Reasoning, the Laws of Logic
Reasoning is “the operation by which the spirit, from two or more known relations, concludes another relation which is derived logically from them.” (CdF) Reasoning is one aspect of rationality, which fundamentally distinguishes man from other animals.
Kreeft explains that the definition of rational includes:
wisdom, intuition, understanding of the nature or essence of a thing (the “first act of the mind”), self-knowledge, moral conscience (awareness of good and evil), and the appreciation of beauty, as well as reasoning and rational calculation (the “third act of the mind”) (SL)
Reasoning also includes judgment (“the second act of the mind”).
The verbal expression of reasoning is an argument, of which one of the forms is the syllogism. (CdF) The following is a famous example:
All men are mortal
Socrates is a man
Therefore, Socrates is mortal
The syllogism works because of the laws of logic, worked on by many Pre-Socratics, such as Parmenides of Elea, but ultimately perfected by Aristotle.
The Laws of Logic
Kreeft distinguishes between the laws of logic and physical laws, saying that, while it may be conceivable for the behaviour of the force of gravity to be slightly or very much different, it is not possible to conceive of the laws of logic being different, they are the result of the immutable nature of God. He says that while physical laws may conceivably be violated by God (e.g Jesus walked on water), logical laws may not be violated — God cannot make the statement all squares have 5 sides true:
—If, of course, God exists. It is not clear what reality these laws are dependent on if there is no God; but in any case they are eternal, unchangeable, necessary truths. If God exists, these laws are descriptions of the nature of God. (SL)
As we later shall see, Aristotle and St. Thomas prove the existence of God. In any case, the laws of logic are necessary truths, true in every world, while the physical laws are contingent truths, which can conceivably be overrided. (SL)
The first law of logic is the Law of Identity, which is formulated by Kreeft to be “a thing is what it is” (SL). While it may seem obvious, this law was first discovered by Parmenides of Elea, and he used it to deny change (in philosophical terms, change is referred to as “motion”). If you recall, the argument went as follows:
If a thing is what it is, then motion is not possible since if it changes, it becomes what it is not. But this violates the Law of Identity since if a thing is what it is, it cannot become what it is not. Thus motion is not possible.
Parmenides was handily refuted by Aristotle, but the refutation will be covered later.
The corollary of the Law of Identity is the Law of Non-Contradiction: “a thing is not what it isn’t; x is not non-x”. (SL)
There is the Law of the Excluded Middle: “a thing is either x or not x. A predicate must be either affirmed or denied of a subject; there is no third possibility. A proposition is either true or false, there is no third possibility.” (SL)
Additionally, there are three more laws which are more explicitly applied in a syllogism.
There is the dictum de omni (law about all): “Whatever is universally true of a subject must be true of everything contained in that subject”. (SL) This means that when I say that all men are mortal, since Socrates is contained within the subject man, he must be mortal too. (SL)
There is the dictum de nullo (law about none): “Whatever is universally false of a subject must be false of everything contained in that subject”. (SL) If I say that all men are not pure spirits, and that Socrates is a man, it follows that Socrates is not a pure spirit.
There is the third principle that “two things identical with one and the same third things are identical with each other”. (SL) Kreeft explains:
For the “third thing” is the “middle term,” the common term with which the other two terms are compared. In the classic example above, “Socrates” and “mortal” are both compared with a common third term, or “middle term,” “men.” …
The negative corollary of principle (3) is that if there are two things, one which is identical with a third thing and the other of which is not, the those two things are not identical with each other. (SL)
All these laws seem self-evident because they are. It is modern logic and philosophy which denies them and places itself into completely escapable conundrums. In the next article, we are going to look at the syllogism proper, as well as the different forms which it can take.