Logic is not a Convention

Technically speaking, you can move the rook diagonally. You’re just breaking the rules.

We like to think of “rules” and “laws” as optional. To the extent we agree on a set of rules, we can sit down and enjoy a game of chess or checkers. But if one party decides to reject the rules – if the rooks start moving diagonally and the knights promote themselves to queens – then the chess game is over, and pieces might start flying.

Language works in a similar fashion. If we all agree on grammatical rules and general vocabulary, we can enjoy a conversation and effectively communicate. But, if one party starts speaking by another set of rules – in a different language – then the communication is over. If you don’t understand the rules, then a new language is indistinguishable from gibberish.

At any point, we can opt-out of the rules of language, and we can form structureless sentences. We can throw chess pieces around. We can break “criminal” law. We can even break social laws and norms. You are free to run around the grocery store in your underwear while shouting nursery rhymes. I wouldn’t recommend it, but it’s certainly possible.

However, it is essential to critical thinking to understand that not all laws are optional.  Specifically, the laws of sound reasoning are not optional; you can’t opt-out of them while making sense. They aren’t convention. Mathematical laws work the same way. 2 + 2 = 4 is not convention. It’s a necessary truth, and it doesn’t matter if you deny it. To the extent you think you’re opting-out of necessary truths, you’re necessarily wrong. These rules are discovered, not created.

This post is an extension of my last article on logic. A number of people commented to say, “Well, which logic are you talking about? There are many different logics out there, so how could you say everything is only grounded in one logic?” This objection, unfortunately, confuses the word “logic” with the concept of logic.

Don’t get me wrong, I am not saying there’s an objective definition for “logic”.  No word has an objective definition. In fact, a huge amount of confusion is caused by people trying to appeal to the “right definition” or “wrong definition”, when ultimately, every word is ostentively defined – we “point” to what we mean. Whether or not our “point” was successful – whether or not the concept was understood by another party – is never a guaranteed thing. Communication is not perfect.

What I mean by “logic” is not “the process of human reasoning.” It isn’t “the conventions of thinking”, or “a school of thought.” It isn’t “a field of study” (though you can study it).

Logic is the inescapable rules of existence. It is what all human reasoning appeals to. These rules are not determined by a committee or culture; they are not optional. They are necessarily tied to all existence; neither logic could be without existence, nor existence without logic. Each implies the other.

If that doesn’t make sense, let me “point” to what I mean by “logic”, by starting with the words “true” and “false”.

Here’s what I mean by “true”. Take the sentence:

“I am having the experience of writing.”

That statement has meaning. It doesn’t matter whether other people share the same definitions “experience” and “writing”. I understand what it means. The statement also possess another quality: what it claims about reality is accurate – I am indeed having the experience of writing. Contrast this with another sentence:

“I am having the experience of eating ham.”

Now, both propositions are sensible. They mean something. But the latter lacks a quality of the former. I am not having the experience of eating ham. It’s precisely this difference – call it the accuracy of the proposition – which we can label as “trueness”. The first proposition has “trueness”– it’s a meaningful claim which accurately describes reality – while the second proposition lacks “trueness” – it’s a meaningful claim that doesn’t accurately describe reality.

Please don’t take this as a linguistic definition of “truth” – I am trying to “point” to what I mean. True-ness and not-trueness are real qualities, regardless of the words you choose to reference them. But, our analysis shouldn’t stop here.

Consider the trueness of the sentence “I am having the experience of writing.” What if we take the following sentence: “It is not-true that I am having the experience of writing.”

There’s an essential relationship between these two claims.  The latter is a perfect negation of the former. To the extent that the first sentence is saying “Such and such about reality is true”, the latter is saying the exact opposite: “Such and such about reality is not-true”.

Here’s what that means: if the sentence “I am having the experience of writing” is true, then it must be the case that the sentence “I am not having the experience of writing” is not-true. That’s what we mean by “not-true” – the negation of “true”.

Thus, a proposition and its negation are necessarily mutually exclusive – otherwise, the proposition hasn’t actually been negated. Again, this isn’t about the definition of the word “negation”. It’s about the concept of what’s happening. If you don’t like the word “negation”, you can choose whatever assortment of syllables pleases you.

I’ve tried to point the conceptual meaning of “true”-ness and “not-true”-ness. Now what about logic? Consider the question:

Why are the categories of “true” and “not-true” mutually exclusive?

Why is the negation of a true claim about reality not-true?

I call it “logic” – the inescapable rules of necessity. It’s not convention – you can’t even choose to break the rules (i.e. you cannot do what cannot be done). It’s not optional; you can’t opt-out. The reason something cannot be “true” and “not-true” at the same time is not cultural. It’s absolutely necessary.

When you see what I’m pointing to, you understand what inescapability means. It’s completely impossible for a negation of something not to be a negation. Just like it’s impossible for an accurate claim about reality to be inaccurate – if it were inaccurate, then it wouldn’t be accurate in the first place!

And why shouldn’t it be otherwise? Because it couldn’t be otherwise. It doesn’t even make any sense to say it could be; it’s nonsensical and meaningless. This does not reflect the laws of thought – this reflects the laws of reality.

When people say “But there are different logics!”, they don’t realize that all thought-processes presuppose the same logical principles. Even if they claim to deny them, they affirm them (but this shouldn’t be surprising, as the rules are inescapable). Precisely, it’s the laws of identity and non-contradiction which every thought presupposes; they are at the bottom of every worldview, whether acknowledged or not. To the extent that anybody denies the law of non-contradiction, they are objectively wrong, and you can know it. This isn’t pigheadedness; it’s necessarily true.

If you think, in theory, there could be a sentence which is both true and not-true at the same time – an inaccurate accurate claim about reality – then your conception of truth isn’t sharp enough. You’ve not thought it through. Negation necessarily means the explicit denial of the truth of a proposition – if it’s negation at all.

This is my attempt to point at logical principles. I’ve not created the rules, but I’ve discovered them, along with many other philosophers. If my communication is ineffective, I will keep pointing with difference sentences. Nothing is more foundational or important in all of philosophy.