Practice with Validity and Invalidity, Etc.

1.  Valid arguments (A) must have all true premises; (B) must have a false conclusion; (C) may have a false conclusion; (D) need not be unsound; (E) both (C) and (D).

No, valid arguments do not need to have all true premises.  Example: 

 P1:  Katy Perry is a porcupine.

P2:  All porcupines live in Yucaipa.

___________________________

C:   Katy Perry lives in Yucaipa.

This is a valid argument (and if you don't see that it is, you have not sufficiently studied this), but it certainly does not have all true premises, does it?  (Hence, (A) cannot be the right answer:  this argument is valid and has all false premises, as a matter of fact).

(B) cannot be true, since this is a valid argument:

P1:  You are a human being.

P2:  All human beings die.

________________________

C:  You are going to die.

(C) is acceptable, on the basis of the Katy Perry argument above (i.e., its conclusion is false, and (C) states only that the conclusion may be false - as in this case it is). 

(D) "need not be unsound" is logically equivalent to "may be sound," and indeed a valid argument may be sound (many are), therefore (D) is acceptable.  Just in case you're in doubt about a valid argument being sound (because you're a thoroughgoing skeptic, say), here's one that is true by definition:

P1:  Only valid arguments may be sound.

P2:  No inductive arguments are valid.

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C:  No inductive arguments are sound.

So (E) is the best response, since both (C) and (D) were demonstrated to be correct.  The best response is always the one that contains the most correct information with no incorrect information.

So, C is the correct answer.


2.  No valid arguments are (A) sound; (B) unsound; (C) ones that contain at least three premises; (D) true; (E) ones in which the conclusion is implied by the premises.

When considering response (A), think about the following argument:

P1:  Professor Fike is a man.

P2:  All men die.

________________________

C:  Professor Fike will die.

Here, the argument is valid.  It is also sound, since all (all) of the premises are, as a matter of fact, true.  So (A) can't be the right answer.  If you don't understand this, you need to re-study the definitions of terms, here.

Is (B) correct?  No. See the Katy Perry argument above.  It is a valid argument, but it is unsound, because at least one of the premises is false.

(C) is false, too.  Here is an example to illustrate why (C) is false:

P1:  Professor Fike is a man.

P2:  Professor Fike came to class in Room LADM 304 on Wednesday, 2/8/2012.

P3:  All men die.

________________________

C:  Professor Fike will die.

This is an argument that contains at least three premises all of which are true, and yet it is a valid argument.  If we assume that all the premises are true (and they are, as it turns out), then the conclusion must be true as well.   

But what about (D)?  If you think (D) isn't correct, you should study this further.  In short, no argument is ever true or false, just as no claim (premise, conclusion, or otherwise) is either valid or invalid.  (It's a category error, like asking what color the number three is.)  So, (D) is true.

But what about (E)?  Since the conclusions of valid arguments are always implied by the premises, and since the item begins with the statement that you're looking for a condition which is not characteristic of valid arguments, (E), too, is unacceptable. 

So, the correct answer is (D).


Sound arguments (A) have all true premises; (B) have all true premises and are for that reason valid; (C) have all true premises and are valid; (D) are valid but may have false premises; (E) have at least one true premise.

Yes, sound arguments do have all true premises.  (So (A) is okay.  But remember:  we're always looking for the best answer.)  This is a matter of the definition of soundness, which you can find here (or, I presume, in the glossary of your textbook, which begins on page 501).

To see that (B) is false, consider this argument:

P1:  2 + 2 = 4.

P2:  3 + 7 = 10.

____________________

C:  Some bears are white.

This is an argument in which all of the premises, and the conclusion as well, are true.  But it is not a valid argument.  There's nothing about the truth of P1 and P2 that necessitates that some bears are white (and the way we're headed, one day relatively soon, it's also possible that no bears will be).  So it's not for "the reason that" an argument has all true premises, that it is sound.  This argument has all true premises, and yet it is not sound.  Even if I changed the conclusion to:

All human beings are mortal,

it would not be sound.  Why?  If you don't know, you should study this.

(C) states (A) again, but adds the condition that sound arguments are valid arguments as well.  This is a better response than (A), because it contains more information, all of which is true.  So, at this point, (C) is the best answer.  If this is not clear, you should study this.

Similarly to (C) above, (D) is false.  By definition, a sound argument cannot include even one false premise.

(E) is, as a matter of fact, true:

P1:  Every argument has at least one premise.

P2:  If an argument is sound, then all of its premises are true.

_________________________________________________

C:  Every sound argument has at least one one true premise.

I have just practiced what I preach (so to speak).  

