What? The problem with that is the argument is just the form, not the truth value of the two premises. All bouncy orange balls are bouncy, all bouncy orange balls are bouncy, but that does not imply "some orange are bouncy", it doesn't follow. Of course the sentence doesn't make sense but the relevant logical issue is just the use of an invalid argument form. — MindForged

Right, the problem is the form in that the form doesn't guarantee that the conclusion is true.

That doesn't mean that the conclusion can't be true. If All guitars are Gibsons and All guitars are Les Pauls, then some Gibsons are Les Pauls. So the conclusion is true in that case. But it's not impossible for the premises to be true and the conclusion false, because we can formulate a version of the argument where the conclusion is that some orange is bouncy.

I don't see the conceptual issue here, these seem like perfectly comprehensible properties some object might have even if they do not in fact have them — MindForged

I was explaining this to aletheist, and I can explain it to you, but it will take a few steps. First, what is the domain you're dealing with in the example you have in mind?

Because empty terms show this argument form to fail and thus Aristotle was wrong to deem it a valid argument, hence Classical Logic was right to distance itself from Aristotle's logic. Following from Russell, take this argument:

All winged horses are horses,
All winged horses have wings,
Therefore some horses have wings.

Clearly the first two premises are true but the conclusion is clearly false, we know there are no horses with wings. So this ought not be regarded as a valid argument in the logical systems developed after Aristotle. — MindForged

It is a valid argument form in Aristotelian logic because statements of the form All A is B must have one or more instances in order to be true (just as with Some A is B).

To give an example using real things:

(1) All tall trees on my property are tall.
(2) All tall trees on my property are trees.
(3) Therefore some trees on my property are tall.

If I have no tall trees on my property then (1) and (2) are not true. And there are no cases where (1) and (2) are true and (3) is false, so it is a valid argument.

Wikipedia gives the rationale for Aristotle's choice.

It is claimed Aristotle's logic system does not cover cases where there are no instances. Aristotle's goal was to develop "a companion-logic for science. He relegates fictions, such as mermaids and unicorns, to the realms of poetry and literature. In his mind, they exist outside the ambit of science. This is why he leaves no room for such non-existent entities in his logic. This is a thoughtful choice, not an inadvertent omission. Technically, Aristotelian science is a search for definitions, where a definition is 'a phrase signifying a thing's essence.'... Because non-existent entities cannot be anything, they do not, in Aristotle's mind, possess an essence... This is why he leaves no place for fictional entities like goat-stags (or unicorns)." [13] However, many logic systems developed since do consider the case where there may be no instances. — Existential import - Wikipedia

Right, the problem is the form in that the form doesn't guarantee that the conclusion is true. — Terrapin Station

But deductive validity requires that the form must guarantee deriving only true conclusions from true premises.

It is a valid argument form in Aristotelian logic because statements of the form All A is B must have one or more instances in order to be true (just as with Some A is B). — Andrew M

Right, but Aristotle stipulated that additional premise; as your Wikipedia quote states, it was "a thoughtful choice, not an inadvertent omission."

It is a valid argument form in Aristotelian logic because statements of the form All A is B must have one or more instances in order to be true (just as with Some A is B). — Andrew M

Sure but as I said empty terms show this to be improper. As your quotesaid, Aristotle stipulated that logic was to regard known existing things and thus empty terms were off the table by fiat, not by argument. But this is kind of ridiculous. It's just true that, for example, mathematicians both use formal logic and do not assume that every entity they quantify over is instantiated. Thus if we followed Aristotle we'd handicap mathematics in pretty ridiculous ways. Logic ought to work just just the same regardless of whether or not there are instances of the things referenced.

Right, the problem is the form in that the form doesn't guarantee that the conclusion is true.
[...]

But it's not impossible for the premises to be true and the conclusion false, because we can formulate a version of the argument where the conclusion is that some orange is bouncy. — Terrapin Station

But that's exactly the point. An invalid argument doesn't mean the conclusion is false, it means the form of the argument is such that the truth of the premises does not necessarily entail the truth of the conclusion. And as Darapti does not guarantee it's rightly deemed invalid.

Right not necessarily, but the conclusion does follow in your example. Your example is actually a bit different structurally, because you're saying that all F that G can also be predicated of are F, and all F that G can also be predicated of are G . . .

But deductive validity requires that the form must guarantee deriving only true conclusions from true premises. — aletheist

Right. I wasn't arguing that it was valid, and I explained why it's not. What I argued is that people gave examples where the conclusion did follow. They didn't give examples where the conclusion doesn't follow.

No, the structure was all F that E can be predicated of are E all F that G can be predicated of G, therefore some E is G. The predicates winged-horse and horse are not the same predicate. Hence it doesn't follow.

