<Lajla> jseamus, again we meet.
<Lajla> Also, classical logic could better be called empirical logic.
<Lajla> It simply takes the rules of interference we 'seem' to have in the 'real world' for granted.
<jseamus> Lajla: my spirit is lifted at the sight of your nick.
<Lajla> My nick is but there to lift your spirit.
<jseamus> Lajla: btb, i agree with your analysis of the nature of logic.
<Lajla> I got into a nasty argument the other day here with [vox] who got angry at us for being too rigorous.
<Lajla> jseamus, well, of course that we have seen the modus ponens be true countless times is no solid proof that it's true _every_ time.
<jseamus> rigour can be good. it can also be of the mortis kind
<Lajla> mortis I only recognise as the Latin genitive of mors?
<Lajla> jseamus: http://thisdomainisirrelevant.net/329
<jseamus> rigor mortis. death rigor
<snoops> the rules of classical logic are not going to be proven false, that is, to lead to inconsistencies, as proofs are already provided using mathematical induction that show they're sound and complete
<snoops> you might not be able to apply it to the world, but that doesn't make classical logic in of itself any less true
<jseamus> Lajla: nice. the one consolation of natural philosophy.
<Lajla> jseamus, ahh, that's just Latin for 'rigour of death'
<Lajla> snoops, nope, they aren't going to be proven false.
<Lajla> Just as much as a logic which rule is {x -> y, x } |= x
<jseamus> Lajla: i was trying oh so hard to make a subtle metaphor. alas...
<Lajla> Instead of y there.
<Lajla> The point is more or less,
<Lajla> íf classical logic describes 'reality'?
<Lajla> THus far we have seen it do so countless times, and not one time false.
<Lajla> But that's of course not a logically sound proof of that it does so infallabily.
<Lajla> Hilbert-style takes the modus ponens as an axiom, if the modus ponens is a universal law of nature is of course the question.
<snoops> see, I never saw classical logic as trying to ascertain truths about the nature of reality, but actually to show the truth of argumentation forms in language
<snoops> as arguments can be true of their form alone
<snoops> regardless of content
<snoops> that's the point
<Lajla> snoops, well, actually classical logic is a form of logic which takes the perceveid universal laws from nature as its rules of interference.
<Lajla> It's empirical logic.
<jseamus> i has to hit teh sack. snoops, i apologize for offending your sensibilities. Lajla, i wish i could stay a little longer in the warm glow of your words, but i gotta go. goodnight.
<Lajla> snoops: http://thisdomainisirrelevant.net/206
<Lajla> 10:08 here.
<Lajla> GMT+1
<Lajla> Sleeps, jseamus.
<jseamus> california
<jseamus> tsorit
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<snoops> it's not empirical, it's a logical necessity.. as in, you can deduce it from reason alone, much like you can do mathematical induction without recourse to the world to see if it's right or not
<snoops> based on what the material conditional means, as well as what it means to know the antecedent, allows you to deduce, solely using reason to find that the consequent is true
<Lajla> snoops, nope, not really,
<Lajla> classical logic is nopt the only logic.
<snoops> of course I know this, hence specifying the material conditional
<Lajla> Classical logic is more or less defined by the modus ponus,
<Lajla> which cannot be proven from the other axioms.
<Lajla> And the modus ponens is observed through the senses as happening in the 'real world'
<snoops> intuitionistic, linear, computability, paraconsistent, modal, the list goes on
<Lajla> But there have been logical systems which do not use the modus ponens.
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<Lajla> Indeed, and all those logics are also consistent.
<Lajla> But classical logic seems to empirically match 'reality', and it's built for that.
<Lajla> 'if x leads to y and x is true, then y is true'
<snoops> while instances occur that show us modus ponens out in the world, that does not entail that we got the idea from the world, or is inductive/empirical in nature.. There are certain mathematical proofs which aspire to our reasoning ability, and they're deductive
<Lajla> snoops, assuming that argument is true, the human reasoning ability and what feels 'natural' to is is still evolved in this world.
<Lajla> And probabily our intuition is evolved to match the needs of our survival.
<Lajla> And applying garbage logic to solve problems on intuition doesn't really aide that.
<Lajla> Sure, the modus ponens feels intuitively correct for humans, but I doubt it would if real observations contradicted if every time.
