By "the science" I do not mean the broad definition -- which even carries over into my favorites like Kant, Hegel, Nietzsche, and Marx -- but whatever the modern beast that is science says.

If I investigate textbooks which academic departments use to teach science -- there is absolutely nothing in there about Jesus or God.

Which paper ought I reference in proving the identity of God? :D

If I investigate textbooks which academic departments use to teach science -- there is absolutely nothing in there about Jesus or God. — Moliere

Yet that wasn't always the case. As Hegel suggests, in The Phenomenology of Spirit, the history of philosophy is like the maturing of a plant. We wouldn't say that the fruit refutes the flower, or that the flower refutes the seed. I believe the same can be said about science. In its contemporary version, it's the end product of a history in which its roots were deeply interwoven with matters of theology, whether we like it or not. It is what it is, as you oossians like to say.

EDIT: Here's the quote:

The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant’s existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another. But the ceaseless activity of their own inherent nature makes them at the same time moments of an organic unity, where they not merely do not contradict one another, but where one is as necessary as the other; and this equal necessity of all moments constitutes alone and thereby the life of the whole. But contradiction as between philosophical systems is not wont to be conceived in this way; on the other hand, the mind perceiving the contradiction does not commonly know how to relieve it or keep it free from its one-sidedness, and to recognise in what seems conflicting and inherently antagonistic the presence of mutually necessary moments. — Hegel

Yet that wasn't always the case. As Hegel suggests, in The Phenomenology of Spirit, the history of philosophy is like the maturing of a plant. We wouldn't say that the fruit refutes the flower, or that the flower refutes the seed. I believe the same can be said about science. In its contemporary version, it's the end product of a history in which its roots were deeply interwoven with matters of theology, whether we like it or not. It is what it is, as you oosians like to say. — Arcane Sandwich

:)

It wasn't always the case, and our ideas have come from these influences. Newton stayed up late doing math to prevent himself from masturbating when he was horny -- it likely helped him in his career.

Still... determining if God exists by modern science can't be done, either way. I like to say that this is a positive thing -- in a way Kant's philosophy is attractive because people can be of any religious persuasion and still believe the same things about the world we experience, and independently believe whatever makes them fulfilled in a moral sense.

The metaphysics of Liberalism :D

I think he has a point with respect to science, though.

Still... determining if God exists by modern science can't be done, either way. I like to say that this is a positive thing -- in a way Kant's philosophy is attractive because people can be of any religious persuasion and still believe the same things about the world we experience, and independently believe whatever makes them fulfilled in a moral sense. — Moliere

The theory of the Big Bang, which is currently accepted in contemporary science, was first proposed by Georges Lemaître, a Catholic priest:

Georges Henri Joseph Édouard Lemaître (/ləˈmɛtrə/ lə-MET-rə; French: [ʒɔʁʒ ləmɛːtʁ]; 17 July 1894 – 20 June 1966) was a Belgian Catholic priest, theoretical physicist, and mathematician who made major contributions to cosmology and astrophysics. He was the first to argue that the recession of galaxies is evidence of an expanding universe and to connect the observational Hubble–Lemaître law with the solution to the Einstein field equations in the general theory of relativity for a homogenous and isotropic universe. That work led Lemaître to propose what he called the "hypothesis of the primeval atom", now regarded as the first formulation of the Big Bang theory of the origin of the universe. — Wikipedia

In his view, the Big Bang was caused by the Christian God.

Heh, fair. I gave an irreverent example of influence -- there are influences which helped people through intellectual difficulties which we don't have to contend with, even.

I have a deep respect for the history of thought. I don't mean to be dismissive of that history, religious or not.

Just... I suppose Kant has influenced me enough, while I don't agree with him (being a materialist, and a realist -- if skeptic), I think he has a point.

Less cryptically -- I believe that the Atheist and the Christian and the Muslim and the other various persuasions can believe in the Big Bang (even if that theory may be false), and believe it means something in a different way.

You lost me here. Can you please clarify what you mean by that? — Arcane Sandwich

For example, you said, "if FTI1 is true, then FTI2 must necessarily be false." Why? Why can't both premises be true?

