No, your reading of it is incorrect because you seem to think it is saying:

All dogs have four legs
Lassie has four legs
Lassie is a dog

...is valid in symbolic logic. It doesn't say that. It says the exact opposite, that this is not valid. — Count Timothy von Icarus

Read it again. The paper says it is invalid, but that symbolic logic "disagrees".

Again, the paper is correct that it is invalid, but the paper is incorrect that symbolic logic disagrees.

If in a given interpretation, P is true, then per that interpretation, for any statement Q, Q->P is true. — TonesInDeepFreeze

That's perfectly clear.

"Dogs have four legs, and Lassie has four legs, therefore Lassie is a dog" is not a valid argument. The conclusion ("Lassie is a dog") may be true, but it has not been proved by this argument. It does not "follow" from the premises.

Now in Aristotelian logic, a true conclusion logically follows from, or is proved by, or is "implied" by, or is validly inferred from, only some premises and not others. The above argument about Lassie is not a valid argument [correct -TIDF] according to Aristotelian logic.Its premises do not prove its conclusion. And common sense, or our innate logical sense, agrees. [correct -TIDF] However, modern symbolic logic disagrees. [incorrect - TIDF] One of its principles is that "if a statement is true, then that statement is implied by any statement whatever."

Yes, disagrees that "a true conclusion logically follows from, or is proved by, or is "implied" by, or is validly inferred from, only some premises and not others."

This is perhaps ambiguous, but it's clarified in the following sentences.

It's not ambiguous. It's as plain as day, with a plain reading:

"Its premises do not prove its conclusion."

'it' refers to the Lassie argument.

"modern symbolic logic disagrees."

That is, modern symbolic disagrees that the Lassie argument's premises do not prove the conclusion.

modern symbolic disagrees that the Lassie argument's premises do not prove the conclusion. — TonesInDeepFreeze

Does that mean modern symbolic logic thinks the premises do prove the conclusion?

That is what the paper says. The paper is incorrect.

Not just incorrect, but incorrect due to egregious sophistry, ignorance or blatant lack of reasoning skills.

That is what the paper says. The paper is incorrect. — TonesInDeepFreeze

There's a paper that says the premises prove the conclusion of this argument?

Dogs have four legs, and Lassie has four legs, therefore Lassie is a dog

I want to see this paper, could you link me?

There's a paper that says the premises prove the conclusion of this argument? — flannel jesus

No, the paper says the argument is invalid, but that symbolic logic says it's valid.

The paper is a polemic against symbolic logic, and it argues (egregiously incorrectly) that symbolic logic regards the argument as valid because symbolic logic says that any true statement (such as "Lassie is a dog") is implied by any statements. In my first post about it, I explained exactly where the sophistry occurs. (There are some typos in my post, but I made edit notes to correct them.)

It's quoted in a post earlier in this thread.

It's quoted in a post earlier in this thread. — TonesInDeepFreeze

There are many many posts in this thread. I don't have any means of efficiently searching for it, so that's why I'm asking you. If you would prefer not to link me up for whatever reason, I suppose I'll just have to accept that.

It's clearly discussing paradoxes of material implication, not arguing that "All A are B and C is B implies C is A," is valid anywhere. In fact it says it isn't valid tout court up above. If that was the point, it could have been stated much clearer and then everything following amounts to a giant non-sequitur. But it isn't a non-sequitur, it's the point of the entire section.

If they wanted to make the point you ascribe to them why wouldn't they use an example like:

All monkeys have tails.
Garfield the cat has a tail.
Therefore Garfield is a monkey.

It would show the absurdity much clearer. But the point is that "has four legs" doesn't imply "is a dog," in that argument, and yet Q → P is always true when P is true, which is incongruous with how Q does not imply P in the other argument. I agree that it could be written clearer, but I think it's pretty uncharitable and ignoring all the context to assume they are claiming what you say they are.

https://thephilosophyforum.com/discussion/comment/916812

Since there were so many typos in my reply, here it is corrected:

Dogs have four legs, and Lassie has four legs, therefore Lassie is a dog" is not a valid argument. The conclusion ("Lassie is a dog") may be true, but it has not been proved by this argument. It does not "follow" from the premises.

