Author Topic: Are you logical? Take The Test And See  (Read 4340 times)

Offline Solitary

Re: Are you logical? Take The Test And See
« Reply #15 on: August 18, 2013, 09:54:55 AM »
Quote from: "entropy"
It seems a little odd to ask whether the syllogisms are true or false rather than valid or invalid. The conclusion could be true even if the major and/or minor premise is false and the syllogism is fallacious in form.

For example, the first syllogism:

All men are mortal.

Socrates is mortal.

[Therefore] Socrates is a man.


The form of this argument is fallacious. It is an example of the fallacy of the undistributed middle [You are not allowed to view links. Register or Login]. Even if the major and minor premises are true, the conclusion does not follow from the premises. Whether or not the conclusion as statement of a claim on its own is true is independent of the prior premises.

That's why I think it would be better to ask if the syllogisms are valid or invalid in form rather than true or false - since "true or false" can refer to the status of each of the premises and the conclusion and the truth or falsity of each is independent of whether or not the form of the syllogism is valid. Or you could ask if the syllogism is sound or not. A sound syllogism is one where the premises are true and the syllogism has a valid form.

You are assuming Socrates the man of history is the premise instead of just being a name. Is it logical to do that? Solitary
There is nothing more frightful than ignorance in action.

Offline entropy

Re: Are you logical? Take The Test And See
« Reply #16 on: August 18, 2013, 12:23:40 PM »
Quote from: "Solitary"

You are assuming Socrates the man of history is the premise instead of just being a name. Is it logical to do that? Solitary

I guess I didn't explain myself very well. You appear to be claiming that the syllogism is false because either the conclusion doesn't follow from the premises or that the conclusion is false (it isn't clear to me which position you are taking). But syllogisms as a form of argumentation cannot be true or false. Truth or falsity is a metaphysical state of a claim or statement. A premise or conclusion is a claim or statement that can be true or false. A syllogism as an argument can be valid or invalid and it can be sound or not sound, but an argument cannot be true or false, only the argument's premises and/or conclusions can be true or false.

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I. Truth, Validity, and Soundness: probably the three most important concepts of the course.

   A. First, let us briefly characterize these concepts.
      1. truth: a property of statements, i.e., that they are the case.
      2. validity: a property of arguments, i.e., that they have a good structure.

         (The premisses and conclusion are so related that it is absolutely impossible for the
                         premisses to be true unless the conclusion is true also.)
      3. soundness: a property of both arguments and the statements in them, i.e., the argument is
                    valid and all the statement are true.
         Sound Argument: (1) valid, (2) true premisses (obviously the conclusion is true as well by the
                        definition of validity).

   B. The fact that a deductive argument is valid cannot, in itself, assure us that any of the statements in
            the argument are true; this fact only tells us that the conclusion must be true if the premisses are
            true.

Offline surly74

Re: Are you logical? Take The Test And See
« Reply #17 on: August 20, 2013, 09:16:40 AM »
Quote from: "Solitary"
You are assuming Socrates the man of history is the premise instead of just being a name. Is it logical to do that? Solitary

then it's another useless trap question. If you can use Socrates as just another name you have to initialize that it's a man's name or a woman's name. If you didn't want to be clever and a trap you would have used John or Jane as the name instead of someone known.
God bless those Pagans
--
Homer Simpson

Offline entropy

Re: Are you logical? Take The Test And See
« Reply #18 on: August 20, 2013, 11:08:17 AM »
Here's another site that goes into what I was trying to get at in my earlier posts:

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Quote
The standard of deductive correctness in an argument is validity. An argument is valid if and only if it is impossible for the premises to be true and the conclusion false. An argument is sound if it is valid and its premises are true. It is important to remember to what the terminology applies: propositions are true or false; sets of propositions are consistent or inconsistent; (deductive) arguments are valid or invalid, sound or unsound. There is no such thing as a valid proposition, or a true argument.

Re: Are you logical? Take The Test And See
« Reply #19 on: August 20, 2013, 02:27:25 PM »
Quote from: "Solitary"
Premises    Conclusion    Follows?    Answer    
 
All men are mortal.

Socrates is mortal.   Socrates is a man.     False
        
Either you are in New York or you are in Philadelphia.  You are not in New York. You are in Philadelphia. True
         
Some dogs are friendly. All dogs are animals.   Some animals are friendly.    True
         
If you won the lottery, you are a millionaire. You are a millionaire.    You won the lottery.     False   

     
No ducks are mammals. No birds are mammals.    Some ducks are not birds.    False.  The third statement has nothing to do with the first two.
         
All humans are mammals. Humans do not have four legs.    Some mammals do not have four legs.    True   
     
Whenever Drug Y is administered, the patient gets better. Whenever Drug Y is not administered, the patient does not get better. Drug Y causes the patient to get better. True, assuming Drug Y is the only variable
         
If you hit the brakes hard, your car will be rear-ended by the car behind you. If you do not hit the brakes hard, you will hit a child in front of you. Either you will hit the child or you will be hit by the car behind you.   False, if you get hit by the car behind you it could send you into the child so you could both hit the child and be rear-ended.  Barring this, the answer would be "true".
         
Whenever you are in Trenton, you are in New Jersey. You are in New Jersey. You are in Trenton.     False
         
Smithville is around 50 kilometres due north of Jonesborough. Jonesborough is around 50 kilometres due north of Browntown. Browntown is closer to Jonesborough than Smithville.    True
"Death can not be killed." -brq

Offline entropy

Re: Are you logical? Take The Test And See
« Reply #20 on: August 20, 2013, 10:13:56 PM »
Solitary - okay, on rereading what you were saying, it is clearer to me now that when you responded with "true" you meant that the conclusion follows from the premises. I still think that it would be better to present the situation as asking if the arguments are valid or invalid rather than putting "true or false" at the end of each statement - that is, it would be better to put "valid argument or invalid argument" at the end of each argument because validity is a term in logic that means that the conclusion of an argument does follow from the premises of the argument.

I also think it would be beneficial to put at least one argument in that has a conclusion that in actuality could be true or false even though the argument is valid (the conclusion does follow from the premises); e.g.:

No dogs have tails.
Fido is a dog.
Therefore, Fido has no tail.

In this case using the "true or false" format you suggested, you would say it was true because the conclusion does follow from the premises. But saying "true" in this case would be confusing to many people because the major premise is false. That's one of the reasons it would be less confusing to use "valid argument or invalid argument" rather than "true or false".

Offline entropy

Re: Are you logical? Take The Test And See
« Reply #21 on: August 20, 2013, 10:28:28 PM »
Quote from: "The Whit"
     
Whenever Drug Y is administered, the patient gets better. Whenever Drug Y is not administered, the patient does not get better. Drug Y causes the patient to get better. True, assuming Drug Y is the only variable

I think this shows the problem with the "true or false" format chosen rather than using the terms "valid or invalid". If the conclusion follows from the premises, the argument is valid, if the conclusion does not follow from the premises, the argument is invalid. In the argument above, the conclusion does not follow from the premises. What you said is correct, if Drug Y is the only variable then the conclusion would have to follow. But the claim that Drug Y is the only variable would then have to be added as another premise to the argument. Given the premises provided in the original argument, the argument is not valid - the conclusion does not follow from the premises provided in the original argument.

 

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