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Anything not existing would not have patterns, pieces or interwoven parts, and would not have structure. Thus the world exists.
Kevin Thomson
I wonder from what evidence you came to that conclusion. You could not have examined many things that do not exist, I think.
Here's an interesting thought... What can we actually logically know with absolute certainty? With no doubt whatsoever, that those things are correct... One thing at least is that you, if you are reading this and thinking about it and experiencing it, you exist. Your Self. You exist, there can be no doubt about that. I would also argue that you can be a hundred percent certain about mathematics. 1 + 1 can't be anything other than 2, when you picture it in your mind. I know some people will disagree on the math part, I've never understood how though... Anyone care to explain?
I agree with all of that, and logical tautologies with absolute certainty.
Maybe someday I will understand the nature of objective reality with absolute certainty. The Holographic Paradigm adds a nice twist here, but its alot to swallow.
Neil
People make mistakes in math. If I add up a long column of figures manually, I am pretty sure to make a mistake.
Of course it is not absolutely certain that a person will not make a mistake in adding a long list of numbers, but it is absolutely certain that if they add the numbers correctly they will arrive at the right answer, and that answer will absolutely always be the same if the numbers are added correctly.
It is absolutely certain that all squares have four sides. If I ask someone to draw me a square, and they draw a triangle instead, does this mean that its not an absolute certainty that all squares have four sides because human error is a factor? Rubbish!
Neil
Of course if they add the numbers correctly then their answer will be correct. That is a tautology. And it is absolutely certain that all squares have four sides, since, again, that is a tautology. Tautologies are just sentences that are true by definition.
I don't think anyone is disputing that.
I think we are all agreed that mathematical propositions are necessarily, and therefore certainly, true. But I wonder whether all necessarily true propositions are true by definition. Take triangles, for example. The simple definition of a triangle is a three-sided figure with straight sides. The fact that its angles add up to 180? is necessarily true, but that is not part of its original definition; it is a consequence of the definition. Similarly, the fact that a certain very large number is prime (if it is) cannot be part of that number's definition if it is not yet known whether it is prime.
I believe some philosophers divide necessarily true statements into two categories:
(a) true de dicto (by definition), and
(b) true de re (as a matter of fact).
An example of (a) would be: "All triangles are triangles" or "All triangles are three-sided figures". An example of (b) would be: "All triangles have angles adding up to 180?".
Is this a useful distinction?
I think we are all agreed that mathematical propositions are necessarily, and therefore certainly, true. But I wonder whether all necessarily true propositions are true by definition. Take triangles, for example. The simple definition of a triangle is a three-sided figure with straight sides. The fact that its angles add up to 180? is necessarily true, but that is not part of its original definition; it is a consequence of the definition. Similarly, the fact that a certain very large number is prime (if it is) cannot be part of that number's definition if it is not yet known whether it is prime.
I believe some philosophers divide necessarily true statements into two categories:
(a) true de dicto (by definition), and
(b) true de re (as a matter of fact).
An example of (a) would be: "All triangles are triangles" or "All triangles are three-sided figures". An example of (b) would be: "All triangles have angles adding up to 180?".
Is this a useful distinction?
