Question about logic.

apeiron

It's in the definition: mutually exclusive, jointly exhaustive. It gets easy with practice.

apeiron

All you are pointing out here is that logic is pure syntax, and has been scrubbed clean of semantics. Which is what I said.

But the OP was about the development of logic. Which was what I was addressing.

Willowz

But, my point is the method. If I understand this properly, in simple terms you are taking the inverse of anything(?)

apeiron

More like the reciprocal in that there is a breaking that usually involves scale as well. The canonical dichotomy is local~global, so in some sense one half ends up shrinking to be as small (or localised) as possible, the other expands to be as large (or global) as possible.

So take something standard like the dichotomy of discrete~continuous. The discrete ends up being the local pole, and the continuous is the global pole. So you could perhaps say, in any given reality, discrete = 1/continuous. The larger you make one value, the smaller you make the other value. Even if we are talking here about qualities rather than quantities!

This is an important point because inverse operations can be of the same scale. For instance, the plus and minus of electric charge seems to be a dichotomy. But really it is only an anti-symmetry. And unstable as a result.

Positive and negative, left and right. These are breakings of symmetry where the scale factor is unchanged and so it is very easy to flip one back into the other. In ontological terms, the symmetry breaking is trivial.

But if symmetries are broken across scale, then the two qualities being produced are, in effect, a long way away from each other. It is no longer easy to annihilate the difference. You can't flip the discrete into the continuous or vice versa because they have moved so far apart as kinds of state.

And then as regards to taking the reciprocal/inverse of anything, of course, you can't do this with just anything. What is the inverse of cat, or plutonium, or Venus? Metaphysics is all about getting in behind these kinds of particular instances so as to extract the fundamental abstract possibilities.

After several centuries of debate, the ancient Greeks came up with a bunch of these dichotomies that we still use. We have refined them, but I don't think we've actually added any critical new ones to them.

Willowz

It's very interesting because it seems you are committing yourself to essentialism. Whereas I and possibly disregardthat take the social constructionism (of science, logic, possibly even math) approach.

apeiron

In fact I clearly argue both. We model reality. But there is also a reality. That can be doubted, but there ends up not being very much point in actually doubting it.

You say you take the social constructionist view. And I just summarised the history of that construction of the syntax of logic. If it seems an argument from essentialism, well that historically was the approach that worked.

disregardthat

Justifying logic is like justifying grammar, logical rules are correct in the same way grammatical rules are correct. In this sense they are arbitrary, but needs no justification.

Willowz

But, they can't be arbitrary and consistent, can they?

disregardthat

How can a logic be inconsistent?

FlexGunship

Are you going for an irony-award with this string of posts? Or was it tongue-in-cheek? If you say that logical rules don't need to be justified and can be arbitrarily defined then there's no guarantee that the resultant set of rules is consistent.

disregardthat

Logic can formally be seen as a method of determining a unique truth value of propositional formulas given the truth-values of the atomistic formulas within. I can hardly imagine logic as such being inconsistent. You are probably thinking of axioms of mathematics.

FlexGunship

Are you saying that the axiomatic foundations of a formal logic system can be arbitrarily defined, or that the system can be arbitrarily defined?

If you're saying the axiomatic beginnings of a logical system can be arbitrarily define, then I'm okay with what you're saying now, but that's certainly not how you started with your first post and is consistent with my earlier post:
Grammar has no such obligation to be consistent and, in fact, it's quite evident in English alone.

disregardthat

To put it like this as I have done before: (not not A) could be said to have the same, or the opposite truth-value of A. The latter would yield a different logic. But the point of the matter is that we do use the word "not" in the way that (not not A) is recognized as A, and for this there needs not be any justification, metaphysical or otherwise.

I don't know what you mean by saying that english grammar is inconsistent. Could you give an example?

FlexGunship

Consistent and inconsistent.
Flammable and inflammable.

disregardthat

This simply shows that the in-prefix is not universally considered a logical "not"-operation, as we don't mean "the opposite of flammable" by inflammable as well as "flammable". But I get your point. This isn't what we mean by logical consistency though.

It is important to note too (before we get into more peculiarities) that it is the intended (understood) meaning of the word or sentence that matters. That we can mean different things by the same word in different situations and contexts doesn't imply any inconsistency.

FlexGunship

If you plan to hand-wave each example as "an exception to the rule" I'm not sure what would satisfy your conditions for exceptions to grammatical rules. Here's a different type of example where a well defined prefix is used when the root is no longer part of the language.

Counterpoint and point.
Countermand and ???.

disregardthat

This is ridiculous, you are the only one saying it's a rule. No one insists on "inflammable" meaning both "flammable" and "not flammable".