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Laabradir33
Alum Member
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Comments
It's valid.
If we take the contrapositive of each statement we get
/C-->/A
/C-->/B
Now this matched out valid argument form 6 https://7sage.com/lesson/valid-argument-forms-4-9-of-9/
and we can conclude /A -some- /B
Do you recognize it now?
Yup - it's valid! You might need to revisit the lessons on validity.
A ---> C
B ---> C
is equivalent to
/C -->/A
/C -->/B
If all /Cs are /As, and all /Cs are /Bs, then it follows that some /As are /Bs.
I like to visualize it:
/B
/A /C /B
/A
So every single /C is both /A and /B. But only some /As are /Bs (there could be infinite /As or infinite /Bs, but as long as more than one /A is a /B, then some /As are /Bs).
To use your example:
If you are smart (A), you pass the LSAT (C)
If you are nice (B), you pass the LSAT (C)
Some people who are not smart (/A) are also not nice (/B)
Thank you so much!
Now it makes sense to me
Good point on revisiting the lessons. I made flashcards and they've helped a bunch!
Can some one clarify how this form is valid??? What I see is an INVALID conclusion from the premises. BUT I also see double word play on the term VALID. The conclusion is inthe contrapositive form of the real conclusion.
So to say the conclusion and it's contrapositive are valid inferences is quite distinct from saying premise one and two MUST bring forth the alleged conclusion.
Here is a clear counter example of why the argument form is INVALID:
All dogs are mammals.
All dogs are canines.
All canines are mammals.
Notice all the claims are true indeed THAT example but it commits a formal fallacy called illicit minor.
Here is another example:
All cobras are snakes.
All cobras are venoumous animals.
All venomous animals are snakes.
Clearly we have true premises and yet the conclusion is FALSE. So we must be clear when we say VALID. Are we talking about transforming a proposition by controposing the proposition or do we mean to refer to THE RELATIONSHIP between the premises and the conclusion.
It is logically valid. I think you may have misread the original post, @roychess.
Are you talking about this form?
A ---> C
B ---> C
/A some /B
/C ---> /A
/C ---> /B
/A some /B
I'm sorry if I'm misunderstanding you, but if I apply your example to the form (A ---> C, B ---> C thus /A some /B), it would be:
All dogs (A) are mammals (C).
All canines (B) are mammals (C).
Some non-dogs (/A) are not canines (/B).
I think this is perfectly valid because I am not a dog and I am not a canine. So there must be at least one (=Some).
Akistotle
The form in your post is not the same as the original post and not the same as mine. Your example is reversed. Your label C is in the wrong spot. Can I use terminology here: the label C is called a middle term because it repeats in the premises and NOT in the conclusion.
So the form is All C are B.
All C are A.
Is distinct from All B are C
All A are C.
So this position of the middle term is important. It can make an argument immediately invalid.
If I did make a mistake can you point it out please?
I referred specifically to the argument form being NOT valid. I agree that a proposition can be contraposed in the conclusion. The problem is that conclusion does not follow from the given premises. That is, there are cases where I can show you I can use that form of argument and find two true premises and a false conclusion. That is what I demonstrated in my first post.
Let me point out again the rhetorical form of logic may define valid differently from deductive reasoning. I can tell you deductive reasoning and mathematical logic express that a valid argument is an argument where the conclusion is impossible to be false with two true premises. That is if the premises are true the conclusion must absolutely be true as well.
What seems to be happening here is you found an true instance of a poor argument form. That is if I substitute different words in the same spot as your form the argument truth value can change. This I demonstrate again:
All men are things that belong to a species.
All men are mortal beings.
All mortal beings are things that belong to a species.
This argument has a middle term named MEN because it repeats in the premises and NOT the conclusion. Notice the argument validity is not based on content value but concepts. Why this is invalid is a concept called distribution.
What the conclusion distributes is NOT distributed in the conclusion. So this a shift in discourse.
Hi @roychess
The original post said:
and I said:
The above is a valid argument form.
Your example of an invalid argument:
Your example can be represented as
A → B
A → C
C → B
and it is an invalid argument form.
Thank you for the correction. I thought the middle term was placed in the first position in the original.
I still need some clarity on how even this form is valid with the middle term in this position.
First in symbolic logic truth tables are used to establish validity. Inference rules are named after truth tables. There are no inference rules that allow this form. Which inference rules establish this form above.
I am aware there is an inference rule hypothetical syllogism but the terms are not in the correct position to use hypothetical syllogism.
Let me show how this form is invalid:
All dogs are mammals.
All cats are mammals.
All cats are dogs.
Contraposing the conclusion gives:all non-dogs are non-cats.
This is still false with true premises.
In symbolic logic:
If something is a dog then it is a mammal. D --> M
If something is a cat, then it is a mammal. C-->M
If something is a cat then it is a dog. C-->D
Controposing the conclusion gives ~D-->~C
If something is not a dog then it is not a cat. The ~ symbol is called tilde and the official symbol for NOT.
I claim this is a case the premises are true and the conclusion is false even in this form.
