Logic Test - i don't get it

[Kenai]

I'll try and break it down.

1) A logically valid argument cannot have all true premises and a false conclusion. This is an axiom of logic. Look it up if you don't believe me. Do you understand that?

2) In this example, all the premises are true and the conclusion is false. Do you understand that?

3) Ergo, the argument is logically invalid. Do you understand that?

4) The combination of (1) and (2) is, actually, a valid proof of the invalidity of the argument in itself, without having to get into how the conclusion doesn't follow from the premises. Do you understand that?

At what point does what I'm saying turn to gibberish?

It all makes sense but where I disagree is in part 2 where you say the premises are true and the conclusion is false. According to the conditions we are given the conclusion is not necessarily false. It doesn't contradict either condition but neither is it wholly supported by it. It is false if you 'take as given' as you suggest earlier but only then.

Everything you are saying makes sense but I fundamentally disagree that the conclusion is false based on the conditions presented, it only becomes false when you add the third condition that all racetracks are routes of transportation but this is not a condition we are originally given it is one that you infer from the context.

I'm not mentally disabled, you don't have to take such a condescending tone.

If you could explain how you've decided the conclusion must be false without needing to refer to anything beyond conditions a and b, I may understand where you're coming from better. As far as I see it, you cannot reach that conclusion without expanding and effectively adding your own third condition (all racetracks are routes of transportation).

 

[Al Vallario]

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[Kenai]

That's adding a third condition to the problem though.

As I edited in above:

If you could explain how you've decided the conclusion must be false without needing to refer to anything beyond conditions a and b, I may understand where you're coming from better. As far as I see it, you cannot reach that conclusion without expanding and effectively adding your own third condition (all racetracks are routes of transportation).

As soon as you add in that extra caveat, you are changing the problem by adding condition c. You're then answering a different logic situation with three conditions not two. In that scenario, yes I agree, of course it's false but that's not what we were being asked to evaluate.

 

[Al Vallario]

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[Killerkebab]

I don't need to add an extra premise to acknowledge that the conclusion is false.

This can't be true, because you do, and have done so here:

It should be taken as given that all racing tracks are routes of transportation. If you add that as an implicit premise, the conclusion is false.

Perhaps the crux of our disagreement is your refusal to acknowledge the fact that all racing tracks are routes of transportation.

I don't see why he should acknowledge that. In this kind of exercise all that matters are the opening statements and what we can draw from them. Any outside knowledge is completely irrelevant to the exercise and should be ignored completely.

 

[Kenai]

I don't need to add an extra premise to acknowledge that the conclusion is false. The conclusion is false regardless of whether or not the argument is valid.

Perhaps the crux of our disagreement is your refusal to acknowledge the fact that all racing tracks are routes of transportation.

To analogise the situation, it's like you refusing to accept "the sky is blue" as a fact, and on that basis arguing I can't declare the conclusion to an argument "the sky is green" false without adding a premise that the sky is, in fact, blue.

No, the crux of our disagreement is not that I refuse to accept that premise is correct (as it clearly is) - I refuse to accept that that premise is part of the situation we were asked to evaluate.

It is an extra third condition beyond the two we were given and thus is not a condition of the situation we were given to evaluate.

We were given two defined conditions and asked to evaluate if a statement is correct given those two conditions. Given those two conditions you cannot decide.

However if you allow that extra condition of all racetracks are routes of transport, then yes, clearly the conclusion is false. I disagree that this condition should be allowed though. I think it is irrelevant whether it is patently true or not, it is not one of the conditions we were asked to evaluate against so we should not evaluate against it.

Our fundamental disagreement is that you feel it is sensible and acceptable to add further conditions based on what you consider given truths, I feel that the problem should be assessed with the given conditions and the given conditions only.

edit - this is where the Pitbull idea was used to help - the conditions in the example didn't tell us that a pitbull was a dog yet it is patently true that a pitbull is a dog. The issue comes down to whether you use that patent truth as one of your conditions or not as it fundamentally changes your outcomes.

 

[Chronictank]

The conclusion is false. A racing track is, by definition, a route of transportation. How on earth could some racing tracks not be routes of transportation? It's patently false.

You cannot possibly reach such a false conclusion as the one provided without a false premise. Yet both of the premies are also true.

Hence, the argument is logically invalid.

That's logic.

If you break down the scenario and explain in terms of x, y and z (removing the context) which is essentially what this test is proving

We can say this because a later question is

7. a. None of the A’s is a B.
b. None of the B’s are C.

