[UNFINISHED] Sense of Logic, On Wittgenstein, Deleuze, and Others
§1: Wittgenstein and the Logocentric Predicament
It is clear that the logocentric predicament is a predicament about our use of logic. Can we just outright reject Sheffer’s proposal of the predicament? Can we say that there was never even a predicament in the first place? Well, Kurt (as a Wittgensteinian) certainly thinks so. Let us go through the second section of Kuusela’s Wittgenstein on Logic as the Method of Philosophy and the Tractatus Logico-Philosophicus by Wittgenstein himself, as well as various other things pertaining to Wittgenstein.
According to Kuusela, Wittgenstein sees that propositions represent states of affairs. Furthermore, Wittgenstein makes a supposedly key division: “on the one hand, propositions represent reality by means of object-referring names that are configured in a proposition in a particular way, corresponding to the configuration of objects that constitute a state of affairs in reality that the proposal represents … On the other hand, the logical constants, i.e. the fundamental or most basic symbols or notions of logic, do not represent or stand for anything in reality” (Kuusela 52). The latter hand has what Kurt, at least from my conversations with him, sees as most important: “There are no logical objects, according to Wittgenstein, in the sense that, for example, the words ‘all’ and ‘some’, the logical connectives, ~, ^, ˅, ⊃, or his notion of the general propositional form are not names of logical objects” ( Kuusela 52).
Fundamental Proposition 1: “For, if there are no logical objects which the logical constants represent, logic cannot be an object of representation, in other words, there are no true/false assertions or theories in logic in the sense of substantial theses about reality, including theses about thought and language as the objects of investigation of logic” (Kuusela 53).
Fundamental Presupposition of Proposition 1: Theory of objects.
Questions to Propostion 1: 1. Why is it the case that if there are no logical objects which logical constants can represent the logic cannot be an object of representation? 2. How does this not suppose what logic is? 3. How can you prove what logic is?
Now, Frege and Russell’s accounts of logic, which are, to us at least, prima facie truer than Wittgenstein’s account, are what we are to look at next, or, rather, more specifically, we are to look at how Wittgenstein handles them. Frege and Russell see logic as having laws, or, more specifically, they see logic as a set of inferential principles, or, at least, Wittgenstein’s conception of Frege and Russell see this. Now, we do not care for the correctness of Wittgenstein’s interpretations, rather we will defend them not knowing whether or not the interpretations are correct. So, again, Wittgenstein’s understanding of Frege and Russell sees that “the axioms [of logic] could be understood as expressing true thoughts or propositions, and therefore as having the same status as the premises and conclusions in an inference” (Kuusela 54–55). In this sense, Wittgenstein views Frege and Russell as doing what Carroll described as the Tortoise Problem: “axioms [for Frege and Russell] figure in inference in the capacity of (what would from Wittgenstein’s point of view be) extra premises whose function is to license transitions between other premises and the conclusion, whereby a correct inference is the substitution instance of a relevant logical law which is asserted as one of the premises of the inference … Rules of inference, if they are regarded as premises of an inference, seem therefore unable to justify the transition from premises to conclusions [due to the Tortoise Problem]” (Kuusela 55). Now Kuusela says that Wittgenstein solves the Tortoise Problem through 5.131–5.132:
If the truth of one proposition follows from the truth of others, this expresses itself in relations in which the forms of these propositions stand to one another, and we do not need to put them in these relations first by connecting them with one another in a proposition; for these relations are internal, and exist as soon as, and by the very fact that, the propositions exist. If p follows from q, I can conclude from q to p; infer p from q. The method of inference is to be understood from the two propositions alone. Only they themselves can justify the inference. (TLP 5.131–5.132)
Kuusela takes Wittgenstein here to be saying that “there is no need to add a rule of inference (a logical law) to an inference as an extra premise. Insofar as an inference from q to p is justified its justification can and, indeed, must be understood as depending on the original propositions involved in the inference” (Kuusela 55). Kuusela furthers, “For insofar as the propositions possess determinate logical characteristics or determinate logical forms — without which it is unclear what propositions they are or whether they are propositions — this suffices for determining whether p can be inferred from q, and for inferring it from q” (Kuusela 55–56). Kuusela sums this sentiment up, “For, again, insofar as p and q are to be propositions with determinate logical characteristics, which is a condition for their figuring in an inference in the first place, then their inferential relations cannot depend on further propositions. Therefore, only q and p themselves can justify the inference” (Kuusela 56). Let us go over this.
