This is how you do it: Take a set, S. Then, you find the compliment of S, which just so happens to be the empty set, ∅ (S-S = ∅). Now that you’ve done this, you’re in a great position because the empty set plays a double role. Not only is it the compliment of S, it is also a subset of S, to the extent that every set contains the empty set. Note that the empty set is thus is both ‘inside’ and ‘outside of S, occupying exactly the paradoxical place which we said a rule for distinction would occupy.
Having done this, you can generate the entirety of the number line by asking how many elements belong to the empty set (=1), and then recursively asking how many elements belong to that set and so on ad infinitum. Ta da. You’ve now digitised the continuum. — StreetlightX
Finite spacetimes can expand just as well as infinite ones. There is no need for them to expand into anything and no need for anything to be outside it. Things just get farther apart, is all.
Put differently, the length of the shortest straight-line trip around the universe (analogous to circumnavigating the Earth along the equator or another Great Circle) increases. — andrewk
Mentalizing, rudimentary or not, necessitates at least some awareness of the other. Agree? — Baden
If you really think this, that mentalizing (in whatever form) does not necessitate at least some awareness of the other (in this case, that an animal can mentalize with regard to another animal without being aware of that other animal), I would say that you're simply wrong. Mentalizing necessitates awareness of the other by definition. If you can't accept that, fine, we'll agree to disagree. As for the rest of your post, the broader issue of animal intentionality is worthy of a separate thread. I'll get involved if you want to start one, but we're somewhat off-topic here. — Baden
But the paper you cite here in defense of that claim doesn't defend it. Byrne is dealing with the issue of "mentalizing" i.e. attributing intentionality to others not mere awareness of others, and he admits of rudimentary mentalizing capacities in other animals in any case. — Baden
You can't account for the rich social life of many animals without positing awareness of others. There's also the mirror test, which suggests self-awareness in some higher mammals such as chimpanzees, elephants and maybe even birds. — Baden
The ever wonderful Edge website posted a wonderful little article by the neuroscientist V. S. Ramachandran regarding the neuoscience of self-awareness. In it, Ramachandran argues that evolutionarily, it's probable that we learnt to recognize 'other minds' long before we learned to recognize our own, and that in fact, self-awareness in fact 'piggy-backed' on our ability to recognize others in the first place. In his own words: "I suggest that "other awareness" may have evolved first and then counterintutively, as often happens in evolution, the same ability was exploited to model ones own mind — what one calls self awareness." The full article is a worth a read, and it's only about three or so pages long. — StreetlightX
But an expanding (or shrinking) universe can only be finite, for physicists and lay people alike. — jkop
Right, certain things cause this "red" thing which is unique in the fact that it is a what it's like experience, something that is radically different than any other physical phenomena. If you cannot see how this is so radically different that pit is not like other physical phenomena of nature- even other very unique phenomena — schopenhauer1
It is not the 'local' (here, now) claims of hypotheses and/or theories which are not verifiable in principle; it is global or universal (everywhere, always) claims that are not verifiable. The 'local' claims may be either verified or falsified, but the global claims may only be falsified. — John
As I tried to make clear in 1934 (L.Sc.D., p34 ; and sections 10 and 11), I do not regard methodology as an empirical discipline, to be tested, perhaps, by the facts of the history of science. It is, rather, a philosophical - a metaphysical - discipline, perhaps partly even a normative proposal. It is largely based on metaphysical realism and the logic of the situation: the situation of a scientist probing into the unknown reality behind the appearances, and anxious to learn from mistakes
Again, provide the full context: — Michael
I admit, a conventionalist might say [your emphasis], that the theoretical systems of the natural sciences are not verifiable, but I assert [my emphasis] that they are not falsifiable either. — Popper
So he's accepting the logical possibility that any "falsification" is mistaken, just as the realist might accept the logical possibility of solipsism or skepticism, but it doesn't then follow that he rejects falsification, just as it doesn't then follow that the realist rejects the veracity of our everyday perceptions and beliefs. — Michael
Falsification of a theory is not equivalent to disproof of a theory, and you appear to be conflating the two in you responses to andrewk. — John
My knowledge of Popper's works is much less than that of physics, but nevertheless I think you may be mistaken here. Did you mean 'logically impossible to verify any theory'? If so, then that matches my understanding of Popper, and agrees with what I was saying.
If you really meant 'falsify' then could you please provide a direct quote from Popper where he says this. — andrewk
Only if you're a scientific realist, right? If you're an instrumentalist then two incompatible theories are both valid if they both make successful predictions about their target subject matter. — Michael
Without knowing anything about science, one can be certain from basic logic that one of those statements cannot be correct. — andrewk
Adding my knowledge of physics to the mix, I can point out that it is the first one. — andrewk
Philosophy's greatest (IMHO) ever contribution to science was Popper's notion of Falsifiability. Any scientist that claims to have a perfectly correct theory of reality needs to go back to university and start learning from the beginning again. ALL theories are only ever currently non-falsified hypotheses. — andrewk
For instance, in Newton's time it was postulated that matter must be (is necessarily) attracted to all other matter according to an inverse square law. Why was matter attracted to matter? Just because. Or perhaps a metaphysician/scientist can or has deduced the law of gravity from a more general law (gravity is just an example, not at all my interest here). Then this "law" is itself either deduced from yet a more general "law" or itself has "just because" status. Infinite regress or bust, in other words. Hence the "shallowness if explanation." — Hoo
NO, my point is that they do NOT treat it is unique. They UNDERMINE it to be just another physical process. But that seems unjustified based on how unique it is compared to say, a force particle/wave or a matter particle. — schopenhauer1
My qualia is part of my existence. We can't discuss someone's qualia without talking about a part of the world which is them. It is unique. There no other state of the world is my qualia. — TheWillowOfDarkness
By definition the scientist and robot do not possess equivalent hardware. One produces their quale of blue when given the pill, the other does not. The difference is already within their existence. — TheWillowOfDarkness
You ask what could bring about the difference, but we already know: a human body with the pill produced the scientist's blue quale, while in the case of the robot body, there was no production of quale. — TheWillowOfDarkness
Suppose we concede the point that evolution and the origin of life has a Godel incompleteness problem and let's ask what that would imply about computational theories of evolution, the origin of life, or even the mind.
Chaitin, I believe, offers a good example of the computational view surrounding that issue. — m-theory
I would argue that animals do have subjectivity- they have a "what it's like aspect". It may not be self-awareness though. — schopenhauer1
Quaila belongs by definition. I am my experience, not yours or anyone else's. You can never access my quaila no matter how much you feel or think like me. It's MY Being and cannot be anyone else's. That's what it means to exist as being of experience. — TheWillowOfDarkness