Conclusion is: All A’s are C’s.

I think this discussion may move somewhere

 

[Al Vallario]

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[Al Vallario]

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[Killerkebab]

This is a poor example.

You're saying that:
All X are Z
All Y are Z
Therefore X is Y

This can or cannot be true. We don't have enough information to make that conclusion... in much the same way as we don't have enough information to make the conclusion in the first example.
Tell us again: what exactly are you arguing?

 

[Kenai]

I'm saying you seem to dispute the falsity of the conclusion, not the premise. That is to say you seem to think it is possible for some racing tracks not to be routes of transportation. That would constitute valid grounds for disagreement.

It isn't a third condition. It is possible to determine the argument is logically invalid with what has been given. The premises are both true, yet they lead to a false conclusion.

Hence the argument is logically invalid. You cannot reach a false conclusion without at least one false premise.

I dispute that the conclusion is false based on the two conditions presented to us. (This bold bit is important and you seem to keep ignoring it)

You assert it is false not because of these conditions but because "all racetracks are routes of transport".

Whilst this is true, it is not part of the scope of the situation we were asked to evaluate.

The conclusion is only false if you allow that third condition - I disagree that that condition should be part of the discussion at all, as it was not one of the two conditions we were asked to evaluate against, be it a patent truth or not.

 

[Al Vallario]

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[Al Vallario]

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[Kenai]

Okay, we're finally getting somewhere.

So you agree the conclusion is false. Bear in mind we're talking in absolutes here. The sky is not blue or green depending on what premises I give you in an argument. It's blue. To say it's green is false. Do you also agree that both the premises are true?

No no no no, I don't agree that the conclusion is false within the confines of the problem we were asked to evaluate (bold again). We are talking within the confines of the question that was posed.

It is false OUTSIDE the confines of that, when you add that "all racetracks are routes of transport" but this was not an original condition. It is not part of the consideration, it's patent truth does not matter as it is not an item for consideration within the confines of the original question.

This is our difference - I am evaluating this using only the given conditions. You are evaluating it using the given conditions and what you consider a given truth

I disagree that such things should be accounted for within the scope of the question that was asked.

 

[Kenai]

Our difference is coming from what we deem an acceptable scope of information to use within our reasoning.

I am using only that which I am given, conditions a and b. Absolutely nothing more, at all.

You are using those, plus the patent truth you infer from the fact racetracks must be routes of transport, despite this not being a specified or defined condition of the logic problem.

I disagree that you should use the context to infer further conditions, be they patent truths or otherwise.

 

[Killerkebab]

Your two opening statements are:
1. Cats are mammals
2. Dogs are mammals

... and the conclusion here was:
Cats are dogs

Whilst 'cats are dogs' doesn't contradict our opening statements, we don't have enough information to make that assertion. The following also don't contradict our opening statement:

All cats are dogs
All dogs are cats
Some cats are dogs
No cats are dogs

None of these (including the 'cats are dogs' conclusion) follow from our opening statements. The conclusion isn't false because cats are clearly not dogs, the conclusion here is false because we cannot come to it using only statements 1. and 2.

 

[Al Vallario]

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[Al Vallario]

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[Killerkebab]

Again, we're talking in absolute terms.

The conclusion is false. You cannot state the conclusion "the sky is green" and tell me whether or not it is false depends on the premises you give me in an argument. It is false no matter what premises you provide.

You can provide certain premises to form a logically valid argument with the conclusion that the sky is green. The argument will be valid, but the conclusion will never be true. The sky is not green.

Crucially, those premises have to be false. There is no way you can deduce, stating only truths, that the sky is green. The same way you cannot state, stating only true premises, the falsehood that some racing tracks are not routes of transport.

To reiterate, I'm not making this rule up. It's an axiom of logic.

Of course the sky is not green. Of course some racetracks are transportation routes. Of course not all Canadians are opticians, and of course cats are not dogs. However, this is not what the logic test is about.

The logic test is about seeing whether the participant can take the information from a finite number of statements and make deductions from these, and these only.

The conclusion "cats are dogs" is false.

The falsehood of the statement isn't dependent on the premises provided in the argument. Cats are not dogs. To say they are is false. I can't believe I'm even having to say this.

You don't have to say it. Hell, I said it before you

You are correct that the conclusion does not follow from the premises. That is because it is impossible to create a logically valid deductive argument that reaches a false conclusion by stating only true premises.

True, but I don't see anywhere in this thread where we've done this...

 

[Al Vallario]

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