I'm not sure I follow. The formal structure of that argument is the following one:

1) If p, then q.
2) p.
3) so, q.

If (1) is false, then (2) is true, and if (1) is true, then (2) is false. — Arcane Sandwich

Okay sure, if you are appealing to the "degenerate cases" of the material conditional then I agree that the former Muslim cannot deny that God exists without affirming that, "If God exists, then God is identical to Jesus," at least if he is consistent. But I'm not sure how useful arguments that depend on such degenerate cases are.

Here you might be right, but only in the sense that both arguments might be valid and yet unsound. — Arcane Sandwich

But isn't that precisely what you meant when you spoke about the possibility of "rejecting both arguments at the same time"?

If so, then that's a powerful reason for rejecting both arguments. — Arcane Sandwich

Why think that?

However, it's still the case that if one of the conclusions is true, then the other one is false, and vice-versa. — Arcane Sandwich

Correct.

The concept of soundness (and unsoundness) applies only to arguments, not to propositions (premises and conclusions), just as the concept of validity (or lack of thereof) only applies to arguments, not to propositions. A proposition (being a premise or a conclusion) can only be true or false. That is at least the modern understanding of such notions. — Arcane Sandwich

On the contrary, a sound conclusion is the conclusion of a sound argument. And as I said, "if either conclusion is sound then both first-premises must be true" (given material conditionals).

This is indeed an argument — Arcane Sandwich

It is not an argument in any substantial sense, and the "arguments" of the OP are similarly insubstantial. Namely, there is nothing persuasive or compelling about them. For example, I could write an OP:

1. If the moon is made of cheese, then pelicans are vegans
2. The moon is made of cheese
3. Therefore, pelicans are vegans

I might follow this with, "Options for resisting the argument." But there is no argument to resist, not in any substantial sense. The person making the argument has the burden of proof in showing the argument to be persuasive or compelling, and mere validity does not succeed in doing this. (Formalizations such as this are only valid consequences, not cases of true inference.)

So rather than give a substantial argument, you've asked TPF users to give substantial arguments against at least one of four propositions (namely, the premises). It's a bit like saying, "I think X. Prove me wrong."

(I would grant that ATI is closer to a substantial argument than FTI, since FTI1 is entirely opaque.)

Since I'm an atheist... — Arcane Sandwich

...the question is actually meaningless to you, and is basically a form of entertainment, if that.

I don't think that's true.

Though the meaning would not be the same kind of meaning.

I care about these arguments because of my history, so they have a meaning -- it's just not the same as those on a spiritual ascent.

And there's nothing wrong with a spiritual ascent, in my worldview. It's only different from what I'm doing.

Due to how the burden of proof works, I don't need to prove a negative — Arcane Sandwich

According to your Wikipedia article you have the burden of proof, for you are the one who spoke.

Or rather, you have simulated a scenario in which someone gives a very opaque argument (FTI), and then you "denied" part of FTI (to quote Wikipedia), so for Wikipedia whoever spoke FTI has the initial burden of proof. So who spoke FTI? No one at all, it seems. It is part of an OP that offers no real argument, and which does not accept the burden of proof for what it claims.

This is good, I feel like we're making progress here, but there's still a lot of distance to cover before we can reach an actual agreement on anything. Right now, we're still trying to settle on the terminology and some of the rules. For example:

you said, "if FTI1 is true, then FTI2 must necessarily be false." Why? Why can't both premises be true? — Leontiskos

Both premises can be true, but they can't both be false. Only one of them can be false.

Okay sure, if you are appealing to the "degenerate cases" of the material conditional then I agree that the former Muslim cannot deny that God exists without affirming that, "If God exists, then God is identical to Jesus," at least if he is consistent. But I'm not sure how useful arguments that depend on such degenerate cases are. — Leontiskos

No, that's not what I had in mind. If I caused such a confusion, then I apologize for that.

Here you might be right, but only in the sense that both arguments might be valid and yet unsound. — Arcane Sandwich


But isn't that precisely what you meant when you spoke about the possibility of "rejecting both arguments at the same time"? — Leontiskos

Yes, indeed.

