## What's wrong with this argument?

• 1k
P1: The application of logic requires premises
P2: Any conclusion the application of logic leads to is true if the premises are true
P3: There is no way for a premise to be determined true or false except relative to another premise
(ex: in order to refute the premise "all humans are green" one must accept the premise "visual perception is more reliable than this idiot" and the premise "I don't see green humans")
P4: A premise cannot determine it's own truth value (I expect people to disagree and I'm waiting to see how)
P5: There is an infinite number of potential premises that can be used in an argument
P6: Consequently there is an infinite number of potential premises that can be used to determine the truth value of a premise
C: Every premise is true if the right premises are used to determine it's truth value
C: Every conclusion is valid if the right premises are used to determine it's truth value

What's wrong with this argument? If it is true then any and all values are destroyed (since they can be reinterpreted as vices) and there is no such thing as certainty. Notice that in disproving this argument you only prove it. The only way to disprove this argument is to do what P3 is saying which is to use different premises to determine the truth value of this argument's premises. It's a critique of the method of philosophy itself
• 8.7k
The only way to disprove this argument is to do what P3 is saying which is to use different premises to determine the truth value of this argument's premises.

Yeah, P3 is fallacious.
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• 8.7k
how so?

By utilizing different logics you can refute a premise.
• 1k
this only restates the problem. Now there is an infinite number of logics to determine the truth value of an infinite number of premises. You renamed "different premises" to "different logics". What prevents me from using absurdist logic?
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You renamed "different premises" to "different logics".

Yes, but their truth value isn't the same across the scope of logic. As an example: contextually, there be an action that is morally wrong but contextually right?
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define: different logics. As far as I know what makes different logics is a different set of starting premises. Also this still doesn't address which logic I should use. The context example is great. I now don't know whether or not I should do what's morally right or what's contextually right. And I can't know by referring to either
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Have at this thread if you care to take 5 minutes to read it.
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the thread is a poll between 3 beliefs about logics. That still does not tell me which belief about logics to pick. In fact it admits to multiple possible answers. You're pushing the problem further and further back but ultimately, there is always one premise/logic/belief about logic that must be accepted without justification. Oh and I edited my last comment
• 8.7k
The context example is great. I now don't know whether or not I should do what's morally right or what's contextually right. And I can't know by referring to either

You can know based on differing logics that would dictate what to do. Ultimately it's a matter of preference when picking what logic to use, there really isn't one definitive logic that can be used or meta-logic. Well, that's not entirely true given that something in all possible worlds can be found to be the most utilitarian preference. But, that's kinda off topic, so I digress.
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Ultimately it's a matter of preference

That's what the argument intends to show
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That's what the argument intends to show

Well, I'm glad that it's a matter of preference; but, I hope this doesn't lead us down the road of nihilistic relativism.
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OMG
I swear. This post was originally titled "on nihilistic relativism" but I changed it. Nihilistic relativism IS the conclusion here unless you're willing to accept arbitrary premises in which case you're still a nihilisitic relativist because you are practising P3. The method of philosophy itself admits of nihilisitic relativism unless you can somehow refute P3 without relying on another premise. In other words you'd have to find a premise that can prove itself (which violates P4). I have failed at doing this over and over again and all of my post were focused on finding such a premise.
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Nihilistic relativism IS the conclusion here unless you're willing to accept arbitrary premises in which case you're still a nihilisitic relativist because you are practising P3.

Well, I'm glad we're on the same page then. I just don't agree with P4 either due to there being things such as synthetic a priori judgments or brute facts to borrow from the Principle of Sufficient Reason. The world seems to operate on firmly based laws that dictate how it is going to behave. My gripe with nihilism is that it is self-defeating.
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I just don't agree with P4 either due to there being things such as synthetic a priori judgments or brute facts to borrow from the Principle of Sufficient Reason

You just agreed with P4 and P3 in that sentence. You have to accept the principle of sufficient reason as a premise in order to show that synthetic apriori judgments exist. If you do not accept the principle of sufficient reason, you'll have to accept the existence of apriori judgments "as preference". Synthetic apriori judgments cannot justify themselves without appealing to the Principle of Sufficient Reason. I'm not saying I don't believe in the principle of sufficient reason, I'm just pointing out it is another one of those "pivots" as I call them. A pivot is a belief that is accepted with no proof or "out of preference". It is like the premise: If A=B and B=C then A=C. No one can prove this but we accept it. The main point of this post is to try to find a COMPLETELY self-justifying belief which means it does not rely on a pivot. I've failed so far. Nihilistic relativism is simply the recognition that "every belief relies on a pivot". This, however, is a pivot of its own and thus unreliable. Maybe this is what you mean by nihilism being self-defeating? But I can't find a more believable pivot anywhere. It is recognized everywhere, even in math, that all of our systems of knowledge are ultimately built on these pivots. Defending a pivot is futile and so I'm trying to find a premise from which we can begin to reason that is not a pivot (that is completely undoubtable and must be accepted by everyone)

My gripe with nihilism is that it is self-defeating.

