The First System was essentially an attempt to build a system of metaphysics, which Peirce defined as "the philosophy of primal truths" and the logical "analysis of conceptions"[23]. Peirce first began studying Kant's "Critique of Pure Reason" in 1855, at the age of about sixteen, and became an enthusiastic disciple from the very beginning of his philosophical career. He later wrote that "I was a passionate devotee of Kant, at least as regards the Transcendental Analytic in the Critic of the Pure Reason. I believed more implicitly in the tables of Judgement and the Categories than if they had been brought down from Sinai" [CP 4.2]. However, he soon became convinced that it would be necessary to make a revision of these, mainly based on the insight that the relations between the categories could be properly expressed in a rather more general way. He noted in a paper written in 1859[24] that the twelve categories may actually be grouped into four classes of three each, and since these classes are more general than the twelve categories, it is these classes, which Peirce went on to rename as `Thing', `Quality', `Dependence' and `Fact', which should in fact be considered the more fundamental, and thus, the categories. In doing so, he also introduced the concept of three developmental stages, which he denoted `Simplicity, `Positivity' and `Perfection' within each of the new categories.
At the same time, he was pondering how to incorporate into his theory the basic insight that he had gained from his earlier readings of Kant's Critique of Pure Reason, that every cognition involves an inference. For Kant there can be no cognitions until the manifold of sense has been brought to unity, and in Peirce's view this reduction can only be brought about by introducing a concept which itself is not a sensuous intuition. This necessitates that every cognition requires some operation upon the manifold to bring it to unity, and Peirce goes on in his theory of judgement to define any operation that takes place on "some information" (i.e. the manifold of sense impressions) which results in a cognition as an inference.
"Every judgement consists in referring a predicate to a subject. The predicate is thought, and the subject is only thought-of. The elements of the predicate are experiences or representations of experience. The subject is never experienced but only assumed. Every judgement, therefore, being a reference of the experienced or known to the assumed or unknown, is an explanation of a phenomenon by hypothesis, and is in fact an inference. Hence there is a major premiss behind every judgement, and the first principles are logically antecedent to all science, which I call a priori."[25]
Peirce goes on to argue that this means in logical terms that the fact that the original major premiss of any syllogism of the type Barbara, which he at this time believed all types of syllogisms could be reduced to, cannot come from experience, but must be given in some way prior to this. It is only minor premisses that can be given by nature in experience. The question is then: where do our original major premisses (or "primal truths") come from? If we make a negative judgement in the form of a proposition such as "this is not green", this cannot be an example of what Peirce calls "unreasoned-upon experience" - experience without prior precedent - since this cognition obviously refers to something known already to the speaker as "green", which the particular experience giving rise to the negative judgement above could not possibly provide. In the same way, unreasoned-upon experience cannot either be universal.
"It is only minor premisses, then, that nature affords us; for all Universal, Negative, Unconditional and Necessary Truths exist and have their truth in the mind. They are true without proof, can have but one basis and must be independent of nature." [Pr. 15f, cited in Murphey 1993, p. 22]
At this point in time, Peirce did not believe that the truth of the axioms or "primal truths" is something that can be demonstrated or proved logically - as a consequence he considered that one can only accept them on the basis of faith. In Kantian terms, these are synthetic a priori statements, the truth of which Kant attempted to solve in his Critique of Pure Reason, but Peirce could not accept Kant's proof on this point, but he did not either seem satisfied with the notion that the truth of the universal axioms, or major premisses - his "primal truths" - must be accepted purely on the basis of faith alone. But since it seemed impossible to inquire at all into the truth of the premisses, then this meant that metaphysics would have to be limited to inquiry into the logical analysis of concepts or ideas - logic must in other words be the key to any ontology. The important distinction Peirce makes in this connection is between the "potentially thought" and the "potentially thought-of": between what is capable of being a sign, and that which is capable of being the object of a sign. Kant's theory of the Transcendental object had implied that there must be two kinds of entities that can be objects of representation: thoughts themselves which can be thought of, and the "things in themselves", which as Kant had pointed out "cannot itself be intuited by us" [A108f]. When something is thought of, this is through its properties, undiscriminated from the thing. For us to become aware of our thoughts, we must subsequently make an abstraction. Peirce however proposed that the process of abstraction could be carried a step further, and that since thought is not a thing, it cannot be merely personal, but rather pure form, which cannot belong to any particular time, space or person.
"A thought is not a thing. Several things may have some quality in common. That is a thought. All the consciousnesses which contain this thought also have the thought of which they are only expressions. Thought therefore is not personal. But pure form.
