Is Aristotelian logic really as powerful as Kreeft says it is? Is formal logic really that ontologically suspect? I thought that Peirce, with his propositional logic enhanced by his logic of relatives and his re-systemization of Kant's categories, did a pretty good job. What do we lose with formal logic that we have with Aristotelian logic, and vice versa?
 Thalidomide Vintage Ad Shirt $22.14 |
 Ape Out Shirt $21.68 |
Thalidomide Vintage Ad Shirt $22.14 |
the problem with symbolic logic is that it's too disconnected from the perceptual and epistemological basis of logic... read a system of logic by js mill to basically what logic was before algebraic logic. even if you do logic diagrammatically like peirce, it still doesn't make any explicit philosophical claims like logic used to, so it's harder for people to see it's philosophical origin.
>even if you do logic diagrammatically like peirce, it still doesn't make any explicit philosophical claims like logic used to,
Could you go more into the nuts and bolts of this please, if you have the time? I thought that Peirce's diagrammatic logic relied on the "software" of his triadic categories and thus made philosophical claims.
i think it's more like he applied his logic to his categories rather than the other way around. in the end the graphs basically can do the same things as symbolic forms of logic, just in a different medium. which is probably why nobody really uses them anymore. I don't know the details.
I thought they were intertwined, that you couldn't have it one way or the other. Peirce's categories were a condensation and original reformulation of Kant's tables of judgments/categories, so in a way they're a kind of pure logic.
Goofy shit. Predicate logic was developed since syllogisms can't be used for math. Look up the problem of multiple generality. Aristotelian logic can't go from
Some cat is feared by every mouse.
to
All mice are afraid of at least one cat.
which is what most people would think of as a pretty basic logical inference
>the problem with symbolic logic is that it's too disconnected from the perceptual and epistemological basis of logic
That's the whole point of logic, to be disconnected from any perceptual and epistemological biases. You've just given a reason symbolic logic is superior.
>Look up the problem of multiple generality. Aristotelian logic can't go from
>Some cat is feared by every mouse.
>to
>All mice are afraid of at least one cat.
>which is what most people would think of as a pretty basic logical inference
If I understand this correctly, Aristotelian logic can only "swim" through genera, it can't ever reach the case? What if you reversed the direction of a syllogism.
>If I understand this correctly, Aristotelian logic can only "swim" through genera, it can't ever reach the case?
This is vague hand waving and shows a real lack of understanding of even Aristotelian logic much less symbolic. The simple reason that syllogisms fail in the example is that the sentences contain two quantifiers "some" and "every" and a valid syllogism can only contain one per sentence. From there it is pretty easy to see how and why predicate calculus was developed to include multiple quantifiers(the predicates). Everything that can be shown using a syllogism can be directly translated into predicate calculus
>This is vague hand waving and shows a real lack of understanding of even Aristotelian logic much less symbolic.
Yeah, I have a lack of understanding, that's why I asked somebody more knowledgeable for additional direction. I don't know why you have to be mean about it. Once upon a time, you didn't understand predicate logic either.
>and a valid syllogism can only contain one per sentence. From there it is pretty easy to see how and why predicate calculus was developed to include multiple quantifiers(the predicates).
It's not easy to see. For starters, why would you want to contain more than one quantifier per sentence? The examples you used, some and every, speak of genera, and they're quite exclusive. Either you have some, or you have all.
Not the anon you are responding too, but he is a goofy butthole plebbitor, disregard his fedora attitude. It’s better to be honest about your lack of understanding unlike 95% of people here who fake read Hegel and Kant
>For starters, why would you want to contain more than one quantifier per sentence?
Do you think the example I gave was a valid logical inference?
>Start with: Some cat is feared by every mouse.
>Logically infer to
>Conclusion: All mice are afraid of at least one cat.
Both of those sentences contain two quantifiers. Predicate logic had a strong motivation from math where similar types of statements pop up constantly, so much so that math is impossible to do with syllogisms.
That makes sense. But why did nobody realize there was a problem with Aristotelian logic? Didn't they realize they needed more precise methods of predication and struggled to do it with Aristotelian logic?
>But why did nobody realize there was a problem with Aristotelian logic?
Why didn't anyone realize heavy rocks didn't fall faster than lighter ones? Aristotelian physics wasn't just deficient in certain areas it was outright wrong and yet his physics lasted nearly as long as his logic(give or take a couple of hundred years). Aristotle was a genius but the people that slavishly followed him for over a thousand years weren't that smart. It's called the Dark Ages for a reason.
>Why didn't anyone realize heavy rocks didn't fall faster than lighter ones?
Because they generally do? Natural motion wasn't capable of describing air resistance, and we technically didn't have direct experimental proof of Galileo's hypotheses until Apollo 15.
>It's called the Dark Ages for a reason.
