And yet — here we begin to break new ground — over and above the facts which evidence, carefully sifted, may attest, there remains the question of the process or proof employed by the mind in arriving at these mediate propositions. What, then, is to be said of our reasoning process itself? What guarantee have we of its accuracy? What gives us the quiet assurance that we reason correctly in formulating mediate judgments? Let the importance of this our last problem be noted. Nearly all our knowledge can be cast into the form of these mediate judgments, which depend upon some marshaling of facts, some intellectual manipulation, some deductive reasoning, some argument, process, or proof. If our reasoning processes themselves are vitiated, then, not all, but the vast bulk of our knowledge must disappear into the night. On the nature of our answer depends the whole possibility of science and philosophy. We have reached another crisis — the last. We may put the question in another way, in order to light up a second train of ideas. Our intellects are capable of three distinct functions, which have recurred like some leit-motiv throughout this essay. By means of intellect, we conceive ideas, we form judgments, linking together no longer the simple ideas but the actual judgments. So far we have established the possible validity of concepts: as representatives of extra-mental natures they may be erroneous, but the error can be tracked. Similarly, we have established the possible validity of judgments, and submitted the criterion of evidence. There remains the reasoning process; not the judgment that are manipulated, but the actual work of manipulation; not the power of judging, but the power of concluding; not the content of our propositions, but their connection and sequence; not our ideas but the “Gang” of our ideas, which needs to be scrutinized and defended. Is the reasoning process itself valid? (Vance, Reality and Truth, 297–298)
There are a number of such general frameworks where the demand to justify the framework from within the framework is always senseless and yet somehow seems incumbent upon us. Thus, although one can prove that a particular argument is valid or rational within the criteria of rationality, one cannot prove within those criteria that rationality is rational or that validity is valid. (John Searle)
The request that [intellectuals] defend reason on the basis of reason is at once impossible and yet mandatory. (Schlag, The Enchantment of Reason, 60)
There is a paradoxical structure that haunts the attempt to ground reason in reason. The parties who attempt at such a justification or grounding must always already rely on that which they are attempting to justify or ground. They are thus threatened by the possibility of a shallow circularity — perhaps even a circularity that is at odds with the idea of reason itself. If, by contrast, the attempt to justify or ground reason is accomplished in ways different from reason, then the effort will have missed the mark. It will have failed to ground reason in reason — resting reason either on dogmatic assertions or on the empty chasm of an infinite regress. All together, this vexing array of disappointing possibilities is called the “Munchausen trilemma”: the attempt to ground reason must in the end rest on (I) infinite regression, (2) circularity, or (3) dogmatic assertion — none of which, of course, can satisfy the grounding ambition. (Schlag, The Enchantment of Reason, 60–61)
Reason leads us to a recognition of its own limitations — and to a recognition of its own immersion in belief. It leads us to recognize that reason depends upon belief. (Schlag, The Enchantment of Reason, 61)
One thing, however, is clear: Reason cannot be indifferent to this predicament. Reason cannot take its dependence upon belief with indifference. The cost of doing so — the cost of blithely presuming the rightfulness or the efficacy of reason — is that reason becomes transformed into its traditional enemies: faith, dogma, prejudice, and company. (Schlag, The Enchantment of Reason, 63)
All of this renders reason quite vulnerable. Reason, understood in this light, exists as an assortment of predicaments: Reason is used to select, monitor, and replace beliefs, yet it is dependent upon belief. Reason is a map to guide us through the unthought, yet remains itself grounded in an unthought that it cannot know. Reason’s identity is in tension with its own ruling normative ambitions. Reason is propelled simultaneously toward the production and the dissolution of contexts. This is manifested often as a tension between critical reflexivity and rational frame construction. For those who are partisans of reason, the attribution of these predicaments to reason is likely to be taken as a kind of criticism. But that is to miss the point. None of these predicaments should be taken as arguments against reason or its use. Rather, they are predicaments that constitute the very identity of reason. (Schlag, The Enchantment of Reason, 78)
