Mentat
- 3,935
- 3
How's it going, Manuel?
Originally posted by Manuel_Silvio
That P([beep]) was a generalization. I used it to prove that incompatibility case for all statements of the form "I [beep] therefore I am" ("I think therefore I am," "I eat therefore I am," "I want therefore I am," etc). Instead of using the specific verb, "think," I used a non-specific variable [beep]. You could say whatever verb in place of [beep] (for example "I discuss therefore I am") and P([beep]) would be a statement like "there need be an I to [beep]" (means, for example, "there need be an I to discuss").
Yes, I know. I was referring to the time when you started to talk about P[bleep] reasoning in the term of functions (like f(x)), and you said that you need not substitute an entity for "P".
Remember you claimed that one can't be thinking if one's not being. The function P([beep])'s value for [beep] = "think" is "there need be an I to think." P([beep]) is the generalization of your premise that thinking (or [beep]ing) and being are firmly bound. There's a reason for my using P([beep]). I took your premise (and generalized it, an action that complicated the matter), then I showed, during that proof, that your premise by which you claim the truth for Descartes' statement leads to a loop along with the same Descartes' statement. This was the loop case in that proof where I said if P = T and Q = T then we'll have a loop. And then I showed even if you put away your premise (eg, you say P = F) and we get P = F and Q = T you won't get much out of it because that would be a paradox. This was the paradox case.
Yes, I understood this as well.
With or without P([beep]), it's clear that statements of form (Q => Q) are ever-true and that they "can't" be used to deduce the truth of Q itself. Take a look at this new formulation of the same proof, perhaps this one works for you.
Well, first I have to point out that Descartes was not trying to deduce the truth of Q, when he made the statement, he was just proving the Evil Demon's attempt to be in vain.
You repeated many times that "if there wasn't an I, who could be thinking?" Let's have your word and say that "thinking" is the "undeniable" companion of "being." Saying this necessitates that "I think" be logically equivalent to "I am."
Descartes' statement is "I think therefore I am." Take "I think" and name it R. Take "I am" and name it Q. Descartes' statement can be expressed as (R => Q). Since R = Q (thinking is always the companion of being), we can always substitute Q with R so (R => Q) becomes (Q => Q). This (Q => Q) is an equivalent of Descartes' statement, (R => Q), by your premise that thinking and being are firmly bound. We know that any statement of form (Q => Q) is ever-true and the truth of Q itself (Q being "I am") can't be deduced from it. This is a non-informative case, a loop. You can't say if Q is T or F (eg, if you exist or not) by knowing that (Q => Q) is true.
It's worth noting that the equivalence of (R => Q) and (Q => Q) was taken from your premise. If you decide to put aside the firm bond between thinking and being then such equivalence can't be claimed and we have a (R => Q) which deduces Q's truth from R's truth like many other plain statements. However, in putting aside the firm bond between thinking (eg, "I think" which is R) and being (eg, "I am" which is Q) you've already accepted that Q's truth is irrelevant to R's truth and deducing Q's truth from R's truth isn't allowed. This is a self-contrary case, a paradox. You can't say R indicates Q when you've previously stated that R and Q are independent (eg, aren't bound).
You are mostly right about all of this. One thing to keep in mind, R does not equal Q, but rather contains Q as a sub-premise. The difference is that R's truth necessitates that Q be true, but Q can be true without R.
Back to Evil Demon scenario, we have the Evil Demon claiming there's no Rene Descartes and Descartes claiming there is indeed a Rene Descartes by deducing from his ability to think of this scenario. Descartes is saying Q (eg, that "he is") is T because he's thinking of an Evil Demon scenario and from his thinking, his being can be directly derived, that (R => Q). Descartes is saying R = Q (eg, one's being can be derived from one's ability to think) and that (R => Q). The loop case happens here: (R => Q) can be turned to (Q => Q) and then Evil Demon can turn back to Descartes and tell him that from (Q => Q)'s truth (from "I think therefore I am"'s truth) Q's truth can't be derived without making a loop and violating the rules of game which are the boundaries of Boolean logic.
Incorrect. The Demon is the one that tried to convince an existent entity that he didn't exist, so it is the Demon that is at fault. Descartes would not tell the Demon "I think therefore I am", but would, rather, say "I can think about what you are trying to convince me of, therefore you are defeating your own purpose".
Something to remember about Descartes (I've read a few of his works now) is that he often starts with a statement or concludes with a statement, but the statement doesn't even need to make sense outside of it's context. He gives the context at some point, and the statement should be evaluated only within the framework of the context.
For those who invented and developed it didn't like what wasn't "productive" and "practical" based on "their" understanding of "practice" and "production."
Searching for non-informative statements you won't find any but those statements that are inherently paradoxical and/or self-referenced. A statement is a sentence that can be assigned a "state" (in case of Boolean logic, either of T and F states). If a statement can be assigned a definite state then it's informative for it surely tells us something about something. There remain those statements which can't be assigned a definite state, these can only be of the above categories and because of their indefiniteness are non-informative.
Well this makes sense. However, Descartes' was making the statement within a context that allowed it to be relevant. It was the conclusion of an entire "lesson", so to speak.
He started out with the Evil Demon, trying to convince Descartes that all of the things that he believed were false. Then the Evil Demon went on to try to convince Descartes that he didn't exist. But Descartes came back at him by (basically) saying that the fact that the Demon is making an effort to convince him (Descartes) that he didn't exist, and the fact that Descartes could think about not existing, proved that Descartes did (in fact) exist. At the end of it, Descartes compacted this reasoning into "I think therefore I am".
No, that wasn't a new context. I was only saying that "I was born 15 years ago" doesn't directly result in "I am 15." Hence, an "I was born 15 years ago therefore I am 15" can't be equaled to an "I am 15 therefore I am 15."
Look at the statement "I was born fifteen years ago": One of it's sub-premises is "I was born", and another is "it's been fifteen years since then".
Thus, the second statement of "I was born fifteen years ago, therefore I am 15" (let's call it Q') is one of the sub-premises of the first statement (P'). This is the same situation as "I think therefore I am", as I have shown before.
Even in the case you talk of 15 subjective years, those auxiliary statements (eg, those that must accompany "I was born 15 years ago" to get "I am 15") are present. Now they solemnly declare that there's a distinction between subjectivity and objectivity. Or they may declare Special Relativity and time dilation. Nonetheless, there should be some statements additional to "I was born 15 years ago" to deduce "I was 15." Your statement is of form (R => Q), R and Q being convertible to each other only under special circumstances, thus it isn't of form (Q => Q).
And neither is "I think therefore I am", as I've shown above.
Response continued on the next post...