The fallacy in this form is undistributed Middle.
What someone has shown is that you can form true premises and a true conclusion with this form BUT it depends what words you use in the form.
The words I chose do not workin this alleged valid form. Is the form valid if I can show a single case where the premises are true and the conclusion false?
Notice please when I say an argument is invalid I can state what fallacy it commits. I am not expressing what I think personally. All invalid arguments commit a fallacy. So when anyone says an argument is invalid the person ought to be able to name the fallacy. That is you are not supposed to claim an argument as invalid and walk away.
I may be missing something here but the original post says:
[Argument #1]
Premise 1: A ---> C
Premise 2: B ---> C
Conclusion: ~A some ~B
This argument is valid because
Premise 1: Dogs ---> Mammal
Premise 2: Cats ---> Mammal
Conclusion: ~Dogs some ~Cats
Premise 1: All dogs are mammals.
Premise 2: All cats are mammals
Conclusion: Therefore, there must be at least one thing in the world that is neither a dog nor a cat.
I believe that the "Fallacy of the undistributed middle" is:
[Argument #2]
Premise 1: All dogs are mammals.
Premise 2: All cats are mammals
Conclusion: Therefore, all dogs are cats.
[Argument #2] is invalid.
I think people in this Forum understand "validity" is not something personal so no worries
@roychess
The conclusion of the original post is an "I" not an "A" on the Square of Opposition. This argument is Figure 3 - AAI and is conditionally valid: Modus Darapti.
It is a conceptually tricky argument form, though, to be fair. It doesn't seem to follow at first glance, but it does.
Well thank for the response. The issue with what you are doing is STILL a problem. The premises are all claims and you swap it for a SOME because you see the sentence would be true. This is not a legit method because of other issues but I must introduce this here a bit. Consider
All unicorns are animals with a horn.
All rhinos are animals with a horn.
Therefore there must be at least one rhino that is a unicorn.
Controposing this gives FURTHER problems if you understand what contrapositive really means and not the symbol manipulation.
The issue here is called existential import: referring to some non-existent object namely UNICORN in the example. SOME we all agree means AT LEAST One. How can something that does not exit refer to at least one? These quantifies are CONTRADICTORY.
With that said you MUST not CHANGE quantifiers without justification. You start with all you must FINISH with all. You switching terms without justification is what Mathematica's changed logic for. This is a fallacy called the existential fallacy: going from an all to a some in reasoning. All fallacies have true instances where the premises and conclusion are true. The point is the fallacy has cases where it will be FALSE-- that is the form is not always 100% true.
Are you saying that it's possible that there are no non-As that are also non-Bs, or, in other words, that there are no non-Cs?
I am saying that the form of the argument alone will not always give the correct conclusion. Your conclusion may be true by itself. Your conclusion is not true solely based on the premises.
What logical forms are supposed to do is provide a UNIVERSAL away of getting conclusions no matter what the subject matter is about.
What appears to me in some cases here is that some people are evaluating the truth of the sentences and making rules based on that. So you make sure the conclusion is true based on you making subjective rules.
I have no doubt all people see that my examples have issues and have the SAME form. I used different words in the same position as their words and the truth value changes hence the invalid status.
The LSAT uses Aristotelian Logic, not Boolean, and assumes that all terms referred to exist. This argument is invalid according to Boolean logic, and conditionally valid according to Aristotelian. Since we use Aristotelian and assume the terms exist, this is a valid argument structure. For reference, it is AAI-3 under the conditionally valid forms.
The problem now is what do you mean by conditionally valid.
Conditionally valid usually refers to actual existing things. I am not giving my opinion here.
Aristotelian logic does not assume anything technically. I am aware people use that terminology but if you evaluate it you will find it to be untrue. It can be true in some cases but not 100%.
Deductive reasoning is about methods that work 100% of the time and no less. Scientific reasoning makes up the rest 0 -99%. This is why PURE deductive reasoning is not a science.
At this very moment I am looking a respected logic book authored by Patrick Hurley:
" for example, the AAI-1, is valid from the Aristotelian standpoint If the subject of the conclusion (the minor term) denotes actually existing things."
There is a thread about IF and ONLY IF arguments and how they work. What Hurley is saying is Equivalent to "if the subject of the conclusion (the minor term) denotes actually existing things, THEN the AAI-1 is valid from the Aristotelian standpoint."
I am sorry you disagree. I am not trying to be a trouble maker here. I would like clarity though just in case I made a mistake.
My logic class used Hurley's book as well, so the definition of conditional validity I'm referring to is the same as yours:
"if the subject of the conclusion (the minor term) denotes actually existing things, THEN the AAI-1 is valid from the Aristotelian standpoint."
So, this is a conditional statement. What the LSAT asks us to do is to assume the sufficient. So, I don't actually disagree with you. You're correct in that Aristotle is not making any assumptions about existence. The point you're missing is that the LSAT is. Since this is an LSAT prep company, we operate on the assumptions the LSAT asks us to make. And you really don't want an LSAT prep course that doesn't, lol.
Nice nugget of info. Thanks.