Since, therefore, (A) and (E) are both correct responses, which one do you choose?  (A) is stronger than (E), because we know that, by definition, an argument has at least one premise, but we also know that, by definition, an argument can have any number of premises as long as it's more than 0, so (A) is a stronger response than (E), since it tells us more about the nature of soundness itself.


Enthymemes (A) are valid as they stand, but with an additional premise become sound; (B) are sound arguments with true conclusions; (C) are invalid as they stand, but with an additional premise would be invalid; (D) are invalid as they stand, but with an additional premise would be valid; (E) are insects that live in Yucaipa and Redlands.

Enthymemes are arguments that would be valid, if only a premise were added.  Here's an example of an enthymeme:

P1:  Murder is wrong.

______________________

P2:  You should not murder.

Here is a valid argument, after the "missing premise" is added (and we don't like missing premises in logic):

P1:  Murder is wrong.

P2:  If something (anything) is wrong, you should not do it.

_______________________________________________

You should not murder.

So (A) is incorrect.

Enthymemes have nothing to do with soundness (none of them are sound), so (B) is ruled out.  

(C) is ruled out, since the whole point of identifying an enthymeme is to demonstrate a missing premise, which, if added, would render the argument valid. (See the Murder argument above.)

(E) is just silly.

(D) is the correct answer, by definition.


The conclusion of every sound inductive argument is true. (A) True. (B) Not true.  (B), because no inductive argument is sound.  Here.


Every argument contains no more than one conclusion. (A) True. (B) Not true.  True, by definition.


Some valid arguments have false premises and a true conclusion. (A) True. (B) Not true.  (A) is the correct response.  Example:

P1: Professor Fike is a shaggy dog.

P2: All shaggy dogs teach logic.

___________________________

C:  Professor Fike teaches logic.


All deductively sound arguments are also deductively valid. (A) True. (B) Not true. (A), by definition.


If an argument is deductively valid, then it may be sound. (A) True. (B) Not true. (A), by definition.


 

Assume each of the following is a deductive argument. In each case, is the argument valid or invalid?


All football coaches are poets. Some poets know how to play football. So, some football coaches know how to play football.

This argument is invalid since it's possible that all football coaches are poets, and some poets know how to play football, but also that no football coaches know how to play football.  The final sentence is the conclusion, and while we all know that as a matter of fact most if not all football coaches know how to play football, nothing stated in premises 1 and 2 necessitate that any football coach knows how to play football:

P1: All football coaches are poets.

P2: Some poets know how to play football.

_________________________________________

C:  Some football coaches know how to play football.

Suppose that Vince and John are the only football coaches, and they're both poets (this meets the stated conditions of P1).  Then suppose that Larry Fike's a poet who knows how to play football (this meets the conditions of P2).  This tells me, nor you, nothing about Vince's and John's ability to play football.  So I cannot infer C, necessarily, even if I assume that P1 and P2 are true.


Blaine is shorter than Rupal, and Rupal is shorter than Kareem. So, Blaine is shorter than Kareem.

 

K

R

B

 

Valid.


Some cows are mammals. Some mammals are brown. Therefore, some cows are brown.  

Jimmy is a cow, and a mammal.  Some mammals are brown, like, say, hypothetically, Smokey the Bear.  I cannot conclude from this that there's a brown cow.  Invalid.  

Any brand of pork produces a green color when put into the flame of a barbecue pit. This item produces a green color when put into the flame of a barbecue pit. So, this item may or may not be a brand of pork.  Valid.  For all we know, the unidentified item is a leg of lamb. But since the writer said, "may or may not be a brand of pork," the conclusion follows trivially from the premises.


Some sentences that end with question marks are not genuine questions. (A) True. (B) False.  You think?  (A)


Some sentences that end with exclamation marks are exclamatories. (A) True. (B) False.  Duh!  (A)


Some valid arguments are sound. (A) True. (B) False.  

P1:  Professor Fike is a man.

P2:  All men die.

________________________

C:  Professor Fike will die.

(A) True (however sad).


“Since” is sometimes, but not always, a conclusion indicator. (A) True. (B) False.

"Since 1961 I've been in this world."  "Since a bird is a mammal, and all mammals are related, and I am a mammal, I am related to a bird."

Nope.  (B) False.  "Since" can be used as a temporal indicator, or it can be used as a premise indicator.


  1. “Accordingly” is sometimes a conclusion indicator. (A) True. (B) False.  
  2. “Therefore” is often a conclusion indicator. (A) True. (B) False.
  3. What determines whether a claim is true or false is our being able to prove it. (A) True. (B) False.

I can't prove that Polaris (the North Star) is precisely 20.739291198 million light years above my head as I sit here in Joshua Tree, California contemplating it, and nor can I disprove it.  But it either is, or it is not.