The Site Definition of ‘proof’ reads “Evidences or arguments establishing a statement (hypothesis or opinion) to be valid, factually accurate, or true.” Link.

The question of what constitutes proof that a statement is true is a vexed and complex one. It ties in with issues of reality, truth, confirmation, evidence, levels of confidence, and thresholds. It also ties in with an important topic in epistemology - what is knowledge and how do we obtain it? This also introduces us to the terms warrant and justification. The subject of logic and reasoning are also entwined with proofs.

It needs to be understood that a statement of fact may be true, but it is not possible to prove, to evidence, or even to assess whether or not it is true.

It is also possible that some statements of fact do not have a binary characteristic of truthfulness. This is particularly true of statements of generality such as:

• Most creatures sleep at night.

• All people believe some things which are not proven.

• Great writers taste life differently.

Assessing the truth of such statements requires one to define the terms carefully. Depending upon how the terms are defined the statement may be true, false, or interpretable.

Establishing the ‘truth’ of an opinion is altogether more difficult. It begins with the fact that an opinion may not have a truth value - it may be neither true nor false. It can also be difficult to even determine whether a statement is a fact, an hypothesis, or an opinion. It can all too often simply be reduced to the way the statement is structured, rather than a fundamental difference of meaning. Consider:

1. I am of the opinion that this problem is insoluble.

2. I hypothesise that this problem is insoluble.

3. This problem is insoluble.

1 is a statement of opinion. 2 is a statement of an hypothesise. 3 is a statement of fact.

Yet all three could simply be taken to be different ways of making the same point.

And therefore one might argue that all three have the same truth value, and degree of confidence and certainty. A literal parsing of the three statements, however, must conclude that 1 and 2 are necessarily true even if statement 3 is false.

It might also be thought, at first instance, that statements of fact necessarily relate to reality. This may be true if the very broadest definition / interpretation of ‘reality’ is used, but otherwise one would have to conclude that the following statements are not about reality.

1. There were numerous Nordic gods.

2. Only fantasies are real.

3. Reality may include the known, the unknown, and the unknowable, but there are far more things to be feared beyond that.

If one adds the following statement to the third one above:

For the fantasies of one’s imagination can be enough to freeze one’s blood, steal one’s soul, and stop one’s heart.

one can see that statement 3 can most certainly be true - but to what extent is it talking about reality? Fear cannot freeze one’s blood. Can it steal one’s soul? Are the fantasies of one’s imagination part of reality?

And then there are paradoxical statements where no truth value can be ascribed:

A lie, once written, is as true as this statement.

or if you prefer:

• A lie, once written, is as false as this statement.

In both cases it’s a self referential paradox to which no final quality of truth / falsehood can be applied.

And there are statements where it is not clear whether either a literal or metaphoric interpretation yields a testable meaning, and yet one feels the statement has some truth sense to it:

• Only fantasies are truly realistic.

• Truth, being stranger than fiction, cannot be believed.

• Only good liars are able to speak the truth convincingly.

• Those who seek peace should prepare for war.

• Fragile dreams sometimes bear the most weight.

• One must never trust a man who claims to be honest.

The last statement also creates another problem; although it is a statement, it is also an injunction.

This site is focussed on wisdom. It attempts to communicate and disseminate wisdom. Wisdom which is incomprehensible to most people defeats that purpose. This site therefore strives to draw a fine line between being precisely accurate with subjects such as truth, proof, and epistemology, and being reasonably comprehensible to all reasonably intelligent and educated readers.

Consider:

Humans are