@kennethamy,
kennethamy wrote:
guigus wrote:If I know that I will walk 300 steps tomorrow, then I can walk 301 simply to prove myself wrong. However, despite my having actually walked 300 steps tomorrow would have been necessarily possible, it would not have been necessary.
First of all, if you do know that you will walk 3oo steps tomorrow, then it follows that you will walk 300 steps to tomorrow. So that if, tomorrow, you walk 301 steps, you will have shown that you did not know that you would walk 300 steps, and not that you knew it, but that you were wrong. What you would then show is that you did not know it in the first place, but you only believed you knew it.
I don't believe you have never doubted any previous knowledge of yours, then tried to disprove it. But if it pleases you, then you can rewrite my post in the following manner - it will make no difference to me:
If, according to some deterministic theory, I must believe I will walk 300 steps tomorrow, then I can walk 301 simply to prove determinism wrong. After which, despite my having actually walked 300 steps would have been necessarily possible, it would not have been necessary.
kennethamy wrote:Second of all, whatever is possible is necessarily possible. That is a theorem of modal logic. And of course, if some proposition is possible (and therefore) necessarily possible, it does not follow that proposition is necessary.
Sorry, but where did I say that a proposition being necessarily possible resulted in its being necessary? What I said is that if you take the necessary possibility
of an actuality to be
identical to that actuality, then that possibility becomes the
necessity of that same actuality.
kennethamy wrote:For example, it is possible (and therefore necessarily possible) that I will take a walk tomorrow. But it is clear that my taking a walk tomorrow is not a necessary truth.
And who said it was?
kennethamy wrote:But you probably mean (since you are confused about what "necessary" means) only that although I might take a walk tomorrow, I don't have to take a walk tomorrow.
The meaning of what I said would include that, yes, at least in English (it seems it is you that are confused about what I did say and what I did not).
kennethamy wrote:And, of course, unless someone forces me to take a walk tomorrow, that is true.
You mean that
will be true. For now it is is just a possibility, since you have no way of being sure about what will happen.
kennethamy wrote:But that has nothing to do with modal logic, or any other kind of formal logic. It just has to do with how we ordinarily use the terms, "possible" and "necessary".
I wouldn't go that far: it has things to do with modal logic, as also with other kinds of formal logic, despite going beyond all of that.
kennethamy wrote:What is possible might or might not happen, but what is necessary has to happen. So, since I might or might not take a walk, it is possible that I will.
And snow is white.
kennethamy wrote:But since I will not be forced to take a walk, I won't necessarily take a walk.
Will not? How can you be so sure?
kennethamy wrote:But, of course, necessarily I will either take a walk or I will not take a walk. Although neither my taking a walk nor my not taking a walk is necessary.
So that you succeeded once again in changing the subject completely! Now could you please go back to my reasoning and point out where exactly I got mistaken? Here it is (just in case):
1. If you actually exist and your existence becomes impossible, precisely then you cease to actually exist: your actual existence and its necessary possibility are simultaneous.
2. If the possibility of your existence were identical to the actuality of that existence, then it would become the necessity of your existence, rather than its necessary possibility.
3. Hence, the possibility of your existence must be both different from the actuality of that same existence and simultaneous to it.
Finally, for being both different from and simultaneous to your actual existence, your possible existence must exist: its nonexistence would require its being either identical or asynchronous to your actual existence.