Now in Aristotelian logic, a true conclusion logically follows from, or is proved by, or is "implied" by, or is validly inferred from, only some premises and not others. The above argument about Lassie is not a valid argument according to Aristotelian logic. Its premises do not prove its conclusion. And common sense, or our innate logical sense, agrees. However, modern symbolic logic disagrees. One of its principles is that "if a statement is true, then that statement is implied by any statement whatever.

Symbolic logic definitely does not hold that that Lassie argument is valid.

That claim in the article is either sneaky sophistry or egregious ignorance. It is a ludicrous claim. It goes dramatically against what obtains in symbolic logic.

Let:

'Fx' stand for 'x has 4 legs'

's' stand for 'Lassie'

'Dx' stand for 'x is a dog'

The argument is:

Ax(Dx -> Fx)
Fs
Therefore Ds

Symbolic not only does not say that that is valid, and not only does symbolic logic say it is invalid, but symbolic logic proves it is invalid.

Here is where the authors try to pull a fast one:

Correct: A valid formula is implied by any set of formulas.

Correct: If P is true, then, for any formula Q, we have that Q -> P is true.

Incorrect: If P is true, then Q -> P is valid.

Look what the authors did:

By saying "'Lassie is a dog" is true", they are adopting Ds as a premise. So, of course,

Ax(Dx -> Fx)
Fs
Ds
Therefore Ds

Or I invite the authors to show any symbolic logic system for ordinary predicate logic that provides a derivation of:

Ax(Dx -> Fx)
Fs
Therefore Ds

Moreover, we prove that classical logic provides that its proof method ensures that the premises indeed entail the conclusion. That is, if the conclusion is not entailed by the premises, then the conclusion is not proved by the premises. And that goes for both true and false conclusions. If the truth that Lassie is a dog is not entailed by the premises, then 'Lassie is a dog' is not provable from the premises.

That's a disgustingly specious and disinformational start of an article. And unfortunate that that speciousness and disinformation is propagated by another poster quoting it here.

Again, look at the exact words in the paper:

"Its premises do not prove its conclusion."

'it' refers to the Lassie argument.

"modern symbolic logic disagrees."

That is, modern symbolic disagrees that the Lassie argument's premises do not prove the conclusion.

That is plain as day. All you need to do is read the exact words. It is amazing that you won't recognize it.

Discussing other aspects of the paper does not change that the paper claims that symbolic logic regards the Lassie argument is valid. Indeed, the paper goes on to give its incorrect explanation of why symbolic logic regards the Lassie argument to be valid.

I somehow find it more plausible that they were trying to highlight the incongruity between the fact "Lassie has four legs" does not imply Lassie is a dog in symbolic logic in the argument:

All dogs have four legs
Lassie has four legs
Therefore Lassie is a dog

And the fact that "Lassie has four legs" does imply Lassie is a dog if "Lassie is a dog" is true. That's the straightforward purpose given the context, particularly since the text is not particularly hostile towards symbolic logic aside from arguing that it isn't particularly helpful for most people's use cases.

This, rather than assuming they are trying to imply an falsehood to cast shade on symbolic logic in an extremely roundabout way using an example obfuscates their point (if that was the point they were making)—doing all this to try to suggest something that is easily verifiable as false for ... what purpose?

IDK, maybe I am letting the principle of charity run amok.

"Its premises do not prove its conclusion," because they they do not stand in the right sort of relation to one another (this is the topic of the paragraph). This is true in a specific sense in Aristotlean logic, which denies as valid arguments in which the premises are inconsistent, arguments with conclusions that would follow from any premises whatsoever, or arguments with superfluous premises. Symbolic logic does indeed disagree with this. I assume this is what "it" refers to because that's what all the context suggests.

In fact it says it isn't valid tout court up above. — Count Timothy von Icarus

It correctly says it is invalid, but incorrectly says that symbolic logic "disagrees". It's right there in the paper. It is amazing that you ignore that plain fact.

If that was the point, it could have been stated much clearer — Count Timothy von Icarus

It was stated in perfect clarity that symbolic logic "disagrees" that the premises don't prove the conclusion.