Right, but Aristotle stipulated that additional premise; as your Wikipedia quote states, it was "a thoughtful choice, not an inadvertent omission." — aletheist

I don't think he's stipulating an additional premise. He's instead saying that predication is only applicable when the subject term refers to something that exists.

That is, for Aristotle, vacuous statements are neither true nor false since the presupposition that the subject term refers fails.

It's just true that, for example, mathematicians both use formal logic and do not assume that every entity they quantify over is instantiated. Thus if we followed Aristotle we'd handicap mathematics in pretty ridiculous ways. — MindForged

Can you give any examples where this issue would be important?

Logic ought to work just just the same regardless of whether or not there are instances of the things referenced. — MindForged

To me it seems analogous to "The King of France is bald". Note that Russell and Strawson disagreed on how to treat this kind of statement, with Strawson defending the view that the presupposition fails (and thus the statement is neither true nor false).

No, the structure was all F that E can be predicated of are E all F that G can be predicated of G, — MindForged

Try that one mo 'gin in Engrish.

Can you give any examples where this issue would be important? — Andrew M

Any time one uses the universal quantifier I would think. "For each natural number n, "n x n" = "n + n". That does not assume there is some existing n, it's just a statement about how to define an abstract operation, whether or not that holds in the physical world. If quantifying did assume existence we'd expect to see, I dunno, every number be instantiated by some collection of elements or weird alegbraic models have mapped onto real things, or every kind of geometry have a corresponding universe modeled on it, wouldn't we?

To me it seems analogous to "The King of France is bald". Note that Russell and Strawson disagreed on how to treat this kind of statement, with Strawson defending the view that the presupposition fails (and thus the statement is neither true nor false). — Andrew M

Well OK, there is a debate here but I'm of the view that one ought to try and use as few different logics as possible. I'm not familiar with what Strawson said here but Russell's general route seems correct (use classical logic if it can give a good answer), though I don't think I actually accept his theory of descriptions to resolve these.

"For each natural number n, "n x n" = "n + n". That does not assume there is some existing n, it's just a statement about how to define an abstract operation, — MindForged

Why would you define an abstract operation, and moreover assign "true" to it (assuming we can even really make sense of that), if it can't be satisfied by anything we plug into the variable (in whatever domain you're working in)?

All winged horses are horses,
All winged horses have wings,
Therefore some horses have wings.

Clearly the first two premises are true but the conclusion is clearly false, we know there are no horses with wings. So this ought not be regarded as a valid argument in the logical systems developed after Aristotle. — MindForged

What? It seems to me that if the premises are true, then the conclusion must also be true. It logically follows.

Having read a little more of the discussion, I think I understand some of what has been said about Russell's view, and maybe he was indeed onto something, but if this is a consequence, it's very counterintuitive.

You're treating the premises in a purely logical manner, but assessing the conclusion with respect to whether it's contingently true in the actual world. — Terrapin Station

That's what I was thinking too. There seems to be a disconnection involved in his assessment.

In modern logic it commits the existential fallacy, it's suppressed premise ("There exists at least one winged horse") is clearly false. — MindForged

But that wasn't in the argument, and it doesn't seem appropriate to interpret the argument in that way.

No, the structure was all F that E can be predicated of are E all F that G can be predicated of G,
— MindForged

Try that one mo 'gin in Engrish. — Terrapin Station

:lol:

It took me a while and several reads to figure out what he was saying, but I think I got it, and it's a lot clearer if you break it up:

No, the structure was:

All F that E can be predicated of are E

All F that G can be predicated of are G

What? It seems to me that if the premises are true, then the conclusion must also be true. It logically follows. — S

Unless you can point to where the winged horses are you cannot say it's valid. If the conclusion of an argument is false in spite of true premises, then the argument for is invalid. There is thus a model where truth is not preserved, that's the definition of an invalid argument.

But that wasn't in the argument, and it doesn't seem appropriate to interpret the argument in that way. — S

"Therefore some horses have wings" has an existential operator, how is that inappropriate to point out when it creates a false conclusion from true premises?

Why would you define an abstract operation, and moreover assign "true" to it (assuming we can even really make sense of that), if it can't be satisfied by anything we plug into the variable (in whatever domain you're working in)? — Terrapin Station

I didn't say it couldn't be satisfied, what I said was that quantifying over all the elements of a set does not entail the set has members who exist (that's a separate set). Winged horses could exist but they do not. So given we know this we infer the invalidity of form. The reason I keep repeating this was because way back you seemed to be saying it was valid:

It does, though. It's the same as "All silver toasters are toasters. All silver toasters are silver. Therefore some toasters are silver." — Terrapin Station

Any time one uses the universal quantifier I would think. "For each natural number n, "n x n" = "n + n". That does not assume there is some existing n, it's just a statement about how to define an abstract operation, whether or not that holds in the physical world. — MindForged

I'm not clear on how the example applies. There's one natural number that satisfies that identity (the number 2). But even if the result were an empty set, I don't see any predication of its members analogous to "all winged horses are horses".

