proving that the Christian God "couldn't exist" is really just pointing out the universal historic fact that concepts are constantly being updated to keep pace with cultural evolution — Pantagruel
That this reality may be a simulation and “in every way the same” as the “real world” is simply the deus deceptor — Mikie
A final observation. It goes regularly unnoticed that the conclusion of Descartes’ argument for the existence of an external material world leaves significant scepticism in place. Granting the success of the argument, my sensations are caused by an external material world. But for all the argument shows – for all the broader argument of the Meditations shows, up to this point – my mind might be joined to a brain in a vat, rather than a full human body. This isn’t an oversight on Descartes’ part. It’s all he thinks the argument can prove. — SEP
Model theory makes mathematics decisively correspondentist — Tarskian
Model Theory is the part of mathematics which shows how to apply logic to the study of structures in pure mathematics. On the one hand it is the ultimate abstraction; on the other, it has immediate applications to every-day mathematics. The fundamental tenet of Model Theory is that mathematical truth, like all truth, is relative. A statement may be true or false, depending on how and where it is interpreted. This isn’t necessarily due to mathematics itself, but is a consequence of the language that we use to express mathematical ideas. — Fundamentals of Model Theory, William Weiss and Cherie D’Mello
So model theory studies the structures that satisfy some axioms; buy the structures themselves are nothing more than formal systems. A set along with a collection of operations and relations.
I think that resolves your concern. One can study a set along with some operations and relations defined on it, without believing such a set is real or has concrete existence or whatever way you are expressing your concern. — fishfry
There are no sets in the real world in the sense of set theory. Show me the set containing the empty set and the set containing the empty set, which is better known by its more familiar name, 2. — fishfry
Profession corresponds strongly to background, expectation, opportunity and the economy. — Vera Mont
Even the dumbest offspring of CEO's and department store magnates are aimed at university from their gold-plated cradle, through top-flight nursery school through tutors at prep school, and if that doesn't work, their parents can buy a test-stand-in or a department chair — Vera Mont
Surely, if I am the only entity in existence, my memories would go as far back as I want them to go? — Truth Seeker
If a simulation is wholly deterministic, there is no added value to run it in the first place — Benj96
For all variables throughout the simulations play are already known by the creators. — Benj96
No, you obviously don't. A pipe-fitter can have intelligent children. — Vera Mont
My primary desire is to make all organisms forever happy (including the dead ones and the never-born ones) but this is impossible for me to do — Truth Seeker
That's me saying something, not fishfry. — noAxioms
then the ∞-th step is taken after that — noAxioms
I agree with fishfry that there is no step that gives us 1 since by definition, any given step gets us only halfway there — noAxioms
First, if the world is simulated, why don't its 'designers' simply 'pop out' at times and leave us with some trace of their existence? — jasonm
Similarly, why don't we sometimes notice violations of the laws of physics? If it's just a simulation, does it matter if the laws of physics are perfectly consistent? — jasonm
I said no such thing!! If you like, you can think of the limit as being the ∞-th item. — fishfry
There is an ∞-th item, namely the limit of the sequence.
The sequence itself has no last item. But the "augmented sequence," if you call it that, does. We can simply stick the limit at the end. — fishfry
then 1 may be sensibly taken as the ∞-th item, or as I've been calling it, the item at ω — fishfry
If it is indeed accomplishing an infinite amount of steps, is there not a step where the sequence gives us 1?
— Lionino
No. — fishfry
I think trouble ensues when you try to apply abstract math to the physical world — fishfry
It bothers me that I don't quite know who runs the show. — BitconnectCarlos
Well I am not sure if I have persuasive or great reasons or arguments against solipsism but I must say that I nevertheless do harbor a strong belief in the existence of the external world. Do you find solipsism to be persuasive and if so, how would you argue for it? — Max2
Is there a name for the logical fallacy that "P is repugnant, therefore not-P." — fishfry
What are your core beliefs? — Truth Seeker
I have a duty of care to them. I have a duty of care to all living things. I do my best to save and improve all lives, but I can't save and improve all lives despite my best efforts. — Truth Seeker
Sorry, Lionino, that's a good point by Bitconnect. I'm really trying to understand. You've already helped me get the first part, I had wrong. Do you recognize how nevertheless you have misapplied it, and assertively? — ENOAH
He routinely makes a mockery of his own "faith." He made the sign of the cross at an abortion rally a few days ago. He stands for nothing. He is neither mentally not physically fit to hold office yet the Democrats bolster him up while others run the show. — BitconnectCarlos
non sequiturs — 180 Proof
8. I wish I had killed myself when I was a child. — Truth Seeker
I never feel good enough. — Truth Seeker
How do we judge evidence if it's not happening consciously? — RogueAI
If that belief about the evidence does not happen voluntarily, how is it happening involuntarily? — RogueAI
Yet Luther did. — BitconnectCarlos
You say the Church admitted a mistake regarding indulgences. So the Church can be mistaken. So there is a truth about Christianity that exists regardless of whether the Church acknowledges it. — BitconnectCarlos
I still think it sounds like you wish to restrict even the opportunity to admire, enjoy, and be edified by Jesus to the teachings of the Church. — ENOAH
If your bishop approves your interpretation and the Pope sanctions it ex cathedra, fine — it won't happen anyway because whatever you may have thought of has been thought of before and addressed —, otherwise, it has been rejected by a reason — Lionino
The Church has given itself that authority. — ENOAH
Your insistence that all talk of Jesus needs to conform to Church teachings makes no other sense to me. — ENOAH
No. The mathematics is pristine. 1/2 + 1/4 + 1/8 + ... = 1 in the same sense that 1 + 1 = 2. Two names for the same thing. May be used interchangeably. Exactly equal. Denote exactly the same real number. — fishfry
There is no ∞-th item of a series. [...] But 1 is the limit, it's not a member of the sequence. — fishfry
We may not like how this train of thought goes, and we might settle for the more intuitive and less troublesome metaphysics, but the possibility of either remains, especially when human minds have issues wrestling with the infinity concept. — Lionino
How does it know where to go next, and at what speed? I think that's a more interesting puzzle. Where are velocity and momentum "recorded?" How does the arrow know what to do next? — fishfry
How much time elapses from travel to point a to point b and where is the object located during that time lapse?
Does the object leave existence between a and b and if it does, what maintains its identity during that interval? — Hanover
They are not supported to the extent that General Relativity is, but given that quantum mechanics and General Relativity are known to be incompatible, it would seem that at least one of them is false, and my money is on General Relativity being false. — Michael
You are right. — Truth Seeker
If objective knowledge is knowledge without reference to a mind, then it follows that no knowledge could ever be objective. But in turn, it makes no sense to have a dichotomy where one side is empty and the label "subjective" applies equally to everything. — Count Timothy von Icarus
But its state is not defined at 1 — fishfry
so we can't have counted up to infinity because there is no last number — Michael
From this perspective, Achilles actually does complete all of the supertask steps in the limit as the number of steps goes to infinity. One might only doubt whether or not the standard topology of the real numbers provides the appropriate notion of convergence in this supertask.
Max Black (1950) argued that it is nevertheless impossible to complete the Zeno task, since there is no final step in the infinite sequence.
But as Thomson (1954) and Earman and Norton (1996) have pointed out, there is a sense in which this objection equivocates on two different meanings of the word “complete.” On the one hand “complete” can refer to the execution of a final action. This sense of completion does not occur in Zeno’s Dichotomy, since for every step in the task there is another step that happens later. On the other hand, “complete” can refer to carrying out every step in the task, which certainly does occur in Zeno’s Dichotomy.
I'm just trying to take the subtle approach. — fishfry