Stumped on Basic Sentential Logic!

[trickster]

Hello all. Well I have started my courses in philosophy and am in week three and stumped already. Logic is such a abstract thing to me and apparently I must be a right brain thinker! Anyways…I have the following question, if anyone can help me out on this, I’d appreciate it very much.

OK All You Logic People out there… .why is the following an invalid argument?
My textbook is "Understanding Symbolic Logic (5th Edition) Virginia Klenk

Example 1
If Tinker is a male cat, then Tinker will not have kittens. (T)
Tinker will have kittens (indeterminate)
Therefore: Tinker is a male cat (indeterminant)

My textbook calls this an invalid argument… anyone know why? Is it because we cannot assign the second statement a T or F value in sentential logic?

Example 2

NOT both Clinton and Dole were president in 1999 (F)
Dole was not president in 1999 (T)
Therefore: Clinton was president in 1999 (T)

The textbook says it’s invalid…I don’t understand how the “not” negates the argument and how to read these things, anyone out there know? The negation thing is difficult for me to understand in terms of how to read the premises of the argument.

It’s chapter one of the most basic of logic courses… After this I have to memorize a Logic Truth Table, still trying to remember the symbols for logic operators…then calculating the arguments and translating english into symbolic language…all by Friday when I get tested… 30% of our course at stake! Help can come in the form of responding to me or praying for a miracle like the world has never seen before…and who are the saints who were philosophers… I might start praying to St. Pope JP II since he was a philosopher too… and maybe Thomas Aquinas… got to pass this test

Thanks all.
Bruce

 

[Charlemagne_III]

I hate sentential logic. But I will pray for you.

Why in God’s name did you sign up for this course? Get out if you can!

God bless.

 

[abucs]

Hello all. Well I have started my courses in philosophy and am in week three and stumped already. Logic is such a abstract thing to me and apparently I must be a right brain thinker! Anyways…I have the following question, if anyone can help me out on this, I’d appreciate it very much.

OK All You Logic People out there… .why is the following an invalid argument?
My textbook is "Understanding Symbolic Logic (5th Edition) Virginia Klenk

Example 1
If Tinker is a male cat, then Tinker will not have kittens. (T)
Tinker will have kittens (indeterminate)
Therefore: Tinker is a male cat (indeterminant)

My textbook calls this an invalid argument… anyone know why? Is it because we cannot assign the second statement a T or F value in sentential logic?

Example 2

NOT both Clinton and Dole were president in 1999 (F)
Dole was not president in 1999 (T)
Therefore: Clinton was president in 1999 (T)

The textbook says it’s invalid…I don’t understand how the “not” negates the argument and how to read these things, anyone out there know? The negation thing is difficult for me to understand in terms of how to read the premises of the argument.

It’s chapter one of the most basic of logic courses… After this I have to memorize a Logic Truth Table, still trying to remember the symbols for logic operators…then calculating the arguments and translating english into symbolic language…all by Friday when I get tested… 30% of our course at stake! Help can come in the form of responding to me or praying for a miracle like the world has never seen before…and who are the saints who were philosophers… I might start praying to St. Pope JP II since he was a philosopher too… and maybe Thomas Aquinas… got to pass this test

Thanks all.
Bruce

Example 1

The conclusion that Tinker is a male cat is invalid because Tinker will have kittens (is a possibility/indeterminate) and if we knew Tinker were a male cat was TRUE Tinker would not have kittens would also be TRUE.

Example 2

The conclusion that Clinton was president in 1999 does not follow from what has been stated.

Logically it might not have been either of them that was president in 1999.

Therefore you can’t say that Clinton was president in 1999, just because it wasn’t Dole. An invalid argument.

If not **Clinton NOR Dole **were president in 1999 was FALSE then if it wasn’t Dole is TRUE , then it would be Clinton. But the first statement says **NOT BOTH Clinton and Dole **were president in 1999.

 

[ClearWater]

Hello all. Well I have started my courses in philosophy and am in week three and stumped already. Logic is such a abstract thing to me and apparently I must be a right brain thinker! Anyways…I have the following question, if anyone can help me out on this, I’d appreciate it very much.

OK All You Logic People out there… .why is the following an invalid argument?
My textbook is "Understanding Symbolic Logic (5th Edition) Virginia Klenk

Example 1
If Tinker is a male cat, then Tinker will not have kittens. (T)
Tinker will have kittens (indeterminate)
Therefore: Tinker is a male cat (indeterminant)

My textbook calls this an invalid argument… anyone know why? Is it because we cannot assign the second statement a T or F value in sentential logic?

Example 2

NOT both Clinton and Dole were president in 1999 (F)
Dole was not president in 1999 (T)
Therefore: Clinton was president in 1999 (T)

The textbook says it’s invalid…I don’t understand how the “not” negates the argument toma
nd how to read these things, anyone out there know? The negation thing is difficult for me to understand in terms of how to read the premises of the argument.

