McGee's counterexample to the Modus Ponens

[Speakpigeon]

p1 If a Republican wins, then if Reagan doesn’t win, then Anderson wins;
p2 A Republican wins;
C If Reagan doesn’t win, then Anderson wins.

Put into the context of the election poll and our memories and beliefs about Reagan, Anderson and Carter, we can still be "tricked". Tricked by what? There is no "it".
EB

Are we though? Compared to the original example, I find it much more natural to read this formulation as "given a Republican winner, if Reagan doesn't win, Anderson has to", thus a valid conclusion.

But that's also what the original argument says.

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

The two "it" both clearly refer to "A Republican will win the election".

I agree that we tend to read something else into the argument but that is not the fault of the argument itself. There is no equivocation or else all arguments contain equivocations.
EB

 

[Jokodo]

Are we though? Compared to the original example, I find it much more natural to read this formulation as "given a Republican winner, if Reagan doesn't win, Anderson has to", thus a valid conclusion.

But that's also what the original argument says.

That's what it says, in its valid interpretation.

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

The two "it" both clearly refer to "A Republican will win the election".

They clearly don't. "If a Republican will win the election is not Reagan who wins, a Republican will win the election will be Anderson" isn't even English.

I agree that we tend to read something else into the argument but that is not the fault of the argument itself. There is no equivocation or else all arguments contain equivocations.
EB

That's a bullshit conclusion. Not all arguments contain equally ambiguous terms.

The argument "elephants are unique in having a large trunk; my car has a large trunk; therefore my car is an elephant" contains equivocation of two readings of "trunk".

The arguments "sloths and manatees are the only mammals that can have a number of cervical vertebrae deviating from the default, 7; a giraffe is a mammal that's neither a sloth nor a manatee; therefore a giraffe has seven cervical vertebrae" is valid because "cervical vertebra" only has one meaning.

 

[Speakpigeon]

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

The two "it" both clearly refer to "A Republican will win the election".

They clearly don't. "If a Republican will win the election is not Reagan who wins, a Republican will win the election will be Anderson" isn't even English.

No. There is no reason based on the argument as worded by McGee not to take both instances of "it" as referring to the same thing, contrary to your assertion here:

"It" is a pronoun, pronouns don't have intrinsic reference but are assigned a referent from context. The context offers "the Republican who wins" in the premise, but in the conclusion, ether thay context is lacking, we're tricked to interpret it as an unrestricted "the winner".

No. Both instances of "it" clearly refer to the Republican who win the election as both instances are subject to the assumption that a Republican will win the election.

Both instances of "it" clearly refer to the same the Republican who win the election because in both cases it is the nearest thing they can refer back to.

So, in both cases we have: If the Republican who win the election is not Reagan who wins it will be Anderson.

Or explain to me what there is in this one particular argument that there wouldn't be in any valid argument that would make the two instances of "it" not refer to the same phrase the Republican who win the election.
EB

 

[Jokodo]

They clearly don't. "If a Republican will win the election is not Reagan who wins, a Republican will win the election will be Anderson" isn't even English.

No. There is no reason based on the argument as worded by McGee not to take both instances of "it" as referring to the same thing, contrary to your assertion here:

They can refer to the same thing, but they certainly don't refer to "a Republican will win the election", which is what you said.

"It" is a pronoun, pronouns don't have intrinsic reference but are assigned a referent from context. The context offers "the Republican who wins" in the premise, but in the conclusion, ether thay context is lacking, we're tricked to interpret it as an unrestricted "the winner".

No. Both instances of "it" clearly refer to the Republican who win the election as both instances are subject to the assumption that a Republican will win the election.

If that clearly is so, you could clearly substitute each of their occurrences with "the Republican who (will) win the election" and maintain all readings, including the one that appears paradoxical. This is not the case. To witness:

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

Unlike in McGee's original formulation, we do not get the feeling that the conclusion is unsupported. It logically follows that this cannot be the only, and crucially not the most prominent reading we give his original formulation - if it were, we'd go away from both versions with exactly the same intuition, the same feeling of a paradox, or lack thereof.

There are interesting questions to ask, such as why we don't naturally read it in this interpretation even though it is clearly available, and even though it is the one interpretation that makes sense. But before fruitfully discussing those, it is necessary to acknowledge that there is an ambiguity.

 

[Speakpigeon]

No. Both instances of "it" clearly refer to the Republican who win the election as both instances are subject to the assumption that a Republican will win the election.

If that clearly is so, you could clearly substitute each of their occurrences with "the Republican who (will) win the election" and maintain all readings, including the one that appears paradoxical. This is not the case. To witness:

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

Unlike in McGee's original formulation, we do not get the feeling that the conclusion is unsupported. It logically follows that this cannot be the only, and crucially not the most prominent reading we give his original formulation - if it were, we'd go away from both versions with exactly the same intuition, the same feeling of a paradox, or lack thereof.

There are interesting questions to ask, such as why we don't naturally read it in this interpretation even though it is clearly available, and even though it is the one interpretation that makes sense. But before fruitfully discussing those, it is necessary to acknowledge that there is an ambiguity.

