Here's another way to look at the difference: the Cartesian product of the natural numbers and the natural numbers is different set, certainly, which ...
That's a step in the right direction. You have to switch from a count noun to a mass noun. Water from a fire hose. But even that's not good enough, be...
I had to double-check but I never posted this! A couple times I wrote a post which contained exactly this point. (This post is what was left.) It woul...
Eh. A procedure, as I'm using the term here, accepts some input and yields some output. You show me a natural number, and I can show you another. What...
Before we even get to the question of what a numeral refers to, you face an issue of what makes any given numeral count as a 1 (or as a numeral, or as...
I think the tricky bit is that philosophers hear "1 finger and 2 fingers make 3 fingers because 1 + 2 = 3," or even "1 finger and 2 fingers must make ...
I keep thinking about how we teach basic arithmetic with applications, and it's a very subtle thing. We say, "If I hold up 1 finger, and then 2 more, ...
I was thinking some days ago that, though I'm not sure what the favored way to do this is, if pressed to define the natural numbers I would just const...
One additional thought. We've alluded to the spatial and temporal metaphors we often use talking about mathematics, but another very common metaphor i...
With regard to the number line, I'll say first that the intuitions most of us have, formed in school days, can be a bit misleading, because we are on ...
Because it doesn't mean that. "Next" here implies a relation, and mathematics is the study of the relations between its "objects," which it is happy t...
No one ever says either of those things. You're arguing with someone in your head who knows no more about mathematics than you do. * Zeno's paradox co...
Sunday Morning By Wallace Stevens I Complacencies of the peignoir, and late Coffee and oranges in a sunny chair, And the green freedom of a cockatoo U...
Maybe for you. For me, that's a theorem. Then this is nothing to do with infinite sequences, infinite sets, or infinity. Your position is that you can...
If I recall correctly, he specifically said "habit" rather than "rule", which suggests naturalizing logic, and indeed I think that's where he was head...
This is exactly right, and it is the sort of move I have been trying to hold up as a triumph of human thought. We cannot list them all, but we can giv...
I can put it another way: what you cannot calculate, you must deduce. Infinite sets obviously present a barrier to calculation. So we deduce. Having d...
This is to spectacularly miss the point. Because we can prove what the result would be, we do not have to actually carry out the pairing of every rati...
That was me. Now, of course, it's true there are issues with counterfactual definiteness in quantum mechanics, and "experiments which are not performe...
God forbid you repeat yourself ... The key word in all this seems to be "all". You might as well bold it each time you use it. Now, it's a known fact ...
In other words, the problem is that you'll never finish. Under this view, there are no functions on any infinite set. Not even f(n)=1. No functions on...
Note that to present the point, Ramsey names his philosophers "A" and "B". Indexicals are very interesting. Their analysis is both interesting and imp...
I see. I would say there's a difference between making a claim about "a subset" and a claim about "any subset"; many of us will treat the former as a ...
And is there an element n of N such that n-1 is not a member of N0? This is a perfectly good argument, but it is not the argument you make about N and...
So are you saying there could be a set such that you could label every member of that set starting with 0, but you could not label every member of tha...
You seem to be arguing that N must be bigger smaller than N U {0} because, well, 0 is left out. Is that right? (Doofus.) But try this: instead of thin...
This is yet another thing from the prolific David Lewis, contextualism, the short version of which used to be that we do know things in everyday life ...
Indeed. Apparently we can't. Is that what JTB is for? Take a step back. Is there any prospect for any kind of theory that would pick out all and only ...
I don't think a JTB account is committed to this. You can, and I think this is quite common, simply be a realist (with whatever restriction). That is,...
I don't know what that is. I was just referring to the form. From ~1 you can next derive ~(1 & 2), so now you have a contradiction. I don't remember w...
I'm not sure this is right. If we say, a person S knows that P when P is the case, they believe that P, and their belief that P is "justified," in wha...
That's kinda the right question and kinda the wrong question. The J in JTB is supposed to exclude cases of epistemic luck: the truth of your belief, i...
Doing much better exceeds my ability, I'm afraid. Bayesian inference is certainly well-suited to formalizing some of these issues, but there are compl...
I want to say a little more about this calculation (in which I've corrected a misplaced decimal): \begin{align}P(Survival\ \vert\ Observations) & = \f...
Because non-physical entities do not have spatial locations or orientations. "Odd" was perhaps too polite; it's simply a contradiction. "Perspective",...
This is the sort of thing that bothers me, Sam. (Are the scare quotes around "looking" an acknowledgement of my question about Nancy Rynes looking beh...
And your explanation is to look at what you take to be the motivations of the skeptics in your story. Is that the discussion you want to have? Everyon...
Take a step back and consider what we're talking about here. I don't keep up with this stuff, but Wikipedia seems to believe there is still no evidenc...
You're trying to make an apple pie with strawberries. @"Hanover" gamely pointed out that people can't see without using their eyes, and all of the rep...
I struggled with the Nancy Rynes video. Is she lying? Is she deluded? Is it all true? Listening to her story, these questions don't really find any pu...
Except the video you posted of Nancy Rynes a couple days ago, saying fits none of those criteria. I watched it ? at the maximum allowable speed, but I...
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