To prove something true, you need to 1) know truth, 2) to agree about it and 3) to verify it on a system.

- The only essential truth we know is causality.

Why 1+1 => 2? Because if you put an apple in an empty bag, then add another, and you count the apples, you will find two apples. The same happens if you-hit-your-head-against-the-wall => you-feel-pain. This mechanism of action and reaction is called causality. We learn the action-reaction mechanism before being born and along all our lives. When something breaks causality, we feel pain, anguish, fear. Imagine you bash your head against the wall, but you don't feel nothing. Imagine you lose a loving one. Imagine you see an UFO or a miracle. All this events break the causality rules in our head and we lose the sense of reality. The only reality we accept is the one we understand, and that is the one which follows the causality mechanism.

A proof is the application of the causal rule over a system.

- Causality is an objective knowledge.

Therefore, we all know the mechanism, and we can share thoughts. You will probably agree that if you speak to a rock, it will not answer as a person would do. Therefore you and me can find the same proof. If we don't agree with causality, proof is impossible. Objectivity about causality is probably the base of all science. There is no deeper truth (for now).

- Proof is finding that a consequence is related to a cause by a system.

As you and me 1) know the causality mechanism, and 2) agree about it, finding a proof is making a causal relationship between a cause and a consequence. Then, we can agree that sunlight makes plants grow (causal rule: sunlight-over-a-plant => plant-grows). Then, we can set a system plant, send the sunlight input (cause or action) and verify growth (reaction). Finding the system that relates action to reaction, or finding specific exceptional reactions can be difficult. But sometimes we find them and agree and reach a proof.

4Furthermore, if we're throwing out deductive proof, then there goes

allproof in one fell swoop. Because surely you can't accept inductive logic as a way of obtaining proof, yet discard deductive logic. – boehj – 2011-06-15T00:59:40.517We can prove many things and proving things would be the entire point of the discipline. Examples are easy. Take Kant's antinomies. They exist because we can prove that their extreme solutions fail in logic. If we could not prove anything then they would not exist. – None – 2019-04-16T11:18:29.550

Strongly related to http://philosophy.stackexchange.com/questions/70/could-cogito-ergo-sum-possibly-be-false

– Muhd – 2014-04-28T23:34:55.397From here: "As we know today, Frege's principles of proof are complete for classical predicate logic." What's subjective about this? The proposition P is '8 is an even number'.

– boehj – 2011-06-14T10:08:52.480`P ∧ ¬P`

is false.