On the contrary, a sound conclusion is the conclusion of a sound argument. And as I said, "if either conclusion is sound then both first-premises must be true" (given material conditionals). — Leontiskos

Yes, but a material conditional can be true for the wrong reasons. For example, if both the antecedent and the consequent are false, the conditional itself is true. It's an odd result, and it's counter-intuitive (intuitively, the conditional should be false in that case, but it isn't). I prefer to reserve the concept of soundness for arguments, but feel free to use it for conclusions in the sense that you just mentioned. It's not a hill that I'm willing to die on.

It is not an argument in any substantial sense, and the "arguments" of the OP are similarly insubstantial. Namely, there is nothing persuasive or compelling about them. — Leontiskos

The way I see it, the qualities of being persuasive and compelling are rhetorical qualities, not logical ones. An argument can be unpersuasive and uncompelling and yet it can still be both valid and sound. Conversely, a formal fallacy can be both persuasive and compelling, and yet it would not be valid nor sound.

For example, I could write an OP:

1. If the moon is made of cheese, then pelicans are vegans
2. The moon is made of cheese
3. Therefore, pelicans are vegans — Leontiskos

That's a modus ponens. As such, it's a valid argument. But it's unsound. The false premise in this case is the second one: the moon is not made of cheese. The first premise is a more interesting case. What should we say about it? Well, given that the second premise is false, the first premise must be true, due to the truth table for conditional statements. But it's true for the wrong reasons: both the antecedent and the consequent are false, which make the conditional itself true (as paradoxical as that may seem).

I might follow this with, "Options for resisting the argument." But there is no argument to resist, not in any substantial sense. The person making the argument has the burden of proof in showing the argument to be persuasive or compelling, and mere validity does not succeed in doing this. (Formalizations such as this are only valid consequences, not cases of true inference.) — Leontiskos

It's an easily refutable, but perfectly valid argument. By contrast, the two arguments in the OP in this thread, while equally valid, are not as easily refutable.

So rather than give a substantial argument, you've asked TPF users to give substantial arguments against at least one of four propositions (namely, the premises). It's a bit like saying, "I think X. Prove me wrong."

(I would grant that ATI is closer to a substantial argument than FTI, since FTI1 is entirely opaque.) — Leontiskos

What can I say? I don't share your notion of a "substantial" argument. An argument is either sound or unsound. There's nothing more to it. Logic is a science (a formal science, just like mathematics). It has nothing to do with persuasiveness, just as algebra or geometry have nothing to do with persuasiveness.

...the question is actually meaningless to you, and is basically a form of entertainment, if that. — Wayfarer

Not really. I'm open to the idea that God might exist, and that Jesus might be God.

According to your Wikipedia article you have the burden of proof, for you are the one who spoke. — Leontiskos

The proofs have already been given, since a proof is (to my mind) the same thing as an argument. As such, proofs can be sound or unsound.

Or rather, you have simulated a scenario in which someone gives a very opaque argument (FTI), and then you "denied" part of FTI (to quote Wikipedia), so for Wikipedia whoever spoke FTI has the initial burden of proof. So who spoke FTI? No one at all, it seems. It is part of an OP that offers no real argument, and which does not accept the burden of proof for what it claims. — Leontiskos

Again, I don't accept your notion of a "real" argument. An argument is either sound or unsound, there's nothing more to it. And since an argument is the same thing as a proof, it follows that I already gave two proofs in the OP. But they can't both be sound. If one of them is sound, then the other one is unsound. That being said, you are indeed right in one of your earlier comments, in that both arguments can be unsound.

Both premises can be true, but they can't both be false. Only one of them can be false. — Arcane Sandwich

Sure, if you rely on the degenerate cases of the material conditional, where a false antecedent or a true consequent guarantees a true conditional. But I think I spoke to that.

What can I say? I don't share your notion of a "substantial" argument. An argument is either sound or unsound. There's nothing more to it. Logic is a science (a formal science, just like mathematics). It has nothing to do with persuasiveness, just as algebra or geometry have nothing to do with persuasiveness. — Arcane Sandwich

Let me show why I disagree.