Ah, you're one of *those* posters. You're like several generations behind when it comes to the history of science. It wasn't as simple as
>Aristotle smart but dumb
>1000+ years of slavish adherence to Aristotle
>Natural motion wasn't capable of describing air resistance, and we technically didn't have direct experimental proof of Galileo's hypotheses until Apollo 15.
What? Galileo had experimental proof of his own hypotheses when he dropped the rocks off the fricking tower.
>Aristotle smart but dumb
Aristotle was smart but he was also wrong about a whole shit load of stuff. His physics isn't only fricked with falling rocks, that's just the simplest most amusing example. He got the basics of motion fundamentally wrong. His biology is frequently wrong as well and a simple examination of how many teeth men and women have would have told him that. You may find this hard to believe but smart people can get shit wrong. What makes someone dumb is mindlessly sticking to an error.
>Surely, he and others in his footsteps would have seen that he had a problem, no?
Again a basic thought experiment like Galileo did with his two bricks and a string would have shown something is screwy with Aristotelian physics. And yet it took over a thousand years for someone to think of it.
>thought experiment
>science
lol, behold the power of the STEMgay
https://philsci-archive.pitt.edu/10964/4/Aristotele.pdf
>His biology is frequently wrong as well and a simple examination of how many teeth men and women have would have told him that.
It is silly of him to have repeated an observation that he didn't test himself, re: the teeth, but his biology is hardly "frequently wrong". Are you doing what he did in having heard someone make a claim, and repeating it without verifying?
>open your mouth Eudoxia, I have to count your teefs for... uhhh... the glory of theoria!
His biology is fundamentally based on teleology. He believed in spontaneous generation. This is getting bizarre, Aristotle was not right about everything. You're so desperate to have his metaphysics be correct by association that you're accepting all kinds of clearly false shit.
>I don't believe in spontaneous generation
>life arose from uhhhh... abiogenesis...
I heckin luv scienze
He believed maggots spontaneously generated themselves on meat. Again another famous experiment like Galileo's was Pasteur putting a glass cover over rotting meat to keep the flies off and showing maggots didn't form thus disproving Aristotle. ARISTOTLE GOT LOTS OF SHIT WRONG
I'll grant you the spontaneous generation, but there's nothing wrong with teleology lol. That doesn't even have anything to do with what is scientifically relevant. It's beyond science. You have a hard time distinguishing between what is scientific and what is beyond science.
>but there's nothing wrong with teleology lol. That doesn't even have anything to do with what is scientifically relevant. It's beyond science. You have a hard time distinguishing between what is scientific and what is beyond science.
That would have been a surprise for Aristotle since he thought teleology was what caused rocks to fall to the ground and for organisms to develop. It was part of his physics and one his four causes. After his physics was junked Christian apologists wanted to save their goofy teleology so they moved it to metaphysics which is "beyond" science in the same way any fantasy is. Teleology exists no where outside your mind and is totally subjective.
>since he thought teleology was what caused rocks to fall to the ground and for organisms to develop.
He would still say the same thing. Rocks fall to the ground through gravity, but why does gravity act the way it does or exist as it does? Teleology. Organisms develop through absorption of nutrients and growth of tissue (Aristotle already knew this much), but why? Teleology.
>Rocks fall to the ground through gravity, but why does gravity act the way it does or exist as it does? Teleology. Organisms develop through absorption of nutrients and growth of tissue (Aristotle already knew this much), but why? Teleology.
Don't forget the gravity fairies and the development trolls. Teleology as presented by you there is totally superfluous. And Aristotle emphatically did not believe in gravity, force at a distance goes against his entire physics. He had no concept of momentum either, for him an arrow in flight was pushed forwards by the air rushing into the space it left behind it.
>Teleology as presented by you there is totally superfluous.
Teleology is the why, not the how. It's no more superfluous than asking why you choose to eat food.
>And Aristotle emphatically did not believe in gravity,
Correct, because he did not know about it.
>orce at a distance goes against his entire physics
No, not really. The prime mover moves at a distance according to him, without being in direct contact with anything.
>He had no concept of momentum either,
That's true.
>Teleology is the why, not the how. It's no more superfluous than asking why you choose to eat food.
I already said above
>Teleology exists no where outside your mind and is totally subjective.
Asking my opinion why on if a rock should fall is superfluous
>No, not really. The prime mover moves at a distance according to him, without being in direct contact with anything.
Again basic failure to understand Aristotle. His first mover had to have direct contact since for Aristotle that's all there was. The Bible thumper crap came later and wanted to hide God from direct observation.
>His first mover had to have direct contact since for Aristotle that's all there was
It didn't. You haven't read his Metaphysics. It's the one odd thing about it, which is that the prime mover does not move through contact, its movement is supposedly as a "final cause", it moves because everything moves towards it of its own accord. A bit like gravity analogically, but obviously not the same unequivocally.
>that's all there was
If that were true then things would not be able to move themselves without external contacts.
