Taking a Look at Modus Ponens ... oh yeah, and P-zombies too!

Real Gone Cat

This idea grew out of a mini-debate regarding modus ponens on the p-zombie thread.

Borrowing terminology from Kant, we may define two types of modus ponens as follows :

- synthetic modus ponens : a modus ponens whose conclusion is not contained in its premise
- analytic modus ponens : a modus ponens whose conclusion is contained in its premise

An example of synthetic modus ponens is :

If it is raining, then I will take my umbrella
It is raining
Conclusion : I will take my umbrella

Clearly, the conclusion has no effect on the premise prior to forming the modus ponens - whether you take your umbrella before looking outside does not effect the weather outside. Thus, synthetic modus ponens adds to our knowledge of the world - it tells us something new about the conclusion.

Two examples of analytic modus ponens are given below, numbered 1 and 2 :

1. If Socrates is a man, then Socrates is mortal
Socrates is a man
Conclusion : Socrates is mortal

2. If Atlanta wins the Super Bowl, then New England loses
Atlanta wins the Super Bowl
Conclusion : New England loses

Both versions of analytic modus ponens have the proper form for a modus ponens argument, and so appear valid. And in both cases, the premises and conclusion may match our observations of the real world and thus be true. But both cases are trivial ! In analytic modus ponens #1, mortality is a condition of being a man and is true of any man (not just Socrates) before the modus ponens is presented. In analytic modus ponens #2, New England losing is logically equivalent to Atlanta winning, and will share truth value before the modus ponens is presented (in fact, the conditional is actually a biconditional).

Again, analytic modus ponens arguments are trivial. They add nothing to our understanding.

One more thing may be said of analytic modus ponens #2 : Arguments of this form are easy to identify since the conditional is actually a biconditional - just form a new modus ponens with the converse of the conditional and check to see if it is also true. Consider the analytic modus ponens #2 given above. Using the converse to form a new modus ponens we get :

If New England loses, then Atlanta wins
New England loses
Conclusion : Atlanta wins

This is also true, as it should be since this is a case of #2. Now consider the synthetic case :

If I take my umbrella, then it is raining
I take my umbrella
Conclusion : It is raining

This is clearly false, since umbrellas do not cause rain. Now consider the case labeled analytic #1 :

If Socrates is mortal, then Socrates is a man
Socrates is mortal
Conclusion : Socrates is a man

Clearly false since Socrates might be my cat.

Which brings us to Chalmers' p-zombie modus ponens :

If p-zombies are conceivable, then physicalism is false
P-zombies are conceivable
Conclusion : Physicalism is false

My claim is that this is an analytic modus ponens #2 argument. Consider the way Chalmers sets up the definition of p-zombies : a world physically identical to our world, but different as regards consciousness. The only way this is possible is if consciousness is already assumed to be non-physical (i.e., physicalism is false), or else "physically identical" would include consciousness!

Another way to show that Chalmers' argument is analytic #2 is to form a new modus ponens with the converse :

If physicalism is false, then we may conceive of p-zombies
Physicalism is false
Conclusion : We may conceive of p-zombies

Clearly this could be true - if physicalism is false, then consciousness is separate from the physical, and p-zombies are easy to conceive of. But then the conceivability-of-p-zombies and physicalism-being-false form a biconditional.

So we see that Chalmers' p-zombie argument, being analytic, is trivial. It adds nothing to our understanding of physicalism, and cannot be used to prove physicalism false.

Michael

If I take my umbrella, then it is raining
I take my umbrella
Conclusion : It is raining

This is clearly false, since umbrellas do not cause rain. — Real Gone Cat

Arguments aren't true or false; they're valid or invalid, and the above is valid.

Another way to show that Chalmers' argument is analytic #2 is to form a new modus ponens with the converse :

If physicalism is false, then we may conceive of p-zombies
Physicalism is false
Conclusion : We may conceive of p-zombies

Clearly this could be true - if physicalism is false, then consciousness is separate from the physical, and p-zombies are easy to conceive of. But then the conceivability-of-p-zombies and physicalism-being-false form a biconditional.

Chalmers' first premise isn't a biconditional. It might be that consciousness is physical but that something else isn't. If so, physicalism is false but we can't conceive of p-zombies.

Although, admittedly this is pedantic. You can phrase it as "consciousness isn't physical" rather than "physicalism is false".

Real Gone Cat

↪Michael

So what do you say about the following :

If pigs can fly, then the moon is made of cheese
Pigs can fly
Conclusion : The moon is made of cheese

Clearly valid. But is there any truth to found?

