Logic question (Well more of a premise, conclusion situation)?

Question

The professor gave us two premises and a conclusion. He said that were valid, but I didn't understand why. He will explain it in the next class, but still I'm curious.

1st Premise: Today is Thursday

2nd Premise: Today is not Thursday.

3rd Premise: Trompetilla the clown is the president of (name of my college).

How is this valid, it doesn't make sense. Am I missing something here?

Answer 1

Some of the parts of the other answers are right, but none is completely right.

"Validity" is a term meaning ONLY that a syllogism fits the rules for what a syllogism is, AND "only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false."

Both premises may be true--but not at the same time. Validity does not care about that issue. It cares about whether the premises are possible to be true (which they may, one at a time,) and the conclusion to be false.

On the other hand, "A deductive argument is SOUND if and only if it is both valid, and all of its premises are actually true. Otherwise, a deductive argument is unsound."

http://www.iep.utm.edu/v/val-snd.htm

There are only 15 "valid" syllogistic forms http://phil240.tamu.edu/LectureNotes/6.1... (see page 5). But there are 256 forms of syllogisms!

So something as stupid as your professor's syllogism can be "valid," but "validity" does not make truth.

Answer 2

El Numero nailed it.

I first thought it was a nonsequitur.

It is not about contradiction because it never said you can only either be a clown or your the president of your college.

Answer 3

The premises are mutually exclusive. They can' both be true. A conclusion drawn from two contradictory premises is meaningless.

Answer 4

In classical logic, any argument having premises that form an inconsistent set is necessarily valid.

Recall the definition of validity: An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false.

An argument having premises that form an inconsistent set satisfies this requirement. It is not possible for the premises, an inconsistent set, to be true. Therefore, it is not possible for the premises to be true and the conclusion false -- again, because the premises cannot be true.

The argument is truth preserving because it will never take us from truths to a falsehood. It will not do so because the premises cannot be true, and hence there is no possibility of going from truths to a falsehood. Arguments with premises that form an inconsistent set, while valid, are of course never sound.

Arguments of this sort are sometimes dismissed as not being arguments at all, precisely because their validity does not depend on the relation between the premises and conclusion. There are, however, systematic reasons for allowing these cases to constitute arguments and thus for recognizing them as valid deductive arguments. It is important to remember that such arguments are valid because they meet the requirement of truth preservation -- they will never take us from truths to a falsehood -- not because the premises support the conclusion in any intuitive way.

Similar special cases of validity involve arguments which have a logically true conclusion, or a logically false premise.

Answer 5

Any two inconsistent premises imply any conclusion. Here's a proof:

1) p or not p - Tautology

2) (not q) implies (p or not p) - 1

3) not (p or not p) implies q - contrapositive of 2

4) (not p and p) implies q - tautologically equivalent to 3

So if p is "today is thursday", and q is "Trompetilla...", then you've got this argument form.

Answer 6

In Logic, a premise is a possible scenario.

So when you have a premise (P)

and also another premise at the same time that is the opposite (not P),

then you are encompassing all possible scenarios.

That means that you can say whatever you want as the conclusion, and it would be a valid logic argument.

Answer 7

My guess: If today is Thursday and Not Thursday, then we assume contradictory statements are true.  So, Trompetilla the Clown is both President and Not President of your college.

Something like that.  I haven't taken any actual philosophy classes, but does that make sense?

Answer 8

Addendum:

Summary: Some people think that considering that in formal logic, from a contradiction you can obtain VALIDLY anything, then, if you have a contradiction in natural language scenarios you can also infer anything. This is called trivialization ( A & ¬A |- B o 'F→ ┴ → G' for any G). Well, what I say is that we have good reasons to think that trivialization is not a feature of the intuitive notion of logical validity. This is why this example seems so strange to you as a valid argument. (it probably is intuitively irrelevant, that from the premises you can actually infer validly that conclusion). Further details below...

--

Well, although bluckleylerose is precisely right, there is a problem with the example of your professor that could make logic look too naïve.

It is argued that, given the fact that in formal classical first order logic bivalence applies, i.e. the principle according to which every sentence is either true or not-true (normally understood as the same of falsehood), in situations concerning natural language we have a lot of phenomena that range out of this principle. When you have a contradiction in a theory, if that theory respects bivalence, then your theory gets trivialized, which means that anything follows.

In natural language (such as English) normal usage, a lot of people believe that it is not only that bivalence does not apply, but even more that we actually have contradictory true sentences not quite as a day being two days, but similar sentences. Let me go straight to the some plausible examples:

Vagueness: You can be in between a moment in which you are in Thursday and in a day after or before. Imagine that you are at 11:59:59..... PM of any Thursday, at which exact moment do we shift from Thursday to Friday? It seems that we be, at least theoretically, in the moment in between the pass from one day to another. It doesn't matter if the moment is just too short, there is a leap still in which you are not in one day or another, but in the middle.

Dialetheism: There are some people who think that from a contradiction not everything follows. So, imagine that you have a sentence like this:

i) Sentence i is false.

From that contradiction we do not trivialize anything.

There are other circumstances in the daily normal life in which you may have contradictory beliefs, but not trivialization. I cannot record another one right now.

--Further:

Yaoi Shonen-ai ignores an important point. The technical notion of logical validity makes contradictions justifiers of all beliefs, and we intuit that it is not the case in a pretheorical notion of logical validity. His professor is not stupid nor his example or position, he probably is pointing to an important matter which is tremendously complicated. At least he is transmitting the orthodoxy as everybody else does.

Syllogisms are just a tiny part of logic, i.e., of valid argumentation. This example, in fact is not a syllogism. So your comment on syllogisms as long as I can see is not relevant. Of course validity is not soundness, except in complete and correct formalisms.

-- Further:

Aß іηito got it completely wrong, but El Numero had an orthodoxical intuition about this, the same intuition that your professor seems to have had. The problem is that the technical (formal, traditional, orthodoxical...) notion of validity supports that from a contradiction anything follows. In formal languages of first order classical logic without a way to represent arithmetic, trivialization is for sure the case. But it doesn't seem to be the case for some natural language arguments or situations, such as those I gave you above or the one put forward by your professor. In cases of vagueness (in which you might be, for instance, in two countries at a time, at the middle of two colour shades, in two epochs at a time, in two states at a time, and so on), or in some other plausible cases of contradictory mental states, those contradictions don't seem to support the following of ANY CONCLUSION. (I can recall an example. I have in mind Gödel's incompleteness theorems. In this case we better think that arithmetic is incomplete, than to think that '4 = 5' is true or some other absurdity)

-- Further:

robespierre: Another great way to formulate this question! But what do you think about the traditional notion of classical validity? Don't you think that there is a problem with the ex falso quodlibet part of the traditional notion of validity?