I care little for a hammer being justified in itself, I only care about my use of the hammer being justified to hit this nail, which is to say, I only care about the hammer being that appropriate thing for my task. I care little for if reason is justified in itself, because, in fact, it could never be. Reason regulates constructions and exists with them. It itself too is constructed in the act of inference, but, of course, our very notion of reason is what is interpellated in inference. This divine idea of reason as independent of inference is an absolute absurdity. Let’s say reason, in itself (by itself; abstracted from relation to the act of inference [the act of deduction]), is unjustified. What does this mean? Well, let’s also say our use of reason is justified, as well. Do we not run into a contradiction here? Hardly, for if our use of an unjustified something is itself justified, then the unjust nature of that something means absolutely nothing, for the seeming contradiction already bridged itself when our use of that something was justified; or, in other words, there is no contradiction because our use of unjustified reason is itself justified, meaning that the unjustified nature of reason was unable to take away from the fact that our use of reason is itself justified. In this sense, who cares for the justification of reason, of inference, of logic, of deduction in itself? We certainly do not! Let us go back to the logocentric predicament as originally outlined by Sheffer himself:
The key thing which pure general logic helps us deal with is the logocentric predicament:
Just as the proof of certain theories in metaphysics is made difficult, if not hopeless, because of the « egocentric » predicament, so the attempt to formulate the foundations of logic is rendered arduous by a corresponding « logocentric » predicament. In order to give an account of logic, we must presuppose and employ logic. (Sheffer, Review of Principia Mathematica, 227–228)
In order to justify reason, we must presuppose and put logic to use, which is to say, in order to justify the very first premise of theoretical construction, we must presuppose that premise is the case and put that premise to use. But, there is an issue here: Sheffer has added another step. The employment of reason (i.e., reasoning) is itself the presupposition of reason. If we are not putting reason to use we cannot presuppose it. Therefore, reason is presupposed in the act of using it. Therefore, the act of the presupposition of reason, which is the act of using it, would be justified if the act of using reason was justified, and thus reason itself would finally have the means to the end of its justification established. This could be a potential breakthrough, so let us put what we have said through ruthless criticism.
The fundamental proposition I have just made is this: the presupposition of reason is the same as the use of reason. How is this the case? Does one not have to presuppose reason to use it? Yes, one does. But, what is this act of presupposition itself? For if the act of presupposition itself involves reason, then it itself is the act of putting reason to use. Therefore, meaning the fundamental proposition we have put forward would be the case. The implications, again, of this fundamental presupposition of our’s are very simple: if reason’s use, i.e., reasoning, and its presupposition were the same, then we would no longer have to justify reason in itself, for the independent justification of reasoning would itself ameliorate any issues of reason itself being unjustified (though, we cannot say that reason is itself justified or unjustified without first supposing that reasoning itself is justified). So, we have now realized the solution to any critique of our fundamental supposition: we are not supposing reason, for reason is only the totality of all processes of reasoning that are justified (which is why reason has limits, but reasoning does not). Rather, we are supposing reasoning is justified, not reason being justified, which is to say, we are supposing our act of putting reason to use is justified, so, never do we suppose reason’s justification, for reason is always already that which is justified but only once the putting to use of reason, i.e., reasoning, has been justified, for reasoning is that tool whose exactness in demarcating the justified from the unjustified is only comparable to itself. Okay, this all sounds great, does it not? It does to me. But still, we address two things: 1. Our conception of reason that has thus far been used in this essay and 2. A risk of infinite regress in regards to the presupposition of reasoning’s justification.