!!! oops, that was supposed to say n x 2 = n + n. Mea culpa.

Anyway, what I'm saying is there doesn't need to be anything that instantiates this for us to reason about it. For Aristotle, logic is supposed to be used for things known to exist. In the above, "For every" is just the universal quantifier yes? That's before the predication. But surely it's fine to reason in mathematics without assuming something in the physical world corresponds to this? (Obviously it does in this case but pure mathematics isn't guaranteed to)

Unless you can point to where the winged horses are you cannot say it's valid. — MindForged

That's not how validity works.

If the conclusion of an argument is false in spite of true premises, then the argument form is invalid. — MindForged

Soundness is about actual truth or falsity. Validity is about assumed truth or falsity. In your example syllogism, under the assumption that the premises are true, it follows that the conclusion is true. Hence, the syllogism is valid.

There is thus a model where truth is not preserved, that's the definition of an invalid argument. — MindForged

You're jumping ahead based on your own assumptions. I'm questioning these very assumptions of yours. You're begging the question.

"Therefore some horses have wings" has an existential operator, how is that inappropriate to point out when it creates a false conclusion from true premises? — MindForged

Why do you think that it must be interpreted in that way, as implying existence? In English, as opposed to symbolic logic, and worded as such, it is more ambiguous than you're making out.

I grant that Russell might have a good point. But you are not making a very convincing case.

Winged horses could exist but they do not. — MindForged

In which case saying anything about winged horses puts us in the domain of things that we're imagining. If we change domains midstream we're equivocating.

Anyway, what I'm saying is there doesn't need to be anything that instantiates this for us to reason about it. For Aristotle, logic is supposed to be used for things known to exist. In the above, "For every" is just the universal quantifier yes? That's before the predication. But surely it's fine to reason in mathematics without assuming something in the physical world corresponds to this? (Obviously it does in this case but pure mathematics isn't guaranteed to) — MindForged

That's fine, as far as I can tell. Aristotle was fine with abstractions and hypotheticals, as long as their use was intelligible. The only issue I've raised is with vacuous statements. But there doesn't seem to be a vacuous statement in your example.

That's not how validity works. — S

um, no. Validity is defined as truth preservation over all cases. As we know the first two premises of the argument are true, yet the conclusion is false, we know the issue has to be with the form of the argument. It's invalid, in other words. As the SEP article in logical consequence says:

The model-centered approach to logical consequence takes the validity of an argument to be absence of counterexample. A counterexample to an argument is, in general, some way of manifesting the manner in which the premises of the argument fail to lead to a conclusion. One way to do this is to provide an argument of the same form for which the premises are clearly true and the conclusion is clearly false. Another way to do this is to provide a circumstance in which the premises are true and the conclusion is false. In the contemporary literature the intuitive idea of a counterexample is developed into a theory of models. Models are abstract mathematical structures that provide possible interpretations for each of the non-logical primitives in a formal language. Given a model for a language one is able to define what it is for a sentence in that language to be true (according to that model) or not. So, the intuitive idea of logical consequence in terms of counterexamples is then formally rendered as follows: an argument is valid if and only if there is no model according to which the premises are true and the conclusion is not true. Put in positive terms: in any model in which the premises are true (or in any interpretation of the premises according to which they are true), the conclusion is true too.
— SEP

Soundness is about actual truth or falsity. Validity is about assumed truth or falsity. In your example syllogism, under the assumption that the premises are true, it follows that the conclusion is true. Hence, the syllogism is valid. — S

It does not follow. If I assume all winged horses are horses and all winged horses have wings, we cannot infer that some horses have wings because we see in the actual world that the first two premises are true yet there are no winged horses. This argument form is known to be invalid in classical logic, it commits the existential fallacy. To make it valid you need a fourth premise that explicitly states that there is at least one existing winged horse. But then we see exactly why the original argument form was invalid.

You're jumping ahead based on your own assumptions. I'm questioning these very assumptions of yours. You're begging the question. — S

What? How am I begging the question when I just stating the definition of semantic logical consequence?

Why do you think that it must be interpreted in that way, as implying existence? In English, as opposed to symbolic logic, and worded as such, it is more ambiguous than you're making out. — S

Because "There is" is more or less always interpreted as an existence claim. We're talking about formal logic, not informal natural language reasoning.

