- I'm working on figuring that out with my question to you.

- :lol:

When you wrote it, you were referring to unnamed posters. Was I one of them or not?

Your intent when you wrote it is not affected by anything I say retroactively.

But you did order it.

You asked for a symbolization to see how the definition of 'valid argument' implies that explosion is a valid argument. I gave you exactly what you asked for.

When you wrote it, you were referring to unnamed photographers. Was I one of them or not? — TonesInDeepFreeze

Is photography mere photon manipulation?

I don't know if you fall into that group. It's hard to spot photographers. They disguise themselves, blending into their environment. That's why I am asking you a question. You have disavowed such a view in the past but I don't understand what alternative route you purport to take.

When you wrote, "There are some logicians in these parts who view logic as mere symbol manipulation", who were you referring to?

(I meant 'posters' not 'photographers'.)

When you wrote, "There are some logicians in these parts who view logic as mere symbol manipulation", who were you referring to? — TonesInDeepFreeze

When I wrote it I wasn't sure whether you fit the bill or not. Time to answer my question:

If you say that logic is not merely symbol manipulation, then what do you say it is? — Leontiskos

Who did you think fits the bill?

It's a simple question.

Why do you get to keep ignoring my question? Why do you think you are entitled to an answer to your question?

• Leontiskos: There are folk in these parts who drive Toyota Camrys.
• Tones: I certainly don't drive a Toyota Camry!
• Leontiskos: What kind of car do you drive?
• Tones: :zip:

If you say that logic is not merely symbol manipulation, then what do you say it is? — Leontiskos

It's mathematics without the math. :roll:

It's mathematics without the math. :roll: — jgill

Incidentally, this is my mother's favorite kind of mathematics. :smile:

Here's some informal logic that is not "mere symbol manipulation":

You said that there are some here who view logic as mere symbol manipulation. So, in such a small domain as this one, you could easily list them. And, since by your claim that there are "some", there is at least one that you have in mind. So, if you can't list any other than me, then we may infer that you meant me.

But you left it open, thus it is insinuation. But you don't have the integrity to say who you mean.

/

To maintain that I don't think logic is mere symbol manipulation, it is not required for me to say what logic is. To maintain that basketball is not mere players' statistics, I don't have to tell you what basketball is; whatever it is, I know that it is not mere players' statistics.

/

At some point, time and interest allowing, I may write a post with more about my own sense of the scope of logic. In any case, I use and recognize informal logic as well as formal logic, and I don't take formal logic to be mere symbol manipulation. That is apparent even by the fact that I have discussed, in your presence, certain English sentences vis-a-vis symbolization, as I even did a few posts ago.

Moreover, so many posts I have written about mathematics and logic, written mention a scope that is not at all confined to mere symbolization.

/

Who did you mean ? If you won't say, then I'll take it you don't have the guts to say, as you are sneaky insinuator. "Joe McCarthy" Leontiskos saying, "I have in my hand a list of posters who view logic as mere symbol manipulation".

Very pleasing to see that the proportion of folk who think the OP argument invalid has dropped from a third to a fifth. That's four people - presumably NotAristotle, Hanover, Leon and one other.

Leontiskos: There are folk in these parts who drive Toyota Camrys.
Tones: I certainly don't drive a Toyota Camry!
Leontiskos: What kind of car do you drive?
Tones: — Leontiskos

Leontiskos: There are people here who think acetone is merely oxygen.

TonesInDeepFreeze: I don't think acetone is merely oxygen.

Leontiskos: What else do you think is in acetone? You must answer that for me to decide whether I meant you when I said that there are people here who think acetone is merely oxygen.

TonesInDeepFreeze: Whatever acetone is, I don't say it is merely oxygen, Who are you claiming thinks acetone is only oxygen.

Leontiskos: It is time for you to answer my question.

TonesInDeepFreeze: You first made the claim that there are people here who think acetone is merely oxygen. If you were undecided about me when you made that claim, then which of the people here, do you claim to think that acetone is just oxygen? It's a simple question, and would be honest to answer rather than being a sneaky insinuator.

Leontiskos: How dare you ask me to name the people I claim to think acetone is just oxygen, when you won't write a post about what your notion of logic is?

