But there's something funny in all that, at least to my ear. It almost seems like we need to already know the truth of our premises in order for the logic to be worked out. But if that's the case then how does logic retain its usefulness in the cases where we do not know the truth value of some conclusion? We may have good reason to believe the premises, but couldn't a novel argument actually be a case where we are proving that the form of our argument is, in fact, fallacious because it leads to a false conclusion?
In which case, what is the point of soundness anyways? — Moliere
Really I'm just fishing for any resources that might detail the concept of soundness more fully to satisfy an intellectual itch I have. — Moliere
So you might even say that soundness is analytically defined as those forms of argument which happen to preserve truth. — Moliere
Or, given that there are multiple systems of logic, we could also say that soundness is relative to some system of rules of inference, and all arguments which follow said rules of inference and also contain true premises produce sound arguments. — Moliere
It almost seems like we need to already know the truth of our premises in order for the logic to be worked out. — Moliere
That's validity. Broadly, validity is defined as "Truth preservation over all cases", or if one wanted to be a douche, "Preservation of the designated value across propositional transformations" (I wrote this in class once and the professor indirectly told me to chill the fuck out, lol). Soundness requires a valid argument and true premises. — MindForged
The conclusion is veridical. — MindForged
Not for the validity. That's the logic part. Soundness (at the object language) does need the argument to be valid but the truth value of the premises isn't a question of logic. The logic is the machinery guiding the inferences, soundness is, like, whether or not the machine is doing a good job. — MindForged
So I keep on thinking -- might it be the case that we use a (now believed valid) form of argument with true premises that then comes to false conclusions? — Moliere
Here's where I'm getting tripped up in talking about soundness. While validity does not rely upon soundness for its conceptual clarity, soundness does rely upon validity -- since it must satisfy both that the argument is valid and the argument uses true premises. That's what I'm trying to get at at least, though I do not think I'm putting it well since I basically just restated validity as you note. — Moliere
Is veridicality the same as soundness? — Moliere
At least with informal logic usually the procedure is to show some kind of argument that uses a form with true premises and a false conclusion to demonstrate that some form of argument is invalid. Granted that's not the same as validity, but that's where I'm coming from in my (admittedly rambly) ruminations; that the demonstration of invalidity, rather than validity, relies upon true premises reaching a false conclusion. — Moliere
I think the language got away from you. The - your - argument above is called "Bramantip," A-A-I in the fourth form. It's valid (with an existential qualification usually not made explicit). But with winged horses it's not sound. But i'm pretty sure you already know this.And obviously there are no winged horses in reality. The problem is with the actual argument form, we are merely using real world things and truth value to bring the flaw in the argument form to light. — MindForged
All winged horses are horses
All winged horses have wings
Therefore some horses have wings — MindForged
No, that was not Bramantip, it was Darapti. Like Bramantip, Darapti is also not a valid argument in modern logic — MindForged
1. All winged horses are horses,
2. All winged horses have wings,
3. There is at least one winged horse,
4. Therefore some horses have wings. — MindForged
Your 3 isn't part of the syllogism. There is always an implied if before every proposition; for the conclusion, it might be if 1 and 2 are true, then.... — tim wood
I find much to disagree with in your post, but this can stand for most of it. There is an implied if in all logic. What the exact content of the if-statement is depends on the context; usually it's not important; and usually it's only a problem when people forget it's there.So there is no implied "If" in Aristotle's logic. — MindForged
I find much to disagree with in your post, but this can stand for most of it. There is an implied if in all logic. — tim wood
And hypothetical syllogisms are discussed in (by) Aristotle. — tim wood
In some arguments it is easy to see what is lacking, but others escape our notice and appear to syllogize because something necessary results from what is
supposed. For example, if one had assumed that if a non-substance is destroyed then
a substance will not be destroyed, and that if those-things-out-of-which are destroyed,
the-thing-out-of-them also perished—when these things have been laid down, it is necessary indeed that the part of a substance should be a substance, but this has not been syllogized through the things taken, but rather premises are left out.
[...]
Again, if it is necessary, if a human is, for an animal to be and, if an animal, a substance, then it is necessary, if a human is, for a substance to be; but it has not yet been syllogized, since the premises are not related as we have said. We are misled in cases like these by the fact that something necessary results
from what is supposed, because a syllogism is also necessary. But ‘necessary’ is more extensive than ‘syllogism’: for every syllogism is necessary, but not everything necessary is a syllogism. Consequently, if something does result when certain things have been
posited, one should not try straight off to lead it back <into the figures>. Instead, one
must first get the two premises and next divide them this way into terms, and that
term which is stated in both the premises must be put as the middle (for the middle
must occur in both of them in all of the figures) — Aristotle
I read you as saying that certain arguments that presuppose existential import are out-of-court because the presupposition is not in all cases justified, and therefor the form of the argument is no good. — tim wood
All winged horses are horses,
All winged horses have wings,
There is at least one winged horse,
Therefore some horses have wings.
