Thread: Propositional logic might be flawed.

Definitions:
Objective = exists independent of anyone's mental state
Subjective = does not exist independent of anyone's mental state

Terminology:
MP = Modus Ponens
MPF = MP is flawless
MV = mental verification that MPF

Argument Part 1:
Let's take MP as an example,
1) A
2) A → B
3) ∴ B
To mentally verify that MPF, you need to think very carefully... but to do so, you must use memory.
1) Your memory is fallible
2) Your memory is fallible → your MV may be wrong
3) ∴ Your MV may be wrong


Argument Part 2:
Let's assume that your memory did not fail you... but you still had to execute a process of thought when thinking very carefully.
1) Your thought process is fallible
2) Your thought process is fallible → your MV may be wrong
3) ∴ Your MV may be wrong


Argument Part 3:
Let's assume that your thought process executed correctly.
Still, MP is not necessarily flawless because "your MV" does not equal "MPF".
"Your MV" is a subjective idea.
"MPF" is an objective claim (of fact).
Therefore "your MV" does not equal "MPF".


Argument Part 4:
We cannot yet use "Your MV necessarily implies that MPF" because it carries with it the burden of proof which has not yet been satisfied, congruent to its generalized form "Your subjective idea that an objective claim is a fact necessarily implies that that objective claim is a fact".


Argument Part 5:
Therefore we may never know whether MP has a flaw.
Therefore MP may have a flaw.
Since MP is a part of propositional logic,

Conclusion:
Propositional logic may have a flaw.


Questions:
1) Is the conclusion true by default? If no, why not?2) I've used propositional logic in this argument, so does the conclusion still hold?
3) In my argument, I assumed that the flawlessness property of propositional logic is objective, is that correct? Why or why not?

Originally Posted by RamenNoodles

Propositional logic may have a flaw.

Or, more likely, your premises and application of logic are flawed (to put it kindly).

Originally Posted by Strange

Originally Posted by RamenNoodles

Propositional logic may have a flaw.

Or, more likely, your premises and application of logic are flawed (to put it kindly).

I think that my application of logic is flawed, because I used propositional logic to try and build a proof that propositional logic is itself flawed, which makes the proof flawed.

Also, there's a commonly used "subjective" meaning which slightly varies from my definition, where the introduction of new information from the individual is taken into account. However, I don't think that either meanings of "subjective" undermines Argument Part 4.

Which premises are flawed?
Which instances of application of logic are flawed?

Originally Posted by RamenNoodles

Which premises are flawed?[/COLOR]
Which instances of application of logic are flawed?

Really?

To mentally verify that MPF, you need to think very carefully... but to do so, you must use memory.

This perhaps the most egregious bit of nonsense.

You don’t need to use your memory. It is a set of rules, like arithmetic so you could write down each step. You could even program a computer to do it. But if you are worried that when adding 2 + 3 you will forget that the first number was 2 by the time you get to 3, then you have bigger problems than formal logic.

But even if we accept that humans are incompetent and the computer is full of. IFA, that is only a demonstration that humans are fallible, not a problem with the rules of logic.

The remains arguments are basically the same (just increasingly stupid)

Originally Posted by Strange

But if you are worried that when adding 2 + 3 you will forget that the first number was 2 by the time you get to 3, then you have bigger problems than formal logic.

I'm not exactly worried, just concerned that we can't reasonably be completely certain that when adding 2 + 3 we won't forget that the first number was 2 by the time we get to 3.

Originally Posted by Strange

But even if we accept that humans are incompetent and the computer is full of. IFA, that is only a demonstration that humans are fallible, not a problem with the rules of logic.

What's "IFA"?
If the rules of logic came from something that's capable of being wrong (memory + thought process) then the rules of logic are also capable of being wrong, correct?

The deterministic universe is,I think a model that is no longer followed.

As thinking beings we are a part of said universe and it can be no surprise that our most fundamental assumption (e.g. the rules of logic) are not completely watertight.

We have to get by on probabilities.

Originally Posted by RamenNoodles

I'm not exactly worried, just concerned that we can't reasonably be completely certain that when adding 2 + 3 we won't forget that the first number was 2 by the time we get to 3.

Even if that were a real problem (and it seems pretty silly) it is not a problem with the rules of arithmetic, it is a problem of human fallibility. The fact that an individual is unable to do addition does not mean that the rules if addition are wrong.

What's "IFA"?

That's weird. I think it should have been "full of bugs".

If the rules of logic came from something that's capable of being wrong (memory + thought process) then the rules of logic are also capable of being wrong, correct?

No. Mathematical rules can be proved to be correct and consistent. (By computer, if you are worried about a human proof.)

But you could believe that everything you think you know is wrong because the human mind is fallible. Maybe the sky isn't blue: go outside and check. Come back indoors and you can remember that it is definitely blue. But maybe your memory is wrong.

So go outside and check. Come back indoors and you can remember that it is definitely blue. But maybe your memory is wrong. So go outside and check. Come back indoors and you can remember that it is definitely blue. But maybe your memory is wrong. So go outside and check. Come back indoors and you can remember that it is definitely blue. But maybe your memory is wrong. So go outside and check. Come back indoors and you can remember that it is definitely blue. But maybe your memory is wrong. So go outside and check. Come back indoors and you can remember that it is definitely blue. But maybe your memory is wrong. So go outside and check. Come back indoors and you can remember that it is definitely blue. But maybe your memory is wrong. So go outside and check. Come back indoors and you can remember that it is definitely blue. But maybe your memory is wrong. So ...

Isn't this just badly written Cartesian Epistemology? If you try puzzle logic from very first principles then you cant prove much ("I think there for I am etc") as as your mind may be prisoner to some sort of evil demon or genius convincing you that simple laws of logic that are false happen to be true. Not much new here unless you bucket 400 year old philosophy as new?