Can logical principles be falsified by experience?

An obvious answer to the question is “no”; experience itself tells us that we cannot falsify logical principles through it. Logical principles are almost seen as axiomatic, in such a way that we cannot deny them. However, are we not mistaken in interpreting our experience through reflection or through looking at the external world that experience itself cannot falsify logical principles? If an answer is obvious, it does not follow that it really is the case. Likewise, as Whitehead said, it would need a very unusual mind to undertake the analysis of the obvious. That is what makes the question difficult to answer.

It could even be easier to answer the question on whether logical principles can be falsified by logical principles. To answer the question whether a logical principle can be falsified by experience is like going around in circles; you do not know what premises to use or even where to start. Accepting that experience can falsify such principles would mean destroying what logic had taught us – that we cannot jump from a posteriori premise/s to an a priori conclusion, or from a priori premise/s to an a posteriori conclusion. But then again, we could also question the reliability of Logic and accept as correct the arguments that are considered as invalid in Logic. However, this should only be the case if Logic would be proven as flawed.

As for “falsification”, we mean by disproving something that which is incorrect, and with “experience”, we mean by using either the internal sense (reflection) or the external sense (sensation). For the logical principles, there is/are no other principles I consider than the three basic principles - Principle of Identity (PI), Principle of Non-Contradiction (PNC), and Principle of Excluded Middle (PEM), and those that can be derived from them.

One could have argued that a logical principle can be disproved by experience in terms of valid but unsound arguments; that there are logically valid arguments but are unsound such as this example:

All birds are winged creatures
All winged creatures are flying creatures
Therefore: All birds are flying creatures

The previous example shows a valid but unsound argument. It is valid as it follows Hypothetical Syllogism but unsound because not all birds can fly such as chickens and ducks. However, validity is not equal with truthfulness, so it does not follow that Logic consider as true others that are not true in experience. In fact, Logic would have established the conclusion as false if the first premise were taken as true and the second premise as false. We can see from here that Logic does not contradict experience that could make the experience reject the truths of logic.[1]

As for the three basic principles, others argue that they are just considered as naturally imprinted on the mind because they seem so. Whether or not this is true (that the principles are not innate), I do not think it is right to say that the three are just groundless presuppositions because they are fundamental principles and are not in need of grounds. These three (fundamental) principles are what I want to call the “transcendental presuppositions” of the mind, as it is impossible for the mind to conceive of ideas without presupposing them. The three principles deal with relations (PI: the relation of the self with the self; PNC and PEM: the relation of the self with its contradictory); the mind cannot conceive and even communicate the object/s of its thought without relations. Thus, there is a need for the presupposition of the three; for if there is none, there will be no knowledge but only scattered ideas.

Furthermore, it is absurd[2] to say that the three principles can be falsified by experience as they are derived from the most basic principle (Principle of Identity / p≡p) and are almost equivalent to each other. One cannot seem to falsify that ‘p is p’ or ‘a tree is a tree’, or to falsify everything that could be derived from them (that ‘p is not non-p’ or ‘a tree is not non-tree’). One cannot even falsify one of the two remaining principles (PNC and PEM) as they are both derived from PI and are logically equivalent to each other. PNC can even be translated to PEM and vice-versa through DeMorgan’s theorem[3]. Hence, if these three are logically equivalent to each other and if experience cannot falsify one of them, then experience cannot falsify all of them.

Lastly, since falsification is about disproving something, let me disprove the proposition “Experience can falsify logical principles”. It cannot be the case that experience can falsify logical principles because even if we can imagine a world wherein we can experience that ‘A is not A’, it does not follow that the Principle of Identity is incorrect. Even if our world changed and that ‘A is not A’ would be held as true, the Principle of Identity (that ‘A is A’) would still be true in our previous world wherein such principle is true. It is the same with the game of chess. Chess is governed by certain rules/principles (or moves), but if these principles or moves are changed randomly, the previous principles or moves of chess will no longer apply to the revised chess game. However, the old principles / old rules are still applicable to the chess game wherein there were no changes done. The logical principles are independent of the external world and are still true even if the world changed. As previously said, they are transcendental presuppositions of the mind, and are, thus, independent of our experience.

Falsifying logical principles through experience is logically impossible[4]. Doing so would negate the truthfulness of the transcendental presuppositions in our minds; and in negating such presuppositions, we cannot even conceive what we have experienced, as we cannot conceive of agreement and disagreement of ideas in the absence of relations.

[1] There are times when other principles contradict experience. E.g. That “Parallel lines do not meet” seems to contradict experience as we can observe that they do if only we would use one point of view, making us incapable of seeing the end of the lines. However, I do not consider such as a logical principle (though it s a postulate in Euclidian Geometry) as such is not derivable from the basic principles.
[2] The term absurd does not necessarily mean that I consider the argument as false.
[3] PNC: ~(p & ~p); while PEM: ~p v p
through DeMorgan’s theorem: [~(p & ~p) ≡ ~p v ~~p ≡ ~p v p]
[4] as Wittgenstein said, the only impossibility is the logical impossibility