A circularity in the definition of being false

Consider the following claims:

To say “Snow is white is true” is to say that snow is white.

To say “Ravens are black is true” is to say that ravens are black.

To say “The Earth is round is true” is to say that the Earth is round.

For someone who accepts these claims, it is natural to think that we can define what it is to be false like so:

To say “snow is white is false” is to say that it is not the case that snow is white.

To say “Ravens are black is false” to say that it is not the case that ravens are black.

To say “The Earth is round is false” is to say that it is not the case that the Earth is round.

And so on.

However, Saul Kripke points out a problem with this definition. The problem is that the concept of negation, of its not being the case, is defined by using a truth-table that makes use of the concept of being false. So we get a circular definition: a definition of what it is to be false in which the concept of being false is used in the definition, because one of the components of that definition is in turn defined using the concept of being false. Below is the truth table which defines negation, with P standing for some proposition.

P	Not P
True	False
False	True

Circular definitions are not acceptable. Kripke’s proposal is as follows: let us be affimativists. In other words, let us suppose that there are no falsehoods. When faced with something one might previously have said is false, one should merely say, “I am very reluctant to endorse that view.”

Reference

Kripke, S. 2015. Yet Another Dogma of Empiricism. Philosophy and Phenomenological Research 91: 381-385.

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