In which case saying anything about winged horses puts us in the domain of things that we're imagining. If we change domains midstream we're equivocating. — Terrapin Station

That's more or less what I'm saying. That's what makes it invalid. The class can't be assumed to have members unless we state that it does. Aristotle didn't see this as a problem because he thought logic ought only consider classes with known existing members, but that's not assumed in mathematical reasoning nowadays. It's too limited.

No, on the contrary, if the premises are true, it follows that the conclusion is true. There is no counterexample to the conclusion of the argument under the assumption that the premises are true. You can't appeal to the actual world, because validity is about logical form, and soundness is about the actual world. You think that the article you quoted supports what you're saying, but it doesn't. You seem to be ignoring the premises and only looking at the conclusion.

Because "There is" is more or less always interpreted as an existence claim. We're talking about formal logic, not informal natural language reasoning. — MindForged

You're not even quoting the wording of the argument, which is funny, given that you're the one who wrote it. There is no "There is" contained in the argument. You're reading that into it, which is the problem.

I grant that there might be a version of the argument where what you're saying applies, but that's a different argument to the one that you presented, and I don't agree that your interpretation is the only possible way that the argument can be interpreted. The wording is ambiguous.

The class can't be assumed to have members unless we state that it does. Aristotle didn't see this as a problem because he thought logic ought only consider classes with known existing members, but that's not assumed in mathematical reasoning nowadays. It's too limited. — MindForged

"A class having members" when we're doing mathematics is a matter of whether we're thinking about things in a particular way or not. If you're conceiving of some class with particular properties, especially so that you could utter a statement a la "All x are F" and assign "T" to it, then that class has members, because the domain is what we're imagining, and an xF exists by virtue of conceiving of it (it exists as a conception, which is the domain we're dealing with).

No, on the contrary, if the premises are true, it follows that the conclusion is true. There is no counterexample to the conclusion of the argument under the assumption that the premises are true. You can't appeal to the actual world, because validity is about logical form, and soundness is about the actual world. You think that the article you quoted supports what you're saying, but it doesn't. You seem to be ignoring the premises and only looking at the conclusion. — S

The problem is the premises are true. Are you seriously denying that all winged horses are horses or that they have wings? If so then it has to be a terminological disagreement. Otherwise you're flat out wrong because no winged horses actually exist. The article I quoted does support me because the real world is a model in which the argument is proven to not be truth preserving. It goes from true premises to a false conclusion. The idea that the actual world doesn't count is absurd. We use logic to come to true conclusions about the actual world all the time.

You're not even quoting the wording of the argument, which is funny, given that you're the one who wrote it. There is no "There is" contained in the argument. You're reading that into it, which is the problem. — S

Read it again. "Therefore some horses have wings" uses existential quantification, that's what "some" is translated as in formal logic. I'm quoting myself correctly. There's no argument here, the argument is considered invalid by logicians for exactly this reason. It does not preserve truth in all models.

I grant that there might be a version of the argument where what you're saying applies, but that's a different argument to the one that you presented, and I don't agree that your interpretation is the only possible way that the argument can be interpreted. The wording is ambiguous. — S

The wording is only ambiguous if you don't interpret the logical terms as they standardly are done. "All" is universal quantifying, "some" is existential quantifying. You cannot validly move from quantifying over a set to saying the set has members who satisfy the conditions to be part of the set. That has to be an extra premise otherwise it commits the existential fallacy. Unless I'm much mistaken, this is the exact argument Russell gives to show why modern logic does not admit this as a valid form.

Are you seriously denying that all winged horses are horses or that they have wings? If so then it has to be a terminological disagreement. Otherwise you're flat out wrong because no winged horses actually exist — MindForged

The truth-maker of any statement in logic is never going to be whether something obtains empirically.

The truth-maker for a conclusion is whether the conclusion follows from the premises. What's the case in the actual world has zilch to do with it.

Except when you give the argument an interpretation, what makes a premise true is going to be some truth maker. We have a model (the real world) and in this model the first two premises are true. But the conclusion is false. This (finding a counterexample in an interpretation) is the most common method checking if a model is valid when doing semantic consequence, just check the SEP quote above. If a false conclusion follows from true premises (and we know those premises are true) it is invalid.

The model-centered approach to logical consequence takes the validity of an argument to be absence of counterexample. A counterexample to an argument is, in general, some way of manifesting the manner in which the premises of the argument fail to lead to a conclusion. One way to do this is to provide an argument of the same form for which the premises are clearly true and the conclusion is clearly false — SEP

Do you just object to model theory? It would be the same with just the syntax route.

We have a model (the real world) and in this model the first two premises are true. — MindForged

The first two premises are about a conception; they're a priori claims about how you're using terms. They're not about the external world.

What you're quoting is about plugging values into variables, by the way. You're winged horse argument isn't variables.