Wittgenstein is saying:
C1: If r follows from p and q, then this movement (the following of r from p and q) can be done
So, what are the premises?
P1: If … then propositions are true
C1: If r follows from p and q, then this movement (the following of r from p and q) can be done
Now, Wittgenstein would object to what we have just said. He will say he is not supposing P1, because that would be modus ponens which is what he is purporting to not be necessarily characterized as an extra premise. Now, why isn’t P1 actually a premise? Kuusela says that Wittgenstein sees that C1 is a proposition, and propositions possess a certain form, that form being a logical form. Therefore, inherent to propositions is logic. Therefore, if modus ponens is a logical or inferential rule, then it is contained in (all[?]) propositions, for propositions are necessarily logical as their form is logical. Therefore, p and q both contain modus ponens, therefore meaning r follows.
Now, we could question why r follows from p and q, but this would be the proof being put forward. Let me demonstrate what I am saying (or, at least, trying to say) syllogistically:
P1: q and p → r
P2: q and p
So, the “form” of this is modus ponens, but, because these are propositions, according to Wittgenstein, it is already there internal to the propositions themselves. But, we could question P1 and P2. But, that is irrelevant to whether the Tortoise Problem has been gotten around.
Fundamental Proposition 2: Propositions have a determinate logical form, and this inherently makes them logical, therefore meaning they contain logical/inferential principles within themselves. Or, as Kuusela says, “the rules governing inference are envisaged as being already implicitly contained in the propositions themselves” (Kuusela 58).
Fundamental Presuppositions of Proposition 2: 1. Theory of propositions. 2. An account of what inferential principles there are.
Questions Against Proposition 1: 1. What are those logical/inferential principles? 2. Why is modus ponens a logical/inferential principle actually the case? 3. Can I just say anything is a inferential principle/rule?
Answers to Questions Against Proposition 1: 1. There are no general inferential principles that universally apply to all propositions because of the answer to question two. 2. In this specific case of the syllogism lined out above (P1: q and p → r; P2: q and p; C1: r), modus ponens is contained in P1 and P2 because of the answer to question three. 3. “The method of inference is to be understood from the two propositions alone,” or, in other words, that method of inference (or inferential rule) that is appropriate or proper to two premises is understood immediately upon relating the two premises (TLP 5.132). Or, to rephrase the answer to question three, with an “if … then” proposition (let’s say this is p), modus ponens is understood to be proper to it and what every accompanies it (let’s say this is q). The answer to question three, therefore, serves as a proof for presupposition two, therefore meaning the only thing that is, thus far, supposed within proposition two that has gone without explanation is presupposition one which the presupposition of a theory of propositions.
Questions to the Answer to Question Three: 1. How and/or why is the method of inference understood from the two propositions alone? 2. When Wittgenstein says “is to be,” is this a normative claim? Are inferential principles, i.e., logical laws, normative then? 3. If they are normative, how does one justify them normatively? 4. If they are normative, what would be the descriptive method for justifying them if not them, i.e., if inferential principles are normative and we are trying to justify this normativity, how could there be any other means to justify their normativity other than those inferential principles?
Answers to the Questions to the Answer to Question Three: 1. When we talk about how it is to be understood, all we must really understand is if the inference is correct, for if it is correct, then so is its inferential principle. 2.
