the contradictions themselves as they appear in such systems are at the end of the day empty words.
— TheMadFool
I don't agree. There's something important going on here. — Banno
There is comfort to be had knowing that the area of the circle is indifferent to changes in logic. The core of Archimede’s insight is derivable even in the event of inconsistency. Truth is not so fragile.
That example would not arrises in the instances given in the cited articles.
Try this one:
Australasian Journal of Logic Paraconsistent Measurement of the Circle
There is comfort to be had knowing that the area of the circle is indifferent to changes in logic. The core of Archimede’s insight is derivable even in the event of inconsistency. Truth is not so fragile.
7mReplyOptions — Banno
In the latter, I surmise, we have to be constantly alert to the possibility that we aren't making some kind of mistake like how mathematicians have to take precautions that they aren't dividing by zero when tackling algebraic problems. — TheMadFool
A contradiction simply doesn't make any kind of sense at all. — TheMadFool
That would not be correct. The logic being proposed is as formal as any. — Banno
Indeed; and yet here we have a paraconsistent logic that begins to make sense. — Banno
Reasoning by analogy with the "imaginary" geometry of Lobachevsky, Vasiliev called his novel logic "imaginary", for he assumed it was valid for the worlds where the above-mentioned laws (law of the excluded middle and the law of noncontradiction) did not hold, worlds with beings having other types of sensations. — Wikipedia
There's a fine line between genius and insanity. I have erased this line. — Oscar Levant
...these laws of thought are, at the end of the day, postulates i.e. they're assumptions. Given — TheMadFool
...there doesn't seem to be any real difference between paraconsistent logic and madness/stupidity as inconsistencies are the hallmark of all three — TheMadFool
...what happens if we do not assume these? Can we find a way to do that, which still maintains a capacity to construct arguments? — Banno
What this thread is about is that this fringe approach to logic has recently shown some interesting aspects of mathematical proof - the example above begins work towards a proof of integral calculus in a paraconsistent logic. — Banno
But here we have a way to perhaps understand these inconsistencies in a coherent way. Madness and stupidity is perhaps to do with incoherence rather than inconsistency.
Hence the somewhat surprising break between consistency and coherence. — Banno
Possible worlds is a quite different area. It explicitly assumes consistency. This does not. Of course, if this could be made coherent, then it might be applied to possible world semantics. — Banno
Nor does it have anything to do with existentialism. But it might be a sort of deconstruction, in which consistency is seen as a special case... — Banno
I don't think these two are different. — TheMadFool
But now it seems that there might be an alternative. Rather than an incomplete yet consistent account of mathematics and language, we might construct an inconsistent yet complete account... — Banno
Now, who'd a thunk non-euclidean space could be useful... — Banno
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