What is he really trying to say? That there is no such thing as a paradox? I sometimes say that all paradoxes are resolved in Enfernity (eternity & infinity). But that has nothing to do with the real world. :smile: — Gnomon
Okay, Devil's Advocate. I'll play.
:naughty:
No, Peirce is not saying that there is no such thing as a paradox, but there is a very clear difference between a polarity and a paradox. A polarity has external relation influence. A paradox does not.
Here is how Peirce explains this using the
Liar's Paradox (links below excerpt) ....
"In Lecture 1 he discusses the sentence, "This very proposition is false."; in Lecture 3 he examines the sentence in the form "What is here written is not true." This sentence, as we know, leads to paradoxical conclusions. I will first consider Peirce's analysis of the problem and then his solution to it.
1.1 The Problem Stated
S1 This very proposition is false.
S2 What is here written is not true.
Peirce argues that the problem with this sentence is that it is logically meaningless or logically nonsense, where nonsense is defined as "that which has a certain resemblance to a symbol without being a symbol. "Each genuine symbol is subject to three systems of formal laws; these are the laws of (1) grammar, (2) logic, and (3) rhetoric. Each symbol to be meaningful must satisfy the formal conditions of grammar, of logic, and of the intelligibility of symbols. This symbol is grammatically correct but
fails to be a genuine symbol because it does not satisfy the formal conditions of logic.
In the case of the above sentence, SI, a logical law, the law of the excluded middle, does not apply. Peirce says,
This is a proposition to which the principle of the excluded middle, namely that every symbol must be false or true, does not apply. For if it is false, it is thereby true. And if not false, it is thereby not true.
A logically meaningful sentence will satisfy the laws of logic. Peirce argues that this logical law does not apply to SI because this symbol has no object. Logic, Peirce says, is concerned with assertoric propositions. He says of assertoric propositions, "Propositions which assert always assert something of an object, which is the subject of the proposition."In the case of SI, however, the proposition "does itself state that it has no object. It talks of itself and only of itself and has no external relation whatever." That is, the subject of the proposition being the proposition itself, the predicate makes no assertion of an object to which the proposition refers. An assertoric proposition, then, makes reference to an external object, but this proposition "talks of itself and only of itself and has no
external relation whatever." "Logical laws," however, "only hold good as conditions of a symbol having an object."
Similarly concerning S2 Peirce says that we get an infinite number of
propositions:
What is here written
The statement that that is false
The statement that that is false
The statement that that is false
and so on to infinity."
<<< There is your infinity that has nothing to do with the real world. :wink:
As you read further into the essay, you will see that Peirce also points out that there is a difference between what is
explicitly asserted versus what is
tacitly asserted.
Liar's Paradox
Peirce's Paradoxical Solution to the Liar's Paradox
referring to "modes of existence" other than reality? What other kinds of existence are there? Do ghosts exist in a parallel universe? Are entangled particles a polarity of different modes of existence? — Gnomon
The part of his statement that you are leaving out is "So in the action and reaction of bodies, each body is affected by the other body's motion". He is not referring to ghosts.
:razz: .... Whether or not this can be applied to parallel universes is left for the quantum physicists to figure out. One of the reasons there has been such interest in Peirce (and renewed interest in Spinoza) is because the most recent findings in physics have pointed to how correct and far ahead of their time these brilliant men were, and all by working these things out by using highly skilled logic. ... And again, 5 centuries BCE, Heraclitus was on the right track with his
Logos.
I will write more later, but for now
Happy Thanksgiving. I am thankful to have a friend like you that I can banter with about such things.
:blush: