But I still don't think that a set is identical to its elements because a single object cannot be identical to multiple of object. So a set is another object, additional to its elements. — litewave
A collection consisting of a phone located in my house and another phone located in my friend's house would be a concrete object too, although some might resist that because the two phones are separated "too much". A collection consisting of my phone and of another phone in a different universe that is in a different spacetime might be regarded as a concrete object because its elements are located in a spacetime but then again, they are in different spacetimes, so this collection transcends a single spacetime. — litewave
And then there is the general property/universal "phone" (or "phoneness") - that which all particular phones have in common - and I guess this would be regarded as an abstract object by almost anyone because unless we identify it with the set of all phones, it seems to transcend spacetime or be located in spacetime in an especially weird way. — litewave
I'm not sure what you mean by "abstract" or "abstraction" here. Is the phone a concrete or an abstract object? Is it a collection of other objects or not? — litewave
Would that mean that "being in that collection of objects [or individuals, per Banno]" is a shared property? Can an object "wander in," so to speak, and partake of that property? This may not be a question about your definition so much as an expression of uncertainty about "property". — J
Yes. So what, if anything, would we want to say about identifying such a set with some property? I take it you don't want "being in set X" to count as a property -- nor could it, on the OP's proposal. — J
The mainstream view among mathematicians is that sets are abstract objects. You can see them with the mind's eye, but not physical eyes. — frank
A set is a collection of objects. An average person surely knows what a collection is. Not so surely a universal. — litewave
Why doesn't aporia lead to intellectual anarchy? — J
Oh, sorry. I thought that's what you were looking for in set theory. — frank
For thousands of years mathematicians would have said that set theory is illogical. It flies directly in the face of Aristotle's finitism, but it solves problems that are otherwise unsolvable. Don't look for an intuitive basis for set theory down in your noggin. It's not there. — frank
Well, in predicate logic you have individuals that have/satisfy a property/predicate. I propose that the property is the set of these individuals. — litewave
Well, I'm trying to describe the concept of set in some intuitive terms. You may say that the concept of set is extra-logical but I wouldn't be able to make sense of logic without it. Like, why are the conclusions in syllogisms necessarily true if the premises are true?
The set is an object that somehow unifies different objects without negating their different identities. One over many. — litewave
Even the extravagant set that Moliere has mentioned above is something in addition to the pebble and the sentence, and this something is a property that the pebble and the sentence share. It is an unimportant property for which we have no word, and being in that set means having that property. — litewave
Good. I like Sartre as an "in" to this approach to consciousness and I'm not particularly bothered by the critique in this context (also, my relative lack of knowledge of Husserl means I can't effectively argue the point anyway). — Baden
I'm trying to fill out above a context (more to come) that I'll try to loop back into a fuller application to body image disorders (including body dysmorphic disorder and eating disorders). — Baden
Yes. So what, if anything, would we want to say about identifying such a set with some property? I take it you don't want "being in set X" to count as a property -- nor could it, on the OP's proposal. — J
What was the question? — Banno
A set is a single object. — litewave
I am the one fighting to make it okay to use AI — Athena
So, for the sake of clarity, the Boltzmann brain comes in because our experiences and memories are consistent with both our living in the world we think we do and with our being Boltzmann brains that might dissolve at any moment. The evidence we have doesn't determine our embracing one theory over the other. — Count Timothy von Icarus
Actually, given some multiverse formulations, it seems that we are vastly more likely to be Boltzmann-like (there are many similar variants) brains than citizens in a lawful universe. Or, even if we are in a seemingly lawful universe, it would be vastly more likely that we are in one that has just randomly happened to behave lawfully by sheer coincidence for a few billion years, and will turn chaotic in the coming moments. In which case, while the case is underdetermined, we might conclude that our being Boltzmann like is vastly more likely. — Count Timothy von Icarus
Now, if we are hardcore Bayesian brainers, what exactly is the wholly predictive mind supposed to do when available data forces it to conclude that prediction is hopeless? It's in a pickle! — Count Timothy von Icarus
(This flaw in multiverse theories that fail to place any real restrictions on the "multiverse production mechanism" (e.g. Max Tegmark's view that all mathematical objects exist) is, IMHO, completely fatal to attempts to offer up the multiverse as a solution to the Fine Tuning Problem, but that's a whole different can of worms.) — Count Timothy von Icarus
This sounds to me a bit like post hoc rationalization, as if one is going to decide on a theory and then allow their theory to be "a selective pressure on which evidence is relevant to consider."
The difficulty here is that you seem to be redefining "theory" to be something that precedes rather than follows after evidence, and such is a very strange redefinition. For example, on this redefinition someone might say, "I have a theory...," and this statement would be indistinguishable from, "I have a prejudice..." The basic problem is that 'theory' and 'prejudice' do not mean the same thing. We distinguish between reasoning and post hoc rationalization, and yet your definition seems to have made such a distinction impossible. It seems to have made impossible a distinction between "following the evidence where it leads," and, "engaging in selection bias in favor of some a priori theory." — Leontiskos
What's the argument here: "There is no problem with identifying pseudoscience because in these examples scientists came around to calling out the pseudoscience?"
Why exactly will science always tend towards correctly identifying pseudoscience? Will this always happen? What's the mechanism? — Count Timothy von Icarus
The 19th century was rife with pseudoscience, and I think developments in scientific methods and the philosophy of science played a significant role in curbing this. — Count Timothy von Icarus
Call me a luddite ... — 180 Proof
Because it's a forum for people to talk with other people. — Outlander