Sure it does, now you know any object that has more or less than three sides cannot be a triangle. In fact that simple knowledge has divided the world into triangular and non-triangular objects. With no reference to the physical world we now know something true about it. Reason is a sharp sword, empirical observation is just the hope your senses are correct. Even your senses depend on reason.
That knowledge was was not from the analysis of physical objects, geometry collapses into algebra. No physical object is necessary to make true statements about them.
Close but no cigar. A statement can be true without evidence, but we can only know it is true with evidence. That might be the evidence of reason alone (dubious at best) or empirical evidence (already demonstrated to be effective).
Empirical means perceptible, whether it is ‘really there’ in some other way is irrelevant. So yes, we are experiencing empirical reality by definition. You cannot reason your way out of a platonic Cave, you can only go where you can already perceive light, so there is no other way to tell if reality is real. So much for the value of unaided reason.
If there is so much as one point on which maths and reality do not agree, they are not identical. We do not live in maths, we live in reality and that is what I think knowledge has to be about to be called knowledge. Theoretically, we cannot make discoveries in maths because it is all there in the most basic principles. We can only discover things about reality.
Unforunately, they’ve only been laid to rest by your so-called reasoning.
You are assuming the empirical perception of reality is the correct perception. Senses can be deceived and, hence, are inherently unreliable.
Why does empirical data *ontologically *be used to validate mathematics?
Before I work my way through the other objections, can you tell me how exactly I am wrong?
If you are not happy to accept the value of any empirical evidence at all, there is no common ground for this debate. I could be a robot or a figment of your imagination… And how do you know that senses can be deceived? Either you sense it or reason operating on sense tells you.
It does not, I’m saying that perceptible reality is different from maths
We’ve demonstrated this several times using several examples. Please review our previous posts. If you are so obtuse that you refuse to acknowledge their validity, then it’s a flaw with your comprehension.
Feelings are subjective. However, let’s use your “logic” to good effect. Since I truly feel God is around me, my feelings are experienced. Since experience constitutes empirical evidence then there is empirical evidence for God. Now, please renounce your atheism or admit you are in total error.
It’s irrelevant whether or not you can do everything mathematically. All that is necessary is to show that mathematics can provide a means to knowledge.
Unlike you, I’m not obstinately rejecting the other sides claim. Empirical evidence is valid but not as the only means to gain knowledge.
Regardless, you can gain knowledge of reality using mathematics.
Then you agree with us as to the validity of empiric epistemologies? A statement can be known to be true true using only reason? Though your senses are very dubious, while reason is not.
Nope. One can perceive a sadness, or a truth, or doubt as well as a screwdriver. physical objects are just part of whats percetible. They are not equal terms.
Physicality is entirely relevant because that’s what you actually mean when you say perceptible.
Prove it then.
No clue what you think Plato’s cave helps you.
Doubt is experienced and not empirically, so that’s one for us and we have repeatedly demonstrated that math does not require empirical data to perform.
It doesn’t matter what your belief is,you are claiming that knowledge is dependent on physical experience. As Russell, all the logicians involved, and history have proven, that is always a logical contradiction and therefore false. We keep demonstrating that belief wrong, but you seem to think that it lets you ignore a logical contradiction. Like I said, you are trying to claim that a broken car must work because its the only one you have.
Again, no one has ever made that argument.
Reason tells you. Simply doubt that anything exists, and all you have left is Dubito, it only takes reason to know that all other perceptions (correct use of the word) could be false. It’s nothing but a function of the mind.
It doesn’t matter what analogy you use or how much you try to justify it. If you make knowledge dependent on physical experience, its a logical contradiction as Russell pointed out.
It is indeed necessary to do so, you perceive physical objects don’t you? Just use standard terms. Your refusal to do so is why we think you are playing games.
Except we keep demonstrating that this is a false statement. So not only do you have faith, you have it in something easily disproven.