Questions to the Answers to the Questions to the Answer to Question Three: 1. How does the first answer not presuppose inferential principles? Wittgenstein would say you can’t suppose them because they are contained within propositions because of his theory of propositions, but when we talk about the specific inference does this not become circular in that the only way we know if a specific inferential principle is contained within the relation of two propositions is through testing the correctness of the inference itself, but that the correctness of the inference itself reflects on the inferential principle, does this not suppose another inference, i.e., that inference of “if the inference is correct, then this reflects that the inferential principle is correct [i.e., applied appropriately/properly],” and would we not therefore have to test this inference, and would it not therefore become circular in that if we are testing the correctness of the inference of “if the inference is correct, then this reflects that the inferential principle is correct,” how could we positively test the correctness of this inference without begging the question, as would we not be supposing that the correctness of the inference reflects the correctness of the inferential principle in making the inference? This is a ramble, I know. I hope you can glean something from it. 2. How does our question to answer one that we just put forward not demonstrate that the first answer leads to circularity? Issue of circularity demonstrated: If I test the inference “if the inference is correct, then this reflects that the inferential principle is correct,” and it comes out to be correct, what is the means of it coming out being correct? Is the result of this test not inferred? And, would I therefore not have to question if the correctness of this inference of the result also reflects the correctness of its inferential principle which it came about by? If I would have to do such a thing, would I not, therefore, be supposing that a test signifies positive reflection, therefore making this whole operation circular? 3. How does our question to answer one that we just put forward not demonstrate that the first answer leads to infinite regression? Issue of infinite regression demonstrated: If I have to infer the correctness of an inference, would I not have to test the correctness of that inference? How does this not keep going on infinitely? 4. Why is it the case that an inference being correct demonstrates that the assumed inferential principle is actually proper to the inference at hand?
Elaboration on the First Answer to the Questions to the Answer to Question Three: We demonstrate correctness through showing that “[the] relevant propositions together constitute a tautology, i.e., that the propositions involved in the inference, taken together, emerge as unconditionally true, or true in all circumstances” (Kuusela 59).
Questions Against the Elaboration on the First Answer to the Questions to the Answer to Question Three: 1. How does this not suppose that tautologies are true in all cases? 2. How does this not suppose the principle of identity as a consistency principle? (the principle of identity as a consistency principle isn’t an inferential principle so even if Wittgenstein is correct about his theory of objects and propositions, specifically that his theory that propositions have a logical form necessarily and that necessarily means inference rules are contained in the propositions themselves, he still couldn’t argue that the principle of identity as a consistency principle is contained in the propositions themselves; now, if the p).
Answer to the First Question Against the Elaboration on the First Answer to the Questions to the Answer to Question Three: “In the one case the proposition is true for all the truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological” (TLP 4.46).
Questions to the Answer to the First Question Against the Elaboration on the First Answer to the Questions to the Answer to Question Three: 1. How can we infer if a proposition is true for all of its truth-possibilities? 2. How can we infer such a thing without questioning the validity of the inference, therefore leading to the assertion of our testing method, therefore leaving us in a vicious circle?
Kuusela’s Admission of Failure: “Importantly, however, such a clarification of what inferences count as correct, as Wittgenstein conceives it, does not constitute an attempt to validate or justify relevant inferences in the sense in which the logocentric predicament, according to Sheffer, excludes such validation as already presupposing what was to be validated. As the point might be put, while inference tokens can be validated, and inference types can be clarified by showing them to correspond to certain general patterns of inference, these inference-patterns themselves cannot be validated” (Kuusela 59).
Question Against His Theory of Propositions: How can you prove that Wittgenstein’s theory of propositions is the case without supposing it?
Fundamental Proposition 3: “An illogical thought, Wittgenstein emphasizes, would not be a thought” (Kuusela 63).
Fundamental Presuppositions of Proposition 3: Theory of thoughts.
Questions Against Proposition 3: 1. How can a theory of thoughts be thought non-circularly? 2. Do inferentially derived theories of thoughts not fall into the issue of circularity? 3. Does Wittgenstein not have a inferentially derived theory of thoughts?
The Wittgensteinian Attempt at Solving the Logocentric Predicament as Fundamental Proposition 4: “As explained, the problem [of the logocentric predicament] can be dissolved by abandoning the conception of the discipline of logic as a science whose task is, first, to establish the logical laws or principles that govern correct inference, language use or thinking, and, second, to prescribe with reference to these laws and principles which inferences count as correct or which modes of language use or thinking count as sensible, whereby certain modes of inference, language use or thinking then emerge as justified or validated” (Kuusela 64).
Fundamental Presuppositions of Proposition 4: 1. Theory of logic.
Question Against Proposition 4: How can we inferentially determine a theory of logic in the first place?
Fundamental Proposition 5: “The propositions of logic are tautologies” (TLP 6.1)
Fundamental Presuppositions of Proposition 5: 1. Theory of logic 2. Theory of truth.
