Part Three

Origin of the First Principles of Reasoning

558. So far we have seen how the intuition of ideal being is proper to the intelligent spirit and necessary for its existence (Part One). Granted that ideal being is present to the spirit, we have shown how the origin of other ideas is explained by means of sensation and reflection. We have also shown that ideas as a whole originate in this way, and have applied the argument to certain broad, general classes of ideas (Part Two). We must now deduce in another way various ideas and cognitions strengthening our theory and making it easier to use. For the sake of clarity, let us begin with necessary, basic cognitions. They are: 1. the first principles of reasoning; and 2. certain elementary and very abstract ideas always taken for granted in human reasoning, without which reasoning is impossible. Once possessed, these first principles and elementary ideas become instruments enabling our mind to perform its noble operations and produce new ideas and knowledge. We begin therefore with the supreme principles of human reasoning.

CHAPTER 1

The first and second principles: of knowledge and
of contradiction

559. Principles are expressed by propositions which, in order to be analysed, must be reduced like mathematical formulae to their simplest expression. When dealing with a formula, mathematicians may reduce it to the expression most suitable for their purposes, provided they do not change the value of the formula or alter the equation.

560. A proposition expresses a judgment, that is, a relationship between two terms, predicate and subject.
Because the principles of reason are judgments, they comprise a predicate and a subject. Therefore the simplest and most natural expression of the principles of reason is that which directly indicates the predicate with one distinct word (or phrase), the subject with another, and the connection between them with a third. Let us take the principle of contradiction as our example.

561. The principle of contradiction, in its simple form, is: 'That which is (being) cannot not be.'
'That which is' is the subject; 'not be' is the predicate; 'cannot' is the copula expressing the relationship between the two terms.
In this judgment, the relationship between being and not-being is impossibility.
We have seen that logical impossibility cannot be thought and is in fact nothing.
The principle tells us that being (that which is) cannot be thought at the same time as not-being. When being and
notbeing are put together therefore, we have both an affirmation and a negation, that is, nothing; not-being cancels previously posited being, and all thought disappears.
The principle of contradiction is simply the possibility of thought.

562. Without this principle, therefore, investigation of other matters is impossible. We cannot doubt its existence, validity or effectiveness. Like any other thought, this doubt presupposes the principle as already valid and effective; we cannot begin to think, to question or reason without presupposing thought, questioning and reasoning. In this way the principle of contradiction is completely safe from any attack. Attacking it demands thought but, in order to think, thought has to be possible, and this is precisely what the principle of contradiction states: we cannot think without thinking! If we think at all (no matter what we think) we admit the principle of contradiction, which states: 'I think or I do not think; there is no middle term, because to think without thinking is impossible.' The principle of contradiction therefore is independent of all human thought and opinion, which is possible only with this principle.

563. Someone might say to me: 'I deny the possibility of thought.' I would reply that to deny the possibility is to think it! I would ask: 'Do you think at all? Your answer is either that you think or do not think; whichever it is, you confirm the principle of contradiction. To invalidate the principle, you would have to reply: "I am thinking while I am not thinking", and this would be ridiculous and meaningless.'

564. But let us return to the analysis of the principle of contradiction which is a proposition expressing the following fact: 'Being cannot be thought at the same time as not-being'; in other words, 'Thought does not exist unless it has being for its object.'
This fact which I have observed and, it seems to me, proved beyond doubt, is the idea of being informing and producing our intelligence (cf. 473-557). Thus we often define intelligence as 'the faculty of seeing that which is' (being). The phrase 'being together with not-being' expresses nothing, and nothing is the opposite of something, of being. By showing that our intellect and reason is the faculty for seeing being, I have also shown conversely that it is not possible to see nothing, which is all that the principle of contradiction affirms.
This principle therefore draws its origin from the idea of being, the form of our reason; it is simply the idea of being considered in its application.

565. As Thomas Aquinas and Bonaventure have said, the principle of contradiction is in a certain sense innate [App., no. 19]. According to them the principle reveals itself from deep in the human spirit at our first use of reason. However it seems more strictly true to say that while the foundation of the principle is innate, the principle itself is not. The reason is as follows.

Principles take the form of judgments and are expressed by propositions. Any principle may presuppose some reasoning except for the absolutely first principle which is not under discussion here. In fact the principle of contradiction can be deduced from a preceding principle, which I call the principle of knowledge, expressed by the proposition: 'The object of thought is being or ens' (cf. 535-536). I reason as follows: 'The object of thought is being; but the phrase "being and not-being" expresses nothing, and nothing is not being. Therefore being and not-being is not an object of thought.'

566. Hence, for the idea of being to have taken the form of the principle of contradiction, I must have used it, that is, have begun to judge and reason. I must have formed a mental ens, nothing, and acquired the ideas of affirmation and negation by thinking, and seen that negation plus affirmation equal nothing.
Judgment and reasoning, although naturally and closely tied to the idea of being and carried out promptly, are only the idea of being in its application, disguised and accompanied by relationships. Our reason needs to be released like a spring from its initial state of complete inactivity. But anything in us resulting from such contingently intellectual movement is acquired. Such is the principle of contradiction in its explicit form of a judgment.