Talk:Incorrigibility

?

I'm guessing I don't understand this right, or maybe it's unclear and the definition needs to be reworked. I don't understand why the Descartes quote is used as an example of incorrigibility. If someone could present a proof showing it to be incorrigible, that would be helpful. By the way I understood it when reading the article, the Descartes quote being incorrigible is true if the quote itself is true, but otherwise is not necessarily (in the absence of some other proof).

Let me put it another way. By definition, to say that "I think therefore I am" is incorrigible is to say that "I think therefore I am" is true if somebody thinks it. But how do you know that it's incorrigible to begin with? One way is to assume the truth of "I think, therefore I am". But this reduces to:

"I think therfore I am" is incorrigible if "I think therefore I am" is true.

But this expands to:

("I think therefore I am" is true if one thinks it to be true) if "I think therefore I am" is true

or (note this reduction is valid because there is no "only if"!):

"I think therefore I am" is true if one thinks it to be true and "I think therefore I am" is true

which is circular.

Note that I didn't use "only if" or "iff" anywhere here: there may be other ways to arrive at the incorrigibility of "I think therefore I am". If there are, they should be in the article to avoid this confusion. Mbarbier (talk) 21:13, 31 December 2007 (UTC)

That's the neat thing about incorrigible statements: they appear circular if you look at them in a "A => A incorrigible" format. How else could A be true just on it's own (i.e. proper basic or incorrigible) without the need of that anchor before the 'if'?

So in your last expansion you wrote is "IttIa is true => (IttIa is true => IttIa is true)", which can be expanded indefinitely, but instead you should ask: is the leftmost statement automatically true by the virtue of nothing else besides being written there?

The property of incorrigibility becomes clear when you zoom inside the statement. And herein lies the criticism of using Descartes' quote, because while famous, it's way overkill to illustrate the point.

Thus let's demonstrate (at least) Type-1 on a simpler version of it: "If I think, then thoughts exist", i.e. "Thinking => thoughts" =: TT.

We define "TT is incorrigible, if TT must be true". One could use the implication arrow and write "TT undeniably true => TT incorrigible", but that might be misleading, because we're more interested in definition than deduction.

Now go ahead and perform TT. By the virtue of (what we define as) thinking, you can't escape having (what we define as) thoughts. The proof is that this holds empirically true whenever you perform it, and you can't build a case where this doesn't happen. (e.g. "If I don't think..." *beep*, you're already thinking that).

Which makes TT true in every possible case, which in turn makes TT incorrigible.

--212.35.18.78 (talk) 08:23, 19 September 2021 (UTC)