Latin’s nequit and non valet, which vary in meaning. Nequit derives from “queō,” meaning an ability, while valet derives from “valeō,” meaning “strength,” or “worth.” In the most literal translation, H should be rendered as “something beyond which a greater is not [even] worth to be thought,” expressing epistemic certainty or epistemic impossibility to think of God as existing in the mind alone. That nothing is worth being thought to be greater than God is the conclusion of Anselm’s argument in P2, especially because of the reductio argument right before S13.

The connotation of “not [even] worth to be thought” does not strike as a logical or metaphysical impossibility; rather, one cannot properly understand the formulas if God exists only in the mind. The argument in P2 is not ontological but epistemic, arriving at neither logical nor metaphysical but epistemic certainty, especially because of a contradiction reached between F and G in S11. It is not about existence from understanding to reality but about understanding what there is in the mind and reality. Anselm does not engage with the fool on whether there is God but on whether one understands what is being denied or affirmed.

3 Anselm on Existence in the Mind

The notion of existence in the mind was assumed by Neoplatonists and served as an important tool in explaining how words have meaning and how knowledge is possible. For an in-depth analysis of Anselm’s philosophy of language and its connection with Augustinian Neoplatonism, see King (2006) and Matthews (2006). For our purposes, it suffices to investigate Anselm’s mentalist approach by which we acquire the meaning of words through the intellect’s ability to think and understand.

Language is the comprehension and use of signs, but it depends on the cognitive powers of the intellect to interpret signs accordingly. An object is a sign when it signifies something to the perceiver and in that way transmits some meaning (smoke signifies fire). Every sign has a significate, which is the name that the sign stands for (this is what we call “fire”). Hence, ordinary language is a system of meaning–bearing signs with particular names attached to them.

Of crucial importance in Anselm’s theory of signs and their classification is M10, where he distinguishes between three kinds of signs: sensible (“signis sensibilibus”), mental or “spoken in our minds” (“in nostra mente dicendo”), and non–sensible (“insensibiliter”). The first category comprises spoken and written signs. Mental representations of sensible signs fall under the second category, while the third category includes concepts and images associated with concepts. The first and third are essentially ordinary language; we speak, write and have mental images associated with relevant texts and speech. The second category is what conditions natural language and without which language, such as the use of signs, would not be possible.

Before we can understand anything or before we name an object, there must be a mental representation of the word or object in our minds. In M10, Anselm invites his readers to envisage a craftsman who, before making something, already has its expression in his mind:

That form of things in one’s reason preceded the creation of things: what is it but a particular expression of things in the reason itself? [J]ust as when a craftsman is about to make a work of his art, he first says it within himself using a mental conception (mentis conceptione). Now I understand the expression of mind or reason here, not when the significant words of things are thought but when the things themselves, either future or already existing, are seen in the line of thought in the mind. (M10, S1–2)

The tripartite distinction of signs follows this introduction where Anselm stresses the mental use of signs as that on which the other two depend (M10, S4). To use a sign, one must understand what it stands for. How can one understand what a natural or an abstract sign stands for without first having said within oneself “using a mental conception”? Except for some immediate designations in natural language (such as the letter “a” standing for a vowel ⟨ɒ⟩), one cannot get the same immediate, ostensive connection between a sign and what the sign stands for as that mental connection in one’s reasoning.

Most importantly, the first and third categories depend on mental language because, without past understanding in one’s mind, language would not exist. Without mental language, ordinary language would be meaningless; it would not be a language—a system of signs capable of transmitting any meaning. In M10, Anselm stresses that we can make things that do not yet exist in reality present to our minds only by thinking about them:

…[N]o other word seems so like the thing of which it stands, or so expresses it [clearly], as that likeness of the thing itself, which is presented in the mind of the thinker. (M10, S11)

As in P2, we can understand these things by examining them with our mental vision, even if we understand that these things do not exist in reality. In M31, Anselm further explains that the contents of our thoughts are of two kinds: images and concepts. Genuine understanding of created things comes not with their images in our minds but through understanding concepts of things. Concepts are likenesses of abstract ideas and images stand as signs to physical objects. To think of an object is to have its image in our minds. Likewise, when the mind thinks of itself, it also has an image of itself, as Anselm states in M33:

Therefore, the rational mind, when it understands itself by thinking, [it] has its own image that comes from within. [T]hat is to say, the image of itself formed in its own likeness, as if by its own impression. [T]he mind can separate itself from its own image only by reflection. The mind’s image is the mind’s verbalization. (M33, S16–17)

Anselm concludes that images and concepts are two tools with which we think, while the true content of our thoughts is the mind itself. The true content of the rational soul is something unchangeable and persistent. Expressions can have more or less accurate descriptions of reality, but what is always true to itself is the contents of the mind, which is the mind itself.