There is no ambiguity in McGee's argument. Substituting "the Republican who wins the election" to all instances of "it" shows there is no ambiguity.You are chasing the wrong duck.

Still, I see you are moving a bit, but you still fail to realise what you yourself now say: "the most prominent reading we give his original formulation"... Exactly. It is WE who give McGee's argument a certain reading, and this even though the argument is perfectly unambiguous as shown by the substitution.

Tell me when you wake up because this is indeed the interesting question. There's no ambiguity in the argument, so why do we do it?
EB

 

[Jokodo]

No. Both instances of "it" clearly refer to the Republican who win the election as both instances are subject to the assumption that a Republican will win the election.

If that clearly is so, you could clearly substitute each of their occurrences with "the Republican who (will) win the election" and maintain all readings, including the one that appears paradoxical. This is not the case. To witness:

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

Unlike in McGee's original formulation, we do not get the feeling that the conclusion is unsupported. It logically follows that this cannot be the only, and crucially not the most prominent reading we give his original formulation - if it were, we'd go away from both versions with exactly the same intuition, the same feeling of a paradox, or lack thereof.

There are interesting questions to ask, such as why we don't naturally read it in this interpretation even though it is clearly available, and even though it is the one interpretation that makes sense. But before fruitfully discussing those, it is necessary to acknowledge that there is an ambiguity.

There is no ambiguity in McGee's argument. Substituting "the Republican who wins the election" to all instances of "it" shows there is no ambiguity.You are chasing the wrong duck.

Still, I see you are moving a bit, but you still fail to realise what you yourself now say: "the most prominent reading we give his original formulation"... Exactly. It is WE who give McGee's argument a certain reading, and this even though the argument is perfectly unambiguous as shown by the substitution.

Tell me when you wake up because this is indeed the interesting question. There's no ambiguity in the argument, so why do we do it?
EB

Whether a certain sentence of the English language is ambiguous or not isn't to be decided by some know it all in France (or for that matter England), it is an empirical question the answer to which depends on whether competent speakers of the language converge on one and only one reading regardless of context. As soon as you find a significant minority assigns it a different reading in at least some contexts, you have successfully demonstrated its ambiguity.

Or in short: linguistic expressions don't have meaning above and beyond that which speakers assign them, and they have all the meanings speakers do assign them in a reproducible manner.

That's how the empirical study of human language works, but you can continue to talk about unicorns and leprechauns and sentences that "clearly" mean something different from what people understand when they hear or read them, and only that, if you prefer. Just don't pretend it has anything to do with the real world, alright?

 

[Speakpigeon]

There is no ambiguity in McGee's argument. Substituting "the Republican who wins the election" to all instances of "it" shows there is no ambiguity.You are chasing the wrong duck.

Still, I see you are moving a bit, but you still fail to realise what you yourself now say: "the most prominent reading we give his original formulation"... Exactly. It is WE who give McGee's argument a certain reading, and this even though the argument is perfectly unambiguous as shown by the substitution.

Tell me when you wake up because this is indeed the interesting question. There's no ambiguity in the argument, so why do we do it?
EB

Whether a certain sentence of the English language is ambiguous or not isn't to be decided by some know it all in France (or for that matter England),

Yet another ad hominem. I'm not sure how you determine I am a "know-it-all" since I never claimed on this forum to know anything outside the contents of my own mind.

You seem to get rather too easily upset. I'm not sure you should have any conversation with me.

Anyway, sure, and it is not to be decided by you either. This is a forum and I give my expert opinion as a competent speaker of English.

it is an empirical question the answer to which depends on whether competent speakers of the language converge on one and only one reading regardless of context. As soon as you find a significant minority assigns it a different reading in at least some contexts, you have successfully demonstrated its ambiguity.

I agree with that but you are an incompetent reader because it is rather obvious that the ambiguity doesn't come from the argument.

I also hope that your qualification "in at least some contexts" doesn't mean you think that ambiguity doesn't depend on the context.

Or in short: linguistic expressions don't have meaning above and beyond that which speakers assign them, and they have all the meanings speakers do assign them in a reproducible manner.

That's how the empirical study of human language works, but you can continue to talk about unicorns and leprechauns and sentences that "clearly" mean something different from what people understand when they hear or read them, and only that, if you prefer. Just don't pretend it has anything to do with the real world, alright?

Whatever.

People can get confused. Having any number of people who read the argument wrong isn't proof that the argument is ambiguous.
EB

 

[fromderinside]

So if I side with Jokodo that the argument reads one way while you alone argue it reads another then how do we determine is pristine or ambiguous? You need to come up with something other than repetition of your personal view. Regardless of your personal view there is a difference between specific and unspecific readings as Jokodo points out. Please address.

 

[Jokodo]

Yet another ad hominem. I'm not sure how you determine I am a "know-it-all" since I never claimed on this forum to know anything outside the contents of my own mind.

You seem to get rather too easily upset. I'm not sure you should have any conversation with me.

