If I say that Hesperus is Phosphorus, I am saying that they are the same object (heavenly body). If I say that Ringo Starr is Richard Starkey, I am saying that Ringo Starr is the same person as Richard Starkey.I believe that what is attempted with the law of identity is to express an unqualified sense of "same". You seem to think it fails. Why? — Metaphysician Undercover
I suppose you can. But then I can define as a whole anything I like. A spoonful of sugar. A rainbow. Six inches of two-by-four. The distance between my front door and the shop on the corner. What counts as a part is defined in relation to that. But each part is a whole in its own right. The leg of a chair. The branch of a tree. The handle of a door. Half of a penny. It's just a convenient trick of language.The distance between your eyes is a whole. — Fire Ologist
"Grabbed" from the physical world is a completely inappropriate metaphor. Nothing is grabbed. Something was defined. In any case, if the whole thing was "grabbed from the physical world", it follows that both halves of it were "grabbed". If they weren't, nothing was "grabbed".You need to grab that finite whole thing first from the physical world to then posit the concept of half of that whole. The half wasn’t grabbed from the physical world. — Fire Ologist
The simple solution is to recognize the difference between an analysis and a dissection. A dissection physically separates an object into separate parts (and the parts then become wholes in their own right). An analysis has no physical impact on the object at all. One can analyse a distance into metres, centimetres, millimietrs or yards, feet and inches or any other units you like. You can analyse it into any fractions you like. All at the same time. The object doesn't change.The simple solution is simply to say that motion isn’t continuous. Discrete motion at some scale is a metaphysical necessity. — Michael
Continuous motion suffers from the same problem. We can imagine sensors at each successive half way point that when passed turn a lamp on or off. Is the lamp on or off when we finish our run? — Michael
The simple solution is to say that motion isn’t continuous. Discrete motion at some scale is a metaphysical necessity. — Michael
If I say that Hesperus is Phosphorus, I am saying that they are the same object. — Ludwig V
If I say that Ringo Starr is Richard Starkey, I am saying that Ringo Starr is the same person as Richard Starkey. — Ludwig V
The problem is that if motion is continuous and if the sensors are set up as stated — Michael
You are just restating - reimagining - Thompson's Lamp thought experiment, which has nothing to do with continuous motion as such — SophistiCat
and repeating once more your baseless conclusion — SophistiCat
I’m using Thomson’s lamp to show that continuous motion entails contradictions. — Michael
You need to grab that finite whole thing first from the physical world to then posit the concept of half of that whole. The half wasn’t grabbed from the physical world.
— Fire Ologist
"Grabbed" from the physical world is a completely inappropriate metaphor. Nothing is grabbed. Something was defined. In any case, if the whole thing was "grabbed from the physical world", it follows that both halves of it were "grabbed". If they weren't, nothing was "grabbed". — Ludwig V
you haven't demonstrated any contradictions in TL — SophistiCat
nor linked it to continuous motion. — SophistiCat
A supertask is not simply an infinite sequence. — Michael
With a supertask we are given some activity to perform and we assume that it is physically possible to perform this activity at successively halved intervals of time. We are then asked about the causal consequence of having done so. — Michael
We do not get to introduce additional (and nonsensical) premises such as "and then the lamp magically turns into a plate of spaghetti, prior to which the lamp was neither on nor off." — Michael
The lamp must be either on or off after two minutes. — Michael
If the lamp is on after two minutes then it is on only because the button was pushed to turn it on, prior to which the lamp was off. — Michael
If the lamp is off after two minutes then it is off only because the button was pushed to turn it off, prior to which the lamp was on. — Michael
The supertask doesn’t allow for either of these scenarios and so is proven impossible in principle. — Michael
I take the point. I may not have stated it accurately enough, but the crucial thing, it seemed to me, is to realize that the limit is part of the definition from the start - not, as I think you're saying, something that is worked out from the sequence itself. — Ludwig V
My point is that once we've entered the realm of speculative fantasy, where do we stop? — fishfry
Yes, but once you have defined your half, you can treat it as a unit and define a half of a half... and repeat indefinitely. What limits that process?And you can’t posit or define or conceive of half without reference to half of some other defined, conceived thing, and that thing must be a whole unit. — Fire Ologist
That's certainly where are problems are. But you need to state this carefully. For example, there are no infinite natural numbers and while numbers are not physical things like stars, they do apply to physical things. The tricky point is that the idea of infinity is embedded in the number system, not some accidental additional property.Infinity applies to numbers. Numbers aren’t physical things, like stairs. — Fire Ologist
Infinity is certainly not a concept and not a physical entity - I doubt that it should be called an entity at all. I would love to know what things apart from the mind "conceive of the unit".There is no infinity apart from the mind that conceives it. There are things apart from the mind that conceives of the unit. — Fire Ologist
Ostensive definition can only work if you know, or can work out from the context, what kind of thing (category) is being defined. When you gesture at a red car and say this is red, you will misunderstand if you take red to mean a car or a wheel or a heavy object.That's not the case. "Object" is not implied. You are simply saying that whatever it is that the two names refer to, it is one and the same. — Metaphysician Undercover
It's not enough to know that the two names have the same referent. You need to know, in Wittgenstein's phrase, where the referent "is stationed in the language".Again, this is not true. When you say Ringo Starr is Richard Starkey, all you are saying is that these two names have the same referent. It is only upon analysis, if one seeks to determine whether it is true or not, or something like that, that one would determine that the two names both refer to a person. — Metaphysician Undercover