Suppose I say that God exists, and you tell me that I've made an assertion rather than an argument. So I give what you view as an "argument":

1. If God exists, then God exists
2. God exists
3. Therefore, God exists

Now apparently this is an argument, which is entirely different from an assertion. Since I have given an argument, you have the burden of proof in addressing the argument. You might say, "God does not exist," and I might say, "That's an assertion, not an argument." So you comply:

4. If God does not exist, then God does not exist
5. God does not exist
6. Therefore, God does not exist

We could do that for eternity, and on my view we are neither arguing nor giving arguments, whereas on your view we are (and I have encountered people who literally did this).

Aristotle tells us that arguments move from premises that are better-known to conclusions that are lesser-known. If it doesn't do that, it isn't an argument. Note too that "better-known" and "lesser-known" can easily be indexed to persons, but that they are also indexed to communities, which is why not all sound arguments for the same conclusion are equal. In fact 1-2-3 is a sound "argument," but I would contend that it is not a real argument at all.

An since an argument is the same thing as a proof, it follows that I already gave two proofs in the OP. — Arcane Sandwich

Well if you "spoke" the proofs then you have the basic burden of proof, no? Your Wikipedia article says that the one who speaks has the burden.

Sure, if you rely on the degenerate cases of the material conditional, where a false antecedent or a true consequent guarantees a true conditional. But I think I spoke to that. — Leontiskos

There's nothing "degenerate" about such cases. That notion has no place in a formal science such as logic.

Let me show why I disagree.

Suppose I say that God exists, and you tell me that I've made an assertion rather than an argument. So I give what you view as an "argument":

1. If God exists, then God exists
2. God exists
3. Therefore, God exists — Leontiskos

Sure, that's an argument. It's a modus ponens. I'll just deny the second premise: God does not exist. That makes the first premise true, but only because both the antecedent and the consequent are false.

Now apparently this is an argument, which is entirely different from an assertion. Since I have given an argument, you have the burden of proof in addressing the argument. You might say, "God does not exist," and I might say, "That's an assertion, not an argument." — Leontiskos

I don't need to formulate an argument of my own to deny the second premise of your argument. The burden of proof is not on me in that case, since I don't need to prove a negative here.

So you comply: — Leontiskos

No, I don't, for the reason that I've stated above.

4. If God does not exist, then God does not exist
5. God does not exist
6. Therefore, God does not exist — Leontiskos

That's a perfectly valid modus ponens. It's easily refutable for a theist. All you have to do is to deny the second premise.

We could do that for eternity — Leontiskos

Sure.

on my view we are neither arguing nor giving arguments, whereas on your view we are (and I have encountered people who literally did this). — Leontiskos

Which is why the arguments in the OP, while being modus ponens, do not have the same structure as the one in your example. Because in your example, the conditional has the form "if p, then p", while the conditionals in the arguments of the OP have this other structure: "if p, then q".

Aristotle tells us that arguments move from premises that are better-known to conclusions that are lesser-known. If it doesn't do that, it isn't an argument. — Leontiskos

A lot has happened in logic ever since Aristotle. The same goes for mathematics, especially geometry. But if we focus on the former, there's nothing similar to (for example) paraconsistent logic in Aristotle's philosophy.

In fact 1-2-3 is a sound "argument," but I would contend that it is not an argument at all. — Leontiskos

It's not a sound argument, at least not to my atheist eyes. It is valid, however. Just not sound.

An since an argument is the same thing as a proof, it follows that I already gave two proofs in the OP. — Arcane Sandwich


Well if you "spoke" the proofs then you have the basic burden of proof, no? Your Wikipedia article says that the one who speaks has the burden. — Leontiskos

Yes, and the proofs are the arguments themselves, because that is what a proof is: a list of premises from which a conclusion follows by deduction.

