Logic?
Mar 23 2013, 4:14 pm
By: payne  

Mar 25 2013, 2:43 am Mini Moose 2707 Post #21

¯\_(ツ)_/¯

Quote from payne
To put it in another way: why can we trust "logic"?
I might as well ask you why we can trust "doubt"? :trollface.jpg:




Mar 25 2013, 3:21 am jjf28 Post #22

Oh bother...

Apologies in advance as i'm sure i'm repeating things.

Define: Axiom

Because logic is based on axioms or "assumptions", the only recourse the philosopher has if confronted with a logic-skeptic/doubter is to show that they already agree with your axioms (common approach below) - or that the stakes are too high to disagree (ie: they would lose the foundation they're using to attack or question logic in the first place).

Common Approach


Most axioms simply come off as so deafeningly obvious (as if english itself entailed it) that no one goes against them past the point "well it looks good but there's a chance its not true" (a position I hold I might add). Very easy to move forward with a system that you both hold to be "probably true" if it lacks competitors, else, how are we going to do (legal system, computers, long list of stuff we hold near and dear).

In the rare case that someone seriously disagrees and legitimately has a different foundation, the philosopher has no case (unless their foundation just so happens to entail your foundation), you can't argue anything using modern logic unless you and your interlocutor agree on something :D

tldr: we trust logic because it looks good and gives us something to work with

Quote
To put it in another way: why can we trust "logic"? Someone trying to answer this question will have to do something that boils down to "using logic to prove logic", which looks like a fallacy I believe.

Circular Reasoning :wob:



Rs_yes-im4real - Clan Aura - jjf28.net84.net

Reached the top of StarCraft theory crafting 2:12 AM CST, August 2nd, 2014.

Mar 25 2013, 12:30 pm Sand Wraith Post #23

she*

I remember when computing truth tables was hip. And now all of a sudden we have this?!

wow times change.

Vrael and MA sum up what I think of the subject. I'll add on that I find knowledge and human existence to be recursive or fractal. Logic, as far as it goes to preserve and derive truths, is a pretty good tool. Same with math with respect to its own uses. The only problems arise when people take things too far and forget the big (or small) picture.

That's when we end up with one or two companies that have multiple monopolies and some people call it freedom. Or any other extremists, for that matter.




Mar 25 2013, 4:50 pm payne Post #24

:payne:

Quote from jjf28
Because logic is based on axioms or "assumptions", the only recourse the philosopher has if confronted with a logic-skeptic/doubter is to show that they already agree with your axioms (common approach below) - or that the stakes are too high to disagree (ie: they would lose the foundation they're using to attack or question logic in the first place).
I do agree to work with logic. I am merely using what I agree with to show how weird it is that we feel like what we have decided to be true had to be true. Where does the "self-evident" come from?
See it this way: with Logic, I seem to prove that Non-Logic might very well exist and be true. Once that is done, I do not see why using Logic is contradictory.

Quote
1. If A is true, then B is true
2. A is true
3. Therefore B is true

The only thing logic told us is that if #1 and #2 are true, then #3 is true (Modus Ponens)

Do you disagree that if #1 and #2 were true that #3 would be true?
Of course I agree, but that is because I agree with the axiom this whole process uses. In my opinion, there could very well be another set of axioms that would render this reasoning "illogical" (since the "other set of axioms" would be considered to consist as "logic").

Ultimately, based on Oh_Man's Wikipedia-link, I guess I believe that coherentism is to be the most logical way of addressing the 'regress argument' since it allows for relative truths to exist (because I'm having a hard time considering any single thing to be true).

:jaff:



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Mar 29 2013, 3:32 pm jjf28 Post #25

Oh bother...

Quote
I do agree to work with logic. I am merely using what I agree with to show how weird it is that we feel like what we have decided to be true had to be true. Where does the "self-evident" come from?
See it this way: with Logic, I seem to prove that Non-Logic might very well exist and be true. Once that is done, I do not see why using Logic is contradictory.

Can't say I've decided anything "had to be true" I regard philosophers that have reached that conclusion about any a-relative (not relative to another system) statement to have failed.

Quote
I seem to prove that Non-Logic might very well exist and be true

I haven't seen you prove that it's existence is possible, I mean I agree it is but show me the money!

In any case, showing that such a position might be true doesn't serve to undermine logic, in the same way that showing someone that a probable premise might not be true doesn't undermine an argument (not claiming logic to be probable btw, I hold to it via axioms/indefensible statements).

Quote
(because I'm having a hard time considering any single thing to be true)

It's true that you (as an entity) think you are able to question your existence :awesome: Even if reality as we know it was fake and you were plugged into the matrix, you would still hold to the truth of this statement. Even if your existence was merely a project of someone else dream, you would still hold to the statement.

You become far more sane and purposeful when you reach the conclusion that objective truths exist, the fact that objective truths exist can be derived from the law of non-contradiction (as support for the consistency of the logical system, not as proof as that would be circular). In a world where objective truths do not exist, there is no purpose to science, any scientific conclusion would be valid as the truth of the conclusion would exist subjectively. There are no moral truths (I see you've got a head start on this school of thought) and thus no grounds for convicting Kony. And perhaps most importantly, there is no room for inquiry we can't arrive at the truth of something when the truth does not exist but floats in a sea of nothingness.

If the statement "there are no objective truths" is true, then there is at least 1 objective truth, namely, that statement itself. If the statement was false, than an objective truth exists ( <-- one of my favorite moments in philosophy ).