So, let us address my first concert. If reasoning is the act of putting reason to use and reason is the totality of all that which is justified, we fall into this issue of reasoning only being able to put forward what is justified, which would be great if that was the case, but because not all processes of reasoning, of inference, are justified, our conception of reason must be revised. So, how are we to define reason if reasoning is the act of putting it to use? “Reason is, in its various forms (inductive, deductive, analogical, abductive, instrumental, practical), a way of moving from one place to another” (Schlag, The Enchantment of Reason, 76). Reason then itself is reasoning. Reason is itself being put to use, any instantiation of reason is reason being put to use. “By what?” which is to ask, “What is putting reason to use?” Must we say the reasoner? Does that answer not presuppose a subject? Could we not say rather, that reason is putting itself to use? If reasoning is reason being put to use (let us forget the previous emphasis on act held earlier in this essay for a moment), then reason is putting itself to use, which is not to suppose reason’s existence for reason interpellates itself ex nihilo, for reason has no possible constitution other than itself, and, therefore, through itself (and this is where our predicament arises), comes to be. Wait, that isn’t right. Reason is the “through itself.” Reason never actually comes to be because reason has nothing to do in itself with Being, which is not to say that it is up in arms with Becoming. Rather, reason is reasoning, there is no idea of reason. Reasoning is just that process of making an inference: of putting up two premises and having them propel you to a conclusion; the propellant, here, is reason. Wait, wait, let us try and think of this differently again.
What are inference rules such as modus ponens? Modus ponens is not an external rule of inference, which is not to say it is immanently within the propositions themselves as Wittgenstein says in the Tractatus. Rather, inference rules represent the different valid forms inferences can take. So, I can say,
P1: p → q
C1: Therefore, q
and all I will have said is that a certain movement of reasoning, a specific form of inference is valid. There seems to be no such thing as inference in itself. Inferences must take a form because they are a movement, as, by the very fact of it being a movement from premises to conclusions, it must take a form as if it did not take a form, it could never direct itself toward the conclusion. But does this not suppose that the conclusion is just laying out there, free-floating? Not at all, as all possible propositions exist within the domain of discourse (expressed through the operator D). Are we not supposing the domain of discourse then? Obviously, one could say we aren’t. Whether there actually is the domain of discourse or not does not matter, for whether these propositions are free-floating independent of our construction or are dependent on our construction does not matter in regards to our position in that once constructed by an entity able to construct propositions it is then free-floating until the entity itself employs reason to move these two free-floating propositions into a relationship with one another. Reasoning is the process of moving from two free-floating propositions (premises) to another single proposition (the conclusion) and inference is the movement from the premises to the conclusion. Does inference then suppose some relation between the premises? Alas, we have arrived at the best way to express what I was previously trying to say: inference rules are those external hands which, contra Wittgenstein, force the propositions into a relationship with one another, providing the propellant required to launch the inference to the conclusion. The issue then becomes “What gives propellant to these inference rules themselves?” This is an issue solely because if inference rules are the propellant to inferences then any inference rule would rely on another inference rule until eventually there was no inference rule behind another, and that inference rule would be left on its own and unjustified. Reasoning is the process of the utilization of inference rules and then the propelled movement, the inference, toward the conclusion that arises out of the easily combustive utilization of inference rules. Our issue is then of inferences and inference rules? Not necessarily, for it is an issue of logic and reason. Let us further delve into this.