In M67, Anselm calls the mind a mirror capable of reflecting itself and God, the greatest essence (summa essentia):

At the minimum, the mind is the clearest reflection of [the greatest essence], as long as it can remember, understand, and love it. The greatness of the mind’s ability to comprehend depends on its similarity to [the greatest essence]. (M67, S3–4)

The mind can reflect itself and God “as long as it can remember, understand, and love.” Thus, existence in intellect is an ability to understand through self–reflection and transmit that understanding in language. The mind, as the source of truth in all linguistic and epistemic capacities, has two criteria of truth: God and itself. When the fool in P2 is called to think of “something beyond which nothing a greater can be thought,” s/he is to activate their mental capacities to reflect the higher truth, examine their own mind and understand this reference to God.

However, the “God criterion,” or divine illumination of the knowing mind, is absent from P2. It stands in the background of P1, but the fool has no access to it. If P2 were to contain an ontological proof of God’s existence, it must have the “God criterion.” Yet P2 is notoriously a one-criterion argument—the intellect’s ability for ostensive linguistic understanding. However, it is not immediately clear why ostension in language is problematic.

4 Augustine and Wittgenstein on Ostension

Neither definition nor description is appropriate when considering Anselm’s formula. Definitions are specifications of references, placing definiendum within particular definiens. The Anselmian formula is nowhere that specific. Descriptions list common features of something. In P2, we have no lists; the formula is not that general. Ostension is a kind of definition in which we give examples by pointing to some specific referent (i.e., “‘White’ is that [arrow square] color”). In this sentence, “that” must go with the act of showing an object exemplifying the color. Unlike definitions and descriptions, ostensions do not have within themselves any linguistic content that stands in some general or specific relationship with the object. Ostensions call attention to the object itself and they appeal to us to investigate the object further.

Augustine is an important source of ostension for both Anselm and, later Wittgenstein. Anselm’s tripartite division of signs in M31 is Augustinian through and through. For Wittgenstein, some aspects of Augustine’s writings on ostension reminded him of his own notion of ostension in the Tractatus Logico-Philosophicus (TLP) (1989)—the main target of his criticisms in PI. Augustine uses ostension in reference to God in several texts, most notably in his Confessions (C) (2009).

One such text starts Wittgenstein’s PI (§1):

When [the adults] themselves named some object, and when they turned while making the sound, I saw and understood what they were naming, when they pointed it out (ostendere). Their intention was revealed by the motion of their bodies, as by the natural words of all people (verbis naturalibus omnium gentium), which they did by the countenance of their faces and movement of their eyes, and by the action of the other body parts, and by the sound of the voice, revealing the affection of the soul (indicante affectionem animi) in asking, having, rejecting, or fleeing from things. Having thus recognized the words and uttered them through sentences which I often heard, I gradually begun to use signs and through them express my wishes. (C 1.8.10.20–11.4)

In the secondary literature, this primitive approach to language goes by the name of “Augustinian picture of language:” words have meaning because they stand in our minds as signs for the objects they signify and that meaning is conveyed through ostension. Augustine’s philosophy of language is much more complex than this description of how a child might learn words from his or her parents. King insists that in C and De Trinitate Augustine postulated no inexpressible private mental language as something on which all ordinary language depends (2014, 307). Perhaps, the term “mental language” here is misleading. Instead, we should speak of intellect’s predisposition to make sense of signs we later use in language and thought. It is not an ability to think before we speak but an ability to even form a thought and a capacity to make meaningful expressions of thoughts. The relationship between this intellect’s ability and thought or language is immediate, for what else can come between the thought and what makes that thought possible?