That's valid. But we know it's not sound since the third premise is clearly false.
Some people try to defend Syllogistic on this point by saying Aristotle thought logic was only concerned with existing things and so it's not really invalid. Of course, this is just stupid. If you try to keep this as valid and say that, for example, Syllogistic doesn't get anything wrong you end up invalidating other argument forms that are considered valid (I can go into this if you want) and you might as well exhaust mathematics since mathematics cannot function with the limited inference resources of Syllogistic (and besides, lots of math (pure mathematics) isn't "real" so this is a death knell). — MindForged
I'm curious about what the problems really are — Andrew M
That Aristotelian and classical logic are distinct will hardly be denied. But it might
well be suggested that the adoption of classical logic did not revise Aristotelian logic
in any interesting sense: Aristotelian logic was perfectly correct as far as it went; it was just incomplete. Classical logic simply extended it to a more complete theory. Such a suggestion would be false. It is a well-known fact, often ignored by philosophers (though not, perhaps, historians of philosophy) that Aristotelian logic is incompatible with classical logic in just the same way that non-Euclidean geometries are incompatible with Euclidean geometry. A central part of Aristotelian logic is syllogistic, and the most natural translation of the syllogistic forms into classical logic is as follows:
AaB | All As are Bs ∀x(Ax ⊃ Bx)
AeB | No As are Bs ¬∃x(Ax ∧ Bx)
AiB | Some As are Bs ∃x(Ax ∧ Bx)
AoB | Some As are not Bs ∃x(Ax ∧ ¬Bx)
Given this translation, Aristotelian syllogistic gives verdicts concerning the validity
of some syllogisms that are inconsistent with classical logic. Consider the inferences
called by the medievals Darapti and Camestros, which are, respectively:
All Bs are Cs
All Bs are As
Hence some As are Cs
All Cs are Bs
No As are Bs
Hence some As are not Cs
Both of these are valid syllogisms. Both are invalid in classical logic. The problem is, of course, one of existential import. Some syllogisms seem to presuppose that various categories are instantiated. It is sometimes suggested that the problem can be repaired by adding the import to the translations explicitly. Specifically, we add the clause ∃xAx to each of the a and e forms. (It would be redundant in the other two.) This is, indeed, sufficient to render all the syllogistic forms classically valid, but the problem with this is that it invalidates other central parts of Aristotelian logic, notably, the square of opposition. The square is:
AaB| AeB
_________
AiB | AoB
where the claims on the top line are contraries; on the bottom line are sub-contraries; and on both diagonals are contradictories. Now it is clear that, once the a form is augmented with existential import, a and o are not contradictories: both are false if
there are no As. For the same reason, neither are e and i.
Another suggested repair is to add existential import to the a form (but not the e), and take the o form to be its negation (∃x(Ax ∧¬Bx)∨¬∃xAx). This validates all the syllogisms and the square of opposition. The oddity of taking ‘some As are not Bs’ to be true if there are no As is clear enough. But more importantly, this repair invalidates another part of the traditional logic: the inferences of obversion. Specifically, obversion permits the inference from ‘no As are Bs’ to ‘all As are non-Bs’; which fails if the e form
is not existentially loaded. Obversion is not in Aristotle, but it is a perfectly standard
part of traditional logic.
It is sometimes suggested that, rather than adding existential import to the translations explicitly, we should take the instantiation of all the categories involved to be a global presupposition.This is a move of desperation. If it is correct, then we cannot use syllogistic to reason, e.g. in mathematics, where we certainly do not make such presuppositions. I don’t think that the traditional logicians who endorsed syllogistic believed this. Moreover, if we were to allow validity to have contingent presuppositions, pretty much anything could be made to be valid.
More importantly, the suggestion really will not save syllogistic. All winged horses
are horses, and all winged horses have wings. Applying Darapti, we may infer that there are some winged horses. The argument clearly generalizes. All As are As. A fortiori, all ABs are As; and symmetrically, all ABs are Bs. By Darapti it follows that there are some ABs. Thus syllogistic allows us to prove that any two categories intersect.
And if it be replied that this is just one of the global presuppositions, take B to be Ā, the complement of A (non-A). It can hardly be maintained that Aristotelian logic
globally presupposes contradictions. This argument requires the use of compound
terms. Again, these are not in Aristotle, but are an established part of traditional
logic.
What we have seen is that, however one interprets traditional logic in classical logic, something has to be given up. Moreover, this is quite essential. For as the last argument shows, traditional logic is, in fact, inconsistent. At any rate, classical logic is not (just) a more generous framework subsuming traditional logic. Prevarication aside, modern logic has given the thumbs-down to Darapti and its ilk.
— Graham Priest
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