>If that were true then things would not be able to move themselves without external contacts.
Besides teleology. He thought the planets orbited the earth because their teleology or purpose was to orbit the earth. But when he said move he meant something else was moving it directly. Force at a distance didn't even start to make sense to him because for Aristotle the vacuum couldn't exist. Everything was indirectly in contact with everything else
>force at a distance goes against his entire physics.
Spooky action at a distance was disliked by most scientists throughout most of the history of science lol. It was usually taken as a sign that something was "missing" from the predominant theory, leading to great scientific development (e.g. general relativity displacing Newtonian gravity).
>He had no concept of momentum either, for him an arrow in flight was pushed forwards by the air rushing into the space it left behind it.
Obviously this doesn't explain Aristotle's error, but isn't that similar to how an airfoil works to produce lift?
>Spooky action at a distance was disliked by most scientists throughout most of the history of science lol
You've badly mangled this quote to support the opposite position. Einstein didn't like quantum mechanics(he's the one who said that) because it effected change at a distance without force.
> It was usually taken as a sign that something was "missing" from the predominant theory, leading to great scientific development (e.g. general relativity displacing Newtonian gravity).
Gravity in both Newton and Einstein is emphatically a force at a distance. There is no necessary connecting material between the masses being effected. You still don't get how far from modern physics Aristotle was. He viewed all motion as a kind of bumper cars and that everything was in contact indirectly with everything else through a chain of bumps.
>Obviously this doesn't explain Aristotle's error, but isn't that similar to how an airfoil works to produce lift?
Aristotle was describing the forward motion of the arrow not a perpendicular lifting force.
>You've badly mangled this quote to support the opposite position.
Who was I quoting? I can name several prominent scientists from Leibniz to Einstein who complained about "occult forces" and "spooky action at a distance."
>Gravity in both Newton and Einstein is emphatically a force at a distance.
There is no force at a distance when you're dealing with curvatures in spacetime.
>Aristotle was describing the forward motion of the arrow not a perpendicular lifting force.
I'm just saying that Aristotle had a particular intuition about physics that works extremely well in some respects. Change a few nouns and give some remedial kinematics lessons and Aristotle would have made for a great aerospace engineer.
>You still don't get how far from modern physics Aristotle was.
https://philsci-archive.pitt.edu/10964/4/Aristotele.pdf
>There is no force at a distance when you're dealing with curvatures in spacetime.
I mean this goes without saying Aristotle would also not have believed in spacetime.
>I'm just saying that Aristotle had a particular intuition about physics that works extremely well in some respects
His intuition is the same common sense that every human has concerning everyday physics. There is nothing unique about it.
>Change a few nouns and give some remedial kinematics lessons and Aristotle would have made for a great aerospace engineer.
He didn't believe in force at a distance or momentum. By remedial you mean throw out all of his physics and replace it with modern stuff. I have no doubt Aristotle could learn it but there is nothing about his physics that is salvageable.
>https://philsci-archive.pitt.edu/10964/4/Aristotele.pdf
You already linked that and I glanced over it. It's the same tired crud about Aristotle being a decent empirical approximation under certain conditions. But his theory was wildly off and in no way comes close to what we have now or even with Newton. You can't even seem to realize how strange it was.
>His intuition is the same common sense that every human has concerning everyday physics.
>You can't even seem to realize how strange it was.
make up your mind moron
You don't think people's intuitions can be strange? You've internalized some of modern physics and think it was always your common sense. It's intuitive that the sun orbits the earth but it's also fricking strange when people claim that.
Strange in what sense? That it doesn't agree with what you learned in a classroom?
Strange in the sense that it is intuitive to me now that the earth orbits the sun. But that is after I went to school.
It sounds like you have a poorly trained intuition.
>Aristotle since he thought teleology was what caused rocks to fall to the ground and for organisms to develop.
You can still have teleology and the theory of gravity, teleology and the theory of evolution, etc. In fact, in practice, educators find it difficult to avoid using "teleological" language to introduce students to the subject, and they feel a strange sense of guilt since it's been beaten into their heads without them understanding what teleology is or why science "avoids" it.
>You can still have teleology and the theory of gravity, teleology and the theory of evolution, etc.
And it's totally superfluous since gravity and evolution fully describe the observed phenomena. It's like claiming fairies also drag things to the ground along with gravity.
>In fact, in practice, educators find it difficult to avoid using "teleological" language to introduce students to the subject
Because people are inclined to personify inanimate objects and natural forces. My little cousin got mad when he tripped on chair and then pushed the chair over to get back at it. Aristotle's teleology is a child's view of the world which is why it is useful pedagogically. It shares mental space with witchcraft and shamanism seeing spirits in nature.
>And it's totally superfluous since gravity and evolution fully describe the observed phenomena
It's only superfluous depending on the scale one asks a question.
