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April 23rd, 2012, 8:07 pm
April 23rd, 2012, 10:46 pm
Pris it’s purely a semantic matter.
What needs to be the case in order from '3+2-5' to be true? Well, it needs to be the case that there exists a number 3 and that there exists a number 2, such that their conjunction is 5. This is the case with any true statement.
April 23rd, 2012, 11:40 pm
(p1) The statement '3+2=5' is true.
April 24th, 2012, 12:01 am
April 24th, 2012, 12:41 am
Okay, so if you don't think mathematical objects really exist, that would imply (by modus tollens) that the statement '3+2=5' is false. But do you really want to concede to that? Mathematics is in-dispensable, since it is the basis of most of our strongest sciences. That would entail an extremely anti-realist view and destroy knowledge all together.
What needs to be the case in order from '3+2-5' to be true? Well, it needs to be the case that there exists a number 3 and that there exists a number 2, such that their conjunction is 5.
April 24th, 2012, 3:14 pm
I repeat, it’s all a matter of semantics--------
April 24th, 2012, 6:21 pm
April 24th, 2012, 10:05 pm
April 26th, 2012, 3:36 pm
Each and every concept is true to some degree.
….while I’ve long wondered whether our concept of numbers might fall flat in the face of infinity. For instance if there are an infinite number of numbers then how can there also be an infinite number of even ones, and odd too, etc, and somehow doesn’t this call into question the legitimacy of infinite universes
April 26th, 2012, 4:19 pm
April 26th, 2012, 5:12 pm
I imagine a race of six-legged humanoids in a distant galaxy who don’t consider us “human” so you still have to attach conditions. Lawsuits have been conducted and won on the basis of such apparent absurdities.
April 26th, 2012, 6:55 pm
Let me reiterate that six-legged Marty who considers himself human but doesn’t consider us so sees the statement as true. So you have to specify at least that what you mean by “human” excludes, say, anything not earthbound. You will have to continue adding conditions until what you’re saying is, “ 'All humans have six legs' is false” provided that which I callI call human has fewer than six legs” which is of course a tautology
April 26th, 2012, 7:54 pm
Pris we simply view the Megillah differently. Yours is black and white with definite outline while mine is fuzzy gray in all diretions
April 27th, 2012, 2:06 pm
2. It does not matter if it is beyond verification. I believe the matter can resolved using a priori reasoning, or at least reasoning to the best conclusion.
(a) The existence of numbers is not impossible.
(b) If the existence of numbers is not impossible, then their existence is either necessary or contingent.
(c) The existence of numbers is not contingent.
(d) Therefore, if the existence of numbers is not impossible, then their existence is necessary.
(e) Therefore, the existence of numbers is necessary (from (a) & (b) & (c)).
Certainly, the existence of physical objects is much more certain since we can perceive them via our senses, but from that it does not follow that supra-sensible objects don't exist.
May 1st, 2012, 4:28 pm
What justification is their for thinking their existence cannot be contingent? My reason for thinking that would be that they are abstract objects, and abstract objects, if they exist, seem to exist necessarily. For how else could an abstract object exist? Contingent things are typically concrete particulars, such as tables, chairs, and persons.