4 very easy arguments. Are they valid?

[Angra Mainyu]

Are the following arguments valid?

First argument (A1).

P1: Joe is either a squid or a giraffe.
P2: Joe is not a squid.
C: Joe is a giraffe.

A2:

P1’: A giraffe is not an elephant.
P2’: Joe is a giraffe.
C’: Joe is not an elephant.

A3:

P1’’: An elephant is not a squid.
P2’’: Joe is an elephant.
C’’: Joe is not a squid.

A4:

P1: Joe is either a squid or a giraffe.
P1’: A giraffe is not an elephant.
P1’’: An elephant is not a squid.
P2’’: Joe is an elephant.
C’’’: Joe is not an elephant, and Joe is an elephant.

If you do not know the answers but you want to know, click

Show

All of the arguments are valid.
In fact, if you realize that A1, A2 and A3 are all valid, it is easy to see that A4 argument is also valid, for the following reason:

A4 contains all of the premises of A3. Hence, the conclusion C’’ of A3 also follows from the premises of A4. Now, C’’ together with P1 make up all of the premises of A1. Thus, the conclusion C of A1 also follows from the premises of A4. Now, C together with P1’ make all of the premises of A2. Hence, the conclusion C' of A2 - namely, that Joe is not an elephant - also follows from the premises of A4. But then, C’’’ follows immediately from C’ and P2’’.

.

 

[Speakpigeon]

I don't want to know your answers.
EB

 

[fast]

Is the flow of each argument such that the conclusions MUST be true if the premises are true? Yes.

Knowing the arguments are valid illuiminates a few things: 1) we know the arguments are deductive and not nondeductive. 2) we know they are not inductive arguments, for only nondeductive arguments are inductive arguments 3) we know the form of the argument will bring a guarentee to the truth of the conclusions if the premises are true.

 

[ruby sparks]

I'm not seeing how A4 is valid.

C contradicts itself.

And does not seem to follow from P1 or P2’’.

No?

 

[Treedbear]

P2' and P2" are contradictory. Or else I just do not get it.

ETA- Either that or an elephant is a type of giraffe in which case C' is false, as well as C"'.

 

[fast]

P2' and P2" are contradictory. Or else I just do not get it.

ETA- Either that or an elephant is a type of giraffe in which case C' is false, as well as C"'.

They are not contradictory.

 

[Treedbear]

P2' and P2" are contradictory. Or else I just do not get it.

ETA- Either that or an elephant is a type of giraffe in which case C' is false, as well as C"'.

They are not contradictory.

P2’: Joe is a giraffe.
P2’’: Joe is an elephant.

If a giraffe is not an elephant and an elephant is not a giraffe then Joe cannot be both an elephant and a giraffe.

 

[fast]

P2' and P2" are contradictory. Or else I just do not get it.

ETA- Either that or an elephant is a type of giraffe in which case C' is false, as well as C"'.

They are not contradictory.

P2’: Joe is a giraffe.
P2’’: Joe is an elephant.

If a giraffe is not an elephant and an elephant is not a giraffe then Joe cannot be both an elephant and a giraffe.

I don’t have a problem with any of that. My issue is with what you said. You said they are contradictory. They are not.

 

[Treedbear]

P2’: Joe is a giraffe.
P2’’: Joe is an elephant.

If a giraffe is not an elephant and an elephant is not a giraffe then Joe cannot be both an elephant and a giraffe.

I don’t have a problem with any of that. My issue is with what you said. You said they are contradictory. They are not.

contradictory adjective
1 Mutually opposed or inconsistent

How can Joe be both a giraffe and an elephant?

 

[fast]

contradictory adjective
1 Mutually opposed or inconsistent

How can Joe be both a giraffe and an elephant?

Definitions—gotta love ‘em!

Joe is not both a giraffe and an elephant.

Case study 1:

P1: I am in South Carolina, and
P2: I am not in South Carolina

It IS the case that one MUST be true.

Case study 2:
P1: I am in South Carolina, and
P2: I am in Florida.

It IS NOT the case one MUST be true.

Case study 1: contradiction
Case study 2: not a contradiction

Hence the difference between a contradiction and statements that are contrary.

When you grasped that there was a problem, you characterized it as a contradiction. That was the mistake you made.

 

[Treedbear]

contradictory adjective
1 Mutually opposed or inconsistent

How can Joe be both a giraffe and an elephant?

Definitions—gotta love ‘em!

Joe is not both a giraffe and an elephant.

Case study 1:

P1: I am in South Carolina, and
P2: I am not in South Carolina

It IS the case that one MUST be true.

Case study 2:
P1: I am in South Carolina, and
P2: I am in Florida.

