Am I correct in saying, Example 2 has an invalid form, and thus invalid argument according to this excerpt, because by changing the set of animals from Lizards to Cats in example 3, keeping the structure of the syllogism the same, one can clearly see the form of argument is invalid with a false conclusion. (+ and since structure/form is same for example 2, form is also invalid in 2) — S100

:up:

I agree with you! I wrote extra details if you're interested.

If you want to show an argument is invalid, you can do that by finding a way for all its premises to be true and its conclusion to be false. Looking at example 2 in that context:

P1 All bunnies are mammals
P2 Speedy the lizard is not a bunny
C Therefore Speedy is not a mammal — Example 2

P1 is true, P2 is true and C is true, but the argument is invalid, why?

The A-level book you quoted substituted in "Wilbur the cat" for "Speedy the lizard" to obtain:

P1 All bunnies are mammals
P2 Wilbur the cat is not a bunny
C Therefore Wilbur is not a mammal — Example 3

P1 is true, P2 is true but C is false.

So the argument is invalid. Since an example of the same argument form was found that had all true premises but a false conclusion.

Some more detail:

The form of an argument doesn't care about who or what specific entities it's talking about, just the relationships between them. You can write down the form of an argument using labels for the things in the statements you make Eg:

P1 All Xs are Ys.
P2 z is not an X
C z is not a Y.

You can recover example 2 by substituting in bunnies for X, mammals for Y, and Speedy the lizard for z.
You can recover example 3 by substituting in bunnies for X, mammals for Y, and Wilbur the cat for z.
That substitution is just like substitution in GCSE (if that's still a thing) algebra!
If an argument is valid, you can substitute in whatever you like for the entities mentioned in it - regardless of what you substitute in, for a valid argument if its premises are true its conclusions must be true.

That presentation gives the argument form example 2 and 3 share. It's invalid, as you've already seen. Wilbur the cat ( z ) is not a bunny ( X ), but Wilbur the cat ( z ) is in fact a mammal ( Y ).

del

del

If @S100 is examined on the material - their post begins with a lengthy quote from an A-level textbook in philosophy - they'd be examined on questions regarding deductive logic. The A-level textbook quote begins:

"Two key terms that you need to understand in relation to deductions and other
forms of argument are ‘validity’ and ‘soundness’. Validity relates to the form of
the argument. Soundness relates to an argument’s premises and its form."

"Deductive arguments have a form which is valid, which just means that if the premises are true, the conclusion must also be true." — S100

Other modes of inference than deductive logic are irrelevant to the question asked by the OP about the A-level textbook examples.

tl;dr for legwork: the second definition of "neither valid nor invalid" the OP references combines badly with the A-level textbook definition of validity, because "neither valid nor invalid" syllogisms in the second definition are actually invalid syllogisms by the A-level textbook definition.

The paper they referenced is dealing with a non-standard definition of validity. I chased it back through its citations (I think). The paper "Lehmann on the rules of the invalid syllogisms" is talking about validity in categorical syllogisms, and claims:

Anne Lehmann makes a distinction between valid, invalid, and neither valid nor invalid syllogisms. A valid syllogism is one in which the conclusion must be true when each of the two premises is true. An invalid syllogism is one in which the conclusions must be false when each of the two premises is true. A neither valid nor invalid syllogism is one in which the conclusion either can be true or can be false when each of the two premises is true

The first concept "A valid syllogism is one in which the conclusion must be true when each of the two premises is true" is the same as validity as discussed in the A level textbook examples.

The second concept "an invalid syllogism is one in which the conclusion must be false when each of the two premises is true" is a sub case of the invalidity concept in the A level textbook - because the conclusion must be false (by definition) when all (both) of its premises are true, it must be invalid in the sense of being able to have all true premises and false conclusions.

The third concept "a neither valid nor invalid syllogism is one in which the conclusion can either be true or false when each of its two premises is true" is another instance of an invalid argument by the A-level book definition - since the conclusion by definition can be false when all the premises are true.

Moreover, the paper of Anne Lehmann's that the article the OP found cites doesn't use the same terms for those concepts, she calls them "valid and perfect true syllogisms", "invalid and perfect false syllogisms" and "indefinite and imperfect syllogisms" respectively. Lehmann's original paper is "Two Sets of Perfect Syllogisms".

All the confusion comes down to the same word being used for slightly different things in different sources. A mangled reference to a 1973 logic note in a corner of research looking at categorical syllogisms vs a standard conception of deductive validity in an A-level textbook.

Thanks for the clarification. :up:

I want to ask you, is it possible to craft a deductive argument with the following characteristics:

1. Neither valid nor invalid

2. Both premises true

3. The conclusion is either true or false

???

By the way...I've made a huge mistake. I deleted the offending posts.

It's not the case that inductive arguments are neither valid nor invalid. They're all invalid.

1. Neither valid nor invalid — TheMadFool

IEP article on validity and soundness (a peer reviewed open access online philosophy encyclopedia, @S100).

A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid. — IEP

You can see from the definition that all deductive arguments are either valid or they are invalid. No in betweens, no exceptions.

2. Both premises true

3. The conclusion is either true or false — TheMadFool

If something satisfies those two conditions, that both its premises are true and its conclusion might be false, that would be an invalid argument with two premises.

It's not the case that inductive arguments are neither valid nor invalid. They're all invalid. — TheMadFool

:up: Inductive arguments are deductively invalid, yeah . That plays a part in setting up Hume's Problem of Induction.

observe all instances of the class — fdrake

Yes, thanks again. You're right on the money.

Note: Being neither valid nor invalid = Being both valid AND invalid

Here's a scenario which might clarify the scenario.

Argument A

1. X% of Americans own a phone
2. John is an America
Ergo
3. John owns a phone

Assume two people are involved in this argument, S1 and S2. S1's accuracy regarding X% is the nearest whole number such that if X% >= 99.5% he considers X% = 100% and if X% < 99.5% he rounds it off to 99%. S2, on the other hand, has an accuracy correct to the 1st decimal place and so for S2, X% >= 99.95% is X% = 100% and X% < 99.95 is X = 99.9%
Now, suppose X% is 99.94%. For S1, X% becomes 100% and argument A becomes valid but for S2, X% is only 99.9% and argument A is invalid.

Assuming the premises are true, the argument A is, depending on the accuracy in the calculation of the percentage, both valid and invalid. It appears that an argument being neither valid nor invalid is equivalent to it being both valid and invalid.

Another example of an argument being neither valid nor invalid, with true premises and a conclusion that can be either true or false will use the same template as above but the entire argument will be made explicit.

1. IF (99% of women who have an abortion feel relief 5 years after an abortion AND Sarah is a woman) THEN Sarah will feel relief 5 years after an abortion

2. 99% of women who have an abortion feel relief 5 years after an abortion AND Sarah is a woman

Ergo,

3. Sarah will feel relief 5 years after an abortion.

As you can see this is the true form of the argument, perhaps all arguments are of this form. It's a combination of a deductive argument with an inductive argument.

1. The deductive part is valid (modus ponens) and the inductive part is invalid (even if the premises are true, the conclusion true or false)

2. The premises are true for both the deductive and inductive parts

3. The conclusion is either true or false.

:chin: