For anyone curious, my Googling says that the trillionth digit of π is 2
@Toadzx
Жыл бұрын
This video feels like it needs a complete list of what the laws of logic are. Like law of non contradiction, and law of identity, ect. Speaking of which I think your last example violates the law of identity. So “existence=green” is NOT logically possible.
@zsoltnagy5654
Жыл бұрын
So it's logically possible, that God doesn't exist, since a non-existing God doesn't contradict or violate any laws of logic.
@ApologeticsSquared
Жыл бұрын
Indeed!
@mikek17
Жыл бұрын
Is it really "generally agreed" that mathematical falsehoods are logically impossible? After all given the definition of logical impossibility in this video, this would mean that all the laws of mathematics are analytic, which is highly questionable. At least, all the attempts I've seen to reduce math to analytic statements rely on certain biconditionals/definitions which may not actually be semantically equivalent to each other (I mean that a good case can be made to the contrary).
@ShouVertica
Жыл бұрын
These videos should really tie into the argumrnt in some way, "logical possibility" is the lowest bar and practically a grammar check for any argument.
@dominiks5068
Жыл бұрын
Are you sure it's generally agreed that mathematical facts are logically necessary? For something to be logically necessary its denial would have to entail a contradiction, as you say... but if mathematics is synthetic (as many think it is), then I don't see how denying 2+2=4 would entail a contradiction
@litigioussociety4249
Жыл бұрын
Mathematics is based on logical axioms. For example, the axiom that a+b=b+a is true in established mathematics. You could have the opposite axiom, but once the axiom is established, then there can't be further determinations that contradict that axiom. To further use the example, in grammar "me and you" and "you and me" are not considered equal due to points of view. "Bob and Doug" and "Doug and Bob" are considered grammatically equal, but not euphonically equal.
@dominiks5068
Жыл бұрын
@@litigioussociety4249 Sure, if we accept certain axioms, then certain truths follow necessarily. That much we agree on! But when we say something is logically necessary, we normally mean that its truth follows just from the meaning of the term + the inference rules of first-order logic (or maybe second-order logic). And it's not at all clear that this is the case for mathematics That's why Frege's theory of mathematics was called Logicism: because it tried to show that mathematical truths follow from analytical truths + FOL alone, which many other theories don't think is possible
@mesplin3
Жыл бұрын
Only God can determine whether two sets are truly equal even if they have the same elements. - A Math Atheist /jk
@Nickesponja
Жыл бұрын
Given how we define 2, +, =, and 4, it follows that 2+2=4. It's an analytic statement. To explain it in more detail, we define 0 as the empty set. We define the successor of a set A as succ(A)=A U {A}. Then we define 1 as succ(0), 2 as succ(1) and so on. The operation + is defined by the rules x+1=succ(x) and succ(x)+y=succ(x+y). As for =, by definition two sets are equal if they have the same elements. Given all of these definitions, it follows necessarily that 2+2=4.
@dominiks5068
Жыл бұрын
@@Nickesponja But whether "the empty set" is the meaning of "2" is the very thing in question! This would mean that everyone who thinks a set-theoretic foundation of mathematics is mistaken (which are like 70% of philosophers) doesn't understand what "I have two children" means
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