Elaboration on Proposition 5: For Wittgenstein, tautologies mean nothing in the sense that “they do not say anything about how things are in reality” (Kuusela 66). In other words, tautologies “describe no states of affairs whose obtaining would determine their truth/falsity” (Kuusela 66). For Wittgenstein, “the truth-value of a tautology only depends on the symbols themselves, on their having been combined in a particular way in the proposition. In this sense, the propositions of logic may be described as analytical, as Wittgenstein does in 6.11” (Kuusela 66–67).
Questions Against the Elaboration on Proposition 5: 1. What makes analyticity justified or true? 2. Does this not suppose a theory of truth?
§2: Going through the Tractatus Logico-Philosophicus
We have identified the key presuppositions of all of Wittgenstein’s fundamental propositions (or at least those propositions we find to be fundamental): a theory of objects, propositions, thoughts, logic, and truth. We will go over each and also put forward questions, answers, objections, and responses in regards to each.
§2.1: Wittgenstein’s Theory of Objects
§2.2: Wittgenstein’s Theory of Propositions
§2.3: Wittgenstein’s Theory of Thoughts
§2.4: Wittgenstein’s Theory of Logic
§2.5: Wittgenstein’s Theory of Truth
§3: Further Remarks on Wittgensteinians
In his “Review of Eli Friedlander, Signs of Sense: Reading Wittgenstein’s ‘Tractatus’,” Kremer says, for Wittgenstein, “logic itself is beyond justification, neither a source of justification nor something to be justified, neither a theory nor a principle, but an ability which pervades all our thinking, even our thinking of objects” (Kremer 654).
Fundamental Proposition 1: Logic is not something to be justified because it isn’t a theory or a principle, rather it is an ability that is binding in regards to thinking.
Objection to Proposition 1: Whether logic is an ability or not does not take away from it having to be justified. That something is binding is not indicative of its validity, truth, etc. (this is the common fallacy committed by the epistemic particularist). That logic is appropriate and proper simply means that it meets its own standards, i.e., that it is logical. The logocentric predicament demonstrates that logic, in its common (i.e., our) understanding, is illogical due to vicious circularity. Whether or not logic puts forward propositions to judge does not change its need to be justified. In other words, if logic is just a method and puts forward nothing, then nothing can be identified. Or, again, in other words, logic is an ability that we can describe, and thus we ourselves can formulate what is happening within the process that is the “ability” of logic.” Now, let us say that logic, as Wittgenstein says, cannot be said but only shown. Let us realize what this means not to Wittgenstein, but to us. If our assertions about logic cannot be “true” in the sense we cannot have anything said about logic, then obviously one couldn’t say that nothing can be said about logic without saying something about logic and thus being in a contradiction, which, by Wittgenstein’s own standard, would therefore be “illogical” in the sense that it is not tautological (which all the propositions of logic are; also, note, that contradictions aren’t illogical for Wittgenstein, rather just necessarily untrue, but again, this supposes his theory of logic and his understanding of thought itself). This is why Wittgenstein says, “Whereof one cannot speak, thereof one must be silent” (TLP 7). But, he only arrives at this conclusion by speaking about what cannot be spoken of, i.e., by speaking about what he calls “the inexpressible” (TLP 6.522). This is obviously mysticism, and Wittgenstein admits this when he says, “There is indeed the inexpressible. This shows itself; it is the mystical” (TLP 6.522). In this sense, it is Wittgenstein, through his mysticism, that is positing logic outside of language by way of language. This obviously puts him in a contradiction, and he admits this (I literally have no idea why people buy into Wittgenstein once they realize he admits his own failures). He admits this when he says, “My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.) He must surmount these propositions; then he sees the world rightly” (TLP 6.54). In other words, Wittgenstein is admitting that he uses language to describe logic, he is admitting he is using the ladder to climb. But, Wittgenstein is saying that after his climb, he throws away his ladder, i.e., he asserts that logic cannot be talked about because “[w]hereof one cannot speak, thereof one must be silent” (TLP 7). Now, Wittgenstein would in a certain sense be able to do this move without falling into a position of illogicality if he could assert that what he is putting forward is all that one can put forward. What I mean by this is that if Wittgenstein could prove that whenever one picks up the ladder and begins the climb, the only correct way to climb would be the way he is climbing in the Tractatus. In other words, if Wittgenstein could prove that his conclusions are the inevitable conclusions when language is employed, then he could say that there is this kind of meta-circle: one always, when employing language, realizes my conclusion. This is why he says that when one “finally recognizes [his propositions] as senseless,” when one finally “understands,” they are then to “throw away the ladder” (TLP 6.54). Now, he does assert that the employment of language always and only leads to his conclusions if language/philosophy is employed correctly/rightly: “The right method of philosophy would be this. To say nothing except what can be said … [it is] the only strictly correct method” (TLP 