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Thread: McGee's counterexample to the Modus Ponens

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    McGee's counterexample to the Modus Ponens

    Here is an interesting example to try your wits...

    This is one philosopher, Vann McGee, who in 1986 proposed a counterexample to the Modus Ponens, no less!

    Here is the thing:
    McGee's counterexample
    https://link.springer.com/article/10.1007%2FBF00355293

    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

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    Quote Originally Posted by Speakpigeon View Post
    Here is an interesting example to try your wits...

    This is one philosopher, Vann McGee, who in 1986 proposed a counterexample to the Modus Ponens, no less!

    Here is the thing:
    McGee's counterexample
    https://link.springer.com/article/10.1007%2FBF00355293

    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
    What's going on is the Principle_of_explosion. He's trying to sneak in a change of premises halfway through the argument. The conviction that "A Republican will win the election." rests entirely on the premise that the polls are accurate. The conditional "If it's not Reagan who wins" requires the polls to be inaccurate. So he ends up saying "if the polls are accurate and the polls are inaccurate", which is a contradiction.

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    Quote Originally Posted by Jokodo View Post
    Quote Originally Posted by Speakpigeon View Post
    Here is an interesting example to try your wits...

    This is one philosopher, Vann McGee, who in 1986 proposed a counterexample to the Modus Ponens, no less!

    Here is the thing:
    McGee's counterexample
    https://link.springer.com/article/10.1007%2FBF00355293

    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
    What's going on is the Principle_of_explosion. He's trying to sneak in a change of premises halfway through the argument. The conviction that "A Republican will win the election." rests entirely on the premise that the polls are accurate. The conditional "If it's not Reagan who wins" requires the polls to be inaccurate. So he ends up saying "if the polls are accurate and the polls are inaccurate", which is a contradiction.
    From a more linguistic perspective, you could say that he's confusing two readings if the English indefinite article "a". It has an unspecific reading which can be paraphrased as "whoever wins the election is going to be a Republican", and a specific one roughly meaning "there is a certain Republican [in our context: namely Ronald Reagan] who will win the election". The conclusion only follows from the unspecific reading, which the context doesn't support. The specific reading is again in contradiction to the antecedent if the conditional.

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    Quote Originally Posted by Jokodo View Post
    Quote Originally Posted by Jokodo View Post

    What's going on is the Principle_of_explosion. He's trying to sneak in a change of premises halfway through the argument. The conviction that "A Republican will win the election." rests entirely on the premise that the polls are accurate. The conditional "If it's not Reagan who wins" requires the polls to be inaccurate. So he ends up saying "if the polls are accurate and the polls are inaccurate", which is a contradiction.
    From a more linguistic perspective, you could say that he's confusing two readings if the English indefinite article "a". It has an unspecific reading which can be paraphrased as "whoever wins the election is going to be a Republican", and a specific one roughly meaning "there is a certain Republican [in our context: namely Ronald Reagan] who will win the election". The conclusion only follows from the unspecific reading, which the context doesn't support. The specific reading is again in contradiction to the antecedent if the conditional.
    This is closer to the real problem, I think. In my view, the ambiguity is actually around "it" in "If it isn't Reagan...". Unpacked, it means "the winning Republican, in the event that a Republican wins." If you plug this into the conclusion, it follows from the premises without contradicting anything.

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    Veteran Member Treedbear's Avatar
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    Quote Originally Posted by PyramidHead View Post
    Quote Originally Posted by Jokodo View Post
    Quote Originally Posted by Jokodo View Post

