Premises Conclusion Follows? Answer
All men are mortal.
Socrates is mortal. Socrates is a man. True or False?
Either you are in New York or you are in Philadelphia. You are not in New York. You are in Philadelphia. True or False?
Some dogs are friendly. All dogs are animals. Some animals are friendly. True or False?
If you won the lottery, you are a millionaire. You are a millionaire. You won the lottery. True or False?
No ducks are mammals. No birds are mammals. Some ducks are not birds. True or False?
All humans are mammals. Humans do not have four legs. Some mammals do not have four legs. True or False?
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 or False?
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. True or False?
Whenever you are in Trenton, you are in New Jersey. You are in New Jersey. You are in Trenton. True or 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 or False? Solitary
For those that were interested in finding out, here are the answers:
Premises Conclusion Follows? Answer
All men are mortal.
Socrates is mortal. Socrates is a man. True
False (False.) Socrates could be a cat.
Either you are in New York or you are in Philadelphia.
You are not in New York. You are in Philadelphia. True
False (True.)
Some dogs are friendly.
All dogs are animals. Some animals are friendly. True
False (True.)
If you won the lottery, you are a millionaire.
You are a millionaire. You won the lottery. True
False (False.) You could be a millionaire without winning the lottery.
No ducks are mammals.
No birds are mammals. Some ducks are not birds. True
False (False.) A duck can be a cotton fabric.
All humans are mammals.
Humans do not have four legs. Some mammals do not have four legs. True
False (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
False (False.) A patient can get better without drug Y.
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. True
False (True.)
Whenever you are in Trenton, you are in New Jersey.
You are in New Jersey. You are in Trenton. True
False (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
False (true.) Browntown is 50 kilometers from Jonesborough, but Smithville is 100 kilometers from Jonesborough, even if it is 50K from Browntown.
Premises Conclusion Follows? Answer
All men are mortal. Yes
Socrates is mortal. Socrates is a man. True or False? True
Either you are in New York or you are in Philadelphia. You are not in New York. You are in Philadelphia. True or False? True
Some dogs are friendly. All dogs are animals. Some animals are friendly. True or False? True
If you won the lottery, you are a millionaire. You are a millionaire. You won the lottery. True or False? False
No ducks are mammals. No birds are mammals. Some ducks are not birds. True or False? False
All humans are mammals. Humans do not have four legs. Some mammals do not have four legs. True or False? 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 or False? True
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. True or False? True
Whenever you are in Trenton, you are in New Jersey. You are in New Jersey. You are in Trenton. True or False? 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 or False? True
> 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 or False?
Indeterminate, because of the vagueness of the statement. Does it mean, "Browntown is closer to Jonesborough than Smithville [is]," or "Browntown is closer to Jonesborough than [it is to] Smithville"?
Frank
Quote from: "mykcob4"Premises Conclusion Follows? Answer
All men are mortal. Yes
Socrates is mortal. Socrates is a man. True or False? True False. Socrates could be a cat.
Either you are in New York or you are in Philadelphia. You are not in New York. You are in Philadelphia. True or False? True
Some dogs are friendly. All dogs are animals. Some animals are friendly. True or False? True
If you won the lottery, you are a millionaire. You are a millionaire. You won the lottery. True or False? False
No ducks are mammals. No birds are mammals. Some ducks are not birds. True or False? False True. a duck can be a form of cotton clothe.
All humans are mammals. Humans do not have four legs. Some mammals do not have four legs. True or False? 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 or False? True False. The patients could have gotten better without Drug Y and something else.
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. True or False? True
Whenever you are in Trenton, you are in New Jersey. You are in New Jersey. You are in Trenton. True or False? 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 or False? True
Quote from: "FrankDK"> 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 or False?
Indeterminate, because of the vagueness of the statement. Does it mean, "Browntown is closer to Jonesborough than Smithville [is]," or "Browntown is closer to Jonesborough than [it is to] Smithville"?
Frank
Browntown is 50 kilometers from Jonesborough, but Smithville is 100 kilometers from Jonesborough, even if it is 50K from Browntown. :-o Solitary
Quote from: "Solitary"Quote from: "FrankDK"> 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 or False?
Indeterminate, because of the vagueness of the statement. Does it mean, "Browntown is closer to Jonesborough than Smithville [is]," or "Browntown is closer to Jonesborough than [it is to] Smithville"?
