Disjunctive syllogism

Hey everyone,

When formulating a disjunction, do both values have to be valid for the disjunction to have any meaning?

So if I said: It must be either X or Y and cannot be anything else.

Is the above a valid form for a disjunction? If yes, does it still work if either X or Y are not true values?

So for example: The chair is either red or bhgytyiu but it cannot be both.

So in the above, X=red and Y=bhgytyiu

Given that Y is gibberish, what does that mean in terms of the validity of the disjunction?

Thanks

I am not sure what you are asking, but a disjunction is a compound proposition, and a compound proposition must consists only of atomic propositions, And all propositions are either true or false. So no disjunct of a disjunct can be gibberish, since if it is, the whole disjunction will have no truth-value.

kennethamy wrote:

I am not sure what you are asking, but a disjunction is a compound proposition, and a compound proposition must consists only of atomic propositions, And all propositions are either true or false. So no disjunct of a disjunct can be gibberish, since if it is, the whole disjunction will have no truth-value.

Okay thanks for your response.

What if one of the propositions is not even possible?

The triangle either has one right angle or two right angles, it cannot be both.

So here X= one right angle and Y= two right angles.

So although neither is gibberish, Y is obviously impossible. Is this a valid disjunction?

I'm sort of confused about the use of some disjunctions I've seen because they come across as begging the question.

A disjunctive syllogism takes the form of:
P v Q
~P
Therefore, Q

Note this simple argument (from Copi,1964) as an illustration:

The blind man has a red hat or the blind man has a white hat. The blind man does not have a red hat; therefore, the blind man has a white hat.

The argument,

1. X is either a 4-sided triangle, or X is a 5-sided square.
2. X is not a 4-sided triangle.
Therefore, 3. X is a 5-sided square.

Is a valid argument. Disjunctive syllogism.

It is (of course) not a sound argument since it has a false premise.

Your "problem" is nothing to do with logic per se which is about validity of an argument, it is about the distinction between "falsity" and "nonsense" of premises. For the purposes of logical analysis these two must be equated as "truth value =0" (aka "false"). Discussion of " truth versus rationality" which is the basis of the assignment of "values" to premises, is a different philosophical ball game. Note the old adage about computers (logic machines) "Rubbish in, gives rubbish out".

fresco wrote:

Your "problem" is nothing to do with logic per se which is about validity of an argument, it is about the distinction between "falsity" and "nonsense" of premises. For the purposes of logical analysis these two must be equated as "truth value =0" (aka "false"). Discussion of " truth versus rationality" which is the basis of the assignment of "values" to premises, is a different philosophical ball game. Note the old adage about computers (logic machines) "Rubbish in, gives rubbish out".

So even nonsense premises can be inserted into a DS as it will always be seen as "truth value = 0"?

The focus of attention should be on whether the value of the premises are "valid" to determine whether the DS is of any use.

Thanks Ken and Fresco, much obliged.

fresco wrote:

Your "problem" is nothing to do with logic per se which is about validity of an argument, it is about the distinction between "falsity" and "nonsense" of premises. For the purposes of logical analysis these two must be equated as "truth value =0" (aka "false"). Discussion of " truth versus rationality" which is the basis of the assignment of "values" to premises, is a different philosophical ball game. Note the old adage about computers (logic machines) "Rubbish in, gives rubbish out".

So even nonsense premises can be inserted into a DS as it will always be seen as "truth value = 0"?

josh0335: The focus of attention should be on whether the value of the premises are "valid" to determine whether the DS is of any use.

Owen phil: [(2+2=4) or (*9*65n6h%%$)], has no truth value at all...it is not a well formed formula.

1. X is either a 4-sided triangle, or X is a 5-sided square. 2. X is not a 4-sided triangle. Therefore, 3. X is a 5-sided square.

Is a valid argument. Disjunctive syllogism.

Forgive me to ask this ignorent question, but where does one use this disjunctive syllogism?

Quote:

josh0335: The focus of attention should be on whether the value of the premises are "valid" to determine whether the DS is of any use.

Then I'm sorry I missed the point of your question (in another forum). I see that the "valid" terminology is straightened out now.

I believe that, in theory logic, aka predicate, aka "first order," aka logic of math (with material implication turned off), aka "the logic that includes the terminology 'well formed formula,'" that Owen phil is correct when he says:

Quote:

Owen phil: [(2+2=4) or (*9*65n6h%%$)], has no truth value at all...it is not a well formed formula.

But I don't believe this is true in the logic of debate (propositional, "material implication" turned on). I think this is your context because you implied your purpose was mostly about "red herrings."

I think that, in the logic of debate, a meaningless premise or proposition is taken as "false," so that the disjunction still works. In the logic of debate, the proposition:

"X is red"

is really two propositions, one being implied by the material implication rule: "Red exists" and "X=Red."

So, if the first proposition is false, then the evaluation stops there, the proposition is considered false, and one never gets to the second proposition "X=Red", i.e. it is thrown away.

I don't know anything for sure, but if I am correct about that, and assuming it is true that X=red, then in the statement:

"X=Red or X=bhgytyiu" you have a True and a False, the expression evaluates to True.

"X=4 sided triangle or X=5 sided square" you have an F, F, since neither exists, so the expression evaluates to F.

But if we start from the opposite direction by asserting that (P or Q) is true, but that "X=4 sided triangle" is false, then "X=5 sided square" evaluates to true, at least in theory.

But, again, I think that in the logic of debate, the argument would still evaluate to "false" unless the beginning assertion included "5 sided squares exist."

A question for kennethamy:

Quote:

1. X is either a 4-sided triangle, or X is a 5-sided square. 2. X is not a 4-sided triangle. Therefore, 3. X is a 5-sided square.

Is a valid argument. Disjunctive syllogism.

Is calling that argument a "syllogism" proper terminology, or are you
just adopting it to be cooperative? I dont' know the answer, but I wonder which logic(s) is implied? Propositional, boolean, predicate?

1. X is either a 4-sided triangle, or X is a 5-sided square. 2. X is not a 4-sided triangle. Therefore, 3. X is a 5-sided square.

4. That is a disjunctive syllogism, and is a valid argument. It is not, however, a sound argument, since it has a false premise.