Objectivism Online Forum

# A, Not A and B

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Having only really started reading about Objectivism in itself about two months ago, I still have a lot to figure out and understand. I found the following quote in an online guide to Objectivism...

Logic, the method by which we sift contradictions from our thinking, is a derivate of the axiom of identity. While the laws and fallacies of logic are numerous, they can be subsumed to three basic laws :

The law of identity : A is A.

The law of non-contradiction : A cannot be not-A.

The law of excluded middle : B can either be A or not-A.

These timeless laws provide the fundamentals of logical thinking. As we will see later, logic is one of the three parts of reason.

I was wondering if someone who understands this could explain the idea of

B can either be A or not-A.

as it seemed to me that it would make more sense if the sentence read "B can neither be A nor not-A", although this is probably due to lack of insight on my part.

Thanks

The TravellingFool

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Yes, that is not a very good statement of the law of excluded middle, if you aren't already familiar with it.

What it is saying as that some entity B cannot have both property A and property non-A. For example, a sports car cannot be both red and not red (at the same time and in the same respect--obviously it could be red at one time and painted a different color later, or it could be red with blue 80s pinstripes ). That is, an entity either has a certain property, or it doesn't; it's either-or, there is no middle ground (thus, the name "the law of excluded middle").

So a better statement of it would be something like: B can have either property A or non-A, but not both, at the same time and in the same respect.

Hope that helps.

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Thanks for that. I'll probably post something else here soon but the more I read, the more this makes sense. Although I've never before equated logic with red sports cars with blue 80s pinstripes.

Ta ta

The TravellingFool

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So a better statement of it would be something like: B can have either property A or non-A, but not both, at the same time and in the same respect.

Ash...

saying that B can either have the property A or not have the property A seems to depart from the strict logic of the statement ... if B subsumes a set of properties, then it can hold property A, but many other properties C, D, etc exist under either A or B ... Thus B can never BE A, unless all other properties C, D etc ... coincide.

The statement seems to hold as its focus the single properties A & B, allowing for extension to subsumed sets of properties ascribed to A & B ... and either B is the same property as A [which would then imply equivalency of all subsumed sets of properties of A and B, if A & B are a collection of properties ] in which case B IS A ...

or else B is not A when the property B differs from the property A. B is thus some different property, or at least one property in its subsumed set is different from at least one property of the subsumed set of properties that define A.

I hope I said that effectively enough to communicate what I have visualized in my mind ....

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The statement seems to hold as its focus the single properties A & B, allowing for extension to subsumed sets of properties ascribed to A & BÂ  ...

... this probably would have been better put saying The statement seems to hold as its focus the single properties A & B, allowing for extension to subsumed sets of properties ascribed to X & Y ... and either B is the same property as A [which would then imply equivalency of all subsumed sets of properties of X and Y, if A & B are a collection of properties ] in which case B IS A ...

...etc.

My original wording even confused me as to the distinction between the properties A & B and the sets A & B.

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I think introducing the idea of sets at this point is unnecessary to get at the main point of the principle and just confuses the issue. But I think you're right that there's a different (and perhaps simpler) reading of the original definition than the one I offered, which is that B either equals A, or does not. But I think the problem with that kind of interpretation and the way it was originally stated is that, in the context of just having offered definitions for the laws of identity and contradiction which state that A is A and cannot be not-A, to then abruptly switch to the notion that B can be either A or not-A can be easily misunderstood by someone who's not already familiar with these laws to mean that A can be B (i.e., not-A) in direct contradiction to the previously stated laws. And that's exactly what I think happened here. I thought introducing the idea of properties would help sort out what was meant by B being able to be either A or not-A (and I also thought it important to add that implied by the either/or setup is the qualification, "but not both").

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I think the law of the excluded middle covers all sorts of predications, so that your first statement of it, Ash, is an application of the law to predications involving properties (I suppose Aristotle would call them accidents). But the law could equally be applied to other sorts of predications. For instance, man is either an animal or a non-animal. Animal here is a predication in the manner of a genus rather than a property. Or also, a particular man is either Karl Marx or non-Karl Marx. And this is predication in the manner of something individual.

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Right, it was only a matter of time, I'm need help again.

With regards to the stolen concept fallacy, how does atheism work?

Is it possible to say that God/some form of higher being does not exist without

inadvertantly implying his/its existence?

This may seem a fairly fundamental question but I am having a great deal of

trouble at the moment actually getting my hands on Rand's texts and therefore

am working solely with material I am able to find on the net and although there is

plenty, it seems primarily for those with prior knowledge of the ideas of

Objectivism and now I'm confused.

Anyone who can help, please do.

Ta ta,

TF

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"is it possible to say that God/some form of higher being does not exist without inadvertantly implying his/its existence?"

In response to this question, I'll ask you: is it possible to say Santa Clause does not exist without inadvertantly implying his existence?

or

"Is it possible to say The Sandman does not exist without inadvertantly implying his existence?"

What about the Tooth Fairy? The Easter Bunny? Johnny Appleseed? Superman, etc etc etc?

What is it about speaking of any of them which supposedly can inadvertantly imply their existence?

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You're misunderstanding the stolen concept fallacy. The fallacy consists of using (and thus accepting) a concept while denying or ignoring some concept on which it logically depends. For example, someone is stealing the concept of morality if he uses that concept while at the same time denying free will, since if there is no choice of what to do, there is no question of what one ought to do.

When an atheist says, "God does not exist," he is not using the concept of God. He is denying it (Objectivists consider God to be an invalid concept, since it is not reducible to anything one perceives).

By the way, the administrators of this forum probably want you to start a new thread when you introduce new topics.

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