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CTK Exchange
parahacker
Member since Jul-10-08
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Dec-12-08, 03:34 PM (EST) |
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"implying falsity"
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This is a)probably a really stupid question and b)possibly the wrong forum for it. But I'm forging ahead. In the article, falsity proves anything, it clearly explains how this is possible and the ramifications. So I'm on the same page with everyone there. But it raised the question in my mind, if falsity implies anything, including truth, how does one imply falsity? 1=2 for example; if we 'assume' that some false premise is true, and it ends up implying 1=2, how do we know that our starting premise is false and that we have not in fact discovered a new universal truth that makes 1=2?
Embracing self-contradiction since 2006
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alexb
Charter Member
2316 posts |
Dec-12-08, 03:44 PM (EST) |
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1. "RE: implying falsity"
In response to message #0
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If you look at the truth table for the implication, you'll find that 1. Falsity implies anything, but also
2. Truth implies only truth, so that it is impossible to derive 1=2 from a "really" true premise. But, in principle, "derivability" is different from "being true". The former is a notion meaningful in formal systems; the latter in the models of formal systems. |
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alexb
Charter Member
2316 posts |
Dec-14-08, 05:49 PM (EST) |
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3. "RE: implying falsity"
In response to message #2
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>I don't understand entirely. The models of formal systems?
>Aren't formal systems models themselves? May be. Think of the axioms of hyperbolic geometry. There are models: on a horn, Klein's in a circle, Poincare's in a circle. >And what about situations like the incompleteness theorems? Godel's incompleteness theorem states that in a sufficiently powerful consistent system there are unprovable statements whose negation is also unprovable. This is proven by constructing an arithmetic model in which there is a true sentence that asserts its own unprovability. >Are they not really true, because they claim that any formal
>system with enough ability to self-reflect will produce
>false premises from true ones? There is nothing in what I said that may, in my view, lead to this conclusion. If you want you may call derivable sentences true. |
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