Logic is a form of reasoning, as logic is the necessary relation of consequence. Logic is not the “science of truth” as, for example, Frege purports it to be. So, what do I mean by “the necessary relation of consequences”? Simple: two premises, once put into a specific relation with one another, necessarily have the consequence that is their conclusion. In other words, we have
P1: p → q
these are two propositions (P) which once put in relation to one another (P1 and P2) then lead to the conclusion
C1: Therefore, q
necessarily. C1 is the necessary consequence of those two relations. A logical conclusion is a logically necessary conclusion. Thus, logic is a specification upon inference making: logic simply qualifies an inference as necessary. What is the basis for this logical conclusion? Inference rules? But would that be a logical conclusion, meaning the logocentric predicament precedes the question of inference? Surprisingly (counter to all that has been previously said), no. I say no only because there is a supposed differentiation. The problem of the inferred justification of inference rules infinitely regressing is itself the problem of logic, for when we say the logocentric predicament is the issue of having to utilize logic in its justification, therefore supposing it is justified, we are doing two things 1. Fallaciously equivocating logic’s use with logic itself and 2. Talking about inferences. Let me further explain this. Just like with reason, which I promise I’ll get back to, logic is actually not very well understood. We know logic is the necessary relation of consequence, but what about logical laws. That something is itself or that contradiction means something is incorrect are both principles supposed to be the case when one makes a proposition, no? The issue is that both the law of identity and the law of non-contradiction are rules that regulate premises:
Law of identity
P1: p is
P2: q is
C1: p and q are respectively themselves
What we have supposed here is simply that something also means that something is itself, or “A is, therefore A is itself.”
Law of non-contradiction
P1: p cannot be q
P2: p is q
C1: P2 cannot be the case
What we have supposed here is simply that something cannot be two logical opposite states at once. In both cases, the law of identity and non-contradiction has functioned as something which regulates the content of premises, which is to say, regulates the premises themselves (as propositions are their contents). Alternatively,
P1: the law of identity is the case
P2: p is
C1: p is itself
P1: the law of non-contradiction is the case
P2: p cannot be q but is also q
C1: p is not the case
Here, the way we even conclude that these laws are necessary is through inference and through inference rules. But, is it not the presupposed meaning of the words that communicate the appropriate inference? Now, things have gotten even more daunting for us, as we now are having to deal with logic, inference, reason, and meaning. Dummett and many who follow his semantic anti-realism argue that meaning precedes logic. Does their very inference not suppose inference rules and a necessary consequence (a necessary inference; logic) from those premises that inference rules put together? Yes, of course, it does. But, do inference rules not require meaning for them to put premises in relation to one another which then lets logic do its work, leading to the production of a necessary conclusion? Here is how we escape this bind. We say, yes logic supposes meaning in the sense that there is meaning, but this is not to suppose the existence of meaning itself. For example, if I say,
P3: Therefore, I’m God
I’m obviously going to come off as insane in that there is no meaning to be taken from P1 and P2. But, why is there no meaning to be extricated from these premises? Simple: because I do not know what the contents of either P1 or P2 mean does not in any let us conclude that they mean nothing, for meaning nothing to us is meaning something. The meaning of “A single melon dog is higher than God Himself” cannot be said to have a universal meaning to all, which is to say, the meaning of the latter proposition cannot be said to have a real, existent, and objective meaning in that those signifiers (words) can always have a subjectively altered signified, but, nevertheless, semantic intention makes any issues that are seemingly damning to us immediately ameliorated in that whether or not the law of identity and non-contradiction are true, the semantic intention is still there; or, in other words, let’s say that I say, “A dog cannot be a cat,” I am, first supposing that something is itself, the law of identity, and then I am, second, supposing a theory of meaning which shows that cat and dog have different meanings, which means I am, in turn, third, supposing that things have two different meanings means they cannot be one another and themselves simultaneously, the law of non-contradiction. So, law of identity, then theory of meaning, then law of non-contradiction, right? Well, when we bring up the law of identity do we not suppose it means something? This is where semantic intent comes into play. That I may not be able to express something without supposing meaning in no way means that the content which I semantically intended has been negated. So, for example, if I said, “Wow, at that based melon dog over there,” and then someone said to mean, “Well, actually, that isn’t a melon dog, because the word dog means llama and that isn’t a llama but some other entity.” Okay, so we know that I was wrong about the meaning of the word per someone else, but nevertheless, that entity I was referring to, which is the entirety of the content intended in the word “dog,” did not stop existing after they said I misreferred to it. So, when we say that the law of identity regulates the content of a proposition, we are saying that it regulates the semantically intended content which means we make no supposition that what we mean actually express that content but only that we intend to, and we can not presuppose that we intend to, because it is the case that we have a semantic intention when we put forward any proposition, for to say otherwise would be to say something that is actually meaningless, which is an impossibility. That my proposition cannot mean or be the same as another contradictory proposition supposes the law of identity and the law of non-contradiction, but this is not a supposition but rather a semantic intention. When the person said that was not a dog but something else, they supposed the law of identity and the law of non-contradiction. So, now, meaning has been taken out of the picture because there was never a presupposition of meaning but rather the act of semantic intention. Thus, we are back to inference, logic, and reason.
