Let me rephrase, since it really wasn't clear, now that I look at it. "I borrowed 3 chickens from my neighbour. Wolf ate them, so I borrowed another 4. Now I owe my neighbour 7 chickens."
While the negative numbers do not exist in nature, their origin is empirical. Those 7 chickens do exist (or existed, until wolf ate 3 of them). The only matter here that makes them negative is the ownership. Negative numbers didn't appear for the sake of themselves, they came to life from subtraction.



I'm not entirely sure if we understand each other on this. No, higher math does not come from empirical observations, it comes from lingering over issues previously thought up, formulated, and proven. I'm talking about that basic fact that their proof relies on validity of proof of each and every law or concept they call upon, down to the axioms. If they are all valid, the only weak point that remains is validity of the axioms.

Now, if we were into discussion about observation and perception defining the truth (or not), I do not dare to go there. I think everything we know about the world is subjective due to our way of perception and experiencing things. Therefore, the real status and behaviour of all there is might be entirely different (or not be at all, according to quantum theory). Question is, how much does it matter to us.

I will look up imaginary numbers as an example of your reasoning and see what's the deal with them, but that will have to wait for tomorrow.

And yes, it's induction. Bad wording on my part, sorry (those words are alike, seriously...).

Even though I haven't seen anything that correlates to such a big number, and I cannot imagine it due to my human limitations, I can induct (hope it's good this time ) subtracting 4 from 9 bazillion would have the same result as subtracting it from 5.
As for zero, the fact that human didn't think up everything right away when he became homo sapiens doesn't mean all his further inventions are not empirical.



There is a distinct difference. Religions claim existence of god cannot be proven and rely on faith. They don't even try. So, do you actually think somebody out there could? Mathematicians do try on the other hand, and do it. I've done some easy proves (and was tought many more, even though I never liked them for purely practical reasons), so based on that I will trust that all the other proves out there were also verified by math community (especially that disproving something previously considered true is an achievement for mathematicians, so they do, at least occasionaly, try).

Preemptively (just in case), let me say I don't want to go into "I'd have to do everything myself" argument.



Elaborate on that, or, if you don't feel like it, point me somewhere online.
I ask for that because physics seems like nothing more than math put to use, at least considering the argument.

Empirical used in here, as I understand, means that something was formulated based on experience gathered from observation.

It will probably end shortly, I for myself will either get convinced or drop it anyway.
Sorry for the derail.

@Verithrax
Your posts appear out of nowhere in the past of the thread!
That's hardly convenient.

Tell the mods to pull me out of mod preview so they show when I actually post them.

Xinemus' post is going to take more time to respond to than I have right now, so you're unlucky target number one.

Math is empirical without being directly observed in every instance.

The recognition of patterns is no less empirical than the observation of patterns, so long as the pattern is of observed things. It is not unempirical to say two pennies weigh less than 784,301,004 pennies, even though the comparison has never been made. It is unempirical to say that the weight is because they participate only mildly in the form of Heavy, there are angels pulling down the balance, or the scale and pennies are strict mental constructs with no real existence (which is where the real hole in empiricism lies, if you have the urge to go the nihilistic route). If two pennies weigh twice as much as one penny and fourteen pennies weigh seven times as much as two pennies and fourteen times as much as one penny, you've got a sufficient basis to talk about the weight of 784,301,004 pennies.

The astrophysics student that most of the people still on this thread know likes to remind me that physics is a more empiric science than biology because of the inclusion of math. (She can usually be goaded to say something less pleasant about theoretical physicists shortly thereafter, but that's not the point.) Math is a quantifying tool and not much else. We have statistics to better quantify bulk research. We have algebra and calculus to describe patterns. Geometry and trigonometry give more information on bodies occupying space and time. I use Xinemus' favorite example, the square root, twice a day to explain to customers why a square yard has nine square feet instead of three--a very empiric reality, regardless of the presence of a 3' x 3' and 1' x 1' square in the house.

I don't know if I've ever said that. I do have this ... problem with life sciences, though that stems from many more things than the fact that they use more arithmetic than mathematics.


This, however, is correct. Most of them are full of crap.

By "borrowed", Kashim means "lent". Lots of Europeans seem to have trouble with those words for some reason. His example makes sense.

How is divide by zero empirical, but multiplication by 0 is not?

how does it empirically work that -X * -y = z but -x + -y = -z

In school, I was always told to just accept this, that is must be this way for other things to work. (with double negatives in english being used to explain how it works. Which doesn't explain addition at all.)

This is not true.

Most religions do claim that G-d can not be proven empirically though.

Quite a difference. There are plenty of ontological, rational, logical, and experiential proofs though.

Part of religion and faith in a god IS faith. That's the MAIN part.

Explaining and proving why the faith is there sort of negates the purpose of faith.

For some religions, not all.

Sometimes faith is just based on faith, but sometimes faith is based on knowledge.

Actually, he means borrowed. People borrow money that banks lend. If he lent three chickens to his neighbor, he doesn't owe his neighbor a thing.

I'd agree with Tajalli. Proving a belief defeats the purpose of faith.

Oh hey, actually I just misread. Ignore!

EDIT: Lots of people seem to have trouble with those words anyway though!

I think the original wording was something along the lines of his neighbor borrowing him four chickens, which is an improper use of the word borrow. The rephrasing is accurate, though.

In Romance languages, there's no distinction between borrowing and lending; the same verb is used for either, and we differentiate based on whether you borrow/lend something from someone or to someone.