It’s chapter one of the most basic of logic courses… After this I have to memorize a Logic Truth Table, still trying to remember the symbols for logic operators…then calculating the arguments and translating english into symbolic language…all by Friday when I get tested… 30% of our course at stake! Help can come in the form of responding to me or praying for a miracle like the world has never seen before…and who are the saints who were philosophers… I might start praying to St. Pope JP II since he was a philosopher too… and maybe Thomas Aquinas… got to pass this test

Thanks all.
Bruce

Gosh! I wish I could be of help, but it’s “Greek” to me!

Good bless you in any case!

 

[Allegra]

Hello all. Well I have started my courses in philosophy and am in week three and stumped already. Logic is such a abstract thing to me and apparently I must be a right brain thinker! Anyways…I have the following question, if anyone can help me out on this, I’d appreciate it very much.

OK All You Logic People out there… .why is the following an invalid argument?
My textbook is "Understanding Symbolic Logic (5th Edition) Virginia Klenk

Example 1
If Tinker is a male cat, then Tinker will not have kittens. (T)
Tinker will have kittens (indeterminate)
Therefore: Tinker is a male cat (indeterminant)

My textbook calls this an invalid argument… anyone know why? Is it because we cannot assign the second statement a T or F value in sentential logic?

Example 2

NOT both Clinton and Dole were president in 1999 (F)
Dole was not president in 1999 (T)
Therefore: Clinton was president in 1999 (T)

The textbook says it’s invalid…I don’t understand how the “not” negates the argument and how to read these things, anyone out there know? The negation thing is difficult for me to understand in terms of how to read the premises of the argument.

It’s chapter one of the most basic of logic courses… After this I have to memorize a Logic Truth Table, still trying to remember the symbols for logic operators…then calculating the arguments and translating english into symbolic language…all by Friday when I get tested… 30% of our course at stake! Help can come in the form of responding to me or praying for a miracle like the world has never seen before…and who are the saints who were philosophers… I might start praying to St. Pope JP II since he was a philosopher too… and maybe Thomas Aquinas… got to pass this test

Thanks all.
Bruce

I never took that class, but the answer seems really obvious to me. Tinker could be a sterile female cat. Not all females have kittens. And in the second example, it’s obvious that a third party could have been president. I don’t know if that is the answer you are looking for though.

 

[St_Francis]

Well, the first one, the last statement doesn’t follow from the first two. If the first two were both true, then the last one would have to be that Tinker was a FEmale cat.

The second one could also have a problem with the “both” set-up of the sentence, altho I think the others are correct about the possibility of a third person’s being Preisdent. However, the both problem could come up in another scenario.

If I say to my two children:

You may both have a piece of pie, then they should split a piece.

In order for them to be able to have a piece of pie *each, *I should say, You may each have a piece of pie.

 

[Lion_IRC]

Example 1
If Tinker is a male cat, then Tinker will not have kittens. (T)
Tinker will have kittens (indeterminate)
Therefore: Tinker is a male cat (indeterminant)

The argument is invalid because the conclusion doesnt follow from the premises.
The opposite conclusion would be true.

(a) If Tinker is a male cat, then Tinker will not have kittens.

(b) Tinker will have kittens

Therefore: Tinker is NOT a male cat (necessary inference)

 

[Lion_IRC]

Well, the first one, the last statement doesn’t follow from the first two. If the first two were both true, then the last one would have to be that Tinker was a FEmale cat…

I would avoid confusing the issue with what other things Tinker might possibly be. Female cat. Neutered cat. Self-impregnating alien space cat…

The only thing the argument subject hinges on is whether Tinker can or cannot be a “male cat”.

 

[Zoltan_Cobalt]

You have all missed the point.

No one has recognized the the relationship between Tinker (a TOM cat) and Clinton.

It should be obvious…

 

[abucs]

The argument is invalid because the conclusion doesnt follow from the premises.
The opposite conclusion would be true.

(a) If Tinker is a male cat, then Tinker will not have kittens.

(b) Tinker will have kittens

Therefore: Tinker is NOT a male cat (necessary inference)

If I am reading it correctly, the statement (b) Tinker will have kittens is indeterminate which means it might be true or it might be false, we don’t know. We can’t say that Tinker is a male cat, only that logically Tinker could be a male cat given the statements.

‘Could’ isn’t good enough In logic to suggest a universally TRUE statement. So we can’t say Tinker was a male cat, but likewise we can’t say Tinker was not a male cat.

Because Tinker will have kittens in indeterminate, then he might be male, or she might be female.

If i’m reading it right.

 

[Lion_IRC]

The statement is indeterminate in the sense that :
…*how can you see into the future *to know that such an event (b) WILL happen.