Augustine could not have postulated that this immediate, ostensive relationship between intellect and its expressible contents is the only way language works, but it is where language and thought have their beginning. As for ostension, we know that Augustine, in the same C, distrusted it and did not consider it the only or the main way humans operate with signs and words, as it is clear from this reference to God:

But who can call upon you without knowing you? For not knowing you one might call instead on something else. (C 1.1.16–17)

Our knowledge of God comes from the conception of God within our minds. Words and thoughts are signs that point to God. Still, for Augustine, our knowing God can come only from God and not from learning about God from hearing or reading. The reason is simple and the same as it will appear for Anselm—language can be ambiguous and misleading. In De Magistro (DM) (1970), Augustine most clearly spoke of the importance of signs in our language and knowledge of things:

As our advancing argument have shown, not even [the wall] can be shown without a sign. For pointing the finger is certainly not the wall but a sign through which we see the wall. Hence, without showing signs (signis ostendi) I can see nothing. (DM 3.6.49–52)

Ostension gives meaning to a sign only when the perceiver has the right mental disposition. Without God present in our minds guiding us in our discernment of signs, there is always the possibility of ambiguity and misunderstanding, “And so, I exist and I ask you to be in me for without you I cannot exist” (C 1.2.15–17). In DM12, Augustine famously remarked that “nothing can be taught by words” (“verbis doceri nihil possit” DM12.40.50). Further in that work, he insists that it is Christ, the true teacher, who teaches us the meanings of what we think and say. Yet we do not hear him speaking in ordinary speech but through understanding within our minds.

As Nawar (2021) pointed out, Augustine considered ordinary language too ambiguous and often equivocal to propose a simple referential theory of meaning. If the Anselmian formula is an ostension that points to God from a mere linguistic understanding towards understanding that God exists in reality (Engelland 2023), then these texts from Augustine have a crucial importance for P2, even without “God’s criterion” openly stated: Words have meaning only from intellect’s cognitive abilities to recognize it, aided by divine presence in our minds.

We can observe a similar approach in TLP: Meaning is captured by the mind alone thinking concepts and objects while its expression occurs in the language of logic and its immediate, isomorphic relation to the world of facts. Wittgenstein never used the term “ostension” in TLP but the notion was the key to his early theory of meaning. We communicate our thoughts through propositions whose main constituents are simple names:

[E]very possible sense can be expressed by a symbol to which the description fits, and every symbol to which the description fits can express a sense if the meanings of the names are chosen accordingly. (TLP 4.5)

Names stand in an ostensive, direct and isomorphic relation to objects:

In a proposition, the thought can be expressed in such a way that elements of the propositional sign correspond to the objects of thought. (TLP 3.2)

That relation is inexpressible in ordinary language; at most, we can give elucidations that have the meaning already known to us:

The meanings of primitive signs can be explained through elucidations. Elucidations are propositions that contain the primitive signs. So they can only be understood if the meanings of those signs are already known. (TLP 3.263)

What changed for Wittgenstein in his middle (1929-36) and later (1936-51) periods is the realization that even for ostension to convey any meaning, it cannot be an isolated account of signs originating from faculties of a mind. In his 1930–32 lectures (LWL) (1980), Wittgenstein was clear about how limited ostension is:

One of the implements of our language is ostensive definition. But with such ostensive signs we have only a mere calculus.

What we call a connection between language and reality is the connection between spoken language and, for example, the language of gestures. If we had no written or spoken language, where then would be the connection? How can you explain one gesture by another? (LWL, 102)

What is needed apart from ostension, or with it, is “written or spoken language.” Without it, how could we ever understand “the language of gestures” pointing to anything? To his question, “Where then would be the connection”? Wittgenstein, at different periods, gave three different responses: logic, language, or practice.

In TLP, logic takes care of itself; the meaning is already present in one’s mind and is ostensively expressed by the sign if the sign is possible:

Logic must take care of itself.

A sign that is possible should also be able to signify. Whatever is possible in logic is also allowed. (TLP 5.473)

For Wittgenstein of the middle period logic gives way to ordinary language, as is clear from LWL (102). In PI, Wittgenstein realizes that for ostension to convey any meaning at all, much linguistic and extralinguistic practice must occur. His notion of “language-games,” which emerged in the early 1930s, became enriched with notions of use and practice, often extending beyond linguistic applications. In PI §185, at the beginning of his rule-following discussion (§§185-242), Wittgenstein shows how simple commands can be interpreted variously and ambiguously.

Wittgenstein proposes an example in which the pupil has learned the series of natural numbers and is taught other series of cardinal numbers. S/he is asked to write the continuation of numbers “0, n, 2n, 3n, etc.” After reaching 1000, the teacher gives the new order “+2,” and the pupil writes 1000, 1004, 1008, 1012.

