
#19
Nov1911, 01:41 PM

PF Gold
P: 2,432

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



#20
Nov1911, 03:17 PM

P: 256





#21
Nov1911, 05:50 PM

PF Gold
P: 2,432

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 antisymmetry. 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. 



#22
Nov1911, 06:07 PM

P: 256

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.




#23
Nov1911, 07:37 PM

PF Gold
P: 2,432

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. 



#24
Nov2111, 11:03 AM

Sci Advisor
P: 1,704

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.




#25
Nov2111, 02:20 PM

P: 256





#26
Nov2211, 03:14 AM

Sci Advisor
P: 1,704





#27
Nov2211, 09:04 AM

PF Gold
P: 735





#28
Nov2211, 09:37 AM

Sci Advisor
P: 1,704





#29
Nov2211, 09:44 AM

PF Gold
P: 735

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: 



#30
Nov2211, 10:46 AM

Sci Advisor
P: 1,704

To put it like this as I have done before: (not not A) could be said to have the same, or the opposite truthvalue 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? 



#32
Nov2211, 11:02 AM

Sci Advisor
P: 1,704

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. 



#33
Nov2211, 11:18 AM

PF Gold
P: 735

Counterpoint and point. Countermand and ???. 



#34
Nov2211, 11:21 AM

Sci Advisor
P: 1,704





#35
Nov2211, 11:23 AM

PF Gold
P: 735

EDIT: However, this is off topic. I took issue with your statement the rules of logic are arbitrary in a similar manner to language. And that they lack the need for justification. Common language to formal logic is not a fair comparison. 



#36
Nov2211, 12:07 PM

P: 10




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