How so?
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Maybe this is what you mean by nihilism being self-defeating?

Yes, I think so. Though, I haven't gone through the logic of it all, it seems to me that nihilism is self-defeating because it presupposes no real alternative to its own logic. It's hermetically sealed and cannot be doubted further.

I have a strange affinity towards solipsism, in that it cannot be logically refuted, yet it's nonsensical. Does that make better sense? Nihilism in my mind falls into the same category.
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Defending a pivot is futile and so I'm trying to find a premise from which we can begin to reason that is not a pivot (that is completely undoubtable and must be accepted by everyone)

Well, yes, we can pivot away; but, you can't doubt the fact that you're doubting, can you?
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hold my beer. In order to go from:
P1: I am doubting
To:
C: I am doubting
I have to accept the premise:
A=A (law of identity)
There is no reason to accept the law of identity (I just happen to irl) aka it is a pivot
Therefore I may or may not not be doubting by doubting

But other than that, "I am doubting" is not very useful even if I don't recognize it as a pivot. I can't get anywhere from "I am doubting" because I can't even go on to say "Therefore I am" because that would require I accept the premise "A being must exist to doubt". While I do accept this premise irl (I can't conceive of it being any other way) that does not validate it.
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it seems to me that nihilism is self-defeating because it presupposes no real alternative to its own logic

While not really nihilism, check out the pyrenean skeptic school. Ask a pyrenean skeptic "Is knowledge possible" and they'll say "I don't know". That how skeptical they are (this is also me btw, I accept pivots like a normal person but I don't think they are permanent or irreplaceable ergo nihilistic)
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Yeah, I'm interested in what others think, given that we fleshed out all the nuances and details of your argument. I'm somewhat at a loss for words given that your logic is airtight and hermetically sealed. In the majority of cases, hermetically sealed arguments are of the religious and metaphysical type. Yours might differ.
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P2: Any conclusion the application of logic leads to is true if the premises are true

We tend to state P2 in reference to deductive logic, but not all logic is deductive. Deductive logic itself, or at least our epistemic and empirical access to it, is derived from repeated experience of consistent relationships (an inductive affair). Even at it's most abstract, "A=A" is not deducible apriori.

The strength of deduction we have empirical access to is actually built on an inductive argument. In other words, deductive logic is only known to be as reliable as the inductive experiments that test them have been repeated.

To say that deductive logic, when properly used, necessitates truth if done from true premises, is in line with how we tend to think about it, but it would be more accurate to sat that deductive logic is the set of observed relationships that have not yet shown inconsistency from true premises.

P3: There is no way for a premise to be determined true or false except relative to another premise (ex: in order to refute the premise "all humans are green" one must accept the premise "visual perception is more reliable than this idiot" and the premise "I don't see green humans")

P4: A premise cannot determine it's own truth value (I expect people to disagree and I'm waiting to see how)

You're essentially saying the same thing with both of these premises, and the issue is you're expecting that certainty emerges from perfect bottom up deduction, when in practice we can only approach it from imperfect top down induction. Let me show you what I mean:

Take a highly uncontroversial and basic premise: a force of gravity exists.

We would normally determine the truth of this premise by conducting an experiment to see if our predictions hold true; the more experiments we run and the more accurate or reliable our predictions become the stronger our confidence is (the closer we get to "certainty"). You can propose that we're relying on other premises which themselves must be tested, such as the premise that visual perception reflects some true aspect of the things it perceives. Likewise we can begin testing this premise as well (getting repeatedly slapped in the face is a good test, as it correlates with other senses, such as touch/pain). The more we test the reliability of visual perception, the more confident we become that it does reflect something true about the external world. Next you might doubt the premise that an external world exists in the first place, which is also something we can test by examining the nature of perception itself (e.g: destroying and restoring one's eyeballs consistently cuts off the flow of visual information from the external world).

As you can see it's not hard to quickly evoke doubt and demand an infinite series of supplementary premises, but the need to continually supply them becomes smaller and smaller as the support for the given argument's premises grows. At some point it becomes ridiculous to keep questioning; there's only so many times we can be slapped in the face with a brute fact before we just accept and roll with it.

Instead of starting from an absolute and certain bottom set of incontrovertible premises, our arguments tend to start somewhere in the middle. Support for conclusions builds upward from premises, and support for premises themselves builds downward, typically via testing, where we only tend to build downward as far as is necessary to be convincing/persuasive/of marginal risk of error with respect to premises.

P5: There is an infinite number of potential premises that can be used in an argument

Yes, such as the "A wizard did it" premise. Not all hypothetical premises are equal, and even if you have an infinite number of supporting premises, the conclusion need not be sound or strong if all the premises are bad, unlikely, or untrue. (you could have an infinite number of premises (assumptions) which pertain to witchcraft and wizardry, and support its existence, and if we could sum them all we would find the chances of wizards existing does not approach 100%.

