McGee's counterexample to the Modus Ponens

Does McGee's counterexample invalidate the Modus ponens?

  • Yes

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  • No

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  • I don't know

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  • The question makes no sense

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Speakpigeon

Speakpigeon

Valued Senior Member
Here is an interesting example for you to try your wits...

This is one philosopher, Vann McGee, who in 1985 proposed a counterexample to the Modus Ponens, no less!

Here is the thing:

McGee's counterexample
https://link.springer.com/article/10.1007/BF00355293
Almost 10 years ago, Vann McGee pushed philosophical doubt beyond another frontier. His attempt to show that modus ponens is not a valid form of inference- and to show this by help of a counterexample and not by envisaging an evil demon confusing us - is proof of the ingenuity of a philosopher's ability to doubt. Other philosophers might be less impressed. They criticize McGee's counterexample, thinking it either rests on confusions or can, in some other way, easily be circumvented. I argue in this paper that such a reaction is unjustified. McGee's counterexample withstands the criticisms raised against it. Should we thus abolish modus ponens? It depends, I think, on what the right theory of conditionals is, and though I will provide some material for deciding this question, in the end, this material will be indecisive.

McGEE'S CLAIM ABOUT MODUS PONENS​

It is sufficient to focus our discussion on one of McGee's counterexamples - others follow the same recipe.
Opinion polls taken just before the 1980 election showed the Republican Ronald Reagan decisively ahead of the democrat Jimmy Carter, with the other Republican in the race, John Anderson, a distant third. Those apprised of the poll results believed, with good reason:

If a Republican wins the election, then if it's not Reagan who wins it will be Anderson.
A Republican will win the election.​

Yet they did not have reason to believe

If it's not Reagan who wins, it will be Anderson.​

This example shows that modus ponens is not an entirely reliable rule of inference. Sometimes the conclusion of an application of modus ponens is something we do not believe and should not believe, even though the premises are propositions we believe very properly. (McGee 1985, pp. 462f.)​

Anyone understands what's going on here?
EB
 
Yes, I understand (I think).

It seems to be no different to any other Modus Ponens:
If X then Y
X
Therefore Y.

The issue here is that people are being asked about 2 distinct scenarios for Y:
Y1 - IF a Republican wins then if not Reagan it will be Anderson.
Y2 - No statement about whether a Republican wins or not, therefore it might be Reagan or a Democrat before Anderson.

Y1 and and Y2 are not the same scenario, even if they are worded the same.
Thus the counterexample is trying to claim:
If X then Y1
X
Therefore Y2

Maybe rewording it as follows might highlight the difference:
Modus Ponens:
If X then Y(assuming X)
X
Therefore Y(assuming X)

And the counterexample being:
If X then Y(assuming X)
X
Therefore Y(not assuming X)

Spot the difference?

So maybe it's just a matter of recognising that Modus Ponens requires the hidden assumption that the Y must always be assuming X.
Does this invalidate Modus Ponens where the concluding Y does not?
Well, no, I don't think so, because the truth seems to be preserved regardless, whether people have a reason to believe in Y(not assuming X) or not.
 
Speakpigeon said:
1. If a Republican wins the election, then if it's not Reagan who wins it will be Anderson.
2. A Republican will win the election.
3. If it's not Reagan who wins, it will be Anderson.
Click to expand...
There's no problem with this, provided we keep track of the entire argument and don't forget premise 2 somewhere along the way.

The point of modus ponens is that it holds that if premises 1 and 2 are both true, then the conclusion 3 logically follows.

So, in this example, if it is true that a Republican will win the election, then it will also be true that if it's not Reagan it will be Anderson.

The "problem" only comes if we backtrack and consider the case where premise 2 is false. In that case, the conclusion (3) can't be derived from premise 1 alone, and there's nothing further to discuss.

So, this isn't a problem for modus ponens as a formal argument structure at all.

