Now whether or not the time-index needs to be a specific instant of time, or could be a duration of time, I don't know - I need to see an argument saying that the notion of time-indexing a proposition commits one to specific instances rather than specific durations. — ProcastinationTomorrow
I'm not sure. I want to say "of course an instant in time makes sense as being some specific point in the temporal continuum" - and to prove that these things exist, I might show you a video of some event or another and then press pause and say - what is represented by that frozen frame is a specific instant in time. Having said that, it does not seem to make sense to view the continuum itself as being made up of such point instants, even if they do exist, since no matter how many such instances you have, since they do not last for any amount of time, you are not going to create a duration of time by adding them together (0+0=0). Could there be a way of taking an instant in time not as a thing itself, but rather as a way of thinking of a duration of time?Another thing. What do you make of the idea of an instant of time? Does it makes sense?
I think time is something that simply can't be ignored. It flows whether you acknowledge it or not and it's part of the definition of almost everything. For instance ''prove'' meant ''test'' in the good old days and that's the reason for much confusion over the adage ''the exception proves the rule''.
The law of non-contradiction (LNC) is defined as the impossibility of a proposition being both true and false in the same respect and at the same time.
From the above we can see that an instant/moment of time is meaningless or, at least, leads to unsolvable paradoxes. I suggest therefore that we give up the notion of an instant of time and always consider time to be an interval - a distance, so to speak, between two points of a clock — TheMadFool
I might show you a video of some event or another and then press pause and say - what is represented by that frozen frame is a specific instant in time. — ProcastinationTomorrow
it does not seem to make sense to view the continuum itself as being made up of such point instants, — ProcastinationTomorrow
since they do not last for any amount of time, you are not going to create a duration of time by adding them together (0+0=0). — ProcastinationTomorrow
Could there be a way of taking an instant in time not as a thing itself, but rather as a way of thinking of a duration of time? — ProcastinationTomorrow
As for the requirement of "same time", in previous discussions I've had people on this forum deny this condition as part of the LNC. I, however, think time is crucial to the meaning of the LNC. — TheMadFool
So if you don't need a conception of time in order to do the calculations (except, of course, practically speaking in the sense that it takes time to mentally calculate), whether mathematical or logical, why introduce it? — Mentalusion
I'm not convinced that's the case. Perhaps some of the issue is that the formalized LNC, -(p & -p), doesn't have anything explicit to say about properties, only propositions, and so is more akin to the math expression. — Mentalusion
In the case of the math expression, "2+1=3", I really don't seen any temporality at all. You could read it the way I was proposing, but I think a more natural reading just sees the expression as an identity that holds absolutely and with regard to temporal sequence. I don't see how a things identity with itself necessarily implicates time. — Mentalusion
If you claim is more of a metaphysical one - that time is inescapably implicit in any claim about anything whatsoever - such that we just can't think anything unless we assume time is present, I guess it's true but probably tautological. It would be like a Kantian category: a condition of thought itself. I wouldn't take that to be a proper subject for propositional logic, though. — Mentalusion
I don't see how 2+1=3 is an expression of identity. You have identified three distinct things, "2", "1", and "3". The "+" symbol says that you add the first two things together, "2" and "1". The "=" symbol says that these things added together are by some standard equivalent to the third thing, "3". — Metaphysician Undercover
whatever is implied is relevant — Metaphysician Undercover
If that is how we must view time then the LNC is meaningless because it requires the notion of an instant of time. Nothing happens in an instant/moment/single point of time. — TheMadFool
You haven't really identified 3 distinct things. You've only identified one thing, the number 3, and the fact that "2+1" is identical to it, or just another way of describing it. — Mentalusion
It's similar to Frege's evening star/morning star example, albeit analytical and not empirical in nature. If you don't see how that's an identity statement having learned arithmetic, I'm not sure I can explain it any more clearly. — Mentalusion
It's also implicit in logic that there are people around who can think, but no one believes that particular implication has any place in the formulation a formal logical system. — Mentalusion
That all said, there is a paradox here, because when we get to discussion metaphysic, ontology, etc. the assumption I think most people make is that our reasoning should be logical. In that case, whatever we say on a metaphysical level is going to be constrained by what we think logic requires. However, when we work out what logic requires, we do so with a naïve, inexplicit understanding about the nature of time. So there is a circularity which is what you might be worried about, but I guess most people would just say it's not vicious and be content to live with some degree of fundamental paradoxality, especially given the proven practical benefits and results logic produces being just what it is now. — Mentalusion
This can all be stated even in a world where time is gunky. — Mr Bee
Gunky? — Metaphysician Undercover
It's continuous, as opposed to discrete? "Gunky" seems to imply a mixture of both. — Metaphysician Undercover
From the above we can see that an instant/moment of time is meaningless — TheMadFool
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