Michael

So what do you say about the following :

If pigs can fly, then the moon is made of cheese
Pigs can fly
Conclusion : The moon is made of cheese

Clearly valid. But is there any truth to found? — Real Gone Cat

The second premise is false. The first premise is true whenever both "pigs can fly" and "the moon is made of cheese" is true. Given that it's a material conditional, it doesn't matter that neither "pigs can fly" nor "the moon is made of cheese" are actually true. Unless you mean the first premise to be an indicative conditional, in which case it would be false.

Terrapin Station

Conditionals do not imply causality. Thinking that they do is one of the dangers of plugging natural language into the structure of a logical argument.

Aside from that, as Michael said, your "clearly this is false" is wrong:

If I take my umbrella, then it is raining
I take my umbrella
Conclusion : It is raining — Real Gone Cat

That is a valid argument. You might say it's not sound, but there's a temptation to say that it's not sound on a misinterpretation of conditionals (such as reading causal relationships into conditionals).

My whole point in that discussion, by the way, was that Michael was ignoring semantic issues with statements in the argument, even though the argument was stated in natural language and the import of it doesn't ignore natural language semantics. What the other person who was saying that the p-zombie argument is essentially question-begging and I were talking about was an issue with the implications of the semantic content of a statement in the argument.

Real Gone Cat

↪Michael

↪Terrapin Station

Aargh! Inelegantly stated on my part (I was half asleep when typing it up). Of course modus ponens arguments are valid or invalid but not true or false. To avoid confusion try this :

- synthetic conditional : a conditional whose consequent is not contained in its antecedent
- analytic conditional : a conditional whose consequent is contained in its antecedent

The reason that I am not using a simple conditional/biconditional distinction is because of conditionals like "If Socrates is a man, then Socrates is mortal", which is clearly not a biconditional, but is analytic by my idea. Perhaps there is some existing terminology for this - my PhD is not in philosophy, sorry.

Then, modus ponens arguments constructed with (what I call) synthetic conditionals add something new to our knowledge. But modus ponens arguments constructed with analytic conditionals do not. Modus ponens constructed with analytic conditonals may clarify or emphasize (i.e., someone who has a vague notion of what it means to be a man may benefit from the conditional that has mortality as the consequent), but they do not really add to the understanding when carefully examined.

I stand by my challenge to Chalmers' modus ponens - the conceivability of p-zombies and physicalism-being-false I believe to form a biconditional. First, if physicalism is (known to be) false, then p-zombies are clearly conceivable. Now Chalmers is claiming the converse (If p-zombies are conceivable, then physicalism is false). From this we must conclude that the two ideas form a biconditional. By my reading of the situation, nothing is added to the understanding by his resulting modus ponens. (And this is just another way of saying that to conceive of p-zombies you must already believe that physicalism is false.)

To Michael : Physicalism is usually understood to be the idea that consciousness is physical. Yeah, I guess some other thing could be non-physical instead, making physicalism about that other thing, but no one makes that claim, do they?

To TS : Did I avoid causality this time? It was not my intent to suggest otherwise.

Cabbage Farmer

An example of synthetic modus ponens is :

If it is raining, then I will take my umbrella
It is raining
Conclusion : I will take my umbrella

Clearly, the conclusion has no effect on the premise prior to forming the modus ponens - whether you take your umbrella before looking outside does not effect the weather outside. Thus, synthetic modus ponens adds to our knowledge of the world - it tells us something new about the conclusion. — Real Gone Cat

I wouldn't say a conclusion "has an effect on" a premise. Conclusions and premises are statements or assertions in arguments. The premises determine what one might validly assert, and thus the validity of inferences.

So far as I can see, this sort of "determining" is merely logical, not causal. When the terms in an argument refer to real objects in the world, the inferential relations in the argument don't generally map onto anything like causal relations between the real objects indicated in the argument. Arguments about umbrellas don't add anything to umbrellas; they help us sort our thoughts about umbrellas. Deductive inferences don't add anything to premises; they help us sort our thoughts on the basis of premises.

Accordingly, I'm not sure I understand your conception of a "synthetic modus ponens". Can you give an example that doesn't involve a future event? My hunch is that the illusion of an "addition" or "effect" has something to do with the fact that the consequent in the conditional, "then I will take my umbrella", refers to an event that has not yet taken place, and more specifically to a potential action with the form of an intention that has yet to be discharged.

