The Instigator
holla1755
Pro (for)
The Contender
ssadi
Con (against)

A Proposition Is Logically Provable If and Only If It Is True

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Voting Style: Open Point System: 7 Point
Started: 6/9/2017 Category: Philosophy
Updated: 1 year ago Status: Debating Period
Viewed: 774 times Debate No: 102965
Debate Rounds (3)
Comments (8)
Votes (0)

 

holla1755

Pro

My claim and my opening argument are given in the ultimate, logical sense of "provability." A logically provable proposition is a proposition for which it is logically possible that some proof of the proposition exists.

It's self-evident that if a proposition is logically provable, then it is true.

The converse is also true. That is, if a proposition is true, then it is logically provable. The argument for the converse is as follows. Suppose a proposition is true. The true proposition's truth is itself evidence that implies the claim that the proposition is true. The true proposition's exhibition in the real world is further evidence that implies the claim that the proposition is true. Since evidence exists that implies the claim that the proposition is true, the proposition is logically provable. This concludes the argument for the converse.

Thus, since the conditional statement "if a proposition is logically provable, then it is true" and its converse are true: A proposition is logically provable if and only if it is true.
ssadi

Con

I thank Instigator for this debate.

DEFINITIONS

If and only if (iff): "A iff B" means that 1- if A, then B, and 2- if B, then A.
Provable: capable of being proven as true or real.[1]

RESOLUTION

Assume that A and B were as follows:

A: a/the proposition is logically provable, and
B: the/a proposition is true.

Then the resolution is: "A iff B" which means both of the followings:

Res.1: If A, then B.
Res.2: If B, then A.

BOP

BOP is fully on Pro, since the resolution is a positive fact claim.


REBUTTALS

Res.1: If A, then B.

Pro barely asserts that Res.1 is "self-evident".

1. Res.1 is the resolution of this debate (i.e., is under question) and needs arguments. "It's self-evident that" is not an argument.

2. "Provable" doesn't mean "proven". So, logically provable doesn't necessarily mean true.

3. Even "logically proven" doesn't necessarily mean "true". For instance, an inductively (logically) proven proposition is not always true (see [2]). E.g., you can compare the concepts of time and space in Classical and Modern physics.[3]

Res.2: If B, then A.

Pro asserts that if a proposition is supposed to be true (i.e., if B), then its truth is evidence that it is true (i.e., then B proves B) and "since evidence exists ... that the proposition is true (i.e., since B), the proposition is logically provable (i.e., then A)". Shortly, Pro barely asserts that if B, then A, without providing any argument for A.

This is just repeating Res.2 of the resolution, and repeating a resolution in a debate doesn't prove the resolution under question.

Consider the followings against Res.2.

A man (M1) tells another man (M2) something (X) and nobody else hears it. There were no cameras etc. to record the event. M1 immediately dies after that. M2 then claims that X was "Take my car for free". Either M1 said so or didn't.

Whatever the truth is, is it logically provable?

What about what you dreamed last night?

I wish Pro good luck in second round.


REFERENCES

[1] https://goo.gl...
[2] https://goo.gl...
[3] https://goo.gl...
Debate Round No. 1
holla1755

Pro

"It's self-evident that" is an argument. It's an argument that is used to justify some claims as unproven postulates instead of proven theorems. I think it's self-evident that if a proposition logically can be shown to be true by starting off with truth and invoking some truth preserving principals, then the proposition is true. If you start off right and follow all the rules, you will end right. Thus, if a proposition is logically provable, it is true.

You say that "provable" doesn't mean "proven." You're right, in a sense. There is, however, another sense in which "provable" means "proven in theory" or "proven in some possible world."

How you go from "provable doesn't mean proven" to "logically provable doesn't necessarily mean true" in your "2." rebuttal is unclear. If you're equating "proven in the actual world" and "true," I disagree with your equation. There may be, and it seems there are, propositions that are not proven in the actual world but are true.

You say that an inductively proven proposition is not always true. I say there are no inductively proven propositions. A proof is more than a mere suggestion of the truth of a proposition. It is a certain assurance of the truth of a proposition. Proof is a part of deductive reasoning, not inductive reasoning.

I provided two arguments in support of my claim that if a proposition is true, then it's provable. You didn't rebut my second argument. My first argument is not a case of mere reiteration as you seem to think. It is a use of additional concepts and language to support my position.

You seemed to attempt to propose a counterexample to my claim that if a proposition is true, then it's provable. But in the end, you awkwardly left off with a question when you could have instead advanced your own position. Whatever the truth is, it is logically provable. The concept of physical information, https://en.wikipedia.org..., and popular belief in science and evidence support my view.
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Debate Round No. 2
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Debate Round No. 3
8 comments have been posted on this debate. Showing 1 through 8 records.
Posted by canis 1 year ago
canis
A proposition is provable if you have the prove that made it possible fore you to make the proposition.
Posted by MrDelaney 1 year ago
MrDelaney
"If you mean logically valid, then the resolution is wrong.
If you mean syllogistically sound, then the resolution begs the question."

Exactly.
Posted by MagicAintReal 1 year ago
MagicAintReal
Yeah, this most certainly hinges on "logically provable."
If you mean logically valid, then the resolution is wrong.
If you mean syllogistically sound, then the resolution begs the question.
Posted by Selenspire 1 year ago
Selenspire
I'm wondering what you mean by "logically provable". A hypothesis can be supported without turning out to be true. This disproving factor can also prove to be completely unknown, so something we think we know to be true could be false. Take the Evolutionary Theory. Scientifically, it is completely supported (not including science with religious bias like Creationism), but some day, we may come across some undeniable evidence, and it will be disproven. Does that mean it was not proven in the first place, despite no longer being considered true?
Posted by Sonofcharl 1 year ago
Sonofcharl
Your stating the obvious.
There would be no point in accepting this challenge.
Posted by PowerPikachu21 1 year ago
PowerPikachu21
This resolution is provable if and only if it is true. If it is true, then it can be proved. If it isn't true, then it can't be proven.

You would go about proving the resolution by citing other propositions which are indeed true. So if you think about it like that, it's kind of meta.
Posted by MrDelaney 1 year ago
MrDelaney
What is your definition of 'logically provable'?
Posted by MrDelaney 1 year ago
MrDelaney
What is your definition of 'logically provable'?
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