Anyway, sure, and it is not to be decided by you either. This is a forum and I give my expert opinion as a competent speaker of English.

it is an empirical question the answer to which depends on whether competent speakers of the language converge on one and only one reading regardless of context. As soon as you find a significant minority assigns it a different reading in at least some contexts, you have successfully demonstrated its ambiguity.

I agree with that but you are an incompetent reader because it is rather obvious that the ambiguity doesn't come from the argument.

That's a category error. Arguments aren't ambiguous or unambiguous, they are valid or invalid. Sentences can be ambiguous. Arguments aren't sequences of sentences, they are webs of propositions. If a representation of an argument contains ambiguous sentences, than that representation is ambiguous in that it can refer to different arguments - each of which is either valid or invalid, but not both.

The sequence of sentences McGee uses in his representation is ambiguous in several ways: There's the issue of the specific and unspecific reading of the article, the issue of what "it" refers to, and the issue of whether to interpret the "will" as a certainty or a probability. In some of its interpretations, it refers to a valid argument (if the sentence "A Republican will win the election" is interpreted as a certainty, and/or the "it" in the conclusion is taken to refer to "the Republican who wins the election"), in others it doesn't.

If we replace the ambiguous sentences with unambiguous paraphrases corresponding to a reading that results in a valid argument, we have no trouble whatsoever intuitively assessing that the argument is indeed valid.

For example:

A1: If a Republican wins the election, then if the Republican who wins the election is not Reagan, the Republican who wins the election will be Anderson.
B1: A Republican will win the election.
C1: If the Republican who wins the election is not Reagan, the Republican who wins the election will be Anderson.​

Here, the conclusion is valid (though it has a presupposition, namely that a Republican wins). Similarly:

A2: If a Republican wins the election, then if it isn't Reagan who wins, it will be Anderson.
B2: It is a certainty that a Republican, whoever it is, will win the election (e. g. because we've consulted a clairvoyant who is never wrong).
C2: If it isn't Reagan who wins, it will be Anderson.​

...again a valid conclusion.

If you replace the ambiguous sentences with unambiguous paraphrases corresponding to different reading, it's similarly clear that the argument is invalid.

A3: If a Republican wins the election, then if it isn't Reagan who wins, it will be Anderson.
B3: It is highly probable that Reagan (who is a Republican so I will refer to him simply as that) will win the election.
C3: If it isn't Reagan who wins, it is highly probable that Anderson will.​

What McGee does is providing a context that prejudices us to read the B sentence in reading B3, but tricking us into believing that we're inside a type 1 or 2 argument.

Argument 3 is invalid, but it shares a representation with a valid argument due to linguistic ambiguities. Argument 2 is valid by virtue of modus ponens, so he's confusing us into believing that the invalidity of argument 3 is a problem for modus ponens, and he's using linguistic ambiguity to do so.

 

[MxM111]

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

McGee's counterexample

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.

I think the problem is the following. Modus ponens principle is a logic principle, not probability principle. If A, then B. Then A happens. 100% happens. No "probably happens". Then B

Applying to the election example, it is misleading to say "A Republican will win the election", because it does not convey the 100% certainty, because we talk about future. Modus ponens does not have time dimention, it just says "this happen therefore that". Change "A Republican will win the election" to "A Republican won the election", then it is true that "If it's not Reagan who won, it is Anderson."

A statement "A Republican will win the election" must mean "we live in the word where the only possibility is a republican wining election", otherwise Modus ponens is not applicable. Then again "If it's not Reagan who wins, it will be Anderson" is completely valid statement.

 

[fromderinside]

A statement "A Republican will win the election" must mean "we live in the word where the only possibility is a republican wining election", otherwise Modus ponens is not applicable. Then again "If it's not Reagan who wins, it will be Anderson" is completely valid statement.

This ^^^^^

captures real conditions in Hungary and US. So your example is bogus.

 

[Speakpigeon]

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

McGee's counterexample

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.

I think the problem is the following. Modus ponens principle is a logic principle, not probability principle. If A, then B. Then A happens. 100% happens. No "probably happens". Then B

Applying to the election example, it is misleading to say "A Republican will win the election", because it does not convey the 100% certainty, because we talk about future. Modus ponens does not have time dimention, it just says "this happen therefore that". Change "A Republican will win the election" to "A Republican won the election", then it is true that "If it's not Reagan who won, it is Anderson."

A statement "A Republican will win the election" must mean "we live in the word where the only possibility is a republican wining election", otherwise Modus ponens is not applicable. Then again "If it's not Reagan who wins, it will be Anderson" is completely valid statement.

This is a red herring. We can modify McGee's counterexample as follows, putting everything in the present:

McGee's counterexample modified:

If a Republican has won the election, then if it's not Reagan who has won it is Anderson.
A Republican has won the election.

Yet they did not have reason to believe

If it's not Reagan who has won, it is Anderson.

It is certainly better this way, but we should all be able to interpret McGee's original in this vein without requiring my assistance.
EB