<snoops> evolution is a naturalistic explanation for what feels certain and correct in us.. a naturalistic explanation is of course going to appeal to the natural sciences.. it's begging the question as to whether we got them from empricial or rational means
<snoops> really, modus ponens looks like a very good case for something that is a priori
<snoops> certainly after deducing it, you never need to test it with empirical sense data again
<Lajla> well, I won't argue that the modus ponens feels more intuitive to most people.
<Lajla> My point is more that in logic itself, it's surely not more 'rightful', if such a concept can even exist in logic alltogether.
<Lajla> Also, the human mind is actualy very bad at proper rigorous logic.
<snoops> I'm not sure what you mean by rightful
<Lajla> snoops, I mean as the 'proper logic'.
<snoops> proper logic?
<Lajla> From where I see it, logic is chiefly an investigation of 'what is true if under the assumption that these things are true', and under 'these things' are also one's rules of interference.
<Lajla> snoops, the logic that is more 'correct'.
<Lajla> Already we see the difficulties at even intuitively defining the concept. =P
<snoops> rightful, proper, correct.. I'm really not sure what you're appealing to - a metaphysical truth that is perhaps currently known about the nature of things?
<snoops> intuitively defining the concept of modus ponens? I think it's incredibly easy to define
<snoops> you define the meaning of the conditional, and state when it is true and when it is not.. and also you can show it is equivalent to not(A and not B)
<Lajla> snoops, no I'm trying to intuitively define your idea of classical logic.
<Lajla> But maybe I misunderstand, rephrase it please.
<Anaximander> are there pointers in modal logic?
<snoops> modal logics include necessary and possible operators
<snoops> box for necessary, and diamond for possibility
<snoops> you can appeal to possible worlds semantics to provide an interpretation
Anaximander anokth
<Lajla> Anaximander, aren't pointers chiefly for programming and instruction sets at max?
<snoops> so for example boxA is true, iff all worlds in the model believe A
<Lajla> To point at a character space?
<snoops> diamondA is true, iff at least one world in the model believes A
<snoops> naturally box and diamond have a relationship to that of universial and existential quantifiers
<Lajla> so I gathered yes.
<Lajla> Can't say I'm well versed in modal logic.
<Lajla> I plead total ignorance.
<snoops> you don't actually need to prove modus ponens.. you can actually just get by with far less.. eg, such as the sheffer stroke that charles sanders pierce first talked about in a paper quite a few years ago, that has the expressive power of propositional logic
<snoops> from X and -(X & -Y) you can deduce Y from the law of non-contradiction
<snoops> you do need negation, that's crucial
<snoops> there are many different model logics, which basically just change the relationship between which worlds can see each other (how they're linked together)
<snoops> modal rather*
<snoops> relationships in the mathematical sense of transistivity, reflectivity, and symmetry
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<Lajla> snoops, you _cannot_ prove the modus ponens from the other rules of classical logic is the point.
<Lajla> It's an axiom.
<Lajla> the fifth postulate.
<Lajla> And many people once too said that all geometry had to be euclidian.
<snoops> A implies B is logically equiv to -(A & -B) and also to (-A or B).. If you A in any of those cases, you can deduce B
<snoops> -(A & -B) by reductio ad absurdum and (-A or B) by disjunctive syllogism
<snoops> so, if you have a problem with modus ponens, you'll also have a problem with reductio ad adsurdum and disjunctive syllogism
<snoops> absurdum rather
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<Lajla> snoops, not really.
<Lajla> It's true that modus ponens grants the option of the reductio ad absurdum
<Lajla> It's not the ONLY thing that grants it.
<Lajla> For one: {x, x -> y } | y AND ' BUSH IS A TOTAL IDIOT´
<Lajla> Also grants it.
<Lajla> A system of modus ponens plus that if 'any' statement is true, it is provable that bush is a total idiot.
[!--extracted from ##philosophy@irc.freenode.net--]
Hey, thanks for the Finnish lesson. That was very nifty.
And sorry for the late response.
So you really did ask me about my Finnish, even though you already knew how rudimentary my Finnish was.:O
All Comments (98) Comments
lalala vulvaaa
fusion each otheeeer
and baby is made
~~ unleeeesss
you haaaaAAAAVEEE
an oblique vagiiinaa
<3
~~~lalala
And sorry for the late response.
So you really did ask me about my Finnish, even though you already knew how rudimentary my Finnish was.:O
/pats
And yes, I have my moments.