What will he say to you? What will you say to him? Will it be sufficient to tell him that you "chose not to" meet with him? — Leontiskos

Right, and is it not also true that if a promise is sincere then one will do what they promised (unless some unforeseen impediment intervenes)? — Leontiskos

Why can't you? — Leontiskos

It doesn't matter whether you put the halving ad infinitum as an antecedent in a conclusion or as a premise - it's logically the same. — TonesInDeepFreeze

But completion is not in your premises. — TonesInDeepFreeze

The definition of a super-task is as you say. But your listed premises don't say anything about completion or ending. — TonesInDeepFreeze

The contradiction is: The lamp is either On or Off T 12:00 and the lamp is neither On nor Off at 12:00.

But that contradiction comes from a set of premises, each of which is not logically true, and dropping any one of the premises blocks deriving the contradiction. It would help if you would at least tell me that you understand that. — TonesInDeepFreeze

It is begging the question merely to declare it is a contradiction that denumerably many tasks can be executed in finite time. — TonesInDeepFreeze

It merely says that metaphysical possibility may be logically possibility and that there's another notion that the article describes ostensively. So is it just the same as logical possibility, and if not what is a proper definition that is not merely ostensive? — TonesInDeepFreeze

I didn't say they end. — TonesInDeepFreeze

Again, the contradiction comes from the conjunction of the premises. — TonesInDeepFreeze

(3) We don't have a satisfactory definition of 'metaphysical possibility' here. — TonesInDeepFreeze

It's not a contradiction in and of itself. — TonesInDeepFreeze

So you think that S can intend that the utterance T will place him under an obligation, and utter T, but not thereby consider themself under an obligation. — Banno

If "...it isn't clear to (you) what obligations are" and you do not think there are such things as obligations, then you are not going to understand what is involved in making a promise. — Banno

I did indeed promise to answer your question, but I am under no obligation to do so".

You don't see this as problematic? — Banno

Then I need provide no answer. — Banno

So this tells me only that you will not be held to your promises. — Banno

OK. You are not a man of your word. — Banno

DO you thinkt hat one can sincerely say "I promise to answer you but I will not answer you".

I'll let you work through it. — Banno

The linked paper sets out an account that hows how sometimes uttering "I promise to do this" is placing oneself under an obligation. — Banno

More than that. "Promises exist" means that there is an illocutionary act that involves placing oneself under an obligation. Such an act occurs in the world, not in some other domain.

Not seeing any ambiguity. — Banno

It is a promise, it is an obligation. — Banno

People make promises. Therefore there are promises. Therefore promises exist. — Banno

What possible reason could there be for not allowing for the same possibility with respect to theories about "transcendental entities"? — Pantagruel

I'm asking you why a narrative that is from the limited human-centric perspective cannot both be inaccurate but also refer to something that in fact exists. Assuming which, yes, the claim that Zeus does not exist (qua "any possible deity") is not logical, that is, is not warranted. — Pantagruel

How could the multiverse be uncountably infinite? — RogueAI

Rather, infinitely divisibility along with the other premises entails a contradiction. — TonesInDeepFreeze

var isLampOn = false

function pushButton()
{
  isLampOn = !isLampOn
}

var i = 120

while (true) {

  wait i *= 0.5
  
  pushButton()

}

echo isLampOn

var i = 120

while (true) { wait i *= 0.5 }

while (true) { }

That makes 0.999999..... = 1 just an illusion created by the notation you have decided to use. It is not a proof. In my opinion. You might have a different idea of what a proof is. — Ludwig V

In my book 0.9 + 0.1 = 1 and 1 - 0.1 = 0.9 and so 0.9 does not equal 1. There's a similar argument for 0.99 and 1 and so on. So far each element of 0.99999....., I have an argument that it does not equal 1. However, I see that your proof involves limits and I know that in that context words change their meanings. So I'm curious. — Ludwig V

P13 Some infinitist claim, however, that at t_b, after performing Thomson’s supertask, the lamp could be in any unknown state, even in an exotic one. But a lamp that can be in an unknown state is not a Thomson’s lamp: the only possible states of a Thomson’s lamp are on and off. No other alternative is possible without arbitrarily violating the formal legitimate definition of Thomson’s lamp. And we presume no formal theory is authorized to violate arbitrarily a formal definition, nor, obviously to change, in the same arbitrary terms, the nature of the world (Principle of invariance). It goes without saying that if that were the case any thing could be expected from that theory, because the case could be applied to any other argument.

P16 At this point some infinitists claim the lamp could be at S_b by reasons unknown. But, once again, that claim violates the definition of the lamp: the state of a Thomson’s lamp changes exclusively by pressing down its button, by clicking its button. So a lamp that changes its state by reasons unknown is not, by definition, a Thomson’s lamp (Principles of Invariance and of Autonomy).

Next would be to examine whether your inference is correct that the problem shows that time is not infinitely divisible — TonesInDeepFreeze

I hope it won't be too long that I'll have time to resume going over your argument with the emendations. — TonesInDeepFreeze

Also, you have a modal operator after a quantifier. — TonesInDeepFreeze

Am I correct that by "we cannot assume pEx(nPx) is true for any logically consistent Px" you mean "For all consistent Px, we have that pEx(nPx) is not logically true"? — TonesInDeepFreeze

When you say "there are no spontaneous, uncaused events," you are ignoring the physically impossible premises of the problem. — fishfry

It would help if you would give one self-contained argument with transparent inferences from start to finish. — TonesInDeepFreeze

I want to get back to looking at this more closely, but in the meantime, do you consider your presentation equivalent with Thomson's statement of the problem? — TonesInDeepFreeze