On the other hand, we also have two different verbs which in most languages including English are coalesced into "to be", which is a source of endless amusement for us.

Verithrax beat me to it on the 'borrow' and 'lend' issue.
It is exactly the reason why I still happen to confuse the two at times.
Out of curiosity, what is the difference between those two words for 'to be'?



Proof by contradiction is based on empirically true basic logic tautology, ~(~p)<=>p.
As for multiplication by zero, I don't think I need to elaborate on that.




Quite empirical.
I have already provided the simplest example for negative numbers addition being empirical.


Which are the ones that claim otherwise?

I can't think of any mainstream religions that actually do claim that there is an empirical proof for God. This may be a case of weasel wording instead of an actual statement. Words like "most" and "some" are incredibly weaselly when used by themselves, as they provide meaning with no evidence. A non-weaselly way to state that sentence would be "Most religions do claim that God cannot be proven empirically, but there are a few notable exceptions such as Fictitious Religion and Made-Up Religion."

This will be pretty long. I'm way behind and have to catch up!

To start with, you all seem to be saying the same basic thing, using different definitions. If I understand, Xavius & crew are saying that math (logic, etc) is emperical because you can take what is observed and deduce more complicated mathematics from it - ultimately, it is based on observation. Xinemus & crew are saying it is not empirical because it is not directly based on observation. This leads everything back to my original post a few pages ago...

People are again making the mistake of equating their conclusions to the theoretical process of empiricism. Empiricism is balanced, and can be used to reach all sorts of conclusions. Can mathematical concepts eventually be reached given a long line of empirical observations? Yes - in fact, that is how they came up. They started with counting the rocks, then grew more and more theoretical, but all of it was based on observation. Does that mean that the conclusion (i.e. later mathematical innovations, like calculus for example) are automatically factual? No. There could be some mistaken observation, or mixed up mathematical theory that leads to a faulty conclusion. We might someday find out that calculus is completely worthless and wrong, and have to scrap the entire field. Can we say that calculus is absolutely and certainly true? No.

It really doesn't matter whether we call math empirical or not - the base questions are:
1. Can truth be reached using empirical methods?
2. Do empirical methods always lead to truth?
3. Can truth be reached using any other methods?

I think we can all agree with #1. I would say no to #2, and yes to #3. The fact is that both Christians and Atheists can use empirical data to "prove" their point. The same is true of just about anything. As I said before, everyone uses the empirical method, but we tend to forget that all information (empirical or otherwise) passes through a filter of what we "know" (i.e. our beliefs) before we reach a conclusion.

The second issue was about the combination of faith and proof. Because of what I said above (all "proof" is filtered by our beliefs), the existence/nonexistence of God can never be proven. None of the central tenants of any religious belief can ever be absolutely, 100% proven to every person. There is, and there always will be, an aspect of doubt. However, do not fall into the trap of believing that "faith" means just taking something and believing it for no reason. In my understanding, the Hebrew concept of faith (which the three biggest world religious are based on) did not describe just believing something random, but examining several bits of evidences, then taking the leap to believe the conclusion, even if it cannot be absolutely proven. That is, in fact, what Christians, Atheists, YECs, OECs, Evolutionists, Jews, Hindus, Scientologists, and followers of every other belief system truly do.

People (Christians and Atheists seem especially guilty of this) like to pretend that their own system is the only one which can be logically reached, and that all others are based on ignorance and manipulation. If you really want to make progress, get past the arrogance, and move on to actually examining the other options. That means reading books by people who don't agree with you, and examining the hard questions. Having done so (somewhat) I believe that Christianity is the most likely - independent of my personal, spiritual position, I believe it is also the most logical, based on "empirical" and "logical" methods.

You don't understand empiricism, however. The scientific method (A codified form of empiricism) does not deal with proof (That's why I've been careful not to use the word "proof" lately - it's misleading.)

Proof is for mathematics and alcohol. Which is why mathematics is an abstract constructed system, and not a direct representation of reality - although empirically demonstrated as an useful model of reality which has predictive powers, it can't be dealt with the way Xinemus has, as if it's a scientific theory. It's not; it's a model, an abstraction. Abstractions don't have truth values; you can't say math is true. You can, however, say it's useful, which is enough.

In empiricism as it is understood by modern science however, we deal with evidence, and not proofs; nothing is 100% certain, but we, through induction and deductive reasoning, are able to reach conclusions based on evidence. There is clearly no real evidence for the existence of god (Or any variation on the theme, like Santa). Thus, we come to the conclusion that it is more likely than not that there is no god.

Theists, at least the reasonable ones, do the same thing except they take random things as evidence for god - like love, or morality, or consciousness. Ultimately that is simply "I do not understand x; x therefore god" which is an ultimately unconvincing argument for the existence of anything.

Though that may look empirical, I do not believe those examples are. They are creating symbols and using rules which depend on the assumption to prove the point. In other words, dividing by zero breaks the rules of mathmatics and renders the math meaningless, but if one was inclined, they would call this a contradiction in math which proves if falseness., and saying that you can't divide by zero, is just apologetics.

Similarly, when you lose 3 red chips, you do not make $15. Rather, you no longer owe $15. You are not losing, but you are also not gaining.

As for religions, many people look at miracles and say they are empirical proofs. A person who does not believe in miracles, will say they have an explanation, even if they don't know what it is.

But the very concept of a miracle, is the concept of empirical proof for G-d's existence.