 

[Lion_IRC]

This is the one that has me baffled. I understand the difference between an invalid argument and an unsound argument. And surely this argument is invalid because neither (a) nor (b), whether true or false, compel us to think that Clinton had to be president in 1999

But why is the first premise indicated as (F) False?

Example 2

NOT both Clinton and Dole were president in 1999 (F)
Dole was not president in 1999 (T)
Therefore: Clinton was president in 1999 (T)

The textbook says it’s invalid…I don’t understand how the “not” negates the argument and how to read these things, anyone out there know? The negation thing is difficult for me to understand in terms of how to read the premises of the argument.

Re-worded
(a) Clinton and Dole were not both president in 1999. (It’s possible that two different people can be president in the same year.)
(b) Dole was not president in 1999
(c) Therefore: There can be no other possibilty other than Clinton was president in 1999 (Obviously there could have been other people who became president apart from Clinton or Dole.)

 

[rIz0]

Understand the concepts of validity and soundness. Look for literature on conditional statements and understand what it is that we are trying to accomplish with respect to the various forms of conditional statements (more than one type of conditional relationship in terms of entailment…also research entailment). Anyway, I will try my best to help and I will only address the first argument (which is likely a material conditional):

If Tinker is a male cat, then Tinker will not have kittens.
Tinker will have kittens
Therefore: Tinker is a male cat

P1 (premise 1): Is a conditional statement. It’s important that you understand the relationship between necessary and sufficient conditions so I will not reveal too much (you are more than capable of just reasoning through this one). But what I have said alone should motivate you to research the topic. Which if you do, I am positive will help you gain clarity.

P2 (premise 2): is an assertion. And as it pertains to this arguments form just so happens to be an assertion that negates (logical vocabulary also…should research) the consequent of the conditional established in P1.

And P3 (premise 3 or more properly the conclusion as indicated by: ‘therefore’) is the affirmation of the antecedent based SOLELY on the NEGATION of the consequent in P1.

Thus, the arguments form is invalid. It denies the consequent to affirm the antecedent. Usually, when you see an argument of this form you will know that it is invalid (proceed with caution though). As tautologies and necessary truths confuse the general framework for discerning which argument forms are logical or not. But that will come later if choose to continue training in logic.

Consider this argument:
If the grass is green then, the sky is blue
the sky is NOT blue
Thus, the grass is green

This argument takes the same shape as the one you have posted. If you see how this is invalid then you will see how the argument you posted is invalid.

Also just a personal note: begin by falsifying the conclusion and then looking to see if the premise could be true while the conclusion false. If the premises can all remain true while the conclusion false then the argument will always be invalid (except in rare occasion involving necessary truths).

 

[Iron_Donkey]

OK All You Logic People out there… .why is the following an invalid argument?
My textbook is "Understanding Symbolic Logic (5th Edition) Virginia Klenk

Example 1
If Tinker is a male cat, then Tinker will not have kittens. (T)
Tinker will have kittens (indeterminate)
Therefore: Tinker is a male cat (indeterminant)

My textbook calls this an invalid argument… anyone know why? Is it because we cannot assign the second statement a T or F value in sentential logic?

The informal intuitive method: try to think of a counter example: Tinker is a spayed female cat for example. Then Tinker will not have kittens, and if Tinker were a male cat then (anything) because she’s not a male cat. This relies too much on the inner meaning of sentences to be a good answer in sentential logic, but this sort of thinking can help you figure out what direction you should be going when you move to the more formal method, at least until you get used to it.

An argument is valid if for all ways whatsoever of assigning True and False to the basic sentences (whether this way corresponds to reality or not) such that the premises are all true, the conclusion is also true.

Correspondingly, an argument is invalid if there is any way whatsoever of assigning True and False to the basic sentence letters so that the premises are all true and the conclusion is false - such a way being called a counterexample. Generally, the best way to show an argument is invalid is to find such a counterexample

The formal sentential method: Translate it into letters: Let A be Tinker is a male cat, B be Tinker will have kittens.

The argument becomes:
A=>not B
B
Therefore A

This argument is invalid if there is any way to assign truth values to A and B such that the premises are true and the conclusion false. Assign F to A, T to B.

Then:

A=>B is F =>F, which is true according to truth table definitions.
B is True
And A is False.

So all the premises are true and the conclusion is false (under this truth assignment, or valuation), and so the argument is not valid.

Example 2

NOT both Clinton and Dole were president in 1999 (F)
Dole was not president in 1999 (T)
Therefore: Clinton was president in 1999 (T)

The textbook says it’s invalid…I don’t understand how the “not” negates the argument and how to read these things, anyone out there know? The negation thing is difficult for me to understand in terms of how to read the premises of the argument.