6.53). Only that way which, that method by which, Wittgenstein climbed up the ladder is the correct, is the right (not in a normative sense), way to climb up the ladder. How would one prove this? And furthermore, does this not suppose that there is ground to stand on once one throws away the ladder? How would one prove that there is higher ground? Does Wittgenstein not deny the possibility of higher ground when he says, “Propositions cannot express anything higher” (TLP 6.42)? Wittgenstein could only prove this through employing his method, which would suppose that his method is the only proper method. This leaves him in a vicious circularity. But, by his own admission, and as we have realized through our analysis, we know that there is no higher ground once he throws away the ladder. This throwing away of the ladder then is the initiation of falling back to the floor which one was climbing away from. This is the vicious meta-circle Wittgenstein is in: he always arrives back at the floor. Wittgenstein’s philosophy then is nothing more than a machine, maybe even a labyrinth because the climb sure as Hell isn’t easy, of suffering. Wittgensteinians are indifferentiable from Sisyphus. “Let’s begin the climb again,” they say, not realizing the ironic illogicality of their whole effort. But, let’s grant that Wittgenstein is correct about all this. Does this solve the logocentric predicament? No, because the logocentric predicament can just become a problem of inference, and inferences can be talked about. This is what all the Wittgensteinians I have talked to have failed to understand. But wait, the Wittgensteinians could argue that it is actually the inexpressible itself which serves as this higher ground. Hence, Wittgenstein’s mysticism. Therefore, proposition 1 supposes a theory of logic, propositions, thinking, etc. but these are mainly irrelevant in that we have either addressed them directly already (see above) or they are trivial in regards to the logocentric predicament. What is relevant in a theory of mysticism.
Fundamental Presupposition of Proposition 1: Theory of mysticism.
Elaboration on the Fundamental Presupposition of Proposition 1: Wittgenstein, in the Tractatus, only uses the word mystical three times: 1. “Not how the world is, is the mystical, but that it is” (TLP 6.44) 2. “The feeling of the world as a limited whole is the mystical feeling” (TLP 6.45) 3. There is indeed the inexpressible. This shows itself; it is the mystical” (TLP 6.522).
Objections to the Fundamental Presupposition of Propoposition 1: 1. By speak, in the context of its opposition to show, Wittgenstein does not mean that one has to draw what one is saying and then show it. Rather, any form of signification is speaking. As Wittgenstein says, “Objects I can only name. Signs represent them. I can only speak of them. I cannot assert them. A proposition can only say how a thing is, not what it is” (TLP 3.221). But, what does it mean to show then? Well, there is a confusing notion being put forth here in that, for Wittgenstein, “The proposition shows its sense. The proposition shows how things stand, if it is true. And it says, that they do so stand” (TLP 4.022). Ultimately, though, we understand his usage when he says, “That which expresses itself, in language, we cannot express by language. The propositions show the logical form of reality. They exhibit it” (TLP 4.121). His proof of the inexpressible, then, is therefore his theory of propositions, in that propositions, according to his theory, have a determinate logical form, which is dependent on the inexpressible (which is Logic, with a capital l). Hence, another circle has been found with Wittgenstein. 2. Furthermore, mysticism fails on the fact that it is dependent on empricism. Deleuze understands this, but in a “different” and “more” “correct” way than all other empiricists (hence why transcendental empiricism is the highest form of empricism, though, in the end, it still suffers from the issues that all other forms of empricism suffer from). If an understanding of logic, which, for Wittgenstein, is key to logic having the unique status Wittgenstein attributes to it, and that understanding must come from perception, then does this not suppose a metaphysic? And, even if there is a perceiving subject, where do we perceive logic? He says, we perceive them in propositions. Now, obviously the next question would be why does it being shown and not able to be expressed mean that it escapes the logocentirc predicament. And we have already gone over that being the case, so I will not address it here, as I have already questioned it to the ground above. Nonetheless, how we know that logic is actually correct, is not something that concerns Wittgenstein. Ultimately, what Wittgenstein leads us to is all propositions and inferences being correct, because we could not make illogical ones to him. In this sense, do we not arrive at a certain trivialism? Wittgenstein says, “Everything we see could also be otherwise. Everything we can describe at all could also be otherwise. There is no order of things a priori” (TLP 5.634). We describe propositions, as a theory is in a certain sense a description. Therefore, again, by Wittgenstein’s own admission, logic is not secure in that it is either a.) dependent on our understanding, in which, it does not take care of itself or b.) it does take care of itself, yet it cannot exist a priori, as “[t]here is no order of things a priori” (TLP 5.634). I’ve confused myself at this point. Let me just put forward one final and fundamental objection. 3. How can we understand something which isn’t expressed, i.e., not given to the understanding, other than the understanding itself?