I'm open to the idea that God might exist, and that Jesus might be God. — Arcane Sandwich

I suppose that's something. But let me make an observation here. I don't generally make it my business to argue for belief in God on this forum. I'm not an atheist, so I do believe that religion has a real referent, it is about a reality, not a 'social construct' or psychological projection. But when you ask the question as what that referent might be, it is very difficult to answer. If it were a straightforward matter, one could point to something by way of definition. But defining the nature of deity or the idea of the Sacred is not at all straightforward. This is why the question tends to fragment into innummerable, and often conflicting, mythological or philosophical accounts. And of course there's nothing remotely like a consensus possible in any of this in today's cultural landscape.

In any case, and in a roundabout way, what I meant by my earlier remark was that for an atheist, the question of the nature of God's existence doesn't matter in an existential sense; it doesn't mean anything for her conception of the nature of existence. It's a theoretical or hypothetical matter. Whereas for the believer, the question has real import: she believes that there is something at stake beyond the hypothetical. Something like the fate of her immortal soul, which, of course, means nothing to those who don't believe it's even a meaningful idea.

As to the question of whether and in what sense Jesus is identical with God, there is, on the one hand, 'I and the Father are One' (John 10:30). But then on the other, Mark 10:18 'Why do you call Me good? No one is good except God.'

I interpret that against a kind of pan-religious perspective which understands the figures in these expressions as archetypal realities. So that here when Jesus says 'why call Me good?', he's gesturing towards his particular self, the ego or persona. That is precisely what Jesus says must die, when He says, 'He who saves his own life will loose it, he who looses his life for My sake will be saved'( Mt 16:25). In other words, 'dying to the self' or the selfish or egoic perspective is required to be 'born again' into the Holy spirit. That 'ego death' is not unique to the Christian faith (although of course, for Christians, Jesus is the archetype.)

But understanding the themes of 'union with the Divine' (in Christianity, called 'theosis' or 'beatification') at least on a literary, if not an existential, level, is necessary to understand what the question of the identity of Jesus with the Divine means.

A very thoughtful and informative post, thanks for contributing it to this Thread :clap:

You're both quite chatty in your most recent posts, but I'm going to need to ask you two if you have horses in this race, before proceeding any further. If not, then you're immoral. Says who? The Boy Scouts, that's who.

There's nothing "degenerate" about such cases. That notion has no place in a formal science such as logic. — Arcane Sandwich

<Sure it does>. And when Frege first tried to introduce the material conditional he was resisted for decades for this very reason.

Which is why the arguments in the OP, while being modus ponens, do not have the same structure as the one in your example. Because in your example, the conditional has the form "if p, then p", while the conditionals in the arguments of the OP have this other structure: "if p, then q". — Arcane Sandwich

But you yourself said that it is a "perfectly valid modus ponens." So what's the problem? What's the difference between a modus ponens where p=q and a modus ponens where p!=q? It seems that on your view there can be no significant distinction between the two modus ponens. You said, "An argument is either sound or unsound. There's nothing more to it. Logic is a science (a formal science, just like mathematics)."

It's not a sound argument, at least not to my atheist eyes. It is valid, however. Just not sound. — Arcane Sandwich

Yes: you think 4-5-6 is the sound argument, right?

<Sure it does>. And when Frege first tried to introduce the material conditional he was resisted for decades for this very reason. — Leontiskos

Mathematicians also like to talk about mathematical beauty, but I reject that notion myself. Aesthetic notions have no place in a formal science.

But you yourself said that it is a "perfectly valid modus ponens." So what's the problem? What's the difference between a modus ponens where p=q and a modus ponens where p!=q? It seems that on your view there can be no significant distinction between the two modus ponens. — Leontiskos

They have different structures. "If p, then p" is not the same structure as "If p, then q".

Yes: you think 4-5-6 is the sound argument, right? — Leontiskos

Of course. It's both valid and sound. But I wouldn't endorse that argument myself, because it's easily refutable. To speak poetically for a moment, it's not a good argument, even though it's both valid and sound.

They have different structures. "If p, then p" is not the same structure as "If p, then q". — Arcane Sandwich

Same structure:

p: God exists
q: God exists

1. p → q
2. p
3. ∴ q

(The structure is modus ponens, and you yourself claimed that 1-2-3 is a modus ponens.)

