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T.Wester, s2635879, Bachelor student 28th or March 2021

In The Critique of Pure Reason, Kant dedicates a large part of his book to the exploration and
explanation of his “transcendental logic”. Logic in the transcendental sense varies greatly from both
traditional and modern logic, these differences will be explored in this essay. This essay will focus primarily
on the question whether the aim of transcendental logic is the same as that of modern-^{1} and traditional-^{2}logic.
In non-transcendental logic (which I will henceforth refer to as “normal logic”), we analyse the truth-
value of certain statements. In modern propositional- and predicate-logic, this analysis happens in an almost
mathematical fashion. For instance, if two true statements are connected with an “∧ (and)” operator, the
result of this equation shall be true as well. Logic in this (normal) sense is used for analysing our thoughts and
arguments.

1 With “modern logic”, I am primarily referring to propositional and predicate logic unless state otherwise.

2 The term “traditional logic” will refer to all logic that is not transcendental before Kant's time, the specific thinkers will be specified in the paragraphs discussing this form of logic.

3 In this essay, I will only ever refer to Kant's chapter on transcendental logic as: “The Transcendental Logic” reserving the term: “transcendental logic” for the concept Kant discusses in this chapter.

Kant separates Logic further into general- and particular-logic. General logic “contains the absolutely necessary rules of thinking, without which no use of the understanding takes place” (Kant,1998,B76). Particular logic on the other hand “contains the rules for correctly thinking about a certain kind of objects” (Kant,1998,B76). Particular logic is also known as the organon of science, which can be seen as the specific method of that field. These organons are called the impure forms of elementary logic. The pure form of elementary logic is a canon of logic itself, of our a priori understanding.

Now we arrive at transcendental logic which Kant claims to be different from both pure and impure
elementary logic.^{3} Kant characterizes both particular and general logic by saying that it “treats only the form
of thinking in general” (Kant,1998,B79), it is therefore “merely formal logic” (Kant,1998,B170). Meanwhile,
transcendental logic is “a logic in which one did not abstract from all content of cognition” (Kant,1998,B80).
This difference is well characterized in Clinton Tolley's work titled “The Generality of Kant's Logic”. In this
work, Tolley states that: “while traditional logic investigates the form of understanding, transcendental logic
studies its content.” (Tolley,2012).

Kant's transcendental logic is not entirely different from normal logic however. In The Transcendental Logic, Kant defines a set of logical functions of which some bear a striking resemblance to operators and quantifiers in modern propositional- and predicate-logic. Under the heading quantity, Kant defines the Universal (∀) and Particular (∃) quantifiers, which both have direct equivalents in modern predicate logic. Furthermore, under relation, Kant defines the hypothetical and exhaustive relations, which are similar respectively to the implication and (exclusive-)disjunction. The differences between transcendental- and normal-logic can be explained in various ways, a few of which I will discuss below.

First, one might be inclined to point out the similarities between transcendental- and normal-logic and assume that they have the same aim. This would imply however that Kant's attempt at making a table of logical functions has failed miserably. Kant's table of functions is not exhaustive (i.e. it does not contain all possible functions), nor minimal (i.e. it does not contain the bare minimum amount of functions with which we can substitute all the other ones). Furthermore, Kant's table contains functions such as the Singular Quantifier, the Infinite Quality and the Categorical Relation which seem to have no place in modern- or traditional-logic. A theory that claims that Kant was attempting to invent modern logic while writing The Transcendental Logic must accept that Kant simply failed at doing so and that Kant's aim was only later realized by the likes of Boole, Russel, Frege, and Peano.

realized by the likes of Boole, Russel, Frege, and Peano. Another method of approaching The Transcendental Logic is by pointing out the differences between it and modern logic and state that Kant was clinging to a (now outdated) form of traditional Aristotelian logic. This would explain why Kant is missing certain functions of modern logic, but it cannot explain the whole table. After all, in The Transcendental Logic, Kant also introduces concepts foreign to Aristotelian logic. The entire section on Modality for instance, is more similar to modern-day modal logic than traditional The entire section on Modality for instance, is more similar to modern-day modal logic than traditional Aristotelian logic.

The aim of The Transcendental logic seems to be neither the same as the aim of modern logic nor is it a repetition of the ideas expressed in traditional logic. The question of what exactly Kant's aim is in The Transcendental Logic remains.