Thing
Feeling
No abstraction can in itself therefore ever be fully realised in human consciousness, only instances (i.e. "expressions") of an abstraction.[27]
In order to cope with the problem of how we can have knowledge of abstractions if they are not in mind. Peirce proposes that there are two types of conceptions that we cannot think, although we can think about them. He writes in a discussion of why we can reason about the infinite, even though we cannot analyse or otherwise really understand it as an abstraction:
" Pseudo-conceptions or conceptions that we cannot think are of two kinds. The first is where the conceptions into which we analyse the pseudo-conception in definition refuse to be combined and are contradictory. And I will in another place give a formal proof that such conceptions represent no thing and are not had.
The second case is where the elementary conceptions do not refuse to be combined, but where our power of synthesizing is inadequate and the combination can never be completed."[28]
If the "synthesizing" in case two above cannot be completed (Kant's "bringing of the manifold to unity"), then there cannot be an effect on the mind in the form of a conscious idea. This means that the mind must be able to cope with ideas that are not brought into consciousness: we can think of them, but we do not need to be able to think them. The problem then is how to know whether these ideas are true or not. Peirce's solution is to say that the "normal way of thinking" yields true statements, which presumes that every statement is true unless it contradicts some other, even meaningless statements. Thus "what is unintelligible is true" if it contradicts nothing else.
This analysis of conceptions provided Peirce with three classes of entities: the thing thought of, the thought and the abstraction. It was these three classes, the enumeration of which he held to be complete, that were to form the basic foundation of his triadic system of logic.
From his studies of Aristotle and the Scholastics, which in turn had originally been prompted by his conviction that the correctness of Kant's table of functions of judgement could not be guaranteed, Peirce arrived finally at the conclusion that the most important object of study for logic was not the forms of the proposition, but rather, the syllogisms themselves. His reasoning was that since the only differences among the propositions that are logically significant are those which affect their role as components of syllogisms, then the study of the syllogisms should precede that of the propositions. Kant had of course in the Transcendental Dialectic of his "Critique of Pure Reason" drawn a different conclusion from Peirce with regard to the nature of the syllogisms, namely that there were actually three types of dialectical syllogism, distinguished from one another by the forms of their propositions. (the categorical, the hypothetical and the disjunctive). The universality and necessity of the categories for Kant rest, then, upon the universality and necessity of the forms of the propositions, which in turn rest upon the dual assertion that all thought is in propositions, and that the classification of the propositions is correct. Peirce's proposal was on the other hand that if the significance of propositional form depends on its use in inference, then the correctness of this classification depends on the further premisses that all thought is inference (rather than in propositions), and that these particular forms are necessary for thought, considered as inference, which led him naturally enough to re-examine the issue of the classification of the syllogisms.
At this time, Peirce had, as mentioned previously, adopted the position, based largely on his somewhat loose interpretation of Kant's prior discussion of this in "Die falsche Spitzfindigheit der vier Syllogistischen Figuern"[29], that all forms of inference, including hypothesis, could be reduced to the first of the four syllogistic figures, i.e. Barbara[30]. Peirce went on to develop this idea further and he explained it, probably sometime around the middle of 1865, in the following fashion:
"Every syllogism can be put into a hypothetical form thus:
Y is X
If Y then X
Z is Y
becomes
but Y (under Z)
Z is X
Therefore X (under Z)"
Where (under Z) Peirce meant that under the hypothesis that Z is true, that is: that Y would be true if Z is. Since X as modus ponens will be assertable if Y is, and since Y is true if Z is, then X is true if Z is.
Here, Peirce is, then, emphasising the hypothetical form of the modus ponens. Murphey points out that it is clear that he had not yet discovered that the three figures of the syllogism could be correlated with the methods of deduction, induction and hypothesis (or "abduction", as he later went on to refer to it). This did not come until later. Thus, at the beginning of 1866, Peirce began on a detailed analysis of Kant's article on "Die falsche Spitzfindigheit...", and of the relations between the three syllogistic figures, and actually succeeded in proving that each of the three figures involves an independent principle of inference. Even though all syllogisms of the second and third figures may in principle be reduced to the first, the argument for making this reduction must in any case be made in the figure from which it is being reduced: "Hence it is proved that every figure involves the principle of the first figure, but the second and third figures involve other principles besides" [CP 2.807] In reaching this conclusion he had been influenced by his reading of Boole's "An Investigation of the Laws of Thought". At the same time he also concluded significantly that "There is no difference logically between hypotheticals and categoricals. The subject is a sign of the predicate, the antecedent of the consequent; and this is the only point that concerns logic."[31]. This substitution of the sign relation for causality as the most basic relation between subject and predicate in the proposition, represents, again according to Murphey, one of the most fundamental advances that Peirce made in this period. The three forms of inference may well be distinct, but if the causal relationship between subject and predicate may be reduced to a sign relation, then this relation must be the most basic form of thought upon which one must build any system of categories.