But I wouldn't endorse that argument myself, because it's easily refutable. To speak poetically for a moment, it's not a good argument, even though it's both valid and sound. — Arcane Sandwich

But just a few minutes ago you said, "An argument is either sound or unsound. There's nothing more to it." Now you want to say that some sound arguments are good and some sound arguments are bad. So clearly there is something more to it.

I'm going to need to ask you two if you have horses in this race, before proceeding any further. — Arcane Sandwich

If you’re asking whether I think it matters, then ‘yes’.

Same structure:

p: God exists
q: God exists

1. p → q
2. p
3. ∴ q — Leontiskos

In this case, if "p" and "q" are both identical to "God exists", then the structure is the following one:

1. p → p
2. p
3. ∴ p

(The structure is modus ponens, and you yourself claimed that 1-2-3 is a modus ponens.) — Leontiskos

There's two types of structures in logic: the structure of arguments, and the structure of propositions. Two arguments can have the same structure (i.e., both of them are modus ponens) while having propositions with different structures (i.e., p → q instead of p → p).

But just a few minutes ago you said, "An argument is either sound or unsound. There's nothing more to it." Now you want to say that some sound arguments are good and some sound arguments are bad. So clearly there is something more to it. — Leontiskos

Nah. I stand by what I said earlier: there is nothing more to an argument than its soundness (or unsoundness). Its validity is taken for granted, because if it wasn't valid, it wouldn't be an argument to begin with (it would be a formal fallacy instead). When I say that some arguments are good and that some of them are bad, I'm speaking poetically. In other words, I'm being rhetorical, not logical. I don't dismiss rhetoric, I simply declare that being persuasive and compelling are within its province, instead of being qualities of the formal science that we call logic.

It was a joking reference to .

There's two types of structures in logic: the structure of arguments, and the structure of propositions. Two arguments can have the same structure (i.e., both of them are modus ponens) while having propositions with different structures (i.e., p → q instead of p → p). — Arcane Sandwich

That's an interesting account, but I don't know of any rule of logic which requires that a modus ponens where p=q magically has a different structure. The validity rules are all the same, so it's not clear what it would even mean to claim that it has a different structure. If you're all about formalism, then the structure is exactly the same.

When I say that some arguments are good and that some of them are bad, I'm speaking poetically. In other words, I'm being rhetorical, not logical. I don't dismiss rhetoric, I simply declare that being persuasive and compelling are within its province, instead of being qualities of the formal science that we call logic. — Arcane Sandwich

Then you have no reason to claim that the modus ponens where p=q has a different structure, apart from poetry. "Poetically they have a different structure, but formally they do not."

On my view if someone cannot see that this is a degenerate case of modus ponens, then they haven't grasped the raison d'être of logic:

1. p → p
2. p
3. ∴ p

...and of course someone who limits themselves to "formalisms" cannot admit the notion of a degenerate case.

That's an interesting account, but I don't know of any rule of logic which requires that a modus ponens where p=q magically has a different structure. The validity rules are all the same, so it's not clear what it would even mean to claim that it has a different structure. If you're all about formalism, then the structure is exactly the same. — Leontiskos

Not quite, because the difference between p → p and p → q affects their truth values. Consider the former case first:

p → p
T__T
F__F

Now consider the latter case:

p → q
T__T
T__F
F__T
F__F

See the difference? In the former case, p → p can never be false, while in the latter case, p → q can indeed be false (in only one case: the second one).

Then you have no reason to claim that the modus ponens where p=q has a different structure, apart from poetry. "Poetically they have a different structure, but formally they do not." — Leontiskos

That's not what I claim. Formally they have different structures, not poetically. The poetry (or rhetoric) has more to do with the question of which arguments are preferable for this or that objective, such as arguing for the conclusion that God exists (or does not exist). In that sense, not all arguments are equally good. But their goodness (or badness) is outside the province of logic, because those are not logical notions to begin with.