>Because people are inclined to personify inanimate objects and natural forces. My little cousin got mad when he tripped on chair and then pushed the chair over to get back at it. Aristotle's teleology is a child's view of the world which is why it is useful pedagogically. It shares mental space with witchcraft and shamanism seeing spirits in nature.
https://aeon.co/essays/without-a-library-of-platonic-forms-evolution-couldn-t-work
>https://aeon.co/essays/without-a-library-of-platonic-forms-evolution-couldn-t-work
Evolution BTFO then since platonic forms don't exist.
>superfluous
Not so
>you already have a complete explanation
Without teleology there is no completeness
>he doesn't know about spirits
Kek. Hylic af
>you (an onions boy): oh no if someone reads aristotle then they will suddenly forget all of our complete system of modern science^tm because of minor and understandable errors that most children already are informed
>actual scientists (chads): science is always incomplete and reading classics is important to be inspired by all the things people like aristotle got right and why and how they got things wrong and also to learn about foundations, perhaps even to challenge them
there is much in science that is teleological, like the action principle
>there is much in science that is teleological, like the action principle
If that is teleology then sure teleology is scientific. But teleology of that sort is useless for ethics since it is impossible to violate the laws of physics. Everything a human has ever done was subject to the action principle. And all teleology groupies are just trying to sneak God and whatever morality they want in the backdoor. Which teleology of your sort would explicitly deny. It is impossible to act differently from that sort of teleology so everything is automatically moral.
maybe you misunderstand, im saying the action principle is garbage and so is your science
"Based on" is meaningless; one who bothers to actually read his biological works can with greater truth say that his biology is "based on" observations, and those observations are explained in part through teleology.
Spontaneous generation is wrong, abundantly granted, but it's not stupid when it's hard to see fly eggs, or when you can't find where the hell an eel's reproductive organs are. It's not some exaggerated or unreasonable defense of Aristotle to remind that he gets things right, or that you're making a bald claim out of proportion. I'm not saying he's "frequently right" either, but I can 100% assert with certainty that neither of us have gone through his biological writings to determine what proportion is right vs wrong, and that his minute observations of chicken embryos should give one some pause before dismissing him outright.
This is nitpicking. You're right, I haven't gone over Aristotle's biology but I do know the glaring errors other people have pointed out. And I've already said above that Aristotle was a genius and that I have no doubt his "minute observations of chicken embryos" were significant for the time. BUT JUST BECAUSE ARISTOTLE SAID SOMETHING DOESN'T MAKE IT TRUE. Like I've said from the beginning this defense of Aristotle in all things is motivated by wanting his goofy ass metaphysics to be grandfathered in to the true club since Aristotle made it up an ARISTOTLE IS ALWAYS RIGHT
This I can agree with as a more moderate take. It's certainly true that Aristotle's saying something doesn't thereby determine the truth. Amicus Aristotle, etc.
>What? Galileo had experimental proof of his own hypotheses when he dropped the rocks off the fricking tower.
this never happened lol
>this never happened lol
Same with Apollo 15 bro. Celestial bodies obey different physics than earth so we couldn't have landed on the moon. Read Aristotle.
>Apollo 15
Now that's a real experiment that happened. The dropping balls off of the Tower of Pisa is a myth and a great example of how the most rabid STEMgays actually despise experimental method.
>Again a basic thought experiment like Galileo did with his two bricks and a string would have shown something is screwy with Aristotelian physics. And yet it took over a thousand years for someone to think of it.
John Philoponus wrote in the 6th century and did in fact disagree with Aristotle on this. That's just the earliest I know of, I would assume anyone who actually had to deal with falling objects of differing weights would also have figured it out.
Probably, the reason it took a long time for it to become The Science was because falling objects of differing weights was not a problem that occured often enough in engineering for enough of The Scientists to modify Aristotle's theories.
That is a sequence of events that has occured often enough in any technical field I'm sure you can think of some more examples yourself, and is not unique either to Aristotle or to medieval Europe.
I am a physicsgay and your tantrum is embarassing.
>Probably, the reason it took a long time for it to become The Science was because falling objects of differing weights was not a problem that occured often enough in engineering for enough of The Scientists to modify Aristotle's theories.
this. you could probably redefine eternal, natural, and violent motion to encompass new discoveries anyway. I always liked to view "natural motion" as a holistic view of motion, one that includes all the properties of motion observed for a given individual in its usual environment.
you'd have to be a crank yourself to think that Socratic Logic is aimed at children.
For the record, I was looking for a better, more mechanistic explanation. Did Scholastic philosophers think it was a problem? Did they try to handwave away the problem? Did they come up with stopgap measures? For what it's worth, Aristotle did recognize all kinds of quantifiers, studied language itself through the Categories, and obviously wrote in complex sentences, rife with all kinds of complicated predication. Surely, he and others in his footsteps would have seen that he had a problem, no?
