The Sun is not what we see when we look at the sun. — AmadeusD

Neither set is countable — frank

The natural numbers are also a proper subset of the rationals, but they're the same size. — Srap Tasmaner

But Cantor showed that there is a way to force them through a chute so that you can count them one-at-a-time. It's interesting that it turns out you cannot do this with the real numbers. — Srap Tasmaner

OK. It depends on what you are doing. I was thinking of the point of origin on a graph, but that's not quite the same as counting numbers. — Ludwig V

I think many people believe that if something is referred to, it counts as an object. — Ludwig V

Numerals get their identity from roles in activities, not from reference to entities.
— Banno
You are not wrong. But now we are getting into trouble with the difference between numerals and numbers. I have a feeling, however, that we may need numbers in order to identify correspondences between numeral systems and perhaps even number systems with different bases. — Ludwig V

But don't we also need 0, as the starting-point? — Ludwig V

I don't have a problem about the timeless present in the case of constitutive norms. But in relation to procedures, I do. For the obvious reason, that a procedure takes place in time. — Ludwig V

You'll find that you can't. — frank

I've just been observing the different stances people are taking. — frank

Ok. I don't object to that. I doubt you can do the same thing for ZFC, though. So are you now suspicious that ZFC might be bullshit? — frank

An object in your mind is called a mental object. An object in your hand is a physical object. An abstract object is something that isn't physical, but it's not simply mental either. — frank

This is at the core of the problems with US politics. — Christoffer

• Benacerraf’s identification problem
• Gödel’s incompleteness theorems shows that set theory cannot fully capture all mathematical truths
• Category theory, topology, homotopy type theory don’t naturally live in the set-theoretic universe

There aren't a lot of experts in phil of math — frank

You have the minority view — frank

You're trying to have your cake and eat it too. — frank

There was a lot of strenuous protesting in this thread to the effect that infinity is a thing. Turns out you actually agree with Meta. Numbers aren't things. They're just elements of language games. — frank

So math is just language games, right? — frank

Wow! Being productive. :up: — frank

It is part of the strategy to ensure Trump does not have to leave office. — Questioner

I think I explained it quite clearly here: — Michael

If “X is cold₂” just means “X causes cold₁ sensations in me”, then:

*instruments don’t measure cold, only predict feelings
*disagreements are merely parallel reports
*learning temperature terms requires introspection
*correction becomes impossible except as etiquette

That is not how the language works, and it is not how science or ordinary life proceeds.

That is orthogonal to the earlier dispute. — Banno

If “hot”, “cold”, “painful”, “harmful”, etc. were mere fictions, then safety thresholds, medical advice, engineering tolerances and so on would all lose their point. Science would be answering questions no one had. That John and Jane disagree as to the temperature of the bath is not a fiction; it's something to be explained. This is lost in your account. — Banno

The only way that "1" can refer to an object called "a number", instead of referring to distinct ideas in the minds of individual subjects is platonism. Platonism is the only way that "1" can refer to the same thing (a number, an object) for multiple people. Otherwise "1" refers, for you, to the idea you have in your head, for me, to the idea I have in my head, and so on. This is the way that values such as mathematical values are presumed to be objective rather than being subjective like many other values. It's known as platonism. — Metaphysician Undercover