On my view if someone cannot see that this is a degenerate case of modus ponens, then they haven't grasped the raison d'être of logic:

1. p → p
2. p
3. ∴ p — Leontiskos

There's nothing degenerate about it. It's a perfectly valid argument.

...and of course someone who limits themselves to "formalisms" cannot admit the notion of a degenerate case. — Leontiskos

Am I limited to "formalisms"? Maybe. Can I admit the notion of a degenerate case, in the context of a formal science? Not really. I don't admit the notion of mathematical beauty either, not within the context of math as a formal science. There are very beautiful objects in nature as well as culture, that have certain qualities like symmetry, but the notion of mathematical beauty only makes sense outside of mathematics, not within it. The same goes for the notion of degeneracy. It only makes sense outside of logic, not within it.

Not quite, because the difference between p → p and p → q affects their truth values. — Arcane Sandwich

It is merely a subset of the truth table where p!=q. The truth values are no different. Or in other words, at no point would someone become alarmed upon learning that p=q. It makes no difference at all. Nothing that was valid where p!=q will become invalid where p=q. This is why representing them with the same letter or a different letter makes no difference at all.

That's not what I claim. Formally they have different structures, not poetically. — Arcane Sandwich

If two things behave in precisely the same manner, then they do not have two different logical structures. The two modus ponens "arguments" under scrutiny behave in precisely the same manner; therefore they do not have two different logical structures (on the formalist's understanding).

Put it this way: when someone gives a modus ponens you don't have to check with them first, to make sure that p!=q. It makes no difference at all. There is no caveat when it comes to modus ponens, no condition where if p=q the rule fails.

The same goes for the notion of degeneracy. It only makes sense outside of logic, not within it. — Arcane Sandwich

You say that but then you want to make an ad hoc distinction between the "structure" of different modus ponens "arguments," so I still have hope for you. :wink:

It is merely a subset of the truth table where p!=q. — Leontiskos

But the problem is that the subset in question only contemplates two cases (T and T, F and F), such that both cases are necessarily true, while the larger set contains a case which is false (T and F).

If two things behave in precisely the same manner, then they do not have two different logical structures. — Leontiskos

Exactly, which is why p → p and p → q don't have the same logical structure: they don't behave in precisely the same manner as far as their possible truth values go. The former is always true, it's a tautology (it's always true, it can never be false). The latter is not a tautology, it is instead contingent (it can be true or false, depending on the case).

The two modus ponens "arguments" under scrutiny behave in precisely the same manner; therefore they do not have two different logical structures — Leontiskos

Their argumentative structure is identical, but their propositional structure is different.

You say that but then you want to make an ad hoc distinction between the "structure" of different modus ponens "arguments," so I still have hope for you. :wink: — Leontiskos

I meant "structure" as in the structure of their propositions, not the structure of their logical form.

Let me refine the argument I gave:

If a logical form need not be isolated, then it "behaves in precisely the same manner" (and therefore does not have a different logical structure...).

That's the key point, namely:

Put it this way: when someone gives a modus ponens you don't have to check with them first, to make sure that p!=q. It makes no difference at all. There is no caveat when it comes to modus ponens, no condition where if p=q the rule fails. — Leontiskos

Call this MP1:

1. p → q
2. p
3. ∴ q

And this MP2:

1. p → p
2. p
3. ∴ p


If MP2 behaved differently than MP1 (in a relevant logical sense), then MP2 would need to be isolated from MP1. In that case every time someone offered up a modus ponens we would need verify whether we are talking about MP1 or MP2. But we don't. Because nothing is at stake. They behave in the same manner (because modus ponens doesn't care whether the first premise is tautological). It makes no difference. And therefore they have the same structure. We don't say that things which do not need to be differentiated have a different structure. MP2 is merely a particular kind of modus ponens. For the formalist it is no more or less modus ponens than any other modus ponens. It is not anything other than modus ponens (and therefore has no different inferential structure).

The difference between MP1 and MP2 is metalogical, and one of course needs to move into the meta-language if they want to understand what an argument really is.

(We actually have a lot of threads on these sorts of topics, so I don't want belabor this for too long.)