>Everything that can be shown using a syllogism can be directly translated into predicate calculus
It actually can't. To this day there is still the problem of transferring essential predication from one to the other. The quantifiers used in predicate logic preclude the possibility of essential predication, making it essentially less generalizable. The example is using "all" and " at least one" as quantifiers does not make sense when establishing an essential predication like "humans are two-legged." According to predicate logic, "all" human beings are not two-legged, and at least one human being is one-legged and two-legged. Yet per the premise, human beings are two-legged, even though predicate logic can't capture this relationship because the predicates introduced subvert the original relationship, which is not quantifiable. Again, sure, it's great for maths, which is purely quantitative, but it ruins other fields of inquiry which might be purely qualitative. The problem transfers over into modal logic, but it requires specific fixes in order to be able to accommodate syllogistic logic, and even still it is questionable whether "possible worlds" actually capture what that kind of predication really is. Form has to suit its content, and all logic is purely form.
> so much so that math is impossible to do with syllogisms.
Maths is not impossible with syllogisms, it just requires rearranging the layout of presentation, which is awkward but by no means impossible. You can derive the same conclusion you just gave by simply including one or more premises and an additional deduction.
Logic is not certain. Modern logicians cannot even decide whether ( A -> B ) -> ( A -> ¬B ) is a valid axiom.
>The quantifiers used in predicate logic preclude the possibility of essential predication, making it essentially less generalizable.
I suppose this isn't a problem when your metaphysical worldview dispenses with essence, full stop. Problem solved!
>obvious sarcasm
>I suppose this isn't a problem when your metaphysical worldview dispenses with essence
The worldview is not relevant. We are talking about whether predicate logic is capable of subsuming the content of another logic. And the answer is it's not. Therefore predicate logic does not fully subsume syllogistic logic. It only subsumes syllogistic logic if you are interested in pure mathematics.
Then why did say
>The quantifiers used in predicate logic preclude the possibility of essential predication, making it essentially less generalizable.
That's a clear metaphysical problem baked into predicate logic.
See below
It's not "baking in" anything, so much as it is leaving room for the discussion of particular possibilities. No one is claiming syllogistic logic forces you to assume the existence of essences. Refer to this post
>( A -> B ) -> ¬( A -> ¬B )
slight correction
Huh? Just do the truth table that's from propositional logic not predicate.
I even did it for you if A and B are false
>( A -> B ) -> ¬( A -> ¬B )
is false and can't so it can't be a tautology. You really have no clue what you're talking about.
Yes, according to the axioms of classical logic, that statement is false due to the introduction of material implication, which is that A -> B = ¬A ∨ B. The reason you are asserting that the statement is false is because of the EXQ axiom which allows for vacuously true implications. But it's not unanimously considered false, because there are systems where ( A -> B ) -> ¬( A -> ¬B ) is axiomatically true, and therefore material implication is excluded as a possibility.
>Yes, according to the axioms of classical logic
So what you're saying is there are other systems of logic? Then just say that instead saying crap like
>Modern logicians cannot even decide whether ( A -> B ) -> ( A -> ¬B ) is a valid axiom.
Classical logic doesn't accept it and whatever logic you're talking about does(far from convinced that such a system is consistent) You can make a system of logic with whatever axioms you like, it's a common pass time in academia. Making sure it's consistent is trickier
>So what you're saying is there are other systems of logic?
No, the point is that there are people who do not agree that the standard system of logic is fully coherent. That includes the statement that there are other "systems", because if you think one system is incoherent, then you will naturally create another which you think is superior. This is not just a question of axioms, the axioms are a question of general relevance and meaning.
>far from convinced that such a system is consistent
You're not convinced that one truth cannot imply the truth and falsity of the same thing? Anyway, I'm not really interested in what you find convincing. If someone did not find the law of non-contradiction convincing, I would not try to convince them beyond the very basics.
It's true. In classical logic, which is widely taught since the 20th century but not before it, the truth value for 0 -> 0 and 0 -> 1 = 1. In connexive logic, which is still considered a viable alternative to classical logic, the truth value for 0 -> 0 and 0 -> 1 = 0. You are probably someone early in college who has just learnt the basic truth tables and thinks they are set in stone. They mostly are set in stone, but there are hiccups you are not aware of like the one I just mentioned. It's probably for the best that professors don't scare you away with "ifs" and "buts" when you are first learning.
>No, the point is that there are people who do not agree that the standard system of logic is fully coherent
Have you found a paradox in classical logic? You're going to be famous bro. If what you really mean by "coherent" is some feeling you have is hurt no one cares.
>You're not convinced that one truth cannot imply the truth and falsity of the same thing?
I was being sarcastic. I already showed your axiom isn't tautological so I'm certain that your system is inconsistent.