Elaboration on the Objections to the Fundamental Presupposition of Proposition 1: Now, let us note, this critique of mysticism (specifically, Wittgensteinian mysticism) does not apply to Bataille’s mysticism. For Bataille’s mysticism is a mysticism which is without mysticism. In other words, the only refutation of Bataille’s theory of nonknowledge is a non-mystical solution to the logocentric predicament itself.
In his “Wittgenstein, Psychologism and the So-Called Normativity of Logic,” Gilad Nir says, “the internal relations between propositions that make up an inference are constitutive of their determinate identity qua propositions. The appreciation of such relations is already presupposed in our understanding of these propositions, and this renders void the need for any mediation between premises and conclusion … Inference, on this view, serves to bring out and articulate the shape of the logical space of one’s language. The harmony between what we understand and how we infer is secured neither by appeal to higher order beliefs about what follows from what, nor by means of instantiating axioms, nor by applying rules of inference. No such mediation between premises and conclusions is needed, since the components of inference are not discretely individuated atoms of belief, which from connections with other such atoms only when some additional act kicks in. Rather, the components of inference are propositions that we understand, and hence propositions that already occupy determinate locations in our logical space” (Nir 170–171). In this sense, “[t]o affirm any proposition,” for Wittgenstein, “one must understand it” (Nir 174).
Fundamental Proposition 2: The key to inference-making is a subject’s understanding.
Objections to Proposition 2: 1. How can understanding itself be understood without first understanding understanding? Vicious circularity is contained in here as long as inference is required. Only a non-inferentialist account allows for the understanding of understanding in that the instantiation of understanding is, at the same time, the non-inferential understanding of understanding. Oddly, this returns us to Kant, in that, for Kant, “Logic is thus a self-cognition of the understanding and of reason, not as to their faculties in regard to objects, however, but merely as to form … In logic the question is only, How will the understanding cognize itself,” or, in other words, “How will the understanding understand itself?” (Kant, Lectures on Logic, 529–530). Circularity on arises insofar as their is a movement between the understanding and the self-cognition of the understanding. But, with a non-inferential account, there is no movement between the two. 2. How could we know our understanding of understanding is the correct understanding when inference is employed? Again, because there are no means within the non-inferential account of understanding, there is no issue of correctness or properness in that there is no means, there is just the immediate and simultaneous instantiation of the ends (the understanding and the understanding of the understanding). 3. Not only does Wittgenstein fall prey to the latter skeptical rebuttal, but he also falls to this one: how can one prove that one’s understanding of propositions is correct? Or, at least, how can one understand that one’s understanding of propositions is correct? And then understand that this understanding of one’s understanding of the propositions is correct? And so on, ad infitium! This demonstrates the infinite regression latently contained within the mechanics of any “inferentialist” account of the understanding. 4. Furthermore, why is this logical space of one’s language, even if one understands it, “correct”? If one asserts it is correct, they fall into the issue of mysticism because logic would be inexpressible and if they assert it is incorrect, then they concede they fall into the logocentric predicament. And, even if one asserts that the logical space of one’s language is beyond correctness and incorrectness (as categories themselves), then they fall into the issues of mysticism lined out above. 5. Furthermore, there seems to be some level of circularity here with Wittgenstein in that he must presuppose that the inferential principle is contained within the relation between the propositions themselves. Now, even if this is the case, it is no matter for our position, for we have given a plethora of refutations to it being the case above. However, we can recognize that it is impossible for the inferential principle to be contained within the relation without presupposing it is there. Now, this obviously goes back to Wittgenstein’s theory of propositions and him having to say that it has a determinate logical form. Now, we have lined out the issues with both his theory of propositions itself and his theory of propositions being the case above. But, he does have to infer this theory of propositions. He has to climb the ladder, by his own admission. Therefore, when inferring his theory of propositions, he must suppose it is the case unless he has a non-inferentialist account (which he doesn’t). In fact, I find the biggest issue with Wittgenstein to be the fact that he treats inference (almost) as non-inferences: “All inference takes place a priori” (TLP 5.133). Now, because he must suppose his theory of propositions when inferring it, we realize that there is no non-fallacious reason, which is not actually a reason at all, for the inferential principle to be contained within the propositional relation. Rather, a non-inferentialist account which has an understanding of the inferential rule isolated would, by way of analytic a priori intuition, solve any issues which pervade all other accounts in that 1. There is no need for experience, hence a priori 2. There is no need for inference, hence intuition 3. There is no need for anything beyond what is expressed, i.e., there is no movement from one point to another, hence analytic.