If they wanted to make the point you ascribe to them why wouldn't they use an example like:

All monkeys have tails.
Garfield the cat has a tail.
Therefore Garfield is a monkey. — Count Timothy von Icarus

Because their point in that paragraph was that "Lassie is a dog" is true but not provable from the premises but that symbolic logic disagrees that is not provable from the premises.

Read the paragraph slowly, line by line, and you will see:

"Its premises do not prove its conclusion."

"modern symbolic logic disagrees."

I somehow find it more plausible that they were trying to highlight the incongruity between the fact "Lassie has four legs" does not imply Lassie is a dog in symbolic logic in the argument:

All dogs have four legs
Lassie has four legs
Therefore Lassie is a dog

And the fact that "Lassie has four legs" does imply Lassie is a dog if "Lassie is a dog" is true. — Count Timothy von Icarus

Whatever you think was meant to be highlighted, or plausible, or your interpretation, the plain fact is that the paper says that symbolic logic regards the argument as valid.

That's enough right there. It's incontrovertible.

But, going on:

The reason they make that claim is to make a strawman against symbolic logic. It's a strawman because symbolic logic does not say the argument is valid. Then they incorrectly argue that the reason symbolic logic says the argument is valid is because "Lassie is a dog" is true and symbolic logic says that any true sentence is proven by any sentences.

the straightforward purpose given the context — Count Timothy von Icarus

Whatever you think the purpose is, it is utterly straightforward that the paper claims that symbolic regards the argument as valid. They incorrectly base that claim on the claim that symbolic logic regards the argument as valid because "Lassie is a dog" is true and symbolic logic says that any true sentence is proven by any sentences.

the text is not particularly hostile towards symbolic logic aside from arguing that it isn't particularly helpful for most people's use cases. — Count Timothy von Icarus

The article uses the Lassie example to argue that symbolic logic departs from common sense logic. But that is a specious argument, since symbolic logic is right with common sense regarding the Lassie argument.

This, rather than assuming they are trying to imply an falsehood to cast shade on symbolic logic in an extremely roundabout way using an example obfuscates their point (if that was the point they were making)—doing all this to try to suggest something that is easily verifiable as false for ... what purpose? — Count Timothy von Icarus

(1) You are obfuscating. Your argument is that they couldn't have meant what they exactly wrote because of something else. It is in broad daylight that they claimed that symbolic logic disagrees that the argument is invalid. And what they say right after is premised on that. Again: They make the claim, then argue that the reason symbolic logic regards the argument as valid is that symbolic logic says "true proven by anything" (by the way, that is not what symbolic logic says, so another false claim in the paper).

(2) The example and argument is not roundabout. And it does not obfuscate their point. It makes their point blazingly clear as they themselves state it right after the example. They try to make symbolic look ridiculous for saying the argument is valid, then incorrectly say what is at root in symbolic logic that allows symbolic logic to say the argument is valid.

(3) The purpose is to present an argument about symbolic logic. I don't why they resorted to egregious sophistry to do that. Why does anyone resort to sophistry? Possibilities include: (a) They think they can get away with it, (b) They got caught up in themselves thinking they had a clever argument, (c) They don't understand symbolic logic ...

IDK, maybe I am letting the principle of charity run amok. — Count Timothy von Icarus

What is that supposed to mean?

Anyway, you continue to evade exactly what they wrote.

In fact it says it isn't valid tout court up above. — Count Timothy von Icarus

No, not tout court. There's an 'however'. They correctly say it is invalid but they also incorrectly say that, however, symbolic logic disagrees.

It's text in broad daylight.

"Winston Churchill was French" does not imply a contradiction. But that does not imply that "Winston Churchill was French" is true. — TonesInDeepFreeze

Of course.



I don't know what to make of your use of "interpretation".

An interpretation, aka 'a model'.

For sentential logic, an interpretation assigns to each sentence letter a value True of value False.

Most commonly this is represented as columns in a truth table.

This is ordinary semantics for sentential logic.

/

I hope my explanation regarding my answer to your question was satisfactory to you. What was your purpose in asking the question?

