The lamp is off at 10:00. I push the button at 10:01, turning the lamp on. Is the lamp on or off at 10:02? The correct answer is "on". You don't get t...
Yes, this is where we have C4 and C5: C4. If the button is only ever pushed at 11:00 then the lamp is on at 12:00 C5. If the button is only ever pushe...
That was a complete description. There are no hidden assumptions. P1-P4 are our premises. C1-C3 follow. And then C4-C6 follow. P1 is implicit in Thoms...
It’s not, it’s a valid inference from the premises. As per P4, the lamp starts off. As per P2, pushing the button will turn it on. As per P3, pushing ...
To reject (1) is to claim that the lamp can spontaneously and without cause be on at 12:00. This is impossible. The lamp can only be on at 12:00 if th...
I don't understand your argument, or at least I don't think you understand my argument. Before we even address the infinite divisibility of time, the ...
More like: P1. The lamp being off must always precede it being on. C1. Therefore, the lamp cannot be modelled over time by the infinite sequence off, ...
If you're referring to the principle of explosion, then sure. The point though is that Thomson shows that the lamp can neither be on nor off after hav...
Yes, that's the basic argument I've been making. The lamp being off must always precede it being on. Therefore, the lamp cannot be modelled over time ...
You're putting the cart before the horse. Before we even consider if and when we push the button it is established that the lamp can only ever be on i...
These are our premises before we even consider if and when we push the button: P1. Nothing happens to the lamp except what is caused to happen to it b...
Yes they do. P1-P3 are always true. C1-C3 follow from P1-P4 and explicitly apply at all times >= 10:00. The fact that the conjunction of these premise...
The lamp is either on or off at t1. But if the button is pushed at t1/2, t3/4, t7/8, and so on ad infinitum, then the lamp is neither on nor off at t1...
I can't preempt someone's disagreement. If someone wants to argue that my conclusion is false then they need to tell me which step in the argument the...
You were when you said this: Benacerraf is not right. His stipulation that the lamp is on (or off) at t1 is inconsistent with the premises of the prob...
It's not true, and so he's not right. These are our premises before we even consider if and when we push the button: P1. Nothing happens to the lamp e...
C3 says it's not. If the button is only ever pushed at 23:00, 23:30, 23:45, and so on ad infinitum, then ipso facto the button is not pushed at midnig...
I address it all here. P1 is an implicit premise in Thomson's argument. He is asking "what happens to a lamp if we push its button an infinite number ...
Because in reality a computer cannot perform two consecutive operations within 10-44 seconds. But we don't need to run the code. We can understand the...
Sure. P1. Nothing happens to the lamp except what is caused to happen to it by pushing the button P2. If the lamp is off and the button is pushed then...
This is the assumption we allow for to examine the possibility of supertasks. But it is still the case that the lamp cannot arbitrarily be on (whether...
I understand how infinite sequences and limits work, as did Thomson. That is why I understand that an infinite sequence of button pushes before midnig...
He doesn't push the button at midnight. He only pushes it at 23:00, 23:30, 23:45, and so on. This is an explicit premise of the problem. Also, pushing...
The first sentence is true and is the proof that "supertasks are senseless" (as Thomson says). The second sentence is false. As mentioned several time...
I also revised my post after posting it. The three implicit premises are: 1) The lamp exists at 12:00 and as per the laws of excluded middle and nonco...
The lamp exists at 12:00 and as per the laws of excluded middle and noncontradiction is either on or off. Given the way lamps work, or at least the la...
P2 is what Thomson's argument tries to prove. The lamp must be either on or off at 12:00, but if the button is pushed an infinite number of times betw...
Then let's rephrase P1 as a question. If the first task is performed at 11:00, the second at 11:30, the third at 11:45, and so on, then how many tasks...
Where is the conflation in my argument? I'll set it out more clearly: P1. If (A) the first task is performed at 11:00, the second at 11:30, the third ...
P2 is what Thomson tries to prove by introducing his lamp. Having performed infinitely many tasks entails a contradiction (the lamp must be either on ...
So from this we make the following argument: P1. If the first task is performed at 11:00, the second at 11:30, the third at 11:45, and so on, then inf...
/uploads/resized/files/47/59ajihgqdgw9obiq.png It is taking this hypothetical premise – that there is no smallest unit of space and time – that gives ...
No, he only argued that "talk of super-tasks is senseless." I simply use this as a refutation by contradiction. If spacetime being infinitely divisibl...
If we're talking about an infinite number of tasks being performed then we are talking about a transfinite number of tasks being performed. I'm not ta...
So his paradox shows that the time between each task in a sequence cannot in principle be modelled by a geometric series, e.g. where the first task ta...
No, I think (as did he) that it successfully shows that supertasks are not possible. Yes. If space and/or time being infinitely divisible entails that...
It's not that complicated. Imaginary numbers have a use – even in electrical engineering – but I cannot have an imaginary number of apples in my fridg...
We can assume that they simply exist in their places or we can assume that they are placed just before the runner reaches the next designated distance...
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