The teacher notices the mistake and the following conversation between the teacher, an observer, and the pupil occurs:

We say to him: “Look what you’re doing!”—He doesn’t understand us. We say, “You should add two; look how you started the series!”—He answers: “Yes! Isn’t it right? I thought, that’s how I should have done it.” — Or suppose he said, pointing to the line: “I continued in the same way!”—It wouldn’t do us any good to say “But don’t you see.….?”—and repeat the old explanations and examples to him.—In such a case we could say something like: This person naturally understands that command, based on our explanations, just as we understand the command: “Always add 2 up to 1000, 4 up to 2000, 6 up to 3000, etc.”

This case would be similar to a person’s natural reaction to a pointing gesture by looking in the direction from the fingertip to the wrist instead of in the direction from the wrist to the fingertip. (PI §185)

A simple order “+2,” an ostension, can have various applications and which application is correct is not obvious to the pupil or us, the readers, for we can easily understand that both applications might be correct. It is not a question of interpreting the order in various ways because we can never end the chain of interpretations (PI §201). Instead, when the context of practice is missing from teaching, an ambiguity in understanding creeps in. We can only say that the pupil misunderstood the teacher in the context of a specific addition known only to the teacher, but that context is missing. As with the pupil, we can only guess it. The last paragraph speaks of this ambiguity since we do not even know this gesture of pointing is pointing, or to what it is supposed to be pointing to.

To draw on a somewhat similar example from DM 3.6, even with “showing signs I can see nothing.” There, Augustine claims that ambiguity results from the inaccuracy of our language. We have seen his solution—the intellect, aided by God (or Christ—the true teacher), can reach the true meaning. In PI, Wittgenstein shows this is not the case. As will become evident in the next section, what accounts for meaning is a common way of acting for language users.

5 Wittgenstein on Mentalism

It is evident from Wittgenstein’s discussions in his later period that understanding cannot be a mental process. For him, mental processes are how we process sense-perception, feelings, emotions and so on. To claim that understanding a word is a mental process is to have a fundamental confusion about what both understanding and mental processes are.

In PI §154, Wittgenstein states that understanding is not a mental state, making this remark one of his most important dismissals of mentalism:

Don’t think even for a second of understanding as a “mental process”!—For it is this way of speaking of it that brings confusion. Instead, ask yourself: in what kind of cases, under what kind of circumstances do we say, “Now I know how to proceed”? That is, if I remembered the formula.

In the sense in which there are processes (including mental processes) that are characteristic of understanding, understanding is not a mental process.

(Increasing and decreasing of a feeling of pain, hearing a melody or a sentence—these are mental processes). (PI §154)

In P2 and in R, Anselm insists on a mere linguistic understanding disconnected from any context besides the words of the formula and presumes that it is enough for a purely mentalistic understanding that God is “something beyond which nothing a greater can be thought.” This, however, is how we must consider sense-perception as a matter of subjective awareness requiring no other criteria of correctness but themselves. But then, awareness of our sense-perception requires neither understanding nor linguistic expression.

Wittgenstein continues in the same vein and insists on the importance of external criteria for linguistic understanding:

The criteria that we apply for “fitting,” “ability,” and “understanding” are much more complicated than they might seem at first glance. That is, the game with these words, and their use in linguistic communication, of which they are the means, is more complicated—the role of these words in our language is different than we are tempted to believe. (PI §182)

How significant is the complication of applying criteria for understanding? In PI §206, amid his discussion of what it means to follow a rule, Wittgenstein paints a rather large picture of what the context of understanding is. It would be helpful if we consider §206 following to be a comment on his earlier discussion in §185:

Imagine you came as a researcher to an unknown country with a language totally foreign to you. Under what circumstances would you say that the people [there] give commands, understand and follow commands, to rebel against orders, etc.?

The shared way of human acting is the reference system by which we interpret foreign language [unknown] to us. (PI §206)

“The reference system” of linguistic understanding extends as far as the entire “shared way of human acting.”⁶ This is perhaps as far away as one can get from the mentalist approach to linguistic understanding. In PI §257, Wittgenstein continues in the same vein and stresses the importance of semantic context being indispensable for meaning anything:

—When you say “He gave a name to the feeling,” one forgets that a great deal must be prepared in the language so that the mere naming is to make sense. And when we talk about someone giving a name to pain, the grammar of the word “pain” must be already presupposed; it indicates the pillar towards which the new word is attached. (PI §257)