>the truth value for 0 -> 0 and 0 -> 1 = 1. In connexive logic, which is still considered a viable alternative to classical logic, the truth value for 0 -> 0 and 0 -> 1 = 0.
Lol and you're accusing me of being an undergrad. Why don't you write out the truth table as an exercise for your "better" logical implication. Does it resemble something? You've turned logical implication into logical and. A trivial error you see in intro logic classes.
>Have you found a paradox in classical logic?
No. You've misinterpreted my posts if that's what you think I said. I only stated that classical logic accepts an absurdity as true, which is that one thing can imply two contraries simultaneously. It's not a paradox, at worst it is a quirk, but it's one which should not be there, because no one generally accepts that kind of reasoning as valid. How can you reasonable justify the belief that A can entail both B and not-B? It's completely irrational. You're fine to hand-wave, but it seems like simply a stubborn desperation to attack a particular figure.
>I already showed your axiom isn't tautological
You showed that it does not accommodate the axioms of classical logic with the use of the material conditional to show that it is false.
>You've turned logical implication into logical and.
There are different ways it is made into a system, but generally the two values I gave are actually considered null values, they do not have a result so they are not strictly equivalent to and. But otherwise yes, it does appear very similar as my example showed, which should've been clarified. Regardless, it's the solution to resolving the given absurdity of a single term being able to imply another term and its negation. This logic has been in use for the majority of history. I don't consider that in itself a valid justification, but it is at least demonstration that you are not justified in considering it a "trivial error."
>intro logic classes.
It seems like they are the only ones you have taken?
>It seems like they are the only ones you have taken?
Bro you just claimed the truth table for logical implication is the same as the truth table for logical and. I'm the one giving the advice that should be followed. Not to mention even with your new truth table for implication your axiom
>( A -> B ) -> ¬( A -> ¬B )
is still not tautological. You have no idea what you're talking about.
>Bro you just claimed the truth table for logical implication is the same as the truth table for logical and.
I clarified that it is not in formalizations of the system.
>is still not tautological.
How is it not tautological, given the axioms of connexive logic?
>How is it not tautological, given the axioms of connexive logic?
Just do the truth table using your logical implication. I've already said this earlier it's a statement of propositional logic with no quantifiers. You can easily work out if it's tautological even using your special logical implication and it's not. You really have no clue what is going on, you learn that in a intro logic course.
>Just do the truth table using your logical implication
I have, and it is true or null for every possible combination of values, which makes it tautologically true.
>I've already said this earlier it's a statement of propositional logic with no quantifiers.
And I did not disagree on that point.
>I have, and it is true or null for every possible combination of values, which makes it tautologically true.
Your logical implication is just logical and. Here is your supposed axiom
>( A -> B ) -> ¬( A -> ¬B )
taking A and B both as false
(F / F) / ~(F / ~F)
F / ~(F / T)
F / ~F
F / T
F
An elementary use of logic shows it's not a tautology. You're wrong and oblivious to how wrong you are.
The truth table is what is in question in that example. Logicians do not agree on the layout of the truth table for implications. What I provided was one of the famous disagreements.
Essences are reasoned to exist through certain chains of induction and deduction. The essence is not a standard of normality or a benchmark, it generally has a more nuanced definition than that. That's not what the point of this discussion is, though. I don't think I necessarily disagree with anything else you stated, so I'm not sure how it conflicts with what I've already said. The point is simply that predicate logic cannot capture one kind of relationship, because of the way it must treat its content.
>Essences are reasoned to exist through certain chains of induction and deduction.
Demonstrate how you can from cases to essence from induction and deduction.
>The essence is not a standard of normality or a benchmark, it generally has a more nuanced definition than that.
It's a good working definition though, isn't it?
>Logicians do not agree on the layout of the truth table for implications.
Lol what!? Bro you're so far gone it's not even worth talking to you. There are ZERO logicians who don't agree with the truth table for logical implication.
>According to predicate logic, "all" human beings are not two-legged, and at least one human being is one-legged and two-legged
I don't know what this means. It sounds like you want to be able to bake properties into your definitions without explicitly claiming them as part of your definition which is a fundamentally dishonest tactic. Not to mention there are one-legged humans which already fricks up your example if you're trying to draw credibility from the real world.
>It's not "baking in" anything, so much as it is leaving room for the discussion of particular possibilities.
You understand why essences are appealed to, right? They're a standard of normality, so we have a benchmark from which we can judge particular cases against. If we have no benchmark (and benchmarks typically come with properties, hence subject and predicate), then how can the particular possibility make sense? We would have no way of grouping them at all, making quantifiers like some and all impossible to use meaningfully.
It's said that you answered the other anon so rudely, because while he wasn't focusing on an aspect that you cared about, his intuition was correct.
>It’s the fragment of natural language that involves statements with a two-place subject predicate structure, where the subject and the predicate terms can be represented as classes of objects, and where the logical relations between statements are determined by relations of inclusion, exclusion, and overlap among the classes.