I think that there some rules that apply in fiction (imaginary stories), because the story needs to have plausibility. But I don't know how to work out what they are. Coleridge, I think it was, said that there needs to be a "suspension of disbelief" for any fiction to work. The reader/audience needs to co-operate and not ask awkward questions. But there are limits. There needs to be some realism for the story to be recognizable at all.My point is that once we've entered the realm of speculative fantasy, where do we stop? — fishfry
I don't quite see why x is the last value, nor why you think that defining the set in that way gets round the point that w is not derived from the criterion from which all the other numbers in that set are derived.s has a greatest number in its domain, and the last value for s is x. — TonesInDeepFreeze
Yes, but once you have defined your half, you can treat it as a unit and define a half of a half... and repeat indefinitely — Ludwig V
I'm missing something here. When I step on a step, do I step on the whole step, or just a part of it. When I sit on a chair do I sit on the whole of it. It depends how you interpret the words, that's all.Only unitary whole things can be touched or stepped on, like a step. — Fire Ologist
I don't quite see why x is the last value, nor why you think that defining the set in that way gets round the point that w is not derived from the criterion from which all the other numbers in that set are derived. — Ludwig V
Infinity is certainly not a concept — Ludwig V
We stop at the single issue being discussed: performing some action at arbitrarily small intervals of time. So taking the code here we assume that each line is run in an instant with the exception of the wait i *= 0.5 line which waits for the specified time in seconds. The logic of the code still behaves exactly as we would expect. Thomson is asking us what is output when echo isLampOn runs. — Michael
If your only solution is to insert the line isLampOn = 'a plate of spaghetti' after while (true) { ... } and before echo isLampOn then you are not answering the question as posed. — Michael
If you cannot make sense of the echo isLampOn line without inserting some arbitrary code before it then you must accept that it doesn't make sense for while (true) { ... } to complete. The arbitrary code you are trying to insert is a smokescreen to disguise this impossibility, exactly like your magic turning the lamp into a plate of spaghetti. — Michael
I think that there some rules that apply in fiction (imaginary stories), because the story needs to have plausibility. But I don't know how to work out what they are. Coleridge, I think it was, said that there needs to be a "suspension of disbelief" for any fiction to work. The reader/audience needs to co-operate and not ask awkward questions. But there are limits. There needs to be some realism for the story to be recognizable at all. — Ludwig V
mathematical modelling of movement is infinitely divisible — Heracloitus
But it's not my only solution. I've said (several times) that "Lamp is on" and "Lamp is off" are also valid solutions. — fishfry
The lamp is on only if the button was pushed to turn it on, prior to which the lamp was off. — Michael
Or, if you want to introduce magic, it is on only if magic turned it on, prior to which the lamp was off. — Michael
So if you want to say that the lamp was on after two minutes then you must accept that at some final time prior to two minutes the lamp was (left) off. — Michael
The supertask doesn't allow for this. — Michael
I'm afraid there was a typo in my last post. I posted "Infinity is certainly not a concept", which is rubbish. I meant to post "Infinity is certainly a concept". Apologies.Meanwhile, in other fields of study, such as philosophy, writers do speak of a concept of infinity. I am not opining here whether, despite philosophical discussions of infinity, infinity is or is not a legitimate concept. — TonesInDeepFreeze
Quite so.If, as suggested, the thought experiment is a kind of fiction, then we see the fiction we're told doesn't mention anything a last moment in the sequence of moments, so the fiction does not disallow us from extending to another fiction in which there is a last moment and such that the value of the action at that last moment is whatever x we want it to be. That is, at all the moments mentioned in the fiction, the lamp is on or it's off. That doesn't preclude another fiction in which there is a last moment in which any number of things can be the case: (1) The lamp is on, (2) The lamp is off, (3) The lamp explodes into bits and is off, or (4) The lamp expands to the size of the sun and is on, or (5) the light transforms into a pepperoni pizza. — TonesInDeepFreeze
I'm not at all clear how the ordinary logic of cause and effect would apply in the context of hypothetical physical laws. But we are clearly not dealing with the ordinary physical world, and that leaves us free to imagine anything at all.In our hypothetical scenario with hypothetical physical laws we are still dealing with the ordinary logic of cause and effect. — Michael
The first sentence is fine. I don't get the second sentence. You seem to be saying that the paradox is real. But mixing up actual stairs with models of stairs just produces a confusion, so the paradox is just an illusion - in my opinion.Modeling is not physical, so the models built with infinity will never pose a problem when descending stairs. There is no paradox because the paradox seeks to mix actual stairs with modeling. — Fire Ologist
Yes, I realized that and was hoping to produce a formulation that would allow a more constructive discussion.You've solved my problem. I need the willing suspension of disbelief to converse with Michael. Indeed, that's the question I asked him. — fishfry
I don't know about Bergson. I think it is clearer to distinguish between "physical division (separation)" and "mathematical division (analysis)".Sounds Bergsonian. Actual movement is indivisible but the mathematical modelling of movement is infinitely divisible. — Heracloitus
There are two cases in play at the moment - "0, 1, 0, 1, ..." and "1/2, 1/4, 1/8, 1/16.." Comments switch between them without always being clear. You are, however, quite right that the first sequence doesn't have a limit and the second one has what we could call a natural limit.I don't recall how we got started on this, but the lamp sequence doesn't have a limit so the terminal state has no natural answer. — fishfry
I'm not at all clear how the ordinary logic of cause and effect would apply in the context of hypothetical physical laws. But we are clearly not dealing with the ordinary physical world, and that leaves us free to imagine anything at all. — Ludwig V
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