    What's going on is the Principle_of_explosion. He's trying to sneak in a change of premises halfway through the argument. The conviction that "A Republican will win the election." rests entirely on the premise that the polls are accurate. The conditional "If it's not Reagan who wins" requires the polls to be inaccurate. So he ends up saying "if the polls are accurate and the polls are inaccurate", which is a contradiction.
    From a more linguistic perspective, you could say that he's confusing two readings if the English indefinite article "a". It has an unspecific reading which can be paraphrased as "whoever wins the election is going to be a Republican", and a specific one roughly meaning "there is a certain Republican [in our context: namely Ronald Reagan] who will win the election". The conclusion only follows from the unspecific reading, which the context doesn't support. The specific reading is again in contradiction to the antecedent if the conditional.
    This is closer to the real problem, I think. In my view, the ambiguity is actually around "it" in "If it isn't Reagan...". Unpacked, it means "the winning Republican, in the event that a Republican wins." If you plug this into the conclusion, it follows from the premises without contradicting anything.
    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.
    But they obviously did have a reason to believe that, because when given the hypothetical "a Republican wins the election" and there are only two Republicans, if one was not the winner then it had to be the other. If p then q. If a Republican wins the election, then it will be either Reagan or Anderson.

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    Veteran Member PyramidHead's Avatar
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    Quote Originally Posted by Treedbear View Post
    Quote Originally Posted by PyramidHead View Post

    This is closer to the real problem, I think. In my view, the ambiguity is actually around "it" in "If it isn't Reagan...". Unpacked, it means "the winning Republican, in the event that a Republican wins." If you plug this into the conclusion, it follows from the premises without contradicting anything.
    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.
    But they obviously did have a reason to believe that, because when given the hypothetical "a Republican wins the election" and there are only two Republicans, if one was not the winner then it had to be the other. If p then q. If a Republican wins the election, then it will be either Reagan or Anderson.
    That was my point. Properly interpreted, there is every reason to believe the conclusion given the premises, so this is not a counterexample to MP.

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    Put simpler, he's substituting a phrase in one meaning ("a Republican" under its specific reading) for the same phrase in another meaning (the unspecific one). So the argument is not entirely unlike saying "elephants are unique in having large trunks. My car has a large trunk. Therefore, my car is an elephant."
    Last edited by Jokodo; 11-01-2019 at 05:43 PM.

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    Quote Originally Posted by Treedbear View Post
    Quote Originally Posted by PyramidHead View Post

    This is closer to the real problem, I think. In my view, the ambiguity is actually around "it" in "If it isn't Reagan...". Unpacked, it means "the winning Republican, in the event that a Republican wins." If you plug this into the conclusion, it follows from the premises without contradicting anything.
    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.
    But they obviously did have a reason to believe that, because when given the hypothetical "a Republican wins the election" and there are only two Republicans, if one was not the winner then it had to be the other. If p then q. If a Republican wins the election, then it will be either Reagan or Anderson.
    One of the premises, restated in an unambiguous form, reads "if whoever wins the election is a Republican..." The other, "a certain Republican will win the election." Those are two different meanings, and you can't freely substitute one for the other and expect to arrive at a valid argument any more than by substituting the two meanings of "trunk",
    Last edited by Jokodo; 11-01-2019 at 05:42 PM.

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    OK, I broadly agree with everything which has been said. I would express the problem differently, though. To my mind, the problem is that our belief in this case is not grounded in the argument.

    This argument is typical of the kind of arguments where we find it difficult to assess validity because it requires that we abstract the argument from the context. If you submit an argument involving Trump or Boris Johnson, people will forget the question about the validity of the argument and focus instead on the question of the truth of the conclusion.

    Our argument here is indeed about a real situation about Ronald Reagan and the Republicans, and we are duly reminded of the opinion polls before the election. This is all an effective massaging of our belief gland and we look at the conclusion of the argument not as part of the argument but as if it was standing on its own and consequently, we all disbelieve the implication because, clearly, if it wouldn't have been Reagan, it would have been Carter.

    Here we assess the conclusion in light of the general context of the actual situation referred to by the argument, including, crucially the opinion poll, and including our own memory and understanding of American politics.

    There is a similar problem in particular with all arguments about God, which have the ability to upset people a lot and throw off their logic.

    The problem, however, is more general. Whenever the argument is realistic and we have some expertise on the subject matter, our own beliefs will come in to derail our logical intuition. This is actualy quite potent. I can look at the Donald Reagan argument here and feel at the same time that the argument is valid and that somehow it doesn't work.

