You're stuck thinking I'm making a certain kind of argument, but I am not. You're not thinking about what I've specifically written, as probably you t...
P1. The lamp is turned on and off only by pushing the button P2. If the lamp is off and the button is pushed then the lamp is turned on P3. If the lam...
You answered pretty fast. That's your prerogative. But it make me wonder whether you're giving much thought to my remarks, as still it would be your p...
I didn't say they end. Again, the contradiction comes from the conjunction of the premises. It is not a given that it is a contradiction in and of its...
(1) The symbols I used are common. The formulas I gave are not complicated. If one knows merely basic symbolic logical notation, then one can read rig...
So I don't understand why fishfry would deny the plain record of the postings here. Not only did I indeed state the axioms of identity theory several ...
From a couple of years ago, not involving fishfry. Probably there are others over the last couple of years. For simplicity, I didn't mention the quant...
At least, if you are ever interested in a formula, but you don't know the use of the symbol, there you have it. Of course, if you're not interested in...
(1) If a set of premises G entails a contradiction, and for any member P of G we have that G\{P} does not entail a contradiction, then we are logicall...
I don't proffer an opinion on that. But I can see that presumably the most likely candidate is "At 11:00 the button is pushed to turn the lamp On, at ...
@"fishfry" Nearly all of these text symbols are quite common: ~ ... it is not the case that -> ... implies <-> ... if and only if & ... and v ... or A...
I stated the axioms of identity theory in multiple posts. Not funny, but true. I did not say that it's not. I'll say again: First order logic with ide...
I'm not rejecting anything. I'm saying: (1) What is the proof of C2 and C3 from the premises? (Though we don't need it, if we adopt my rP6.) (2) Inste...
Infinite divisibility doesn't entail a contradiction. Rather, infinitely divisibility along with the other premises entails a contradiction. Moreover,...
An interesting point is that while we can express the indiscernibility of identicals as a first order schema, we can express the identity of indiscern...
We quantify over them in the meta-theory not in the object theory. That is what an axiom schema is. For example (leaving out some technical details he...
I stated explicitly several times that that is what I mean by 'identity theory'. I recall having seen the term used professionally before, and so I ad...
Benacerraf: "A. Aladdin starts at to and performs the super-task in question just as Thomson does. Let t1 be the first inistant after he has completed...
If Benacerraf is not skipping the condition, then where does he recognize it? What essential difference is there between Aladdin/Bernard and Cinderell...
'=' is primitive. But there is more to say. So indeed, let's go back to square one: '=' is primitive in logic (first order logic with equality, aka 'i...
I think those examples and a common informal context are okay. They suggest that, for example, a rock is not a set. My point is that it would only be ...
@"Michael" Next would be to examine whether your inference is correct that the problem shows that time is not infinitely divisible (or that it is not ...
@"Michael" @"fishfry" I haven't yet read all of Benacerraf's paper, but at least where he disscusses Aladdin and Bernard, it seems to me that he's not...
The same set can be specified in two different ways: {the door, the floor, the roof ... the balcony} {x | x is a feature of the house} Okay. In casual...
@"Michael" Two presentations that are equivalent. I would like to know how C2 and C3 are derived in Michael's version. That is rC1 and rC2 in my versi...
I was quite relaxed when I provided the information. The argument shows that the premises entail a contradiction, so at least one of the premises must...
I won't refer you to a source. I'll refer you to this: Definition: .999... = lim(k = 1 to inf) SUM(j = 1 to k) 9/(10^j). Let f(k) = SUM(j = 1 to k) 9/...
I didn't say that a house is not a house. I said a house is not a set. What things separately? Nor can I. That doesn't entail that a house is a set. A...
The adjective 'is potentially infinite' has no mathematical definition that I know of, including in alternative theories. The adjective 'is infinite' ...
Who says anything about probability when merely mentioning that .9... = 1. We prove that .9... = 1, from the definition of the notation '.9...'. '.9.....
By the premises, there is no third state. Indeed, even if not a premise but a definition: Df. 'On' means 'not Off' there is no third state. No, Thomso...
The crank writes, " that the elements of a set may be concrete objects." If the elements cannot be concretes and can't be abstractions, then what can ...
If the attribute is color then there are six orderings based on that attribute: red ball, white ball, blue ball red ball, blue ball, white ball blue b...
I would think of those as aspects of the house, not members of the house. I wouldn't think of a house as being a set. There are sets of aspects of a h...
Questions are not interruptions. And no level is required to ask questions. When someone lies about your posts and incessantly posts disinformation ab...
There's plenty of detailed information and explanation posted in this thread. If you have any questions, or wish to learn more, then it's as simple as...
The incessant crank says, "Tones attempted to hide this behind sophistry by replacing the continuity of the real numbers with the density of the ratio...
The crank's latest posts are again a welter of blatant sophistry. If only one's time were infinite to write out out all that should be said about his ...
The crank says, "The deep stuff gets booted off the main page, being for most, undistinguishable from shit." The crank can't discern irony, even when ...
(1) The completeness theorem is: If a sentence is entailed by a set of premises then the sentence is provable from that set of sentences. Or, equivale...
proof implies truth, but truth does not imply proof. Suppose we have a consistent set of axioms for mathematics (the set theory axioms will do nicely)...
@"Michael": I see now that a few of my previous comments, while not incorrect, were not helpful for understanding the problem. I'm still at provisiona...
@"fishfry": Probably some of these points you already know ; I'm mentioning them just to fill out the picture. If PA here is first order, then PA does...
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