In PI §269, Wittgenstein envisions a situation in which no “behavioral criteria” exist for linguistic understanding. At most, perhaps s/he believes in understanding a word, but if s/he fails to support her/his understanding, it is the instance of the so-called “private language” that does not exist:

Let us remember that there are certain behavioral criteria for not understanding a word: that it means nothing to him, that he does not know what to do with it. And criteria for the fact that he “believes he understands” the word, associates a meaning with it, but not the correct one. And finally, criteria for ensuring that he understands the word correctly. In the second case one could speak of subjective understanding. And sounds that no one else understands but I “seem to understand” could be called a “private language.” (PI §269)

Here, we can think of the fool hearing the formula from P2 but behaving as if “it means nothing to him, that he does not know what to do with it.” Like Augustine, Anselm never postulated a private language in connection with existence in the mind. He never proposed that we have unspoken language for understanding anything that cannot be expressed in plain language. Rather, he presumed that the formula is intelligible to everyone within the common linguistic context. However, with the mere linguistic intelligibility of the formula, we cannot ask the fool to accept that God exists in her/his intellect if the fool hears and understands every word.

In PI §258, Wittgenstein invites a reader to imagine a diary about some recurrent sensation. Someone writes the sign “S” next to the date on which s/he felt that sensation. The interlocutor, however, immediately objects to this rudimentary activity: “—I want to note firstly that a definition of the sign cannot be expressed.” A possible definition would be a kind of ostensive one pointing inwardly to what the diary–keeper experiences on the days s/he writes an “S.” However, what would that definition be? Would it be a definition of “S” as (1) a mark in the diary, denoting (2) some specific sensation or (3) a whole series of sensations noted as “S”?

Why “a definition of the sign cannot be expressed [aussprechen]?”⁷ The most literal meaning of “aussprechen” is to “pronounce” and “verbally express.” The sign “S” is a formulation of a private sensation, much like a definition, but it expresses nothing meaningful. Between the three possibilities, (2) and (3) will result in equivocation and (1) is self-referential use of sign. Sensations have a beginning, a duration and an end. The mark “S” in the diary can mean anything related to many manifestations of “S.” By itself, it cannot be the criterion of sensation.

Wittgenstein concludes there exists no “criterion of correctness” for a private sensation:

But in our case I have no criterion for correctness [Kriterium für die Richtigkeit]. One would like to say here: whatever seems right to me is right. And that is just what it means that here there can be no talk of “correct.” (PI §258)

Ostensive, inward pointing to one’s sensation is very different from a conventional sign that ostensively stands for it. In the second case the language-game is missing (see PI §96).

What the fool in P2 is asked to understand, by Wittgenstein’s standards, is to reach epistemological certainty via the linguistic understanding reached in a contextual vacuum. The criterion of the correctness of the formula is the linguistic understanding of that formula. However, if the language-game is missing (although it is present in P1 but the fool has no access to it), then the fool will never have the intended understanding. Epistemic certainty that one has in a mental event is not what the fool can reach when s/he hears the formula. The reader does not know why the fool says, “There is no God.” Anselm never provides that context, either (except that s/he is “stupid” (stultus) and “fool” (insipiens) in P3, S12). However, hearing the formula with no independent criterion of correctness gives no linguistic understanding and the argument fails at the start.

An ostensive reference between language and the object of description is what Wittgenstein calls in PI §293 the model of “object and designation” (“Gegenstand und Bezeichnung”), a semantic model of TLP. The section has a famous “beetle-in-the-box” thought experiment in which beetles are compared to private sensations and linguistic descriptions are attempts to share the beetle with others. The problem with the model of “object and designation” is that the thing in the box does not belong in the language-game at all, not even as a something:

For the box might even be empty.—No, [one] can “divide through” this thing in the box; it cancels out, whatever it is.

It means: If one constructs the grammar of the expression of sensation on the model of “object and designation,” then the object falls out of consideration as irrelevant. (PI §293)

Wittgenstein is clear about what constitutes a correct linguistic use: “One can’t guess how a word functions. One has to look at its application and learn from it” (PI §340). An action of guessing would be like comparing one’s reading of the word with the contents of one’s mind as if it is a dictionary in the mind (PI §265) always ready to be consulted. Wittgenstein shows that use as the application of words is the only way to learn and come to know the meaning of linguistic signs (PI §432).

Earlier, he reinforces this point: “You learned the concept ‘pain’ by learning language” (PI §384). Nothing in the mind alone can teach us concepts without first acquiring them through the active use of ordinary language. Whatever the “inner process” might be, it must be supported by external criteria whenever we express it in our language: “An ‘inner process’ requires external criteria” (PI §580).

While we learn concepts through language and understand them through correct use, our inner sensations are given to us, and the terms “understand” or “know” do not apply to them. The latter is what in OC Wittgenstein calls “hinges” (die Angeln), propositions beyond any epistemic doubt (OC §§341–43), and a “grammatical proposition” (grammatischer Satz) that exclude any doubt in principle (OC §58). Wittgenstein provides examples: “I.e., the questions we ask and the doubts we raise are all based on the fact that certain propositions are exempt from all doubt; they are, as it were, the hinges upon which they turn” (OC §341). One such proposition is “I am in pain,” where doubt is excluded entirely by the person who utters this proposition.

Aikin and Hodges insist that Anselm’s “something beyond which a greater nothing can be thought” is a hinge-proposition, something beyond doubt, a grammatical proposition in no need of proofs (2013, 138). This is a significant misunderstanding of both Anselm and Wittgenstein. For Anselm, one needs to understand the meaning of the formula to acknowledge that it is true. Anselm’s argument (and all seven formulas within) requires understanding, which is a basic act of knowing something. Hinge propositions, however, are of a kind whose truth is self–evident and requires no proofs; they are non–epistemic in principle, for they cannot be known in principle. One cannot claim to know or understand that they are in pain; one is simply feeling pain.

For Wittgenstein, hinge propositions are those in which “a mistake is not possible” because it is “logically excluded:”

With the word “certain” we express complete conviction, the absence of any doubt, and with this we try to convince the other person. This is subjective certainty.

But when is something objectively certain?—When an error is not [even] possible. But what kind of possibility is that? Shouldn’t the error be logically excluded? (OC §194)

I cannot be in pain and doubt it. According to Moyal-Sharrock, “hinge certainty is animal through and through” (2021, 150). Wittgenstein writes on this animal certainty: “That means I want to understand it as something that lies beyond justified and unjustified; in a manner of speaking, as something animal” (OC §359). However, nothing in the words “something beyond which a greater nothing can be thought” is certain beyond any doubt or self–evident. Brice insisted that once we learn the hinge-proposition, “this particular hinge-proposition has worked its way out to become an actional, unreflective certitude” (2022, 83). The Anselmian formula is anything but unreflective.

Anselm’s ostensive referential to God formula has no meaning to the fool in P2 if the language-game of P1 is absent. The opening lines of Anselm’s R confirm that P2 must presuppose the Christian context and that Gaunilo is no fool:

Since it is not the “fool” who reprehends me and against whom I spoke in my work but no fool and a Catholic speaking on behalf of the fool, it will suffice for me to respond to the Catholic. (R1, S1)

The issue, then, is with the formula itself. On the one hand, it has no meaning outside of the language-game of P1. However, it gives no knowledge because it has no independent–of–itself reference containing any criterion of correctness. P1 cannot serve as this criterion because of the formula’s wording. It meant to be independent of faith reference to God, clear enough to reach epistemological certainty that God must be thought to exist in reality. The only way the formula could be self–referential and meaningful at the same time is if it pointed to an inward sensation, which is not the case. If so, it would never be an epistemic reference to God within and outside the mind, which is what Anselm intended it to be. Speaking ostensively of an external reality as if it is an inward sensation is what mentalism does.

6 Conclusion

We can now answer Russell’s question—“where the fallacy lies”—concerning Anselm’s argument in P2. It lies in the argument’s assumption that isolated from the extramental context, linguistic understanding of the formula implies existence in the mind. Understanding is not a mental process; it can only come with our knowledge of how to use linguistic signs referring to objects of our understanding. Wittgenstein proved that to understand a word means knowing how to use it (PI §102). It is the use of the formula that should determine its meaning and not the other way around; it is the use of the formula that should be the criterion of its correctness.

Wittgenstein’s case for the fool can be made by claiming that in P2, Anselm makes a false move: Understanding of the formula implies existence in the mind alone which, in turn, implies extramental existence of God based solely on what the formula states. An analysis of Wittgenstein’s texts has shown this move is permitted only when used in ostensive references to one’s sensations; however, these are neither epistemic nor require linguistic expression. The question of one’s understanding of God or a claim that God exists in reality is not that kind of reference.