P6: Consequently there is an infinite number of potential premises that can be used to determine the truth value of a premise
C: Every premise is true if the right premises are used to determine it's truth value

This is not the case. There are a potentially infinite number of premises (in the same way that there are infinite numbers) that can contribute to the inductive strength of an argument, but not all premises contribute an equal amount of inductive strength. (e.g: evidence that wizards don't exist contributes less to the inductive argument for heliocentrism than astronomical observations and orbital predictions does). Very quickly the vast majority of the room for doubt can be eliminated and we're left with hypotheticals that contradict a lot more than the premises of our actual arguments (see: wizards)
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I agree with everything you just said. The problem is this:
At some point it becomes ridiculous to keep questioning

Is a matter of extracting a should from an is. There is nothing in deductive/inductive/abductive logic that tells you when to stop questioning nor what to question or what premises to start testing. Ultimately, the practise of logic requires extracting shoulds from ises. The real issue here is that explaining the world in terms of "a wizard did it" is perfectly justifieable and consistent due to P5 and P6. It's just all of those who explained it through "a wizard did it" happened to die because they couldn't use that explanation for anything practical. Had they been able to, we would also be saying "a wizard did it". The sad thing is, it's not abduction that leads to truth, it's natural selection based on practical utility. There was a time when "God did it" and "Gravity did it" were equally likely propositions. Had someone discovered an applicable use for the former, it would have become the standard. Therefore, it is futile to claim that one has obtained truth through abduction. All one gets is to survive
• 3k
P4: self referential propositions.

P6 does not follow from P5.

C: Every premise is true if the right premises are used to determine it's truth value
C: Every conclusion is valid if the right premises are used to determine it's truth value

Every true premise is true - but the it was true anyway.
Every valid conclusion is true if true premises are used in a valid argument.

Now here's the problem: what is "true"; how is it defined? Godel, having a problem with that, fell back to the well-defined notion of provability. Had he been able to define truth within logic, then he wold have created a sentence that asserted it's own falsehood. I.e., if it were true, then it was false; if false, then true. Ok in ordinary language, but a catastrophe in logic.
• 1k
uhhhh. Why did you just change a premise and both conclusions and then continued to argue as if you're dealing with the same argument?
P6 does not follow from P5.

If there is an infinity of possible premises, and any premise can be used to validate another premise, then there is an infinity if possible premises by which to validate premises
• 2.1k
C1: Every premise is true if the right premises are used to determine it's truth value
C2: Every conclusion is valid if the right premises are used to determine it's truth value
These are too vaguely stated to know what they mean.

I'm guessing that by C1 you mean 'For any proposition P, we can find a set of premises from which that proposition follows'. That gets us nowhere however, because P is a premise from which P follows, and so is ((1=1) -> P).

Further it is vulnerable to inconsistency unless we exclude propositions that are self-contradictory. For example, would you be happy to apply it to the proposition P:'0<>0'?

Certainly for any non-self-contradicting proposition we can construct a logical theory in which it is true. But that doesn't mean that theory is useful, or has any relevance to our lives.

The only way to disprove this argument is to do what P3 is....
It's best to avoid saying things like this. Unless the argument is presented in formal logic, with the rule of inference used to justify each step clearly stated (eg 'Modus Tollens on lines 4 and 5'), it is easily invalidated, simply by pointing out that no formal justification has been provided for one or more of the steps. Breaking up a verbal attempt at persuasion into numbered lines does not constitute a formal proof.
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If there is an infinity of possible premises, and any premise can be used to validate another premise, then there is an infinity if possible premises by which to validate premises

2+2=7 is one of the infinity premises. It does not validate 3+3=6. Any premise cannot be used to validate any premise.
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I'm guessing that by C1 you mean 'For any proposition P, we can find a set of premises from which that proposition follows'. That gets us nowhere however, because P is a premise from which P follows, and so is ((1=1) -> P).

Correcc

For example, would you be happy to apply it to the proposition P:'0<>0'?

My happiness has nothing to do with it. It IS possible to apply it even for self contradictions which is a problem. I would never do that because it doesn't make sense but it is possible.

If we exclude self-contradictions, certainly for any eligible proposition, we can construct a logical theory in which it is true. But that doesn't mean that theory is useful, or has any relevance to our lives.

So, are you saying that the main reason we construct logical theories is because they are useful and relevant to our lives? If so I'd agree but then you'd be basing logic purely in practical value. You'd also only be pushing the issue one step back. Now, one has to choose which aspects of his life he wants to use to base his decision on which premises to use for the system of logic he builds. So instead of
Arbitrary premise -> arbitrary logic
No it's
Arbitrary "life impact" -> arbitrary premise -> arbitrary logic
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yeah you can
P1: arithmetic is correct
P2: 2+2=7
3+3 = (2+1) + (2+1) = 2+2+2= 7+2=9
Therefore the premise: 3+3=6 is false

This is stupid math but it is still consistent
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I think you're confusing a hypothetical proposition with an argument. (Actually, that's pretty good on short notice; not to be confused with good for anything.)
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uhhhh. Care to elaborate? I thought you meant 2+2=7 as a premise so I used it as one
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besides I never said any premise can be used to validate any premise. I said that there is an infinity of premises capable of validating any one premise. Those are not the same thing
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