Frank
Jonesborough is 50 kilometers from Smithville, and Browntown is 100 kilometers from Smithville. Smithville---is 50 K from Jonesborough---and Jonesborough is 50L from Browntown---and so Browntown is closer to Jonesborough than Smithville. :-o Solitary
You're missing the point. I understand the geography. The question is ambiguous. Does it mean, "Browntown is closer to Jonesborough than Smithville [is],"or "Browntown is closer to Jonesborough than [it is to] Smithville"? The former would be false, because Browntown and Smithville are both 50K from Jonesborough. The latter would be true for the reason you gave. By leaving out the part in square brackets, you leave the statement open to interpretation.
Frank
I'm having a hard time making sense of this one. Its probably the wording becuase it's horrendous...or is that the point?
the two statements don't seem to matter to each other either. The question is can some ducks not be birds? You say False (thereby all ducks are birds) but then say a duck can be a cotton fabric.
No ducks are mammals. (meaning anytime you have a mammal you know it's never a duck)
No birds are mammals (a bird can never be a mammal, so based on this, ducks can never be a mammal and neither can a bird, not knowing if ducks can be birds).
Therefore:
Some ducks are not birds. TrueFalse (False.)
(we don't know if ducks can be birds or not. Not enough to go on so for me the answer is True, some ducks, not all, could be birds or not birds...but some could be.)
If it was false then either all ducks had to be birds or not birds. A duck can be a cotton fabric but not all ducks are cotton fabrics, some could be and some could still be birds.
"Duck" in this case is ambiguous. The word can refer to a bird of the family Anatidae, a cloth, a type of vehicle ...
It's not a logic test, it's a are you fucking paying attention test..
Quote from: "FrankDK"Quote from: "Solitary"Quote from: "FrankDK"> 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 or False?
Indeterminate, because of the vagueness of the statement. Does it mean, "Browntown is closer to Jonesborough than Smithville [is]," or "Browntown is closer to Jonesborough than [it is to] Smithville"?
Frank
Jonesborough is 50 kilometers from Smithville, and Browntown is 100 kilometers from Smithville. Smithville---is 50 K from Jonesborough---and Jonesborough is 50L from Browntown---and so Browntown is closer to Jonesborough than Smithville. :-o Solitary
You're missing the point. I understand the geography. The question is ambiguous. Does it mean, "Browntown is closer to Jonesborough than Smithville [is],"or "Browntown is closer to Jonesborough than [it is to] Smithville"? The former would be false, because Browntown and Smithville are both 50K from Jonesborough. The latter would be true for the reason you gave. By leaving out the part in square brackets, you leave the statement open to interpretation.
Frank
If you understand the geography you know they all can't be 50K from each other when the are all in line with each other. One has be on the bottom and farther away from the one on top.
I didn't write the test, but it is obvious to me that it is asking if Browntown is closer to Jonesbourogh than Smithville is even if it doesn't say is if they are both are 50K from each other, or it wouldn't even be asking the question which would be obvious when they are the same distance apart that is a given.
"The former would be false, because Browntown and Smithville are both 50K from Jonesborough." Where does it say that? Am I missing something? It says Browntown is 50K from both, so how can they all be 50K from each other when one is on the bottom and one is on the top? :-k
Would you like me to provide the second test? Those are not my answers to the test. Solitary
Quote from: "FrankDK"Quote from: "Solitary"Quote from: "FrankDK"> 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 or False?
Indeterminate, because of the vagueness of the statement. Does it mean, "Browntown is closer to Jonesborough than Smithville [is]," or "Browntown is closer to Jonesborough than [it is to] Smithville"?
Frank
Jonesborough is 50 kilometers from Smithville, and Browntown is 100 kilometers from Smithville. Smithville---is 50 K from Jonesborough---and Jonesborough is 50L from Browntown---and so Browntown is closer to Jonesborough than Smithville. :-o Solitary
You're missing the point. I understand the geography. The question is ambiguous. Does it mean, "Browntown is closer to Jonesborough than Smithville [is],"or "Browntown is closer to Jonesborough than [it is to] Smithville"? The former would be false, because Browntown and Smithville are both 50K from Jonesborough. The latter would be true for the reason you gave. By leaving out the part in square brackets, you leave the statement open to interpretation.
Frank
:oops: My bad! My explanation was wrong, but the answer was correct, it should have been Browntown is 50 kilometers from Jonesborough, but Smithville is 100 kilometers from Jonesborough, even if it is 50K from Browntown. :Hangman: Solitary
> If you understand the geography you know they all can't be 50K from each other when the are all in line with each other. One has be on the bottom and farther away from the one on top.
