Can We Prove Anything?

[GrowingSmaller]

Still we have confirmation bias and motivated reasoning, motivated perception etc...

For example, is the sky cloudy today? (were you more aware of that, or philosohy until I posed the question?)

Some psychologists restrict the term confirmation bias to selective collection of evidence that supports what one already believes while ignoring or rejecting evidence that supports a different conclusion. Other psychologists apply the term more broadly to the tendency to preserve one's existing beliefs when searching for evidence, interpreting it, or recalling it from memory - Wikipedia.

 

[zippy2006]

No, we always need to start from axioms.

This is a common modern sentiment. Underlying it are two assumptions that classical philosophy would find overtly strange:

1. A proof or demonstration by definition starts with axioms.
2. Axioms are ungrounded and in some sense arbitrary or at least merely stipulations common to a community or race.

Now "axiom" does have that flavor, but "first principle" or "self-evident truth" does not. In any case, saying that nothing can ultimately be proven because axioms cannot be arrived at syllogistically ignores a great deal of philosophy and epistemology. Syllogistic reasoning has traditionally only been understood to be a single part of the reasoning capacities of the human being.

 

[quatona]

This is a common modern sentiment. Underlying it are two assumptions that classical philosophy would find overtly strange:

1. A proof or demonstration by definition starts with axioms.
2. Axioms are ungrounded and in some sense arbitrary or at least merely stipulations common to a community or race.

Now "axiom" does have that flavor, but "first principle" or "self-evident truth" does not. In any case, saying that nothing can ultimately be proven because axioms cannot be arrived at syllogistically ignores a great deal of philosophy and epistemology. Syllogistic reasoning has traditionally only been understood to be a single part of the reasoning capacities of the human being.

Hmm. I didn´t mean to use "axiom" in the way you defined it (with that touch of arbitrariness to it). I meant to use it as sort of "inescapable premise". These premises can not be "proven" (and from within the frame of reference they are used in they needn´t be "proven", I may add.).
So it seems to me that you and I do not really disagree (beyond possible disagreements on usage of certain words).

 

[Ken-1122]

Can We Prove Anything in some kind of ultimate sense?

I think its not possible in math, as demonstrated by Godel, the overall system being either inconsistent or incomplete. So proofs are kind of conditional. (?) But perhaps his proof about formal systems hits 'rock bottom'. (?) Anyway.....

Is it possible in any other realm?

Yes I prove things all the time.

Ken

 

[durangodawood]

Yes I prove things all the time.

Ken

For example.....?

 

[Ken-1122]

For example.....?

Specific mathematical equations, (base 10) actions that have taken place, personal preferences, and the list goes on.

Ken

 

[durangodawood]

Specific mathematical equations, (base 10) actions that have taken place, personal preferences, and the list goes on.

Ken

Yeah, we talked about math already.
Go ahead. Prove a personal preference.

 

[Ken-1122]

Yeah, we talked about math already.
Go ahead. Prove a personal preference.

Things I can prove
*1+1=2 (Base 10)
*I stand over 5 feet tall
*I prefer the taste of sweet over bitter

Need I go on?

Ken

 

[durangodawood]

Things I can prove
*1+1=2 (Base 10)
*I stand over 5 feet tall
*I prefer the taste of sweet over bitter

Need I go on?

Ken

None of those can be proven without resting on certain unprovable assumptions.

 

[Ken-1122]

None of those can be proven without resting on certain unprovable assumptions.

Care to list some of these "unprovable assumptions" that you speak of?

Ken

 

[durangodawood]

Care to list some of these "unprovable assumptions" that you speak of?

Ken

There's the old standby brain-in-a-vat. Maybe you dont stand anything tall.

 

[Ken-1122]

There's the old standby brain-in-a-vat. Maybe you dont stand anything tall.

Brain in a vat? Stand anything tall? I'm afraid I don't speak gibberish; care to repeat that in English?

Ken

 

[FrumiousBandersnatch]

...However, it does mean that theories can be proven wrong.
When such evidence is encountered that refutes a theory or hypothesis, you have successfully "proved it to be wrong".

...But you can NEVER be certain that the next black person you examine won't have blue eyes.

However, it would take only one example of a black person with blue eyes to refute the idea.
At which point it would be proven absolutely that the hypothesis is incorrect.

Nice explanation.

Yes, it's true in principle; but in practice, even falsification isn't absolutely certain; falsification is far more effective and reliable than verification, but, like any human endeavour is fallible itself. Multiple falsifications of an hypothesis via independent means or methods will get you as close to absolute certainty as makes no practical difference, but you can never be absolutely certain. I'm absolutely certain of that

 

[FrumiousBandersnatch]

Brain in a vat? Stand anything tall? I'm afraid I don't speak gibberish; care to repeat that in English?

'Brain in a vat' is solipsism lite - the idea is that the information your senses tell you could be entirely fake, and, in true Hammer Horror or Twilight Zone style, you're just a brain floating in a jar, being fed convincing sensory information by the stimulation of your nerves.

I suppose the modern equivalent would be being in the Matrix.

If you were just a brain in a jar, you wouldn't have a body to measure, so you wouldn't be any measure of tall (you wouldn't stand anything tall).

 

[durangodawood]

Thank you Mr Bsnatch, for doing the work for me.

 

[Chriliman]

'Brain in a vat' is solipsism lite - the idea is that the information your senses tell you could be entirely fake, and, in true Hammer Horror or Twilight Zone style, you're just a brain floating in a jar, being fed convincing sensory information by the stimulation of your nerves.

I suppose the modern equivalent would be being in the Matrix.

If you were just a brain in a jar, you wouldn't have a body to measure, so you wouldn't be any measure of tall (you wouldn't stand anything tall).

Lets assume for a second that the truth is that we're all brains in vats. How could this truth be proven true?

If it were proven true, wouldn't the next question be "why are we all brains in vats?" Implying a higher more complex reason for why we're all brains in vats. Which would then show that the fact that we're all brains in vats is actually not the absolute truth(it would be a fact) because it raises more questions and implies an even more meaningful truth that beckons to be understood.

 

[durangodawood]

Lets assume for a second that the truth is that we're all brains in vats. How could this truth be proven true?

If it were proven true, wouldn't the next question be "why are we all brains in vats?" Implying a higher more complex reason for why we're all brains in vats. Which would then show that the fact that we're all brains in vats is actually not the absolute truth(it would be a fact) because it raises more questions and implies an even more meaningful truth that beckons to be understood.

It cant be proven true. And no one said it could.

 

[Chriliman]

It cant be proven true. And no one said it could.

It's a hypothetical.

I'm curious as to how you're so certain that this truth can't be proven true? Was it proven false to you? This is the only explanation for your apparent certainty.

 

[DogmaHunter]

Nice explanation.

Yes, it's true in principle; but in practice, even falsification isn't absolutely certain; falsification is far more effective and reliable than verification, but, like any human endeavour is fallible itself. Multiple falsifications of an hypothesis via independent means or methods will get you as close to absolute certainty as makes no practical difference, but you can never be absolutely certain. I'm absolutely certain of that

I can not rationally argue against this.
I have to concede. You are correct.

Perhaps I'll rephrase and say that such falsification is as close to "certain" as it can rationally get?

 

[durangodawood]

It's a hypothetical.

I'm curious as to how you're so certain that this truth can't be proven true? Was it proven false to you? This is the only explanation for your apparent certainty.

Yes. Its a hypothetical situation that destroys any certainty of sensory input.