In this case the claim that plays the role of the first premise also plays another role -- outside the argument -- as a contingency plan or conditional intention of the speaker. Or less plausibly, a role as a sort of educated guess about oneself: "Knowing me, if it's raining tomorrow, I'll take my umbrella".

Of course the argument doesn't tell us whether the premises are true in fact. Given premise 2: The fact of your subsequent choice to take your umbrella would determine premise 1 as true, and the fact of your contrary subsequent choice to leave the umbrella at home would determine premise 1 as false.

Either way, it's your future action, not the argument, that "adds something" to the world in this case, something that was not "contained" in the world until you acted. The argument has even less power to determine your choice than your own prospective affirmation of the plan featured in premise 1. To the contrary, in this case it's your choice to take the umbrella, if it's raining, that determines the truth of the conclusion and the soundness of the argument.

Perhaps "temporal logics" are designed to put a formal stamp on such considerations. Temporal logic aside, I recall that some philosophers have spoken as if the truth-values of statements referring to future states of affairs are always already determined, as if the world were one Great Fact for all time.

Consider this variation:

If it's raining tomorrow, I'll take my umbrella
It's raining tomorrow
Therefore I'll take my umbrella

Now both the second premise and the conclusion "add something" to, or rather skirt ahead of, our present view of the facts. This isn't due to the general form of the inference (modus ponens, I'm told), but rather due to the relative temporal positions of the relevant facts and the present recitation of the argument.

From an epistemic point of view, this is just a temporal variation on a more general theme. The following argument contains a premise that purports to "add" to my knowledge of the facts, since I don't actually know whether it's raining in Shanghai:

If it's raining in Shanghai, I'll wear red
It's raining in Shanghai
Therefore I'll wear red

But since I don't know whether it's raining in Shanghai, I don't know whether that premise is true.

How's that for a biconditional?

andrewk

- synthetic conditional : a conditional whose consequent is not contained in its antecedent
- analytic conditional : a conditional whose consequent is contained in its antecedent — Real Gone Cat

The question is what does 'contained in' mean? The question cannot be resolved because in Kant's time - and it was he who was so terribly insistent on the synthetic/analytic distinction - logic was not sufficiently well understood to allow a clear definition of what that means. So we cannot know how he might have attempted to define 'contained in' using the more precise modern tools.

A natural approach would be to say that 'contained in' means that the antecedent is a conjunction of propositions, one of which is syntactically identical to the consequent. In that case we may or may not be able to say that:

(1) IsBachelor(x,t) -> IsUnmarried(x,t)

is analytic, where IsBachelor(x,t) means 'x is a bachelor at time t'.

Here are two logically equivalent, but syntactically different, possible definitions of the atomic formula IsBachelor(x,t):

(2) IsUnmarried(x,t) & IsAdult(x,t) & IsMale(x,t) & IsAlive(x) & IsHuman (x,t) & (for all t') (t'<t -> IsUnmarried(x,t'))

(3) IsAdult(x,t) & IsMale(x,t) & IsAlive(x,t) & IsHuman (x,t) & (for all t') (t'<=t -> IsUnmarried(x,t'))

With interpretation (2), the proposition (1) is analytic, but with interpretation (3) it is not, because the consequent of (1) does not appear in (3).

unenlightened

I tend to think that the analytic/synthetic distinction is a matter of choice.

1. All swans are white.

2. https://commons.wikimedia.org/wiki/File%3ABlack_Swan_at_Martin_Mere.JPG

Choice: (a) that's not a swan because all swans are white.
(b) ok some swans are black.

Or compare, 'all electrons have a negative charge, therefore that particle with the same mass and a positive charge is not an electron - let's call it a positron.'

Numi Who

↪Real Gone Cat

A few observations to share:

1.) Logical thinking in ancient Greek times grew out of an industry - to train paying clients on how to argue their cases in court.

2.) Logical thinking was not the only kind of thinking going on - there was also Rhetoric - which is all about persuading people (whether you speak the truth or not) (and it includes things like body language and emotion), and which was taught by Sophists (hence the phrase 'twisted sophism' when confronted by a deceitful and erroneous propositions) (though they actually taught a lot of things, getting a somewhat bad rap). Today rhetoric is taught to unscrupulous used car salesmen and trial lawyers, hence its continued lowlife image.

3.) There are fallacious forms of modus ponens (which you pointed out).

4.) Other terms for modus ponens would be 'Rules of Thumb' or 'Generalizations' or 'Likely Probabilities' or 'Not hard-and-fast laws of nature'.

Taking a Look at Modus Ponens ... oh yeah, and P-zombies too!

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