> I didn't write the test, but it is obvious to me that it is asking if Browntown is closer to Jonesbourogh than Smithville is even if it doesn't say is if they are both are 50K from each other, or it wouldn't even be asking the question which would be obvious when they are the same distance apart that is a given.
>> "The former would be false, because Browntown and Smithville are both 50K from Jonesborough." Where does it say that? Am I missing something? It says Browntown is 50K from both, so how can they all be 50K from each other when one is on the bottom and one is on the top? :-k
> Would you like me to provide the second test? Those are not my answers to the test. Solitary
This shouldn't be this difficult.
I didn't claim that they are all 50 K from each other. The problem states this:
Smithville
50 K
Jonesborough
50 K
Browntown
So Smithville is not closer to Jonesborough than Browntown is. Both Smithville and Browntown are 50 K from Jonesborough. The distance between Smithville and Browntown is irrelevant. The writer of the test made an assumption, and you happened to make the same assumption.
If it's a logic test, then it should test logic. If a question is ambiguous, then your answer requires an assumption, which isn't logical. If you allow assumptions to be made, none of the other examples can be true or false. The truth or falsehood depends on what assumptions you make and accept.
Here's another similar question:
If a red house is made of red bricks, and a brown house is made of brown bricks, what is a green house made of?
The accepted answer, glass, isn't logical. It's true, but not logical. The "if-then" logic offered in the stem of the question should have you answer "green bricks" if you are being logical. To get the "school solution," you have to make an assumption.
Frank
Quote from: "FrankDK"> If you understand the geography you know they all can't be 50K from each other when the are all in line with each other. One has be on the bottom and farther away from the one on top.
> I didn't write the test, but it is obvious to me that it is asking if Browntown is closer to Jonesbourogh than Smithville is even if it doesn't say is if they are both are 50K from each other, or it wouldn't even be asking the question which would be obvious when they are the same distance apart that is a given.
>> "The former would be false, because Browntown and Smithville are both 50K from Jonesborough." Where does it say that? Am I missing something? It says Browntown is 50K from both, so how can they all be 50K from each other when one is on the bottom and one is on the top? :-k
> Would you like me to provide the second test? Those are not my answers to the test. Solitary
This shouldn't be this difficult.
I didn't claim that they are all 50 K from each other. The problem states this:
Smithville
50 K
Jonesborough
50 K
Browntown It doesn't say that. It says Browntown is 50K from Jonesborough, and 50K from Smithville, not Smithville 50K from Jonesborough. Isn't logic fun? :lol:
So Smithville is not closer to Jonesborough than Browntown is. Both Smithville and Browntown are 50 K from Jonesborough. The distance between Smithville and Browntown is irrelevant. The writer of the test made an assumption, and you happened to make the same assumption.
If it's a logic test, then it should test logic. If a question is ambiguous, The question is not ambiguous at all, you are the one putting assumptions into it. Honest. then your answer requires an assumption, which isn't logical. If you allow assumptions to be made, none of the other examples can be true or false. The truth or falsehood depends on what assumptions you make and accept.
Here's another similar question:
If a red house is made of red bricks, and a brown house is made of brown bricks, what is a green house made of?
The accepted answer, glass, isn't logical. It's true, but not logical. The "if-then" logic offered in the stem of the question should have you answer "green bricks" if you are being logical. To get the "school solution," you have to make an assumption.
Frank
:oops: My explanation was wrong even if the answer was correct. It should be:Browntown is 50 kilometers from Jonesborough, but Smithville is 100 kilometers from Jonesborough, even if it is 50K from Browntown. Sorry about that! My bad. But the answer is still correct even if I explained it wrong. It is a difficult question and why I got confused explaining it, but it is all logical. Solitary
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 [//http://en.wikipedia.org/wiki/Fallacy_of_the_undistributed_middle]. 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.
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 [//http://en.wikipedia.org/wiki/Fallacy_of_the_undistributed_middle]. 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
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.
http://philosophy.lander.edu/logic/tvs.html (http://philosophy.lander.edu/logic/tvs.html)
QuoteI. 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.
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.
Here's another site that goes into what I was trying to get at in my earlier posts:
//http://cas.umkc.edu/philosophy/vade-mecum/2-1.htm
QuoteThe 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.
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
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".
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.