So, back to logic. In order to determine logic’s relationship to inference rules, we must finish analyzing the nature of the two logical laws of identity and non-contradiction. So, meaning is not being supposed by the person differentiating between a dog and that entity which I am mistakenly calling a dog, for semantic intention still intends toward something (which is also why my previous cosmology of the nothing wasn’t self-refuting, as people such as Leo purported it to be, in that quite literally a semantic intention intended toward nothing would be the absence of semantic intention, but I digress). Rather, what was supposed was those two laws of logic in that the differentiation between the semantically intended content required the law of identity and the law of non-contradiction. Was that supposition justified? It matters not as of now, for what we can do is leave meaning, it is completely done with. These two laws of logic, therefore, regulate the content of premises that inference laws move together and then logic-as-propellant propels the movement of the inference that reaches the conclusion as a necessary consequence of the premises (and this is the necessary relation of consequence). Okay, so, let’s first address the two laws of logic and their supposed primacy. Whether or not either of these laws are the case, I would argue, does not necessarily have negative implications for inference rules:
P1: p → q
Can we come to this conclusion without the two laws of logic? Possibly, yes. How so? Well, let’s run through it! Whether or not p or q mean anything does not matter. For example, if p and q are the same then the point is still proven, whether or not p and q mean things opposed to one another again doesn’t mean anything. Whether or not p and q are even themselves does not necessarily mean that our first premise cannot be the case. So, in the case of → what can we say? Do things not get exponentially more complicated for us here (of course they do, duh!)? If → actually means ^, then instead of saying p implies q, we are now saying if p and q, then p, therefore q, but this of course doesn’t follow modus ponens. Therefore, what we must do is if one could get around such an issue? If it is not possible to get around such an issue, what will be of our thought? Will it expire in its short and glorious run into the late evening? Hardly, it will continue on. How? Let us continue and you will see explosions of life painted across the page, each word an instantiation of hope for the future of our thought.
In regards to meaning, semantic intention is still the case. So, in a world without either two logical laws, one could refer to a dog, but one could say that the dog one is speaking of is actually a not-dog, but semantic intention gets around this issue as we have already shown. So, whether or not the law of the identity is the case does not actually matter in regard to meaning and therefore in regard to the content of the propositions (in a barebones sense, i.e., p is still p, for if we are only without the law of identity, then p could not be p and not-p, but p could be anything else; same as the →, → could be anything else, it couldn’t be, though, not-→, but, again, semantic intention solves the issue of → not meaning implication, for it does not have to be itself [as the law of identity is not the case], but that begs the question of what itself is, and if it has not been given an identity in the first place then semantic intention solves for the issue of people using the symbol differently, and even if it has a previously determined identity, the law of identity only leads to an increase in complexity [everything must be translated into one’s understanding of identity, so, for example, if → meant dog for me, but → meant not-dog for another, then I would simply just have to translate my understanding for a moment]). But, one may say that we are doing a false equivocation here, for our example of semantic intention has to do with a metaphysically existing entity, and identity on a metaphysical level is much different from identity on the logico-epistemological level we are implicating it to operate on. Fair enough, so if I refer to q as p, and another sees q as r, and I refer to r as x, and they refer to p as y, and I see y as z, then all I must do, for me, is say “q as p” which, for them, would mean “r as y” but “r as y” would simply mean for me “x as z,” so once I realize that “x as z,” for me, means the same thing as “r as y” for them, then I could simply get around this issue, through the communication of semantic intention. In other words, there is no issue with saying that A is B, for semantic intention can solve this issue by revealing that my A is another’s C and that my B is another person’s Z. So, the real issue then is dropping the law of non-contradiction. If I say, y as r, and by y they think not-y and y, and by r they mean r and not-r, then we have an issue because now I cannot translate any of this through the communication of semantic intention, for I would be saying “y as r,” and they would say back to me “y and not-y as r and not-r.” I cannot in any way reconcile the contradiction here, no? If my A is also not my A, for all contradiction (this is the business of illogic as we can now clearly see) is permitted, then