And to repeat myself a little, I have no grounds to show axiomatic statements (namely about objectivism) to be true, my only recourse is to show that you already believe them be true or to give up :kame:

Post has been edited 4 time(s), last time on Mar 29 2013, 5:41 pm by jjf28. Reason: clarity/typos



Rs_yes-im4real - Clan Aura - jjf28.net84.net

Reached the top of StarCraft theory crafting 2:12 AM CST, August 2nd, 2014.

Mar 29 2013, 8:23 pm Vrael Post #26



Quote
In a world where objective truths do not exist, there is no purpose to science, any scientific conclusion would be valid as the truth of the conclusion would exist subjectively.
All scientific conclusions are subject to the rigor undertaken by the experiments which claim to support them. Science would still be purposeful in such a world because it already is entirely based on subjectivity. The only difference is in this world, we say that past a certain point of "subjective" rigor, we call a thing "true" instead of "likely," which wouldn't be possible if "objective" truths did not exist.

I also hate the use of objective and subjective in this context. Objective implies an object, a goal against which to measure an action. In such a sense, all "objective" comparisons are "subject" to the object which defines the standard of comparison. Change the object, and the "objective" comparison changes. "Objective" and "subjective" is just nonsense trying to sound fancy. If you mean "transcendent" or "universal", or "inherent in the structure of the universe" etc, use those terms instead of "objective."



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Mar 31 2013, 10:04 am JaFF Post #27



This may be of relevance to this discussion.



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Apr 29 2013, 10:21 pm Esponeo Post #28



Why are you people still posting here? As usual, I am here to ruin your day. In this case by simply providing the answer.

You may find it in Less Wrong's Meta-ethics sequence, in particular the section on where recursive justification hits bottom.



None.

Apr 30 2013, 9:03 pm Vrael Post #29



Quote from Esponeo
Why are you people still posting here?
Pot and the kettle :P


I read the article, and didn't find it particularly enlightening. There is no answer here:
Quote from name:Where Recursive Justification Hits Bottom
I do think that reflective loops have a meta-character which should enable one to distinguish them, by common sense, from circular logics.
The author asserts that there is a class of circular logic which is simply "ok," and common sense will tell us when a given argument based on circular logic qualifies as having the meta-character of a "reflective loop" which makes it "ok."

It's the same nonsense you find everywhere else. I have nothing against making assumptions if they seem reasonable, but why on earth is this author pretending that some assumptions have some transcendental meta-quality that distinguishes them from others, if the point of the question is that we don't know if that's true or not? Not only is this author using circular reasoning, he's using circular reasoning to justify circular reasoning!



None.

May 1 2013, 6:54 pm Heinermann Post #30

SDE, BWAPI owner, hacker.

Quote
1. If A is true, then B is true
2. A is true
3. Therefore B is true

This looks like:
1. A ⇒ B
2. A
Conclusion. B

We then prove the following: (A ∧ A ⇒ B) ⇒ B

Assume A ∧ A ⇒ B.
1. A ∧ A ⇒ B
2. A (I2, simplification, from 1)
3. A ⇒ B ^ A (E9, commutative law, from 1)
4. A ⇒ B (I2, simplification, from 3)
5. B (I3, modus ponens, from 2 and 4)

∴(A ∧ A ⇒ B) ⇒ B

This is stuff from my theoretical foundations of computer science book (course code 03-60-231 at the University of Windsor). (EDIT: I accidentally swapped the order of the above but the result will still be the same)

Quote
If acts of punishing the innocent were wrong, then God would not have killed all the Egyptian firstborns for the sins of their Pharaoh.
God killed the Egyptian firstborns for the sins of their Pharaoh.
Therefore, punishing the innocent is a righteous act.
Let A = acts of punishing the innocent is a righteous act
Let K = God killed the Egyptian firstborns for the sins of their pharaoh.

We have
1. ~A ⇒ ~K
2. K
Conclusion. A

Prove: (~A ⇒ ~K ∧ K) ⇒ A
Assume ~A ⇒ ~K ∧ K.
1. ~A ⇒ ~K ∧ K
2. ~A ⇒ ~K (I2, simplification, from 1)
3. K ∧ ~A ⇒ ~K (E9, commutative law, from 1)
4. K (I2, simplification, from 3)
5. K ⇒ A (E19, not sure what it's called, from 2)
6. A (I3, modus ponens, from 4 and 5)

∴(~A ⇒ ~K ∧ K) ⇒ A

Again, from my book. I didn't skip any steps and only used the base axioms we were given.
Just thought it would be neat for people to see it mathematically.

EDIT: I think we were allowed to just list them from our individual assumptions, but the first few steps shows that there is no cutting corners.

So the alternative would be,
P1. ~A ⇒ ~K
P2. K
C. A

1. ~A ⇒ ~K (from P1)
2. K (from P2)
3. K ⇒ A (E19, not sure what it's called, from 1)
4. A (I3, modus ponens, from 2 and 3)

∴A

I don't think there can be "loops" using this method.

Post has been edited 3 time(s), last time on May 1 2013, 7:06 pm by Heinermann.




May 1 2013, 8:21 pm Sand Wraith Post #31

she*

@Hercanic:

Consider Russel's Paradox: https://en.wikipedia.org/wiki/Russell%27s_paradox




May 22 2013, 11:17 pm Sacrieur Post #32

Still Napping

What Heinermann posted is called symbolic logic. It's basically a way to show the logical connectives between statements.



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