It IS NOT the case one MUST be true.

Case study 1: contradiction
Case study 2: not a contradiction

Hence the difference between a contradiction and statements that are contrary.

When you grasped that there was a problem, you characterized it as a contradiction. That was the mistake you made.

Contradiction

In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other.

The bolded "usually" implies not necessarily opposites of each other. And I think you'll agree that there is a logical incompatibility between Joe being a giraffe and also being an elephant.

 

[Lion IRC]

P2' and P2" are contradictory. Or else I just do not get it.

ETA- Either that or an elephant is a type of giraffe in which case C' is false, as well as C"'.

They are not contradictory.

P2’: Joe is a giraffe.
P2’’: Joe is an elephant.

If a giraffe is not an elephant and an elephant is not a giraffe then Joe cannot be both an elephant and a giraffe.

Yep.
If a giraffe was a 'type' of elephant then A2 P1 is false.

I have to wonder what's the point of stacking up all those separate premises (3 unrelated arguments) then attempting to tie them to a 4th syllogism, the conclusion of which not only doesn't follow, but actually contradicts its own premisses.

Is this thread some kind of satirical send-up of transgenderism?

Can Bruce be Kaitlin? Can an atheist be a priest? Can a bat be a bird?

 

[Treedbear]

...
I have to wonder what's the point of stacking up all those separate premises (3 unrelated arguments) then attempting to tie them to a 4th syllogism, the conclusion of which not only doesn't follow, but actually contradicts its own premisses.

Is this thread some kind of satirical send-up of transgenderism?

It's prudent not to underestimate Angra Mainyu.

 

[fast]

Definitions—gotta love ‘em!

Joe is not both a giraffe and an elephant.

Case study 1:

P1: I am in South Carolina, and
P2: I am not in South Carolina

It IS the case that one MUST be true.

Case study 2:
P1: I am in South Carolina, and
P2: I am in Florida.

It IS NOT the case one MUST be true.

Case study 1: contradiction
Case study 2: not a contradiction

Hence the difference between a contradiction and statements that are contrary.

When you grasped that there was a problem, you characterized it as a contradiction. That was the mistake you made.

Contradiction

In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other.

The bolded "usually" implies not necessarily opposites of each other. And I think you'll agree that there is a logical incompatibility between Joe being a giraffe and also being an elephant.

Definitions, I swear!

It’s explanatory definitions like that which underlies the continuation of confusion. “Logical incompatibility” overstates the matter. It’s like defining “false” as “not true.” Or “invalid” as “not valid.” It quick and helpful, but the nuances go by the wayside. We can explain that all inductive arguments are nondeductive arguments and distinguish them from deductive arguments, but those air bubbles; they’ll escape...gotta watch out for ‘em.

Stipulative definitions are made up definitions that do not necessarily adhere to usage for meaning as is the case with lexical terms. Some stupulative definitions that are designed with purpose in mind are BETTER than others. There is an underlying theme at play and it has to do with collective exhaustivity. It’s why logicians gravitate towards very specific definitions.

 

[Treedbear]

... There is an underlying theme at play and it has to do with collective exhaustivity. ...

I think together we've succeeded in that effort. I concede ...

P2' and P2" are contradictory contrary to each other. Or else I just do not get it.

ETA- Either that or an elephant is a type of giraffe in which case C' is false, as well as C"'.

ETA - I hope I'm using the word concede correctly.

 

[fast]

P2’: Joe is a giraffe.
P2’’: Joe is an elephant.

If a giraffe is not an elephant and an elephant is not a giraffe then Joe cannot be both an elephant and a giraffe.

Yep.
If a giraffe was a 'type' of elephant then A2 P1 is false.

I have to wonder what's the point of stacking up all those separate premises (3 unrelated arguments) then attempting to tie them to a 4th syllogism, the conclusion of which not only doesn't follow, but actually contradicts its own premisses.

Is this thread some kind of satirical send-up of transgenderism?

Can Bruce be Kaitlin? Can an atheist be a priest? Can a bat be a bird?

When she was asked “where did you go?” she responded “I was home by 12:00.”

Why? Because what she thought was more important was what time she got back and not where she went. Still, you and I can separate one question from the other without allowing the answer for the question not asked distract us from seeing that the response didn’t stand good as an answer.

Discussing form can be difficult because we are easily blinded by the obvious untruths that distract us from the specific issue at hand. I can give you directions that will lead you from point A to point B, but when you discover that my directions were from my reverse travels that led me down a bunch of one way streets, you’re gonna focus on the fact the directions do you no good, but I promise, if you walk the trip, all will turn out just right.