the possibility of the communication of semantic intention breaks down. Therefore, we can now say that the law of non-contradiction is what is most important, but does the law of non-contradiction not imply the law of identity? Not at all, for if A never has its identity determined, it still matters not in regards to the fact that not-A is not going to be A. But why though? Because A is A? What if A is not-A? Well, that is only an issue if the law of non-contradiction is not the case, for the law of identity itself does not exclude paraconsistency and dialetheic logics, for example, rather it is the law of non-contradiction (as well as the certain level of bivalence in regards to truth derived from the law of exclusive middle which is not really that much of a concern to us as of right now. For, we can say that A cannot be not-A. Here is the thing though, the law of identity regulates the contents of propositions, i.e., the propositions by themselves. The law of non-contradiction doesn’t do such a thing, however.
So, what comes first? The laws of logic? Logic as the necessary relation of consequence? Inference rules? Inference? Reason? Reasoning? Without the law of non-contradiction, logical explosion takes place, but, the principle of explosion, i.e., the principle that holds that anything can be inferred from a contradiction, is still an inference rule. Therefore, inference rules don’t necessitate the law of non-contradiction. But, let us go back to the law of identity for a moment. If A doesn’t have to be itself and it also can be not-A, are propositions not lost to us? How can semantic intention solve this? Is semantic intention not just a way to intersubjective agreement? This is where our approach fails. Instead of arriving at “objectivity,” we arrive at intersubjective agreement.
So, we must begin again, noch einmal. Meaning is still not the issue though. Rather, it is the fact that the content of the propositions that inference rules regulate is regulated by the law of identity and non-contradiction. We are talking about neither of these laws in a metaphysical sense, for it is the fallacious equivocation between the identity of the content of a proposition and the identity of Being that Nietzsche made in his critique of the law of identity. Becoming being the case does not affect our usage of identity here, for words, meaning, etc. have no meaning in themselves, but are rather a method of transmitting information to another. The issue is not that the word, meaning, etc. itself cannot be stable for the one put forward the proposition, but rather, that the communication cannot be stable. Nevertheless, I can know what I mean, no? Can I not still construct a philosophy that only needs translation? Is this not what we have previously proposed, though? In regards to what we have said about this issue of the content of what the inference rules regulate being regulated by the laws of logic, can we not say that the “[l]ogical laws govern inferences” (Patton, “Laws of Thought and Laws of Logic after Kant,” 2)? What does it mean to regulate the content of propositions though? If all propositions are free-floating, not needing any construction, then propositions, without the law of identity, would mean nothing and could not be determined to be anything for they came to be within the body of discourse ex nihilo. But, if propositions are constructed, which is way easier to warrant, then we can say that semantic intention is given to them and that they have no identity in themselves but are rather given an identity in their construction, though, that identity is not a constant in that when subjects interact with a proposition they construct its meaning for them, i.e., what it means to them. Is there an issue if we say, contra Leibniz, “Everything is what it is not.” It seems there is only an issue if the law of non-contradiction is the case. There is another way to view the law of identity. We could view it as “a consistency concept” (Logikal, “When we say that the law of identity doesn’t exist, does it mean it’s always A=A is always false or that A=A is not always true?”). We could see that the law of identity allows us to say that “[i]f one argues that A means one thing & later uses A in a different context that is a fallacy” (Logikal, “When we say that the law of identity doesn’t exist, does it mean it’s always A=A is always false or that A=A is not always true?”). In this sense, the consequence of the absence of the law of identity is this:
P1: p is q
P2: q cannot be r
C1: p cannot be r
P3: p is r
P4: q is r
C2: p is q
So, here we’ve proved our first premise by using p in two different ways. Per the law of identity, this would be fallacious. Without the law of identity, the law of non-contradiction could not say that P2 and C1 are in contradiction without P3 and P4, for what if the identity of p changed in the act of proposition making? Ah! Now we see the importance of the law of identity: semantic intention loses its status as a constant intention, i.e., the semantic intention of p in C1 could be different from the semantic intention of p in P3. Could one not just clarify their semantic intention then? Could they not say I have p1 and p2? Well, what if the identities of both p1 and p2 changed? We would then have an infinite regression.