As in the concept/meaning of self as "that which is purple and square" vs. "that which is orange and circular" or any some such? And this in relation to "there both is and is not a self"? — javra

This makes no sense to me. — Janus

In other words, the first question addresses this very affirmation which you more recently added:

That said, the self has no definitive definition, so introducing such a thing in the context of discussing whether anything could be the same in different contexts or thought under different perspectives seems incoherent from the get-go. — Janus

While the second question I asked addresses this:

The very proposition of "there both a) is a self and b) is no self" has (a) and (b) addressing the exact same thing - irrespective of how the term "self" might be defined or understood as a concept, the exact same identity is addressed The proposition has nothing whatsoever to do with two different interpretations of what "self" means and has everything to do with "the self" both occurring and not occurring at the same time.

So your critique completely misses the issue addressed regarding contradictions and the possible lack of such in the proposition "(the understanding of reality R entails that) there both is and is not a self". "Self" remains identical, but the usage of "is" can in principle be interpreted in two different ways - this, at least, within the context of certain Indian philosophies - thereby potentially equating to the more verbose proposition that "selfhood occurs from the vantage of mundane reality which is illusory but selfhood in no way occurs from the vantage of ultimate/genuine/non-illusory/nondual reality - for there can be no selfhood in the the complete absence of any duality with other - and both these actualities (in semi-Kantian terms, that actuality of the phenomenal world of maya and that nondual actuality/reality which can only be utterly non-phenomanal and, hence, purely noumenal) co-occur at the same time (again, this within certain Indian philosophies)". And such an affirmation would not be logically contradictory.

------

Consider the following substitutions which do not suffer from such ambiguities: Render (A implies B) as "the presence of water implies the presences of oxygen" and (A implies notB) as " the presence of water implies the absence of oxygen": do the two statements not contradict one another? — Janus

Of course they do. Just as much as saying that "the car C is completely green and completely red at the same time and in the same respect* ". And this as I upheld in the post you initially replied to: again, most often, the proposition that A entails both B and notB will be logically contradictory.

* p.s., to be clearer, this with the understanding that any shade of brown is neither green nor red, but brown.

"the presence of water implies the presences of oxygen" and (A implies notB) — Janus

I haven't followed your posts, so there may be context I need. But at least at face value:

"the presence of water implies the presences of oxygen"

is not an "if then" statement, since 'the presence of water' and 'the presence of oxygen' are noun phrases, not propositions.

the proposition that A entails both B and notB will be logically contradictory — javra

I haven't followed your posts, so there may be context I need. That said, (1) What is your context? Classical logic? Some other formal logic? Notions in everyday reasoning? (2) By 'logically contradictory' do you mean the proposition implies a proposition of the form P and ~P? Or something else?

The principle/law of thought which sometimes goes by the name of "the law of noncontradiction", this as articulated by Aristotle (with possible ambiguities as to whether the law applies only to epistemology or also to ontology at large here acknowledged).

What is your statement of the principle?

In short, A and not-A cannot both occur at the same time and in the same respect.

Would allow simplifying that to:

For any statement A, it is not the case that both A and not-A.

Would allow simplifying that to:

For any statement A, it is not the case that both A and not-A. — TonesInDeepFreeze

Is that a question or an affirmation?

Consider: The statement, "Water can be green", does not allow for "water can be green" and "water can be not-green (e.g., blue)".

So what I said does not simplify into what you've written.

If I understand, you take

It is not the case that both water can be green and water can be not-green.

as an instance of the law of contradiction. (?)

Do you also take

It is not the case that both water can be green and water cannot be green

as an instance of the law of contradiction?

If I understand, you take

It is not the case that both water can be green and water can be not-green.

as an instance of the law of contradiction. (?) — TonesInDeepFreeze

No, the exact opposite. Hence the concluding sentence to you in my last post.

However, the statement "water can be green and water can be non-green (e.g., blue) at the same time and in the same respect" will be an instance of the law of noncontradiction.

I don't find that one can properly express the principle linguistically without "at the same time and in the same respect" - or this phrasing's semantic equivalent - being affirmed.

I'll check back in tomorrow.

An interpretation, aka 'a model'. — TonesInDeepFreeze

Ah.

But that does not imply that "Winston Churchill was French" is true in all interpretations, but it does imply that "Winston Churchill was French" is true in at least one interpretation. — TonesInDeepFreeze

Can we say the proposition "Winston Churchill was French" is A? If so, if A is True, what do you make of the following table?



In the interpretation where ¬(a → (b ∧ ¬b)) is T, A is always T.