Some possible examples are numbers and the logical law of non-contradiction.

The function fits the bill, proving the law of non-contradiction, no matter what P is.

This is quite likely if, as Plato pointed out, the law of non-contradiction does not hold for changing things in the world.

The principle of non-contradiction has seemed absolutely undeniable to most philosophers.

This is the logical complement of the law of non-contradiction.

The law of non-contradiction (which states that contradictory statements cannot both at the same time be true) is still valid.

So Plato's law of non-contradiction is the empirically derived necessary starting point for all else he has to say.

The law of non-contradiction is a rule of logic.

(Subsequent philosophers have found other reasons for supporting the principle of non-contradiction).

However, in doing so, he shows that the law of non-contradiction is not the more fundamental of the two:

One difficulty in applying the law of non-contradiction is ambiguity in the propositions.

Buddhism contains a philosophy called Catuskoti that rejects the law of non-contradiction.

Aristotle clarified the connection between contradiction and falsity in his principle of non-contradiction.

Time is not a concept, since otherwise it would merely conform to formal logical analysis (and therefore, to the principle of non-contradiction).

Every Christian would find it useful to get acquainted with the basic principles of logic such as the law of non-contradiction.

Then Socrates goes on to demonstrate the contrary of the commonly accepted part using the law of non-contradiction.

Special evidence comes from the principle of non-contradiction, and natural evidence is that which is gained empirically.

Thus the proof might, after all, beg the question against a kind of skepticism radical enough to put in doubt the rule of non-contradiction.

Instead, Christians can begin dialogues with non-Christians with common ground such as the law of non-contradiction.

Ravi Zacharias claims that most Eastern philosophers reject the law of non-contradiction.

The traditional source of the law of non-contradiction is Aristotle's Metaphysics where he gives three different versions.

The law of bivalence does not hold in intuitionistic logic, only the law of non-contradiction.

He thought innovatively about traditional propositional logic, the principle of non-contradiction and the law of excluded middle.

We would need extraordinary circumstances to arise before we abandoned laws like the Law of Non-Contradiction.

According to both Plato and Aristotle, Heraclitus was said to have denied the law of non-contradiction.

Law of noncontradiction: "Nothing can both be and not be."

This is quite likely if, as Plato pointed out, the law of noncontradiction does not hold for changing things in the world.

This is the logical complement of the law of noncontradiction.

The rule of noncontradiction is one of the ways I should have checked my assumptions.

This violates the law of noncontradiction and, by extension, bivalence.

So Plato's law of noncontradiction is the empirically derived necessary starting point for all else he has to say.

Americans operate by the law of noncontradiction.

One difficulty in applying the law of noncontradiction is ambiguity in the propositions.

Then Socrates goes on to demonstrate the contrary of the commonly accepted part using the law of noncontradiction.

Aristotle says that the foundations of thought and discourse, like the principle of noncontradiction, can be doubted only in speech.

The unity of truth is a fundamental premise of human reasoning, as the principle of noncontradiction makes clear.

The traditional source of the law of noncontradiction is Aristotle's Metaphysics where he gives three different versions.

According to both Plato and Aristotle, Heraclitus was said to have denied the law of noncontradiction.

The study of first principles, such as the law of noncontradiction (logic), which Aristotle believed were the foundation of all other inquiries.

Bertrand Russell asserts a distinction between the "law of excluded middle" and the "law of noncontradiction".

Parmenides, employed an ontological version of the law of noncontradiction to prove that being is and to deny the void, change, and motion.

Rather than starting with experience, Aristotle begins a priori with the law of noncontradiction as the fundamental axiom of an analytic philosophical system.

The Persian philosopher, Ibn Sina (Avicenna), once wrote the following response to opponents of the law of noncontradiction:

The concept of "one true faith" is also based on the basic philosophical law known as the law of noncontradiction: two propositions that contradict each other cannot both be true.

The law of noncontradiction is merely an expression of the mutually exclusive aspect of that dichotomy, and the law of excluded middle, an expression of its jointly exhaustive aspect.

Personal subjective perceptions or judgments can only be said to be true at the same time in the same respect, in which case, the law of noncontradiction must be applicable to personal judgments.

The Structure of Explanation Aristotle makes a basic point about the structure of explanation or demonstration (apodeixis) in the Metaphysics while arguing for the priority of the principle of noncontradiction.

The law of noncontradiction is found in ancient Indian logic as a meta-rule in the Shrauta Sutras, the grammar of Pāṇini, and the Brahma Sutras attributed to Vyasa.

It is inadequate as a criterion because it treats facts in an isolated fashion without true cohesion and integration; nevertheless it remains a necessary condition for the truth of any argument, owing to the law of noncontradiction.

The law of noncontradiction, along with its complement, the law of excluded middle (the third of the three classic laws of thought), are correlates of the law of identity (the first of the three laws).