I am glad we have gone beyond the dogma of practical action, for it has revealed that practical presuppositions are not as important as we thought. But, let us put the issue of reason to rest. What is reason? Reason, “defined by the logicians,” is a faculty “of drawing inferences mediately” (Kant, Critique of Pure Reason, A299/B355). But, for Kant, reason is also “real” and not just logical (Critique of Pure Reason, A299/B355). So, “since a division of reason into a logical and a transcendental faculty occurs here, a higher concept of this source of cognition must be sought that comprehends both concepts under itself” (Kant, Critique of Pure Reason, A299/B355-B356). This exigency pushes Kant to describe reason as “the faculty of principles” (Kant, Critique of Pure Reason, A299/B356). For Kant, the syllogism is a “derivation of a cognition from a principle” (Kant, Critique of Pure Reason, A300/B357). “[T]he understanding may be a faculty of unity of appearances by means of rules, then reason is the faculty of the unity of the rules of understanding under principles” (Kant, Critique of Pure Reason, A302/B359). Kant brings up immediate inferences, or consequentia immediata, which are just the process of having a single premise and then a conclusion immediately inferred from that premise. He gives an example, “That there are three angles in a figure enclosed by three straight lines is immediately cognized, but that these angles together equal two right angles is only inferred” (Kant, Critique of Pure Reason, A303/B360). What immediate inference, therefore, supposes is that “the inferred judgement already lies in the first one, so that it can be derived from it without the mediation of a third representation” (Kant, Critique of Pure Reason, A303/B360). This could only be the case if the paradigm of logical analyticity was the case and if analytic a priori intuitions were justified. My analytic a priori intuition can only come out of an understanding of a concept and its constituents. It is only through understanding that three straight lines coming together to create a polygon will yield as many angles as there are sides, that we can immediately infer that a three-sided polygon will yield three angles. Therefore, supposing we do have an understanding of a concept and its constituents, then we can say that immediate inferences are possible. But, does this not suppose the law of identity? What could establish such a thing? In the introduction to Fanged Noumena, Ray Brassier and Robin Mackay say, “As we saw, Kant’s idealist subordination of real difference to conceptual identity depends upon the logical identity, whose paradigm is the identity of subjective apperception (‘I = I’)” (29). Let us note then, the theoretical explosion that occured in my pondering about this. We must understand that all is needed to establish the law of identity is an understanding of identity itself. Or, rather, a conceptualization of identity, for to conceptualize identity is to conceptualize conceptualization. For identity is a specific conceptualization (or understanding) of something. The conceptualization of identity is to instantiate identity on a conceptual level… I don’t know where this is going. Back to Kant!
