#non-contradiction

[chrissbiblenewsletter]

Logic depends on identity (everything is itself), non-contradiction (nothing is both true and false), and excluded middle (every statement is true or false). These principles enable valid reasoning

[orwellrand-blog]

Atlas Shrugged Triptych by DecoEchoes

[eidetisch]

non-contradiction and metaphysics

Two frequent themes of Aristotle's account of science are

(1) that the first principles of sciences are not demonstrable and

(2) that there is no single universal science including all other sciences as its parts.

“All things are not in a single genus”, he says, “and even if they were, all beings could not fall under the same principles” (On Sophistical Refutations 11).

Thus, it is exactly the universal applicability of dialectic that leads him to deny it the status of a science.

In Metaphysics IV (Γ), however, Aristotle takes what appears to be a different view.

- First, he argues that there is, in a way, a science that takes being as its genus (his name for it is “first philosophy”).

- Second, he argues that the principles of this science will be, in a way, the first principles of all (though he does not claim that the principles of other sciences can be demonstrated from them).

- Third, he identifies one of its first principles as the “most secure” of all principles: the principle of non-contradiction.

As he states it,

It is impossible for the same thing to belong and not belong simultaneously to the same thing in the same respect (Met. )

This is the most secure of all principles, Aristotle tells us, because “it is impossible to be in error about it”.

Since it is a first principle, it cannot be demonstrated; those who think otherwise are “uneducated in analytics”.

However, Aristotle then proceeds to give what he calls a “refutative demonstration” (apodeixai elenktikôs) of this principle.

Further discussion of this principle and Aristotle's arguments concerning it belong to a treatment of his metaphysics (see Aristotle: Metaphysics).

However, it should be noted that:

(1) these arguments draw on Aristotle's views about logic to a greater extent than any treatise outside the logical works themselves;

(2) in the logical works, the principle of non-contradiction is one of Aristotle's favorite illustrations of the “common principles” (koinai archai) that underlie the art of dialectic.

See Aristotle's Metaphysics, Dancy 1975, Code 1986 for further discussion.

via: http://plato.stanford.edu/archives/spr2012/entries/aristotle-logic/

[ontologicalshakedown]

~(p & ~p)