Talk:Modus ponens
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One of the "conversation" chapters in Gödel, Escher, Bach is by Lewis Caroll, and is about MP and how it can be extended to absurdity. -- Tarquin 05:58 Aug 27, 2002 (PDT)
I'm putting in an article about that. To help, can someone clarify if "modus ponens" is the correct term to use with this argument:
- ∀x∀y:equalsame(x,y) ⇒ x=y
- equalsame(a,b)
- ∴ a=b
In other words, does the existence of the quantifiers prevent me from calling this "modus ponens"?
--Ryguasu 23:34 Dec 3, 2002 (UTC)
I would insert the step
- equalsame(a,b) ⇒ a=b
which follows from 1 by specialization. Then the remainder of the argument would be modus ponens. AxelBoldt 03:24 Dec 4, 2002 (UTC)
Is this the same as a sylogism?
Contents |
[edit] self-referential premises
If the argument is modus ponens and its premises are true, then it is sound. The premises are true. Therefore, it is a sound argument.
For the purposes of my following statements:
- this argument
- the argument whose text you see here
- the referenced argument
- the argument referred to in this argument, whose soundness is argued
I assume "the premises are true" in the second line refers to the the premises mentioned in the first line, the premises of the referenced argument, as opposed to the premises of this argument, the argument presented here directly. The premises of this argument are not well premised as true by the second line due to expectations of the reader that the premises of the referenced argument are to be addressed explicitly at this point. However, the use of the definite article over the possessive pronoun suggests that the author is not referring to the referenced argument for this premise...
In short, I just realized you're messing with people.
And to lead into this modus ponens with "instances of its use may be either sound or unsound" is pure genius since this instance may indeed (or ininterpretation) be either.
You got me all worked up.
[edit] Psychology
I've heard that the "modus ponens" is considered something every man is born with (in order to be able to make transactions, like: - "I give you A, if you give me B" - you give me B -> I give you A), while the "modus tollens" is something that needs reflection first. I don't exactly know if this is true/unargued, but this should be mentioned perhaps. Also I've heard that the full name of the modus is "modus ponendo ponens" (and his 'counterpart' "modus tollendo tollens"), if this is true, it might be added too.
I don't want to change this by myself, because I'm not really sure whether it's true or not, as mentioned.
[edit] Truth Tables
Should the truth tables of modus ponens be added to this article? --Vince.Buffalo 05:41, 19 August 2006 (UTC)
[edit] Trivial Truth
Could someone include some discussion of the following problem ...
Here are the truth functions of modus ponens:
((P > Q ) & P) > Q
1 1 1 1 1 [1] 1
1 0 0 0 1 [1] 0
0 1 1 0 0 [1] 1
0 1 0 0 0 [1] 0
*
Underneath the main (conclusion) operator, all lines of the truth table are true, hence the argument is valid.
But there is a problem once you start filling in the variables. The usual example is If one is a man, then one is mortal. Socrates is a man, hence Socrates is mortal. That works. P is true, Q is true, and the conclusion, by the magic of modus ponens comes out true. But what about this: If the moon orbits the earth, then I am wearing white carpenter's pants. Again, the first premise, P, is true. And take my word for it that the second premise, Q, is also true. Given the foregoing, the conclusion is valid. But why? It doesn't seem like the moon orbiting the earth should have any bearing on what I am wearing today, does it?
There are only two ways I have to deal with this, and I hope someone can help. First is simply to say that propositional logic doesn't account for modalities--whether the moon necessarily or possibly orbiting the earth has any impact on my choice of pants. Granted, modal logic, temporal logic, fuzzy logic, and some applications of predicate logic capture all of that. But as to basic bone-headed propositional logic, the conclusion seems odd, because it leaves open the possibility of a modus ponens sentence returning an invalid result--which it shouldn't be able to do.
So I think I have a second answer that works better. Because basic propositional logic doesn't account for time, modality, probability, etc. Given that, propositional logic describes a world in which all true propositions are necessarily related to each other (or necessarily not related to each other.) For instance, in the world that propositional logic can describe--every time a butterfly flaps its wings, there either must or must not be a hurricane.
That's about all I have to describe it, but I'd love to hear what anyone else has to say.
Thx.
I think you misunderstand the notion of a logically valid argument. A valid argument is one in which the conclusion is *guaranteed* simply by virtue of the form of its premises. In your example, you seem to just be assigning truth-values to propositions. It makes no sense to say "given that the earlier two propositions are true, the conclusion is valid," since validity is a property of arguments, not of individual propositions (a common category mistake people make when first learning about logic). "Validity" just means "truth-preserving."
In standard form the modus ponens argument similar to yours would go:
1. The moon orbits the earth.
2. If the moon orbits the earth, then I am wearing white carpenter pants.
3. Therefore, I am wearing white carpenter pants. (1,2 modus ponens)
In this case, 3 is guaranteed by 1 and 2. Whether or not the argument is *sound* has to do with the truth of 1 and 2, and what I believe you are saying is that 2 is absurd (false). This does prevent the argument from being sound, but the argument itself is still valid.
[edit] eliminated link to "falsity implies anything"
I stated this incorrectly in the history page - modus ponens is just a form, and as such truth-value assignments are irrelevant. My real justification for deleting the link is that it really is too unrelated to an article on modus ponens (it would go well in an article on conditional statements).