The issue of the logocentric predicament is an issue of means, it the issue that the justification of logic is through logic. Circularity requires steps to make a circle. Keyword: steps. If we just have a singular proposition which in itself contains is justification, then this whole issue of use lined out the beginning need not be dealt with. In fact, reasoning, logic, inferences, inference rules, all of them, all we have tediously spoke of thus far, they will be preceded by such a thing. But, what this self-justifying proposition must do is entail something, entail that basis which henceforth seemed impossible to uncircularly justify: ? I have no idea what it is as of now… Is it logic, reason, or inference? All three are intimately bound with one another. Logic, in one of its forms, is propelled by inference rules and regulates an inference by making it necessary (following the arbitration of the inference rules). Logic, in another of its three forms, takes the form of logical reasoning, i.e., non-contradictory reasoning. The latter two forms of logic are, in fact, synonymous, in that, logic is assumed to propel itself, which is to say, the inference rules are representation of a certain movement of logical reasoning. But, if we said here, we needed to justify logic in its synthetic form (in the sense that it is the synthesis of the latter two forms of logic), we would end up employing it in the form of a non-contradictory and necessary inference. So, logic cannot be option, nor can inference, and if our goal is to avoid illogical reasoning as it is basically just skeptical and trivial explosion, then reason is out of the picture too. All there cannot constitute their own bases, which is why we need this self-justifying proposition (which is in a certain sense similiar to an axiom, but not really in that an axiom is something which one cannot dispense with whether one wants to or not, which isn’t indicative of its truth, whereas, this self-justifying proposition doesn’t take itself to be true, because that would be a movement of presupposition, and this self-justifying proposition supposes not even nothing). But, if we put forward this self-justifying proposition, it will justify itself, but what else? I argue that the first thing it must justify is not reason, for reason can justify itself in that it can be illogical and the standard for justification for the illogician is anything, so, specifically, what this self-justifying proposition needs to justify is logical reasoning and logical necessity, i.e., synthetic reason. But, we speak of two forms of reason, what it the third? Simple: analytic reason, the laws of logic. So, what comes first, synthetic logic or analytic logic?
[argue that there is a fourth sense of logic and it is the science of logic as the study of truth, so when why ought i prefer to truth to untruth is asked, you can defer to logic because if we are assuming logic to be the case then you automatically ought to prefer truth to untruth, this then terminates in the question of logic versus illogic] [also would this self-justifying proposition not be contained within logic because it is justifying itself as true which is what the science of logic conditions? Basically here you need to escape the whole issue the theoretical primitive fell into which was that it was also the a priori essence of unjustification and justification therefore terminating in illogic]
[What if we had the I of pure apperception/transcendental apperception/etc., what if the “I think” Kant speaks of was this self-justifying proposition we are speaking of]
After having talked to Erik, I have concluded this order:
- We have, first, the self-justifying proposition [maybe dispense with this notion, but don’t be afraid to test new theories], and out of it we have
- Second, we have those concepts of consistency, the law of identity, the law of non-contradiction, etc. [maybe collapse stage 2 and 3 into one another? How do we layer them?]
- We then have inference rules, justified not through inference, which inferring inference rules is the problem I speak of in the parenthetical note in stage five, but through non-inferential justification.
- Inferences are then justified through inference rules, which then gives them the status of that which logic as a science judges: truth, stage five
- We then have logic as the science of truth, for truth is the condition of that inference that took place as the fourth stage which was justified by the inference rule that preceded it (but are inference rules not true? They are not recuperated into the science of logic, truth, unless they are treated as inferences, in which a new problem, which I will explicitly say in a moment, needs to be addressed. Now, it is only once a premise is treated as a conclusion [i.e., as an inference] that its truth becomes of concern, and once it is treated as a conclusion it itself becomes a conclusion [i.e., an inference] because we will be questioning its premises, and this will go on infinitely until we find something without viciously circular or infinitely regressive suppositions, or something with no suppositions at all [which is what we hope the first stage to be])