Fundamental Proposition 3: “[I]t is the propositions, or rather their behaviour, which give us the [inferential] rule” (Zwicky, “Wittgenstein and the Logic of Inference, p. 675).
Objections to the Proposition 3: 1. How can this be put forward without supposing his theory of propositions? 2. The objections to his theory of propositions done above in section two point two.
Zwicky’s Admission of Failure: “These internal relations cannot themselves be represented by propositions because they (the internal relations) are inseparable from that which propositions possess in virtue of being able to represent reality at all. In other words, the representation of internal relations would require the representation of (general) logical form, since internal relations include general logical form in what they display. But no proposition can represent general logical form; therefore no proposition can adequately represent an internal relation” (Zwicky 676).
Elaborations on Zwicky’s Admission of Failure: This latter admission demonstrates that Wittgenstein’s theory of propositions and logic depend on his mysticism, which we have already demonstrated to be untenable above.
Wittgenstein’s Admission of Failure: “What can be shown cannot be said” (TLP 4.1212). This supposes that there is something to be shown which, according to Wittgenstein, can only be shown and not said, therefore meaning communication of any answer to an accusation of begging the question denies itself per Wittgenstein’s own admission. “The holding of such internal properties and relations cannot, however, be asserted by propositions, but it shows itself in the propositions, which present the atomic facts and treat of the objects in question” (TLP 4.122). This further demonstrates the fact that Wittgenstein’s theory of propositions and thus his understanding of logic depend only one what can be shown, but, as we just went over, this mystic “basis” is not a basis at all, only a movement of throwing away the ladder, leaving the climber to hit the floor and die due to internal injuries induced by the collision.
Zwicky’s Admission to the Correctness of Our Elaboration: “[Wittgenstein’s] mysticism with regard to logic (which for him comprised essentially these structural features) was motivated at least in part by the genuine paradox which here confronts us: at the formal level, although we appear to understand universal syntactic or semantic claims, universal languages are demonstrably impossible to construct; and the impossibility of universality conjoined with our apparent comprehension of the concepts which cannot be expressed appears to extend to natural language as well” (Zwicky 678).
