Stating beliefs is easy, defining truth is not.
Do you want to give it a try?

But, this is exactly the issue I discuss in the my third post, which is on my blog page, but not here. Rushing to office now, later.

Thanks!

Please feel free to point out any obvious flaw or shortcomings in my arguments. That would help a lot!
If I may ask, you seem to have had a formal education in Philosophy?

Then what is your opinion on my chain of thoughts? Even if they are informal statements. It seems that it's very important to you to have a formal argument.
I plan on writing about paradoxes, and how they relate to human emotion and language next - in the same series of posts, related to this.

I do it because it is fun for me, but it's not entirely clear to me what value they would end up adding for others.

Look at what you're doing here. Is it even possible to formalize the issue you're trying to address?(Note the thread next door.) I'm not sure. And there's another point there: informal reasoning is generally not quite deductive. How do you formalize analogies? Can you formalize salience? There's no harm in trying, but things are just different out here than they are in mathematics. — Srap Tasmaner

Running a little busy, but will think about it a little more and then respond. You raise valid and interesting points.

But, even if formalizing it could be a pain, why is formal reasoning such a pillar in philosophy ( apart form the usual " concise, clear and expandable" argument), and what place does informal reasoning then have in the picture of Philosophy? You or anyone would be doing me a favor by pointing it out to me. Thanks!

I do not think formal reasoning can encompass all of available Philosophy - precision often comes with a cost.

That's what I think you're thinking about. — Wayfarer

Nope, not really. Reality is not what I had in mind.

See, when you compare the reality of numbers to reality of empirical objects, you do so assuming that the truth in statements referring to both of them respectively is the same truth, enabling you to make the comparison. Otherwise it would be apples and oranges right?

A is true, B is true. How does the way we arrive at A compare to the way we arrive at B?
But, if I say A is T ( T for true), and B is T' ( some other form of truth), there is no simple way to make that comparison.

I think I understand, but just to be sure...

Because the result is empirical, it may be possible to disprove the result by empirical means, and then your inference becomes a reductio of one or more of the empirical premises.

Any of that make sense? — Srap Tasmaner

You do refer to the principle behind falsification right?

So as I understand, you are saying that the act of inference from empirical evidence consists of two parts, one is the act of assertion, and the other is the inference from empirical evidence.

The way I understand is that statements or theorems in mathematics are a way of saying the same thing (assertion), but we want to explore the various ways in which we can say the same thing.
Or, to put it even more simply, we want to find out the set of all statements which have the property of truth, given a certain set of assumptions.
Empirical inferences as you say require an additional conformity to an additional set of rules.

But, in all of this process we have always assumed that the truth we obtain from mathematical statements is the same as the truth from empirical inferences. There is a singular notion of truth here, and I wanted to explore ( which is what the ideas in the blog are about), if this is indeed the case - I do not think that such is the case.

It is always a pleasure to read a well thought out argument! Thank you!

Yes of course.
I am not proposing a different theory - things are fine just as is. In fact further down the blog I make the statements that truth needs to be a single truth/false structure to make math so powerful.

But then, the implications seem to be that this is not the same truth which we refer to in normal language.
( Still exploring and thinking on this)

I am not even 100% sure if the empirical truth and the one arrived at from deductive reasoning on axioms is the same truth. How do we establish that? Is the end result being the same enough to establish that? One works on predictions ( You predicted 4 apples will be left), and another is based on deductive reasoning. One goes beyond the physical universe as well, and is true irrespective of the boundaries of space/time. But this is not a question that I have explored yet. In common language it seems to me, that you could have a slightly different truth to statements.

You are committing yourself to an interpretation too quickly I think.

If you had simply answered yes, you would have seen why I asked that question. :)
Anyways, later!

You lose mobility of thought. Truth becomes the unchangeable anchor. Of course, the universe continues to evolve no matter what. — Rich

Do you think this is true?

So you are worried about time?
You also seem to assume there was one ( thing such as truth) in the first place. Some of your sentences seem to be contradicting others.

lose something from what?

Completely missed the point I am afraid.

I thought McEnroe was praising her, since he said that he would rank somewhere like 1200 and she 700, 500 rank above him. People only quote half to grease the matter.

Yes, it makes perfect sense.
Empirical truth indeed seems a little different.
But I think you are spot on regarding mathematical truth - Axioms have a property of truth and it is preserved through deductive reasoning. Yes, my point in the second post is that it is necessary to have the same property assigned to all mathematical statements - else the power in the language of mathematics would not exist.

And thank you for such a kind welcome. I admit I was waiting to be ridiculed as an amateur :)

I think the main distinction between the truth in physical sciences and mathematics is that the truth in physical sciences carry the weight of predictions, which add to their legitimacy, but at the same time those statements are based on more assumptions, one of them being that the pattern they seek to quantify, explain and predict will hold through future data.