What is True?

[Mocca]

What can we be sure of as true? More specifically, which types of statements can be true? (As an example if I wasn't completely clear, mathematical statements can be confirmed as true, such as 1=1.)

 

[TeddyKGB]

Just thinking out loud for a bit...

Something is true if it is validly derivable from axioms.

 

[Edx]

We can never be absolutely sure of anything.

 

[egon101]

Perhaps no one has been truthful enough about what truthfulness is.

~Nietzsche

 

[Mocca]

Well... I'm sure that 1 = 1.

 

[Forest]

Well... I'm sure that 1 = 1.

I believe that too.

But are you sure that 1=1 everywhere, all the time?

 

[Forest]

Just thinking out loud for a bit...

Something is true if it is validly derivable from axioms.

And axioms are true because, why?

 

[Forest]

We can never be absolutely sure of anything.

Are you absolutely sure about that?

 

[MoonlessNight]

And axioms are true because, why?

It doesn't matter if the axioms are true as long as we recognize that the truth we are speaking about is describing the relationships between the axioms.

 

[Forest]

It doesn't matter if the axioms are true as long as we recognize that the truth we are speaking about is describing the relationships between the axioms.

How can you know you are speaking any truth, unless you know the axioms are true?

 

[DailyBlessings]

"What is true?" is a very different question than "What can we be sure of as true?"

 

[MoonlessNight]

How can you know you are speaking any truth, unless you know the axioms are true?

Because we are speaking about what would happen if these axioms were true. Whether the axioms themselves are true or not, the relationships resulting from those axioms are a form of truth because they describe what would happen necessarily given those conditions. Whether this corresponds to any sort of reality or not is, of course, another story, but it is a form of truth.

For instance I can show that if n^2+5n+1 was ever even (for an integer n) then every number of that form bigger than that one would be even as well. The problem? No number of that form is actually even (which can be proven as well). But the relationship that I noted in the first sentence, i.e. that if one number of that form was even than more would have to be even, is true even though it has no real bearing on any actual numbers. It is a similiar situation when one derives relationships from axioms.

 

[TeddyKGB]

I believe that too.

But are you sure that 1=1 everywhere, all the time?

Yes. 1=1 is an exemplar of an axiom, not an observation or a prediction.

 

[Edx]

Are you absolutely sure about that?

Yes, because we arent talking about the universe here we are talking aboiut if its possible to be absolutely sure our understanding of anything is absolutely correct. As long as possibilities remain we can never have absolute knowledge, since for something to be "absolutely" true there can be no other possibilities.

 

[elman]

What can we be sure of as true? More specifically, which types of statements can be true? (As an example if I wasn't completely clear, mathematical statements can be confirmed as true, such as 1=1.)

Helping people in need is a good thing.

 

[Forest]

Yes, because we arent talking about the universe here we are talking aboiut if its possible to be absolutely sure our understanding of anything is absolutely correct. As long as possibilities remain we can never have absolute knowledge, since for something to be "absolutely" true there can be no other possibilities.

If you can "never be absolutely sure of anything", I still don't understand how you can be absolutley sure about that statement.

Because if you are absolutely sure about what you are saying, then you can be absolutely sure about something.

 

[Forest]

Yes. 1=1 is an exemplar of an axiom, not an observation or a prediction.

So you are saying axioms are just accepted as true, by faith.

 

[Edx]

If you can "never be absolutely sure of anything", I still don't understand how you can be absolutley sure about that statement.

Because if you are absolutely sure about what you are saying, then you can be absolutely sure about something.

You are playing word games, like asking if its possible if God could make a rock so heavy he couldnt lift it.

Look its quite simple, really. Even if what we believe is correct, that doesnt mean we can know with absolute certitude that it is correct. How could we? Even hypothetically? As long as there are other possibilities, no matter how improbable, we can never know absolutely if what we think we know is 100% absolutely correct. And since there is no way we cant be sure we're not all just in The Matrix or some kind of Zen Dream where nothing is real, possibilities will always remain.

This is exactly why science calls fields of study "theory".

 

[Edx]

So you are saying axioms are just accepted as true, by faith.

I believe he is saying that we formed mathematics to explain how the universe works. 1=1 and 1+1=2. We formed those rules, we can say absolutely that based on these rules that that is the answer. But that doesnt mean we can say absolutelly that the universe conforms to theser rules, and therefore cannot know that 1=1 all of the time. We can only say it quite probably is. We already know that at the Quantum level very strange things happen, so I like mathematics is likely wrong at some level.

 

[TeddyKGB]

So you are saying axioms are just accepted as true, by faith.

In the mathematical sense, an axiom establishes a system of deduction. It need not be true to be useful.

In the philosophical sense, an axiom is a self-evident truth. That is, its denial or negation entails a contradiction.