Upon closer reading of Kant, it becomes clear that his aims are different from those of modern logic. And furthermore, that the seeming similarities between transcendental and modern-logic are only surfacelevel. For instance, the aforementioned similarity between the hypothetical judgement and the logical implication falls apart quickly upon further investigation. Of the hypothetical judgement, Kant gives an example: “If there is perfect justice, then obstinate evil will be punished” (Kant,1998,B98). Kant goes on to point out that while this statement contains two propositions, “Whether both of these propositions in themselves are true remains unsettled here.” (Kant,1998,B98). This already indicates that Kant's table of functions does not contain the functions of modern predicate- and propositional-logic. The hypothetical function displays a relation between a ground and a consequent, which is a function absent from modern logic. The same goes for the exhaustive function. This function is not a mere disjunction as in modern logic. The exhaustive function contains all possible realities such as: “Either France is a monarchy, or France is a Republic”. When we compare this to a logical disjunction we can immediately see the difference: “Either France is a monarchy, or Germany is a republic”. In this latter formulation, we can see that not all the possible objects are included. Furthermore, in the modern logical disjunction, there is no actual relation between the two parts. Germany being a republic has no seeming effect on France being a monarchy.

Now that we have proven transcendental logic to be neither an attempt at formalizing modern logic, nor a repetition of traditional logic, we are left with the question of the exact place transcendental logic occupies. Some philosophers from the Leibizian tradition claim that traditional logic “had been based on the assumption that all judgments were, in effect, what Kant himself would now call analytic judgments, the fact that Kant had shown this assumption to be false required that he introduce a parallel logic to cover the new kind of judgment, and in this way supplement the old logic.” (Tolley,2012,4). This view has come under heavy criticism however, because of sections in Kant's first Critique pointing out that transcendental logic only concerns itself with synthetic a priori thinking. Paton claims in his work Metaphysic that while traditional logic “is concerned with the necessary rules, or the necessary form, of all thinking”, transcendental logic “studies only, the rules of synthetic apriori thinking” (Paton,1936,222).

Both of these views are criticised in-depth in Tolley's work “The generality of Kant's transcendental logic”. Firstly, Tolley criticizes the so-called domain-exclusive view from the Leibnizians in the same way Paton does, “the domain-exclusive interpretation stands in direct conflict with Kant's persistent description of the traditional logic as a genuinely ‘general or universal [allgemeine]’ science” (Tolley,2012,8). Tolley goes on to argue that instead of viewing the distinction between normal- and transcendental-logic as a difference in domain, we should see it as a difference in aim. “[The] discussion of the analytic/synthetic distinction, insofar as Kant claims there that this distinction is not one that pertains to the ‘logical form’ of judgments at all, but instead pertains to their ‘content [Inhalt]'”. Tolley states that this is a sufficient reason to believe that any reading of Kant in which he seems “to exclude a species of judgment from the jurisdiction of the traditional logic” should be “viewed with considerable suspicion.”. Secondly, Tolley criticizes Paton's view, drawing from Kant the fact that “the categories extend themselves farther than sensible intuition, because they think objects in general [überhaupt], without seeing to the particular manner Art in which they might be given” (Kant,1998,B309). After which, Tolley claims that “this makes it hard to see how a science concerned with such elements [this science being logic] should nevertheless have its focus restricted by conditions imposed by sensibility” (Tolley,2012,9,bracketed addition by me).

It remains then that transcendental logic must be different in aim. In other words, we use transcendental logic for entirely different analyses than normal-logic. Realizing this we see that Kant's table of functions contains functions of the understanding, not logical operators. The aim of transcendental logic is the analysis of the content of the understanding, not it's form. Reading Kant in this way explains the missing logical operators in the table of functions. For instance, the missing conjunction operator (∧) is irrelevant to Kant's project because it simply states two statements to be true. Such as statement is not a new act of the understanding for it has no difference from stating the truth of two things separately.

In conclusion, one who claims transcendental- and normal-logic to have the same aim would be mistaken. Furthermore, one who considers their domain to be different is also mistaken. The true difference between transcendental- and normal-logic is that the former analyses the content of understanding while the latter analyses the form. This view has the most textual support and logical coherence.

**References**

Kant, 1998. Immanuel Kant, The Critique of Pure Reason, Cambridge University Press (1998).

Paton, 1936. Herbert James Paton, Kant's Metaphysic of Experience, Macmillan (1936). Tolley, 2012.

Clinton Tolley, “The generality of Kant's transcendental logic,” Journal of the History of Philosophy 50(3), pp. 417-446, Johns Hopkins University Press (2012).