But this particular set of premises is circumlocutionary anyway. An equivalent argument with a clearer flow would be:

1. If a Republican wins the election and Reagan doesn't win, then Anderson will win.
2. A Republican will win the election.
3. Reagan will not win the election.
4. Therefore Anderson will win.

or, if you prefer to leave things open as to which Republican candidate will win, and cover all bases explicitly (better):

1. Either a Republican or a Democrat will win the election.
2. If a Republican wins the election and Reagan does not win, then Anderson will win.
3. A Republican will win the election.
4. If Reagan does not win the election, then Anderson will win.

You may have noticed that there are 3 premises there leading to the conclusion, which means we don't really have a modus ponens any more. But we could fix that by having two separate modus ponens arguments leading to the conclusion.

Bottom line is: this "counterexample" only appears to raise an issue because it deliberately obscures part of the full picture. The apparent problem can be fixed if we, as logicians, are more honest about the argument being made. Moreover, I emphasise that the problem isn't "real" in the sense of invalidating the original logic; it's only "real" in the sense that it causes avoidable confusion in the person hearing the argument.

Baldeee has said essentially the same thing in a different way.

All we need here is a more honest logician, as opposed to the kind of logician who likes to jump out of the bushes shouting "gotcha!" at unsuspecting people.
 
Baldeee said:
Yes, I understand (I think).

It seems to be no different to any other Modus Ponens:
If X then Y
X
Therefore Y.

The issue here is that people are being asked about 2 distinct scenarios for Y:
Y1 - IF a Republican wins then if not Reagan it will be Anderson.
Y2 - No statement about whether a Republican wins or not, therefore it might be Reagan or a Democrat before Anderson.

Y1 and and Y2 are not the same scenario, even if they are worded the same.
Thus the counterexample is trying to claim:
If X then Y1
X
Therefore Y2

Maybe rewording it as follows might highlight the difference:
Modus Ponens:
If X then Y(assuming X)
X
Therefore Y(assuming X)

And the counterexample being:
If X then Y(assuming X)
X
Therefore Y(not assuming X)

Spot the difference?

So maybe it's just a matter of recognising that Modus Ponens requires the hidden assumption that the Y must always be assuming X.
Does this invalidate Modus Ponens where the concluding Y does not?
Well, no, I don't think so, because the truth seems to be preserved regardless, whether people have a reason to believe in Y(not assuming X) or not.
Click to expand...

An argument is valid if the conclusion follows from the premises. This is formally expressed by the word "therefore", meaning "For that reason or cause, consequently or hence". Thus, it is not true that Y2 is asserted not assuming the premise that X.
There are no two scenarios because both Y1 and Y2 assume X. We are not being asked anything except to consider the argument as written and worded, and the argument's form is that of the Modus ponens, which presumably is valid.
So, no, I don't spot the difference since there is no difference relatively to other Modus ponens arguments.

If there is a difference, you haven't put the spotlight on it.
EB
 
Speakpigeon said:
An argument is valid if the conclusion follows from the premises. This is formally expressed by the word "therefore", meaning "For that reason or cause, consequently or hence". Thus, it is not true that Y2 is asserted not assuming the premise that X.
There are no two scenarios because both Y1 and Y2 assume X. We are not being asked anything except to consider the argument as written and worded, and the argument's form is that of the Modus ponens, which presumably is valid.
So, no, I don't spot the difference since there is no difference relatively to other Modus ponens arguments.
Click to expand...
What McGee is trying to do is set up a modus ponens where the logical conclusion is not actually true.
You accept that much, I trust?

To do this he is providing an argument of the form:
If X then Y.
X
Therefore Y.
Agreed so far?

The Y in the premise (Y1) asks people their belief starting with the assumption that the Republicans will win.
So within Y1 is the inherent assumption Of a republican win (X).

He has also polled those people about their belief but without any such initial assumption, and in this case they can not believe that “if not Reagan then Anderson will win”.
I.e. a democrat would like win if Reagan didn’t.
This is Y(2), and it is, per McGee, false - I.e. the people do not believe it is true.

So he has gone from
If X then Y1
X
Therefore Y1
(I.e. modus ponens)
but is then trying to claim that the conclusion (Y1) is false since Y2 is false.

The flaw in his argument is actually two-fold here:
First is that, as I have tried to explain, he is trying to use equivocation (between Y1 and Y2) to disprove the conclusion.
And secondly, at no stage is the conclusion actually shown by McGee to be false, which is necessary to show the modus ponens example invalid.
At best he is showing that people have no reason to believe the conclusion, (equivocation between Y1 and Y2 aside).
But having no reason to believe it does not mean the conclusion is false.
In his modus ponens, the conclusion is true, and remains true irrespective of belief in it.
It remains valid.
 
Baldeee said:
What McGee is trying to do is set up a modus ponens where the logical conclusion is not actually true.
You accept that much, I trust?

To do this he is providing an argument of the form:
If X then Y.
X
Therefore Y.
Agreed so far?

The Y in the premise (Y1) asks people their belief starting with the assumption that the Republicans will win.
So within Y1 is the inherent assumption Of a republican win (X).

He has also polled those people about their belief but without any such initial assumption, and in this case they can not believe that “if not Reagan then Anderson will win”.
I.e. a democrat would like win if Reagan didn’t.
This is Y(2), and it is, per McGee, false - I.e. the people do not believe it is true.

So he has gone from
If X then Y1
X
Therefore Y1
(I.e. modus ponens)
but is then trying to claim that the conclusion (Y1) is false since Y2 is false.

The flaw in his argument is actually two-fold here:
First is that, as I have tried to explain, he is trying to use equivocation (between Y1 and Y2) to disprove the conclusion.
And secondly, at no stage is the conclusion actually shown by McGee to be false, which is necessary to show the modus ponens example invalid.
At best he is showing that people have no reason to believe the conclusion, (equivocation between Y1 and Y2 aside).
But having no reason to believe it does not mean the conclusion is false.
In his modus ponens, the conclusion is true, and remains true irrespective of belief in it.
It remains valid.
Click to expand...
I understood your reasoning the first time round, but your explanation isn't convincing me.
The premises in McGee's argument don't ask people about their beliefs. Both premises seem true to me and everybody seems to agree with that.
The conclusion is a conclusion! It is asserted under the assumption that the premises are true, which is why there is the key word "therefore". And we all understand that, presumably.
McGee's doesn't say that the conclusion is false. He says that people "did not have reason to believe" it.
EB
 
Speakpigeon said:
The premises in McGee's argument don't ask people about their beliefs. Both premises seem true to me and everybody seems to agree with that.
The conclusion is a conclusion! It is asserted under the assumption that the premises are true, which is why there is the key word "therefore". And we all understand that, presumably.
McGee's doesn't say that the conclusion is false. He says that people "did not have reason to believe" it.
Click to expand...
I am only going by what you have posted in the OP:
"His attempt to show that modus ponens is not a valid form of inference..." - one can not show modus ponens is invalid without showing that the conclusion is false.
"Those apprised of the poll results believed, with good reason..." - this is with regard the premises, i.e. the premises are believed, with good reason - not that they are necessarily true.
And your very question in the poll asks whether the counterexample invalidates Modus Ponens - again, one can't do that unless one can show the conclusion false.

Thus McGee is very much saying that the conclusion is false, otherwise we're simply not discussing the issue of invalidating Modus Ponens.
I understood your reasoning the first time round, but your explanation isn't convincing me.
Click to expand...
Perhaps if you actually engaged in one of the threads you post, if you actually post your position on this matter, for example, one might actually start to find out what is preventing you from being convinced.
But that's up to you.
 