    I agree with what has been said. However, the wording of the argument seems good enough and wouldn't in itself cause the problem. The problem arise because we read what are essentially the same sentences differently depending on whether they are part of an implication or the conclusion. This only happens because we are biased by being primed by our own expertise on the subject of American elections.

    I will also add to this the interesting comment made by serious people...
    EB

    Three philosophers from Dartmouth defended modus ponens against McGee's example. They claim to find three confusions in McGee's argument, confusions that, if removed, leave modus ponens unchallenged.

    First, modus ponens preserves truth, not grounds for believing or probabilities. A real counterexample would have to use modus ponens to go from true premises to a false conclusion. Second, an analogue of modus ponens for grounds or probabilities must not confuse good grounds or high probabilities for the premises separately with good grounds or high probability for the conjunction of the premises. Finally, the probability of a conditional must not be confused with the conditional probability. (Sinnott-Armstrong, Moor, Fogelin 1986, p. 300)
    https://link.springer.com/article/10.1007%2FBF00355293

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    Quote Originally Posted by Speakpigeon View Post
    OK, I broadly agree with everything which has been said. I would express the problem differently, though. To my mind, the problem is that our belief in this case is not grounded in the argument.

    This argument is typical of the kind of arguments where we find it difficult to assess validity because it requires that we abstract the argument from the context. If you submit an argument involving Trump or Boris Johnson, people will forget the question about the validity of the argument and focus instead on the question of the truth of the conclusion.

    Our argument here is indeed about a real situation about Ronald Reagan and the Republicans, and we are duly reminded of the opinion polls before the election. This is all an effective massaging of our belief gland and we look at the conclusion of the argument not as part of the argument but as if it was standing on its own and consequently, we all disbelieve the implication because, clearly, if it wouldn't have been Reagan, it would have been Carter.

    Here we assess the conclusion in light of the general context of the actual situation referred to by the argument, including, crucially the opinion poll, and including our own memory and understanding of American politics.

    There is a similar problem in particular with all arguments about God, which have the ability to upset people a lot and throw off their logic.

    The problem, however, is more general. Whenever the argument is realistic and we have some expertise on the subject matter, our own beliefs will come in to derail our logical intuition. This is actualy quite potent. I can look at the Donald Reagan argument here and feel at the same time that the argument is valid and that somehow it doesn't work.

    I agree with what has been said. However, the wording of the argument seems good enough and wouldn't in itself cause the problem. The problem arise because we read what are essentially the same sentences differently depending on whether they are part of an implication or the conclusion. This only happens because we are biased by being primed by our own expertise on the subject of American elections.

    I will also add to this the interesting comment made by serious people...
    EB

    Three philosophers from Dartmouth defended modus ponens against McGee's example. They claim to find three confusions in McGee's argument, confusions that, if removed, leave modus ponens unchallenged.

    First, modus ponens preserves truth, not grounds for believing or probabilities. A real counterexample would have to use modus ponens to go from true premises to a false conclusion. Second, an analogue of modus ponens for grounds or probabilities must not confuse good grounds or high probabilities for the premises separately with good grounds or high probability for the conjunction of the premises. Finally, the probability of a conditional must not be confused with the conditional probability. (Sinnott-Armstrong, Moor, Fogelin 1986, p. 300)
    https://link.springer.com/article/10.1007%2FBF00355293
    It's true that a confusion of absolute truth it's partly to blame, but even without that the apparent paradox disappears once you substitute all occurrences of "a" and "it" for unambiguous paraphrases. The argument then becomes either obviously invalid because it rests on substituting a term for one if a different meaning, they become contradictory, or the conclusion actually does follow, or at the very least the premises are no longer supported by the context and therefore or intuitions about the conclusion become irrelevant.

    For example, a. Specific reading of "a Republican" in the first premise implies a shape shifter who will take in either Reagan's or Anderson's form. Disambiguating "it" as "the Republican who wins" produces a valid conclusion with the second premise as a presupposition, etc.

    I challenge you to find an unambiguous paraphrase that doesn't suffer from one if these problems!

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