TonesInDeepFreeze: Well, this started with you making the claim. So, it is natural to first get clear who you meant. And, if you can't say a single person other than me, then that leaves only me.

Leontiskos: What car do you drive?!

Here's one:

Leontiskos insinuated rather than openly stating.
To insinuate instead of openly stating is dishonest.
Leontiskos has been dishonest.

That is logic that is not mere symbol manipulation.

Here's more logic that is not mere symbol manipulation:

Even just one counterexample refutes a universal generalization. So the argument above refutes that I regard logic to be mere symbol manipulation. And this argument does too!

So, if you can't list any other than me, then we may infer that you meant me. — TonesInDeepFreeze

I actually said, "When I wrote it I wasn't sure whether you fit the bill or not." So no, not primarily you.

But you left it open, thus it is insinuation. But you don't have the integrity to say who you mean. — TonesInDeepFreeze

Rather, you asked for information that you would misuse and I did not give it to you. I only gave you the information that pertained to your person.

To maintain that I don't think logic is mere symbol manipulation, it is not required for me to say what logic is. To maintain that basketball is not mere players' statistics, I don't have to tell you what basketball is; whatever it is, I know that it is not mere players' statistics. — TonesInDeepFreeze

Pretty amazing how many miles you will run to avoid a simple question.

Who did you mean ? If you won't say, then I'll take it you don't have the guts to say, as you are sneaky insinuator. — TonesInDeepFreeze

Paranoid, much?

TonesInDeepFreeze: I don't think acetone is merely oxygen. — TonesInDeepFreeze

Not a great analogy, to say the least.

Leontiskos: What else do you think is in acetone? — TonesInDeepFreeze

The formula for acetone is (CH₃)₂CO. Notice how simple that was.

- Three posts on this? Have a drink, or take a nap or something.

This all comes from the conversation that emerged after you insisted that NotAristotle needs to follow a rule:

The rule is completely unambiguous:

If P v Q is on a line, and ~P is on a line, then we may put Q on a new line. — TonesInDeepFreeze

That characterization is a good example of logic-as-symbol-manipulation, and @NotAristotle's difficulty had to do with the nature of logic or inference. This question of "symbol manipulation" is therefore quite relevant to the question of how to understand validity vis-a-vis explosion. Burying your head in the sand and refusing to address the heart of the issue is not a great look.

We might say, "1 is simply a consequence of 2." — Count Timothy von Icarus

I think that's right. I think you've got the horse pulling the cart.

I mentioned quia demonstrations vs. propter quid demonstrations earlier. Supposing that the two definitions do rightly overlap, it would seem like 1 would be a quia demonstration (going from effects backwards), while 2 actually gives us the "why." — Count Timothy von Icarus

I don't see this as relevant. I don't see that propositional logic has a causal or metaphysical direction in any obvious sense. For example, why think that (1) would be a quia demonstration? Because the "effect" of a valid argument is the necessary relation between premises and conclusion that (1) captures? It's hard to see this as an "effect" in any strict sense.

1. An argument is valid when it is impossible for the premises to be true and the conclusion false; — Count Timothy von Icarus

On the standard (non-Tones) interpretation of (1), I would say that this represents a kind of static, non-directional construal of validity. It's about possibility space, not primarily deducibility. On this standard reading of (1) I think (1) and (2a) are coterminous, are they not? I think (1) properly captures a necessary formality of valid arguments; I just think Tones interprets it badly. On the standard interpretation, there is nothing mistaken about (1).

The effect issue is sort of ancillary. The issue is that 1 only follows from 2 given elements of logic that seem to be more a bug than a feature—that do not comport with common standards of "good reasoning."

As Priest says:

The notion of validity that comes out of the orthodox account is a strangely perverse one according to which any rule whose conclusion is a logical truth Is valid and, conversely, any rule whose premises contain a contradiction is valid. By a process that does not fall far short of indoctrination most logicians have now had their sensibilities dulled to these glaring anomalies. However, this is possible only because logicians have also forgotten that logic is a normative subject: it is supposed to provide an account of correct reasoning. When seen in this light the full force of these absurdities can be appreciated. Anyone who actually reasoned from an arbitrary premise to, e.g., the infinity of prime numbers, would not last long in an undergraduate mathematics course.

Now, what is now orthodox comes out of people being uncomfortable with where logic had been previously, fixing perceived problems, so if those moves were properly motivated, others attempts for satisfactory resultions seem like they should be too.

Graham --"logic is a normative subject: it is supposed to provide an account of correct reasoning."

Agree.

This is tangential (in that it is about logic but doesnt really relate to the original post), but what would you say about this argument? Is it viciously circular? --

if modus ponens is logical then any argument of the form [P, P->Q] implies Q.
modus ponens is logical.
therefore, "any argument..."

The effect issue is sort of ancillary. The issue is that 1 only follows from 2 given elements of logic that seem to be more a bug than a feature—that do not comport with common standards of "good reasoning." — Count Timothy von Icarus

In Aristotelian terms, we would say that (1) is a proper accident of validity. It is not the essence of validity, and yet every valid argument will possess the character of (1).

As Priest says — Count Timothy von Icarus

:up: That's what I've been saying for months. :smile:

Now, what is now orthodox comes out of people being uncomfortable with where logic had been previously, fixing perceived problems, so if those moves were properly motivated, others attempts for satisfactory resultions seem like they should be too. — Count Timothy von Icarus

I don't know if I quite followed that.

I think the degeneration of logic has a lot to do with what said.

Is it viciously circular? — NotAristotle

See my post <here> and the excerpt contained therein <here>.

Thanks for the links. So then I think Gensler would say the argument I have is similar to the first of his two circular proofs for modus ponens. The circularity is, interestingly, a result of the structure of the argument, not because of any specific premise.

My version of the argument is missing the inductive element that would cause the argument to be justified, if still circular. It's like a track record argument for perceptual abilities.

Perhaps, in addition to an inductive argument for modus ponens, an argument from coherence can be made. For instance it seems that if modus ponens failed, then MT or RAA would also fail.

1. If MP could be false, then RAA could be false.
2. But RAA is not false.
Therefore neither is MP.

(MT isnt a premise, however the argument is structurally MT). That is to say if MT is veridical, and so is RAA, then that would guarantee the truth of MP.

The circularity is, interestingly, a result of the structure of the argument, not because of any specific premise. — NotAristotle

Yes, but I think that all arguments are, structurally, modus ponens. This goes back to the earlier point about whether all arguments are modus ponens, or whether all arguments utilize a material conditional. Tones is claiming that the metalogical inference uses a material conditional, and is not merely a modus ponens, and that this is why he thinks inconsistent premises automatically* make an argument valid.

1. If MP could be false, then RAA could be false.
2. But RAA is not false.
3. Therefore neither is MP. — NotAristotle

You're right that the conclusion utilizes modus tollens, but here is the way that modus ponens is operating metalogically:

• (1 ^ 2) → 3
• (1 ^ 2)
• ∴ 3

When I deny that the '→' in the first premise is a material conditional, what I mean is that no legitimate metalogical move is available whereby the degenerative uses of the material conditional are utilized. It is only the logical connector needed for a modus ponens, not a material conditional in its full degenerative sense. So there is no permissible metalogical argument as follows:

• (1 ^ ~1) → 2
• ∴ 2

* Note that "automatically" is my word, not Tones'. Let us preempt his quibble.

"So there is no permissible metalogical argument as follows:

(1 ^ ~1) → 2
∴ 2"

Agree, I think; correct me if I have this wrong: by metalogical I take you to mean a logical "move" (such as MP) that is not identical to its truth function.

Apparently, it is not just arguments with contradictions that are problematic.

If it is settled that any premise in an informal argument is demonstrably false, it is unclear whether such an argument's conclusion can be true and yet the argument still be valid, where a valid argument is signified only as an argument that operates with the material conditional. If all valid arguments use the material conditional, arguments with some false premises could seem to still have a true conclusion.

But this seems wrong, at least to me. If any premises are false, a valid argument will result in a conclusion that is necessarily false, according to my non-standard understanding of validity in an informal context.

You may agree. But if you do, then any argument that is valid will turn out to be, in the relation of premises to conclusion, either [true true], or [false, false]. But that is the truth function of equivalence. Indeed, were you to exclude [F, F] as a degenerate case, your resulting truth functionality for a valid argument [T, T] would be truth functionally equivalent to "conjunction." You may argue that either of those truth functionalities is the case, and yet that an argument is still structurally but metalogically MP, although what you meant by calling an argument structurally and metalogically MP would be unclear to me.