Baldeee said:
I am only going by what you have posted in the OP:
"His attempt to show that modus ponens is not a valid form of inference..." - one can not show modus ponens is invalid without showing that the conclusion is false.
"Those apprised of the poll results believed, with good reason..." - this is with regard the premises, i.e. the premises are believed, with good reason - not that they are necessarily true.
And your very question in the poll asks whether the counterexample invalidates Modus Ponens - again, one can't do that unless one can show the conclusion false.
Click to expand...

We all understand that in the actual election, if Reagan hadn't won the election, it would have been Carter. However, as you should know, we don't assess validity on whether the premises or the conclusion are actually true or false.

Do you not accept that the following argument is valid (assuming "election" here too stands for "the 1980 US presidential election)?

If Reagan didn't win the election, then Anderson won the election.
Reagan didn't win the election.
Therefore, Anderson won the election​

Isn't that 100% unambiguously valid?

Baldeee said:
Thus McGee is very much saying that the conclusion is false, otherwise we're simply not discussing the issue of invalidating Modus Ponens.
Perhaps if you actually engaged in one of the threads you post, if you actually post your position on this matter, for example, one might actually start to find out what is preventing you from being convinced.
But that's up to you.
Click to expand...

Do you not accept that the argument in itself is valid?

If a Republican wins the election, then if it's not Reagan who wins it will be Anderson.
A Republican will win the election.
Therefore, if it's not Reagan who wins, it will be Anderson.​

EB
 
Speakpigeon said:
However, as you should know, we don't assess validity on whether the premises or the conclusion are actually true or false.
Click to expand...
I know, and I have not said otherwise.
McGee aims to show that his example is invalid, and to do that he is arguing that the conclusion is false.
Because unless he shows it is false then he can't show that the argument is invalid.
But instead of showing that it is false, he relies on the mere belief that the conclusion is false.
Do you not accept that the following argument is valid ...
Isn't that 100% unambiguously valid? ...
Do you not accept that the argument in itself is valid?
Click to expand...
If you can show where I have said otherwise, maybe it'll be worth responding to these questions.
 
Speakpigeon said:

McGEE'S CLAIM ABOUT MODUS PONENS​
It is sufficient to focus our discussion on one of McGee's counterexamples - others follow the same recipe.
Opinion polls taken just before the 1980 election showed the Republican Ronald Reagan decisively ahead of the democrat Jimmy Carter, with the other Republican in the race, John Anderson, a distant third. Those apprised of the poll results believed, with good reason:

If a Republican wins the election, then if it's not Reagan who wins it will be Anderson.
A Republican will win the election.​
Yet they did not have reason to believe
If it's not Reagan who wins, it will be Anderson.​
Click to expand...
​

So when are you going to present this supposedly "new" and threatening revelation? Valid argument (correct form or template) doesn't mean a sound argument on that basis alone, in terms of what it outputs. The premises have to be true or certain to yield a true or unassailable conclusion (that people could confidently believe in). How can the premises be certain when the antecedent circumstance engendering them is a potentially vulnerable poll rather than, say, a trip to the future and back?​
 
C C said:
So when are you going to present this supposedly "new" and threatening revelation?
Click to expand...
What revelation?!
I asked a question:

Anyone understands what's going on here?​

I never promised any revelation! Have you been drinking?

C C said:
Valid argument (correct form or template) doesn't mean a sound argument on that basis alone, in terms of what it outputs. The premises have to be true or certain to yield a true or unassailable conclusion (that people could confidently believe in). How can the premises be certain when the antecedent circumstance engendering them is a potentially vulnerable poll rather than, say, a trip to the future and back?
Click to expand...
Sorry, I'm uncertain about what you are trying to say.
EB
 
Speakpigeon said:
What revelation?!
I asked a question:

Anyone understands what's going on here?​

I never promised any revelation! Have you been drinking?


Sorry, I'm uncertain about what you are trying to say.
Click to expand...

Not surprising, if you're in such an addled state that you can't even remember the assertion made in the title of this thread.
 
I think the question has been answered. Clearly, there is a good understanding of what's going on here.

Thread closed.
 
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