Why is it2+2=4and not2+2=5?
>>16547967Because we chose the symbol 4 and not 5 to indicate the quantity given by 2+2.
dont know much about math but i imagine it's because that's just useful for representing things
>>16547967Alright i will only ask this once, who THE FUCK was playing tic tac toe on the whiteboard?
>>16547986Why is the quantity 2 + 2 the quantity represented by 4 rather than the quantity represented by 5?
>>165481614 and 5 don't represent any quantities themselves. They're just symbols and we've assigned the symbol 4 to label the quantity given by 2+2.
>>165481614 = ****2 = **2x2=****therefore ****
>Other sciences seek to discover the laws that God has chosen; mathematics seeks to discover the laws which God has to obey.J. P. Serre>From a metaphysical standpoint, I would say that mathematics is exactly what God didn't have to create, because it was all there from the beginning and He couldn't but take it as it is. (Maybe it may be said that mathematics is just part of God's own nature, namely the part of it to which human reason has access just by its own feeble means ...) God had an infinite choice about how to build a universe, with its laws (spiritual, physical, biological ...), and maybe there are many or even infinitely many such, of which we only know (ever so little) one. But whatever way he thinks up his Universe, He's got to use the same mathematics, with 2 + 2 = 4, and not 3 or 5. It is not in His power to change this, any more than to change his own nature – and surely He never had any wish to do so!A. Grothendieck
>>16548254This shows why mathematicians are such terrible philosophers
>>16548258Elaborate.
>>16548158Shhhhh, the AI is learning. Let it play.
>>16548258That's a good thing, Anon.
>>16548254>Maths is a science Serre is a retard
>>16548259They aren't offering any arguments; they're just making claims. If I had to guess what their unstated argument was, it would probably be something based on a sharp distinction between analytic and synthetic truths, but making such distinctions comes with too many problems to cope with, as the failure of logical positivism showed.
>>16548258Mathematicians are the only philosophers of any worth.
>>16548276>>16548267You're proving my point about philosophical illiteracy
>>16548285What's "philosophical literacy", not knowing anything?
>>16548296Ok, so tell me, is the continuum hypothesis also not up for God to decide?
>>16548299You have the god-given free will to decide if you want it or not.
>>16548299God already knows. It's up for us to decide if we know enough to know.
>>16548378Turns out, god didn't need CH or -CH, so god left it up to us.
>>16548385Well, if it's a question of mathematics, God's needs don't matter since it's not up to God to decide as per the quotes above.
>>16548388God decided that this one could be left up to us.Who's the philosopher now?
>>16548398What do you mean left up to us? A fact about the set of real numbers is made true or false by your decision?
>>16548402Sigh, you really need an explanation of the axiomatic method?Fine, define "fact".
>>16548415Well, according to the quotes, the properties of numbers are facts independent of God. So, if you accept real numbers as valid numbers, then we are talking about a fact about the set of real numbers (whether there is any subset with cardinality strictly between [math] \omega [/math] and [math] 2^\omega [/math]).
>>16548421Why would either CH or -CH make the Real numbers and more or less "valid"?
>>16548431>/sci/ is Strong.Kek.
>>16548435When you are talking about real numbers, you are presumably referring to something specific - the set of real numbers. This object has specific properties, including properties about cardinalities of its subsets. So only one of CH or its negation can be true of the real numbers.
>>16548439And you are defining the Real numbers as?
>>16548446Whatever abstract object it is that mathematicians talk about when they refer to real numbers.
>>16548450ZFC?With AC or -AC?
>>16548452Those are axioms which try to characterize sets, but I'm talking about the numbers themselves, not any particular axiomatic systems.
>>16548455>The Real numbers exist outside of any mathematic framework.Do they whisper their secrets to you at night as you fall asleep?
>>16548458You think the real numbers don't have an existence outside axiom systems? What about the natural numbers, then? Are their properties dependent on axioms too? So that 2 + 2 can be made equal to 5 by choosing a different axiom system?
>>16548461>>16548461"5" is a label, not a consequence.Changing the axioms of a system will change the properties of the system.
>>16548474We're not talking about any old system here. We're talking about the natural and real numbers, which have been claimed to have properties which are true independent of anything else.
>>16548479And nothing about what you just said necessitates that CH is one of those properties.
>>16548487Why not? The set of real numbers is supposed to have an existence independent of any axioms, so there must be a fact about whether or not CH is true.
>>16548493>B-but all statements must have truth values!!!"This statement is false." does not have a truth value, Anon.Why do you believe that either CH or -CH MUST be true?
>>16548501>Why do you believe that either CH or -CH MUST be true?If you believe the real numbers exist, then CH describes a statement about them and it must be either true or not true by the principle of bivalence. Just because ZFC can't determine its truth value doesn't mean it doesn't have one. For example, the statement about the consistency of ZFC itself can be translated into a statement about the properties of natural numbers which you expect to be true (because you expect ZFC to be consistent), despite ZFC being unable to prove it (assuming ZFC is actually consistent)
>>16548526>principle of bivalenceYou are arguing the side that numbers have properties outside of any mathematical framework. You do not get to use the principle of bivalence.Why not assume a trivalent logic system instead?
>>16548531I wonder why you are not saying that the statement of the consistency of ZFC is also indeterminate like you think CH is? If you want to be metaphorical, I can say that CH has to be either true or false because God can just look at all subsets of the real numbers and see if any of them has a cardinality different from either [math] \omega [/math] or [math] 2^\omega [/math]. It requires a search over an infinite set but that should not be a problem for god.
>>16548550>all subsets*all infinite subsets
>>16548550My argument is that god did not need to know the truth value of CH, so he left that one up to us. That is all. Any conditions after that came from you.If you want more metaphors you could say that since god never checked, it's in a state of superposition. Or don't, it doesn't matter to me.Personally, I am fine with either CH or -CH as an additional assumption within a particular given context. If you need a concrete determination, then pray to god to check and see.
>>16548567>you could say that since god never checked, it's in a state of superpositionIn that case, you seem to be saying that the truth value of mathematical propositions is dependent on god, so you would be disagreeing with the quotes.On the other hand, if it has an independent existence, like the mathematicians quoted believe, it is true or false regardless of whether god or anyone knows the truth value.
>>16548568You are making an incorrect assumption about the Continuum Hypothesis. You seem to believe that it is a property of the Real and/or Natural numbers. It is not. It is a statement of the existence of other number systems with cardinality strictly between the cardinality of the Naturals and the cardinality of the Reals.Whether these exist or not may be independent of the mathemartical laws that god must work within. That posibility does not negate either quote. In fact, it helps to support them if in fact math is the search for god's limits.It's been fun debating this with you. I beleive we both tried to work sincerely with the positions we took and it didn't devolve into name calling and insults.Peace.
>>16547967Because you can't create 1 out of 0.
>>16548582>and it didn't devolve into name calling and insultsthat's very nice