Not ____ can be read “it is not the case that ___”

Do the letter thing again: let A be “Clinton was president in 1999” and B be “Dole was president in 1999”. Remember that whether an argument is valid has absolutely nothing to do with whether or not the premises ARE true, only if the conclusion must be true if they WERE true. (For example. the argument “All cats are purple”; “If all cats are purple, then cheese is made out of microwave radiation”; therefore “cheese is made out of microwave radiation” is perfectly valid, even if it is kind of stupid.)

This argument then becomes

NOT (A AND B)
NOT B
Therefore A

Note that NOT ___ is true whenever ___ is false, and vice versa. So NOT (A AND B) is true so long as (A AND B) is false, which is the case so long as at least one of A, B are false.

Again, intuitively, it is possible that someone other than Clinton or Dole was president in 1999. Now, Clinton actually was president in 1999, but that doesn’t actually matter - the question is, if all you knew was that Clinton and Dole were not both president in 1999 and also that Dole was not president in 1999, is that alone enough for you to be certain that Clinton was president?

So again, to do this legitimately, try to find a valuation that is a counter example - assign T and F to A and B in some way so that each premise is true and the conclusion is false.

Good luck on your exam.

 

[trickster]

I hate sentential logic. But I will pray for you.

Why in God’s name did you sign up for this course? Get out if you can!

God bless.

Your right Charlemagne! Intro to Logic is a requisite for a major in Philosophy…I can see the value though of understanding how arguments are constructed from one truth to the next. It comes in handy I would think in apologetics down the road…so I will struggle on… do pray, thank you.

Bruce Ferguson

 

[trickster]

Example 1

The conclusion that Tinker is a male cat is invalid because Tinker will have kittens (is a possibility/indeterminate) and if we knew Tinker were a male cat was TRUE Tinker would not have kittens would also be TRUE.

Example 2

The conclusion that Clinton was president in 1999 does not follow from what has been stated.

Logically it might not have been either of them that was president in 1999.

Therefore you can’t say that Clinton was president in 1999, just because it wasn’t Dole. An invalid argument.

If not **Clinton NOR Dole **were president in 1999 was FALSE then if it wasn’t Dole is TRUE , then it would be Clinton. But the first statement says **NOT BOTH Clinton and Dole **were president in 1999.

thank you Abucs. That’s great. So, am I looking at the premises and saying that because there is so much “indetermination” about Tinker that the argument is not valid. Sentential logic requires we assign the premises a “T” or “F” value, right? I am still not clear on how to read “Not Both” as a negative. Do I read “Not”, or “Not both”? That is the part I still find confusing…I know a bit about translating english into symbolic language, but this english phrase confuses me with respect to symbolic language.

Bruce

 

[trickster]

Gosh! I wish I could be of help, but it’s “Greek” to me!

Good bless you in any case!

Me too Clearwater at this point… so just pray for a miracle as huge as Fatima! (which is a prayer that I pass the course!

Thanks.

Bruce

 

[trickster]

I never took that class, but the answer seems really obvious to me. Tinker could be a sterile female cat. Not all females have kittens. And in the second example, it’s obvious that a third party could have been president. I don’t know if that is the answer you are looking for though.

Hi Allegra. I think that is part of it. That allows us to give the premises a “T” or “F” but how it translates into symbolic language… (like a computer language) that is the part I am struggling with though… not to worry, I have only been a philosophy student for three weeks… so I imagine there will be many times of confusion for me moving forward.

Bruce

 

[trickster]

The argument is invalid because the conclusion doesnt follow from the premises.
The opposite conclusion would be true.

(a) If Tinker is a male cat, then Tinker will not have kittens.

(b) Tinker will have kittens

Therefore: Tinker is NOT a male cat (necessary inference)

Thank you Lion IRC… I am starting to get it. I am a right brain thinker and work from general to specific. so I miss a lot of the information that you underline… that is great. it is a challenge for me to be more of a right brain thinker - and focus on the details as a means of seeing the general conclusion. Great!

Bruce

 

[trickster]

Well, the first one, the last statement doesn’t follow from the first two. If the first two were both true, then the last one would have to be that Tinker was a FEmale cat.

The second one could also have a problem with the “both” set-up of the sentence, altho I think the others are correct about the possibility of a third person’s being Preisdent. However, the both problem could come up in another scenario.

If I say to my two children:

You may both have a piece of pie, then they should split a piece.

In order for them to be able to have a piece of pie *each, *I should say, You may each have a piece of pie.

St. Francis…I understand how you see things, and I agree with you. In sentential logic (symbolic logic) we take those english statements and represent them by logical operators of which I have five to work with at an elementary level…so you have indicated very clearly that the statements are ambiguos (spelliing) and as others pointed out, the conclusion does not follow the premises … what ever happened to common sense eh?
Thank you.

Bruce