In addition to the lack of additional quantifiers (hence two-place), it sounds like "swimming among genera" to me, if we understand "genera" to be classes such as what was described.
>You've just given a reason symbolic logic is superior.
for math sure, but not necessarily for empirical science and especially not for philosophy. I don't think Aristotelian logic in particular is the final solution for philosophy and definitely not for empirical science but we can still do better than modern symbolic logic.
>but not necessarily for empirical science and especially not for philosophy
No you've got it totally flipped around. If logic was more laden down with biases it wouldn't have the authority that it does in any field. If I could just say someones logical derivation was just a consequence of their epistemological assumptions that would make logic worthless.
without making epistemological "assumptions" science and philosophy are impossible though. it sounds like you're just prejudiced against the possibility of an epistemology that's anything more than some guy's speculations. logic would never even exist if not for Aristotle's epistemological assumptions that primary substances are the basis of all knowledge.
>it sounds like you're just prejudiced against the possibility of an epistemology that's anything more than some guy's speculations
I don't want some dude sneaking in bogus fantasies and claiming it's logic.
> logic would never even exist if not for Aristotle's epistemological assumptions that primary substances are the basis of all knowledge.
Laughable. Logic is in no way dependent on "primary substances". This is is just metaphysics wankers desperately trying to get some kind of credibility. Clear lines drawn between Aristotle's logic and his metaphysics, one is universally recognized(though superseded by symbolic logic) and the other has been discarded for hundreds of years.
thou shalt not block the way of inquiry
also it seems like you have a lot of prejudice against the guys who created the logic you love... aristote, peirce, russell, and whitehead were all philosophers who sought not just to create symbols to manipulated by mathematicians but to clarify the epistemological motives of their logic and explain its efficacy. neither did they just create logic out of the blue but were motivated by their "bogus fantasies" in creating it. there is no point in having disdain for every area of inquiry that isn't certain and respected yet and there's no reason we can't all one day agree upon claims that go beyond the proper way to manipulate the symbols.
>there is no point in having disdain for every area of inquiry that isn't certain
Logic is certain though unless you're denying that. You're trying to sneak in metaphysics trash and claim it is part of logic. If Aristotle had only come up with his metaphysics and not his logic and other philosophy he'd be nothing but a footnote.
well your insistence that epistemology and metaphysics are "trash" and "bogus fantasies" is just epistemological and metaphysical trash and bogus fantasies that you are trying to sneak into logic.
you can't just ignore problems because people don't agree on them yet.
I didn't insist on anything being trash. I was being sarcastic about disposing with essences to solve a problem. I was hoping you had more to say about logical systems having "baked in" metaphysical assumptions.
>Logic is in no way dependent on "primary substances"
this is not what he said, why you sound so illogical?
is it really a problem and not just a flaw in the language used for the saying?
ontologically that statement can mean 2 different things, both are understandable and can be reasoned with. but the words used is the issue.
>both are understandable and can be reasoned with.
They can't be reasoned with using syllogisms. That is one of the reason predicate logic was developed and superseded Aristotle.
>is it really a problem and not just a flaw in the language used for the saying?
The sentences have two quantifiers. Syllogism can only deal with one per sentence. Predicate logic was developed in part to deal with multiple quantifiers.
Kreeft is the world’s biggest moron and pseud, Aristotle is influential but irrelevant at this point.
What power does he attribute to it? I like the clarity and simplicity of the syllogism, but it seems like its use for discovery is limited (to use the famous example of "all men are mortal" and "Socrates is a man", how do you prove these two premises just using the syllogism? Observation and dialectical arguments seem to have to fill in here), and its best use seems rather to be clear exposition.
It's good for in the wild (real world) (outside academia)) critical thinking, spotting fallacious reasoning, etc.
Intuition>logic
>taking A and B both as false
When A and B are taken as both false, the result is null, because 0 -> 0 = null. Not false. Once again, if you don't understand the axioms, you can't construct a valid truth table.
On the other hand, in classical logic, this statement is true: If a dog walked on the moon, monkeys are plants. This is a true statement according to classical logic. In connexive logic, this statement would have a null truth value.
>When A and B are taken as both false, the result is null, because 0 -> 0 = null. Not false. Once again, if you don't understand the axioms, you can't construct a valid truth table.
Bro valid truth tables don't have null values. If it has a null value whether or not it is a tautology is meaningless. It's not even logic at that point
>Bro valid truth tables don't have null values.
Yes, they do. Buy a textbook introduction to connexive logic.
> If it has a null value whether or not it is a tautology is meaningless
Null is supposed to represent meaningless, because there are meaningless statements. It is still logic, just a logic that is less absurd.
>Yes, they do. Buy a textbook introduction to connexive logic.
