Laws of Logic

In the last post, we quoted Carin Robinson’s claim:

For instance, where we use the laws of logic, let us remember that there are no known/knowable facts about logic. These laws are therefore, to the best of our knowledge, conventions not dissimilar to the rules of a game.

Law

I intend to discuss Robinson’s claim in a bit more detail shortly, but first consider the meaning of a law in its plainest sense. In the USA there is a law that you must pay your taxes for the previous year by mid April. What does this law do? Presumably the purpose of the law is to get people to pay their taxes by that time. Without the law, they would likely not pay by then, and if there were no rule that you have to pay taxes at all, people presumably would not pay taxes. So the law is meant to make something happen, namely the payment of taxes by a certain date, something that otherwise might not happen.

Rules of a game

What about the rules of a game? Consider the game of hide and seek. Wikipedia describes it in some detail:

Hide-and-seek, or hide-and-go-seek, is a popular children’s game in which any number of players (ideally at least three) conceal themselves in a set environment, to be found by one or more seekers. The game is played by one player chosen (designated as being “it”) closing their eyes and counting to a predetermined number while the other players hide. For example, count to 100 in units of 5 or count to 20, one two three and keep counting up till it reaches twenty. After reaching this number, the player who is “it” calls “Ready or not, here I come!” and then attempts to locate all concealed players.

This is partly a factual description, but it is also attempting to give the rules. It seems to be a rule that the players who are hiding have some amount of time to hide, and it would seem to be a violation of the rules if the seeker simply starts the game by announcing, “I see everyone here, so I’ve found everyone,” without there being any time to hide.

What do these rules do? Are they like the law?

Yes and no, in different respects. You can certainly imagine a player breaking the rules in the above manner. So the rules, like the law, are meant to make something happen, namely the players act in a certain manner, and they are meant to exclude what might happen without the rule, just like the law.

There is a difference, however. If a player did the above, they would not be playing the game at all. It is possible to go about your life and not pay any taxes; but it is not possible to play hide-and-seek without there being a space or time for people to hide. In this sense, the law excludes some possibilities for life, but the rule of the game does not exclude some possibilities for that game; it simply describes what the game is. It does exclude possibilities that would be rules for other games. So it excludes some possibilities; but not possibilities for the game of hide and seek.

Facts

Why does Robinson say that there are no “facts” about logic? The English word “fact” is taken from the Latin factum, which means “done” or “made.” This is not accidental to the claim here. There is nothing making things follow the rules of logic, and for this reason Robinson asserts that there are no facts, i.e. nothing made to be the case in the realm of logic. Precisely for this reason, you don’t have to go out and look at the “facts”, i.e. things that are made to be the case in the world, to determine whether or not a statement of logic or mathematics is correct or not.

Laws of Logic

Robinson argues that since the laws of logic don’t make anything be the case in the world, they must be conventional, like “rules of a game”. But in our discussion of the rules of a game, we saw that such rules do exclude certain types of possibility, while they constitute the game itself, and therefore do not exclude any possibilities for the game. How would this work if the rules of logic were rules of a game? What sorts of possibility are excluded by the rules, and what game is constituted by the rules?

As we said, it is possible to break the rules of a game, although when you do, you often stop playing the game by definition. It it similarly possible to break the laws of logic?

If we take the game to be a certain sort of speaking, yes, it is. It is possible for someone to say the words, “Blue things are not blue.” It is possible for someone to say the words, “All cats are mammals. Alvin is a cat. Therefore Alvin is not a mammal.” Someone doing this, however, is not playing the particular game in question. What is that game? I suggest we call it “speaking sensibly about reality.” Someone who breaks the laws of logic, by that very fact, fails to speak sensibly about reality, just as someone who breaks the rules of hide-and-seek fails to play the game.

The rules of hide-and-seek are conventional, in the sense that you could have other rules. But if you did have other rules, you would be playing a different game. In the same way, if you had rules other than the laws of logic for your speaking game, you would be doing something entirely different. You would not be doing what we are normally trying to do when we speak, namely speaking sensibly about reality.

Up to this point, we have actually succeeded in making a certain sort of sense out of Robinson’s claim. But does it follow, as supposed, that logic tells us nothing about reality? We pointed out in the previous post that this is not true. But why is it not, if the laws of logic are conventions about how to speak?

Do the rules of hide-and-seek tell us something about the game of hide-and-seek? Clearly they do, despite the fact that they are conventional. They tell us most of what there is to know about the game. They tell us what the game is, in fact. Likewise, the laws of logic tell us how to speak sensibly about reality. Do they also tell us about reality itself, or just about how to speak about it?

They do, in the way that considering the effect reveals the cause. Reality is what it is, and therefore certain ways of speaking are sensible and others are not. So to tell someone how to speak sensibly is to tell them something about reality. However, there is another difference between the laws of logic and the rules of a game. The rules of a game are conventional in the sense that we could have different rules and different games. And similarly, if we didn’t want to follow the “conventions” of logic, we could speak nonsensically instead of trying to speak sensibly about reality. But there is not some possible alternate reality which could be spoken of sensibly by using different “conventions.” In this sense, you can call the laws of logic rules of a game, if you wish. But they are the rules of the game of understanding, and there is only such game, not only in practice but in principle, and the rules could not have been otherwise.