The notion of an actual infinite makes zero sense if, as per my assumption, actual means what it seems to mean to wit, completed in one sense or another for it flies against the definition of infinity as being necessarily that which can't be completed. — TheMadFool
Maths, set theoretical infinities, kind courtesy of Georg Cantor, is an altogther different story as maths is essentially an axiomatic system, anything goes so long as you don't contradict yourself within one. — TheMadFool
Where does one find a definition of 'actual' that includes 'completed'? — TonesInDeepFreeze
It might go the same way it came (per Mary Tiles). — frank
What do you mean by that? And are you referring to her book 'The Philosophy Of Set Theory'? If so, what in particular do you have in mind from that book? — TonesInDeepFreeze
Page 3, last paragraph. — TonesInDeepFreeze
she's laying out an existing viewpoint. It's not hers. — frank
Read page 4 where she explains the problems that arise from the fact that set theory is unproven — frank
At that point in the book, she is entertaining the idea that talk about infinite sets is not to be taken seriously. Of course, the book is a presentation of various points of view about infinity, so by saying "might" she's making clear that at that point she is not herself saying that talk about infinite numbers is not to be taken seriously. — TonesInDeepFreeze
That sounded better. — frank
by saying "might" she's making clear that at that point she is not herself saying that talk about infinite numbers is not to be taken seriously. — TonesInDeepFreeze
I really thought English wasn't your first language. — frank
's basically what I said when you first took exception: — TonesInDeepFreeze
's basically what I said when you first took exception:
— TonesInDeepFreeze — frank
It's basically what I said when you first took exception: — TonesInDeepFreeze
It might go the same way it came — frank
Read page 4 where she explains the problems that arise from the fact that set theory is unproven: — frank
since she doesn't say anything about "set theory is unproven" or even what one would mean by "set theory is unproven". — TonesInDeepFreeze
Read the whole introduction. — frank
I still think English isn't your first language. You're doing great, though. — frank
I still think English isn't your first language. You're doing great, though. — frank
Your sophomoric sarcasm is misplaced. — TonesInDeepFreeze
You are inference impaired. — TonesInDeepFreeze
What's interesting about this is that whereas it is quite easy to see how mathematics (at its extremes) makes no sense, everything else knowable is EXACTLY the same. It's just more difficult to see. — synthesis
(2) A count is the result of counting. "The count of the books is five."
A number (we're talking about natural numbers in this context) is a count in sense (2). That doesn't preclude that a number is a mathematical object. — TonesInDeepFreeze
We better dispense with that notion. It's nuts. A number is not a book. — TonesInDeepFreeze
So the numeral does not denote a book, but rather it denotes the number that is paired to the book in the bijection (or, in everyday terms, in the pairing off procedure we call 'counting'). — TonesInDeepFreeze
We don't say "''1' denotes 'War And Peace' and '2' denotes 'War And Peace' together with 'Portnoy's Complaint'". That's crazy. — TonesInDeepFreeze
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