My truth table has donuts and puppies as possible values. Just admit you're wrong man. It will be better for you in the long run. A truth table with more than true and false is not a truth table. And like I already said I can't even begin to imagine what you think a tautology is if you can't use certain truth values in the logical proposition.
>My truth table has donuts and puppies as possible values.
That would be ridiculous, so I would reject it. Null is not absurd, especially in the example I gave which clearly has a null truth value.
Not all the truth values, only the ones that don't make sense.
I'm not sure if you're the same poster, but you both need to read introductions to this logic. It's not something I made up personally. It was the standard for all logical discourse prior to the 20th century, and for some it still is. It was only replaced to make certain operations easier in mathematics. If you refuse to believe that an outcome can be meaningless or null, that is your problem, and not logic's.
Look I can show a contradiction isn't inconsistent
A / ~A
but you have to use my special logical and where all the truth values for it are null. Logicians BTFO
Kreeft has an entire chapter that answers your question. Why is this place so hopelessly infested with pseuds that can't even do the bare minimum and actually research what they purport to comment upon?
>Kreeft has an entire chapter that answers your question.
NTA but what chapter? in this book?
The Introduction:
Section 3 - The Two Logics
it's pretty dumb lol, I just finished reading it
The sad thing is, the rest of this book is extremely insightful. I cleared up a lot of misconceptions and confusions about Aristotelian thinking just by flipping randomly through the pages (e.g. Aristotle thinks through "intension" more than "extension", or at least more through intension than we're used to, which explains why he sees genera as "contained in" individuals rather than the opposite way around, like we do in scientific taxonomy).
Most of Kreeft's problems with formal logic come from metaphysical gripes which I don't think are inherently present in formal logic whatsoever. I feel like if Kreeft understood the founders of formal logic, Frege and Peirce, he would have a much different conception of predicate logic. Both were committed realists, especially the latter, who took much from Scholastic realism.
If anything, Kreeft's assertions about Aristotelian logic being "more natural" than formal logic make zero sense. Aristotelian logic only handles basic propositions, yet almost all speech happens with multiple subjects and quantifiers ("valency"). In that way, formal logic is more suited to everyday reasoning because it is capable of handling the problems that are thrown at us every day.
The polemics detract from what is otherwise a very direct and concise introduction to the topic that pretty much anyone can pick and benefit from. He should have saved the polemics for a separate book, their inclusion invites unnecessary controversy.
Well, it wasn't really a distraction. He included it mostly in one chapter in the beginning (which he offers readers the opportunity to skip it with no harm done) and (what wasn't mentioned earlier) an appendix at the end of the book.
The whole book is aimed at Christian wackos that want to home school their kids. It's fetishization of Aristotle has more to do with the fact the he's old and traditional than any real philosophical issue.
it's a really good book though. and I think most "Christian wackos" would be too stupid to get anything out of it
Some other books by the illustrious Peter Kreeft
Socrates' Children Volume I-4
Forty Reasons I Am a Catholic
Angels and Demons: What Do We Really Know about Them?
How to Destroy Western Civilization and Other Ideas from the Cultural Abyss
Ha!: A Christian Philosophy of Humor
Your Questions, God's Answers
The man is a cranky polemicist aimed primarily at children and under educated fundamentalists.
I don't really see any problems with these titles. He seems to be a devout Catholic.
The polemics serve to remedy the apparent discrepancy regarding what aspect of logic a beginner should pursue. You could say that they were unneeded but where this book shines is in introducing you to controversial debates in a non-clinical manner.The problem manifest in this thread is that a group of individuals believe that a beginner text that haven't read should satisfy complicated divisions in the philosophical landscape. I blame OP for this.
>Most of Kreeft's problems with formal logic come from metaphysical gripes which I don't think are inherently present in formal logic whatsoever
Which is why his justification is dependent upon philosophical reasoning. Its a flawed book but not for the reasons anons in this thread think. Either way, no book could ever give us a through overview of a antique tradition but Kreeft makes for a wonderful beginner text
?t=102 is an insightful look for who exactly this book is meant for (even though the man literally tells you this in the introduction)
>Its a flawed book but not for the reasons anons in this thread think. Either way, no book could ever give us a through overview of a antique tradition but Kreeft makes for a wonderful beginner text
I don't think the book is flawed insofar as the content, for its content, is great. Kreeft just has a poor understanding of how Aristotelian logic relates to everything else.
>im a pseud because i dont wanna read a book published by a crank academic through something called "St Augustine's Press" that argues for a patently false conclusion
lol
>I am enough of a moron to open up a discussion about a topic I am entirely misinformed upon
lmao
i'm pretty well-informed on this topic, which is why I don't need to read crank books on vanity presses in order to follow a discussion
Formal logic is a house of cards. It is very impressive but has nothing underneath.
you live in a house of dick
>Is Aristotelian logic really as powerful as Kreeft says it is? Is formal logic really that ontologically suspect?
yes
/thread