§4: Deleuze and the Logocentric Predicament
I have long suspected that Deleuze has something to offer us in regards to the conversation about the logocentric predicament since I first read his Logic of Sense. Now, I have had and still to partly hold some animosity toward Deleuzians and even Deleuze himself (just as I hold more animosity for Wittgenstians rather than for Wittgenstein himself; it is also ironic that Deleuze’s relationship with Wittgenstein was one of “hate” [Deleuze did not like Wiggy!]). But, when Deleuze really leaves obfuscating issues as well as being crystal clear (which he can do quite well when he actually tries) in terms of his explication, he becomes quite the enjoyable read. In fact, Logic of Sense is such a splendid little book! I recommend that we should all, at some point, read it closely, or at least, read it in a beneficial manner. What does Deleuze have to offer us in regards to the logocentric predicament though? Well, nothing more but also nothing less than some sense…
[go over all his theories and how they relate to the logocentric predicament; in section 3 identify those fundamental propositions, try to refute and question them to the ground of course; point out the presuppositions of each of the fundamental propositions, and then cover each of those fundamental presuppositions either in section 4 if they are not a greater theory or in section 5 if they are a greater theory, e.g., his theory of denotation. ALSO, definitely make diagrams, esp. the ones you have in your notes]
§6: Wittgenstein Contra Deleuze
§7: Deleuze Contra Wittgenstein
§8: Wittgenstein Avec Deleuze
§9: Deleuze Avec Wittgenstein
§10: Some Preliminary Notes and Thoughts to the Development of Neo-Rationalism
Paul Boghossian says, “no-one has been able to explain, clearly enough, in what an act of rational insight could intelligibly consist … The question is whether we can be said to have some sort of non-discursive, non-ratiocinative, insight into their natures, an insight that would disclose immediately, and without the help of any reasoning whatsoever, that all instances of MPP are truth-preserving” (“Blind Reasoning, p. 231). Boghossian asks, “What sort of relation obtains between a thinker and a property, when the thinker has ‘rational insight’ into its nature? Or … when the thinker has a rational insight into its nature, when he is simply able to see that when his MPP premises are true so must be its conclusion?” (“Blind Reasoning, p. 231). These are tough questions, and the process of answering them are even more difficult. What is their importance though? Why do we care for rational insight? Laurence Bonjour in his book In Defense of Pure Reason says,
I am invited to asses the cogency of inferring the conclusion that David ate the last piece of cake from the premises, first, that either David ate the last piece of cake or else Jennifer ate it and, second, that Jennifer did not eat it (perhaps because she was at work for the entire time in question). In a way that is parallel to the earlier examples, the obvious construal of this case from an intuitive standpoint is that if I understand the three propositions involved, I will be able to see or grasp or apprehend directly and immediately that the indicated conclusion follows from the indicated premises, taht is, that there is no way for the premises to be true without the conclusion being true as well. It is obvious, of course, that I might appeal in this case to a formal rule of inference, namely the rule of disjunctive syllogism. But there is no reason to think that any such appeal is required in order for my acceptance of the inference as valid to be epistemically justified. Nor, in light of our earlier discussion, is there any reason to think that such a rule would not itself have to be justified either by appeal to the same sort of apparent a priori insight at a more abstract level or else to other rules or porpositons for which an analogous sort of justification would be required. (p. 105–106)
Bonjour’s account of a priori or rational insight would allow us to be epistemically justified in our acceptance of inference rules such as modus ponens. I suggest that it could be through a theory of direct acquaintance that we answer Boghossian’s question of what relation obtains and why does that relation allow us to glean anything when a rational insight “occurs” (our reworking of rationalism, internalism, and foundationalism will all be very skeptical in regards to time in order to avoid any theist’s critique of us that speaks of temporal regress). This move of following and developing direct acquaintance would, it seems, allow us to be able to answer Boghossian’s pressing and important questions as well as not lapse into an inferentialist account of justification. To get past the “fatal circularity” that Boghossian brings up, we can simply argue that there is no presupposition of being able to justifiably infer according to MPP for the internist, or at least for us and our internalism, in that, that is a non-inferentially justified belief, justified through that direct acquaintance which comes out of rational insight.
§11: Perception, Concerns and Worries
I have always been skeptical of perception and its validity. It seems that everyone has those intuitional beliefs which they don’t even try to prove and instead just hold as true (though I have gotten rid of all of those in the sense that I hold they are true). Now, my intuition that sense perception and what it senses, what it perceives, is not the whole story is not an intuition of some higher realm such as heaven, far from it in fact. Instead, I simply have never been convinced of my perception not in the sense of hallucination or in the sense that everyone sees different things. Rather, I find that if one were to purport that experience serves as the basis of logic, for example, or its justification, an inevitable circularity arises. Furthermore, I find no good reason to believe that perception contains some factor that gives its some unique justificatory status. I find some comfort in Locke, but I also find worry:
Locke’s formulation of the doctrine of intuition contains key elements that suit it for an account of a priori knowledge of analytic truths. As the “first act of the mind,” intuition is epistemically prior to other modes of knowledge; no regress looms. Though it may involve a comparison of concepts that were given in experience, it does not depend upon some further experience that is the relation of those concepts: the relation is intrinsic and the perception of it infallible. And it promises to be the foundation for our knowledge of demonstrative truths as well. (McGrew, Internalism and Epistemology, p. 97)
I find comfort in having intuition as our base, but I find worry in the element of experience still being, though only minorly, present.