In any case, I am not sure I agree that an argument is MP in any formulation, as putting an argument in terms of MP would seem to lead to the result that every argument had an "infinite regress" of premises. What I mean is:

P
P→Q
Therefore Q

Is really..

(P^(P→Q))→Q
P→Q
P
Therefore Q

Is really...

((P^(P→Q)→Q)^(P→Q)^P)→Q
(P^(P→Q))→Q
P→Q
P
Therefore Q

Ad infinitum.

Agree, I think; correct me if I have this wrong: by metalogical I take you to mean a logical "move" (such as MP) that is not identical to its truth function. — NotAristotle

Yes, something like that.

If all valid arguments use the material conditional, arguments with some false premises could seem to still have a true conclusion.

But this seems wrong, at least to me. If any premises are false, a valid argument will result in a conclusion that is necessarily false, according to my non-standard understanding of validity in an informal context. — NotAristotle

<A valid argument with a false premise will result in a false conclusion>

That seems intuitively correct. This may be close to what @Count Timothy von Icarus was fishing for. The idea is that valid arguments preserve falsity, and not just truth.

But in fact this does not turn out to be correct. For a counterexample, <All bugs are mortal; Socrates is a bug; Therefore, Socrates is mortal>. More generally, explosion will yield truths and falsehoods alike.

were you to exclude [F, F] as a degenerate case — NotAristotle

This paragraph is unclear to me, but the degenerate case of the material conditional that I am thinking of is [F X]. [F F] does not strike me as degenerate.

What is at stake here is a direction of evaluation. "The antecedent is false, therefore the conditional is true," is parallel to, "The premise is false, therefore the argument is valid." It is not the value of the conclusion that is at stake, but the validity of the argument (which has to do with guarantees regarding the value of the conclusion).

In any case, I am not sure I agree that an argument is MP in any formulation, as putting an argument in terms of MP would seem to lead to the result that every argument had an "infinite regress" of premises. — NotAristotle

I think every argument does have an "infinite regress" of premises in that way. This is just to say that logical inference (modus ponens) is not capturable in formal or truth-functional language. Trying to capture it in that schema results in an infinite regress.

More simply, modus ponens can be thought of as "follows from," and every inference relies on the notion of "follows from."

the validity of the argument (which has to do with guarantees regarding the value of the conclusion). — Leontiskos

Yes, agree. :up:

every inference relies on the notion of "follows from." — Leontiskos

That inferences relies on -follows from- is surely true of deductive arguments; that inductive arguments rely on inference would seem to be true, but I do not know if I would characterize the inference in an inductive argument with -follows from-.

If any premises are false, a valid argument will result in a conclusion that is necessarily false — NotAristotle

A valid argument with a false premise will result in a false conclusion — Leontiskos

Incorrect.

P1. If I am a human woman then I am a human
P2. I am a human woman
C1. Therefore, I am a human

The argument is valid. It's modus ponens. P1 and C1 are true. But P2 is false.

Also:

P1. If I am a woman then I am English
P2. I am a woman
C1. Therefore, I am English

The argument is valid. It's modus ponens. C1 is true. But P1 and P2 are false.

Just to be clear, your post makes it look like Leontiskos was making that assertion; that is not true as Leontiskos was not making that assertion; only I was making that assertion.

If I were to represent your first argument symbolically, the first one would be:

P→Q
~P
Therefore Q.

But that is clearly not a valid argument. So why is it that the way I've represented your argument does not align with the original non-symbolic argument?

If I were to represent your first argument symbolically, the first one would be:

P→Q
~P
Therefore Q. — NotAristotle

These are two different arguments:

P1. If I am a human woman then I am a human: P → Q
P2. I am a human woman: P
C1. Therefore, I am a human: Q

P1. If I am a human woman then I am a human: P → Q
P2. I am not a human woman: ¬P
C1. Therefore, I am a human: Q

The first is valid, P1 is true, P2 is false, and C1 is true
The second is invalid, P1 is true, P2 is true, and C1 is true