Don’t let the truth (of premises or conclusions) distract you from the issue of form, just as you’d advise me not to accept her response regarding time distract me from the issue that was in fact at hand... where did she go.

P1: Joe is either a squid or a giraffe.
P2: Joe is not a squid.
C: Joe is a giraffe.

A2:

P1’: A giraffe is not an elephant.
P2’: Joe is a giraffe.
C’: Joe is not an elephant.

A3:

P1’’: An elephant is not a squid.
P2’’: Joe is an elephant.
C’’: Joe is not a squid.

A4:

P1: Joe is either a squid or a giraffe.
P1’: A giraffe is not an elephant.
P1’’: An elephant is not a squid.
P2’’: Joe is an elephant.
C’’’: Joe is not an elephant, and joe is an elephant.

Look at what’s bold. Can we get from P2” to the part bolded in C’” without regard for the truth? In other words, if X is Y (and never mind if it’s true), could we comfortably accept what follows from that, which in this instance happens to be a trivial truism; after all Joe is an elephant entails Joe is an elephant. Don’t be tempted to deny the entailment of that by chance the truth is that Joe is a groundsman for a zoo.

Why, because it’s all grounded on if’s. If it’s true that all dogs are cats, then it necessarily follows that all dogs are cats. Now, you can go underline the other part of the conclusion and find various lines to get you to that conclusion.

It’s not about soundness; it’s about validity. Kind of like how my map directions wasn’t about helpfulness for driving instructions.

 

[Angra Mainyu]

I don't want to know your answers.
EB

In light of that, I let you know that in order to address some of the points made by other posters, I will disclose the part that is hidden by quoting it in the next post.

 

[Angra Mainyu]

I'm not seeing how A4 is valid.

In the part that is hidden in the OP, I explain why if you realize that A1, A2 and A3 are valid, it is easy to see that A4 is also valid. I will quote that part:

All of the arguments are valid.
In fact, if you realize that A1, A2 and A3 are all valid, it is easy to see that A4 argument is also valid, for the following reason:

A4 contains all of the premises of A3. Hence, the conclusion C’’ of A3 also follows from the premises of A4. Now, C’’ together with P1 make up all of the premises of A1. Thus, the conclusion C of A1 also follows from the premises of A4. Now, C together with P1’ make all of the premises of A2. Hence, the conclusion C' of A2 - namely, that Joe is not an elephant - also follows from the premises of A4. But then, C’’’ follows immediately from C’ and P2’’.

C contradicts itself.

No, it does not. But C''' does.

And does not seem to follow from P1 or P2’’.

No?

It does follow from P1, P1', P1'', and P2'', as explained in detail above - well, in detail if you realize that A1, A2 and A3 are valid. If you do not, then if you let me know, I will explain why those are valid as well.

 

[Angra Mainyu]

P2' and P2" are contradictory. Or else I just do not get it.

ETA- Either that or an elephant is a type of giraffe in which case C' is false, as well as C"'.

No, P2' and P2'' are not contradictory, at least not by their form, though you might argue that it is a contradiction to claim that something is both a giraffe and an elephant by the meaning of the words, but that would not allow you to derive a contradiction without further premises that are not (by their form) tautologies, since you would need the semantic claim.

The argument A4 is valid, though, and the premises are contradictory together, even if they are pairwise not contradictory.

 

[Angra Mainyu]

Yep.
If a giraffe was a 'type' of elephant then A2 P1 is false.

I have to wonder what's the point of stacking up all those separate premises (3 unrelated arguments) then attempting to tie them to a 4th syllogism, the conclusion of which not only doesn't follow, but actually contradicts its own premisses.

The conclusion contradicts its own premises, contradicts itself, but does follow. In fact, if you realize that A1, A2 and A3 are valid, it is easy to see why A4 is valid (if you click to see the hidden part in the OP, that is explained in detail).

Now, the point of stacking up those premises is to try to shed some light on the matter after the confusion resulting from this thread. You will notice that the premises were chosen from there.

Is this thread some kind of satirical send-up of transgenderism?

No. Why would you suspect that?

Can Bruce be Kaitlin?

Yes. In fact, Bruce Jenner is Kaitlin Jenner: the two proper names refer to the same person.

Can an atheist be a priest?

Yes. For example, priests who come to realize that atheism is true do not stop being priests if they keep working at that and pretend they are Catholic.

Can a bat be a bird?

Here "can" needs disambiguation, but in the most common ordinary, I'm pretty sure not. On the other hand, there is no contradiction in asserting - for example - that biologists got it wrong (or lie, or whatever) and bats are actually birds. It is absurdly improbable, but not contradictory.