Summary: Metaphysics (page 4)

To undertake this essential inquiry, thought must rest on the most solid principles. But what can be the most unshakeable of all principles ¹?

It is the principle of non-contradiction, which Aristotle, without explicitly naming it as such, defines as follows:

It is impossible for one and the same thing to be, and at the same time not to be, with respect to the same thing and from the same perspective ².

This principle applies not only to things but also to ideas: human beings do not contradict themselves in their thinking — they cannot simultaneously assent to two opposing propositions.

The principle of non-contradiction is nevertheless denied by some philosophers. Aristotle here refers to Heraclitus.

However, Aristotle does not attempt to demonstrate this principle. As a principle, it is by definition indemonstrable: if it required proof, we would simply regress through an infinite series of causes, and it would cease to be a principle: It is quite impossible for there to be a demonstration of everything without exception, since that would be to lose ourselves in infinity, and in that way there would never be any possible demonstration ³.

In reality, there is no need to defend this principle against attack: it is inherently unassailable, and requires neither foundation nor demonstration.

Indeed, any proposition that seeks to challenge the principle of non-contradiction is neither true nor false — it is, quite simply, devoid of meaning. To make such a claim is to say nothing:

Such a man, in so conducting himself, has little more to do with us than a plant has ⁴.

Any word, by its very nature, upholds the principle of non-contradiction. Indeed, one cannot name a thing without affirming that the thing either is or is not such a thing ⁵.

If this were not the case, the opponent would have to stop speaking altogether.

But does not the same word sometimes carry multiple, contradictory meanings? In reality, each meaning, taken individually, does not contradict itself. All that is needed is to define clearly the meaning we assign to the word in any given sentence.

If the principle of non-contradiction were false, everything would become indistinguishable from everything else ⁶. A trireme would be no different from a wall or a man — if one could, at will, affirm or deny anything and everything ⁷.

Aristotle connects this doctrine to Protagoras, who claimed that man is the measure of all things.

According to this view, if someone believes that man is not a trireme, then man is indeed not a trireme. But if contradictory propositions are equally true, then man is a trireme ⁸.

This doctrine also calls to mind Anaxagoras' position: All things are mixed together ⁹.

In response, Aristotle argues in the Metaphysics that this doctrine merely demonstrates the contradictory nature of the indeterminate — which may well be true. But to invalidate the principle of non-contradiction, one would have to show that the determinate is contradictory, which it is not.

Moreover, action itself upholds the principle of non-contradiction. After all, even our opponent implicitly accepts it: they consider it harmful to fall into a precipice, since they instinctively avoid doing so.

Action thus provides empirical confirmation of the principle of non-contradiction.

From this, we may reasonably infer that, as it seems, everyone believes in something absolute ¹⁰.

Some argue that truth is a matter of degree — for instance, that 4 = 5 is more true than 4 = 1000. Yet the notion of "more or less true" implies the existence of an absolute truth, to which one may be more or less close.

If a thing can potentially become its opposite, it cannot actually be its opposite.

Why, then, is the principle of non-contradiction denied by some? It stems from the observation of the sensible world: If they have adopted this opinion — that contradictories and opposites can coexist — it is because they have observed that opposites can arise from one and the same source ¹¹.

The senses do indeed present us with contradictory information: The same food tastes good to some and tastes bad to others ¹².

Yet this phenomenon reveals the weakness of the senses, which are easily deceived. Returning to the example of food: while wine may seem pleasant to one person and unpleasant to another, the flavour itself does not change.

Thus, the principle of non-contradiction is confirmed: We have established as the most assured principle of all principles that never can two opposite assertions be true at the same time ¹³.

Upon this principle, the science of being as being is founded.

Aristotle then introduces a second indubitable principle — one later known to the Scholastics as the principle of the excluded middle: Moreover, it is not possible that between two contradictory propositions there is ever a middle term ¹⁴.

To illustrate: 'A door is either open or closed.' There is no third possibility.

¹ Book Γ, 3
² ibid.
³ Γ, 4
⁴ ibid.
⁵ ibid.
⁶ ibid.
⁷ ibid.
⁸ ibid.
⁹ ibid.
¹⁰ ibid.
¹¹ Γ, 5
¹² ibid.
¹³ Γ, 6
¹⁴ Γ, 7