A question on logic.

[MarionetteDarner]

In propositional, categorical and predicate logics, premises are either true or false, and arguments are either valid or invalid. All arguments are valid unless true premises give rise to false conclusions. A simple example of a valid form would be P -> Q, P Therefore Q. An invalid form would be P -> Q, ~P Therefore Q. The premises represent truth values, and the conclusion is either valid or not.

Now for my question. In class the other day, I inadvertantly called a conclusion to an argument false, and my professor jumped all over me. I had no opportunity to simply apaologize for the mistake, and I made no attempt to debate the issue, but after I thought about it, the more I thought I ought to have argued the matter.

I would contend that it is possible to make an argument a statement. That is, we can easily say "if it is true that P -> Q, P, then it is also true that Q." To restate: if the premises are true, then the conclusion is true. Therefore an argument is really just an elaborate statement.

Do I have a case?

 

[Wiccan_Child]

In propositional, categorical and predicate logics, premises are either true or false, and arguments are either valid or invalid. All arguments are valid unless true premises give rise to false conclusions. A simple example of a valid form would be P -> Q, P Therefore Q. An invalid form would be P -> Q, ~P Therefore Q. The premises represent truth values, and the conclusion is either valid or not.

Now for my question. In class the other day, I inadvertantly called a conclusion to an argument false, and my professor jumped all over me. I had no opportunity to simply apaologize for the mistake, and I made no attempt to debate the issue, but after I thought about it, the more I thought I ought to have argued the matter.

I would contend that it is possible to make an argument a statement. That is, we can easily say "if it is true that P -> Q, P, then it is also true that Q." To restate: if the premises are true, then the conclusion is true. Therefore an argument is really just an elaborate statement.

Do I have a case?

An argument is a special form of statement, yes, just as disproof is a special form of proof.

 

[MarionetteDarner]

An argument is a special form of statement, yes, just as disproof is a special form of proof.

I've not dealt with disproof. I've only done reductio ad absurdum. How does disproof work in formal logics?

 

[The Nihilist]

The answer that counts is that even if you are right, it's a dumb reason to antagonize your professor. Let it go.

 

[Wiccan_Child]

I've not dealt with disproof. I've only done reductio ad absurdum. How does disproof work in formal logics?

A disproof is any argument that shows that a proposition p is false. As such, a disproof of p is a proof of ¬p. I'd elaborate, but I am drunk. G'night

 

[daniel777]

everything is an argument.

 

[MarionetteDarner]

A disproof is any argument that shows that a proposition p is false. As such, a disproof of p is a proof of ¬p. I'd elaborate, but I am drunk. G'night

Oh, then I have done that, but I haven't distinguished that from a regular proof.

 

[MarionetteDarner]

The answer that counts is that even if you are right, it's a dumb reason to antagonize your professor. Let it go.

I did let it go. I was just wondering. I think your answer is the correct one though.

 

[MarionetteDarner]

everything is an argument.

I'm not sure this is correct.

 

[Yekcidmij]

In propositional, categorical and predicate logics, premises are either true or false, and arguments are either valid or invalid. All arguments are valid unless true premises give rise to false conclusions. A simple example of a valid form would be P -> Q, P Therefore Q. An invalid form would be P -> Q, ~P Therefore Q. The premises represent truth values, and the conclusion is either valid or not.

Now for my question. In class the other day, I inadvertantly called a conclusion to an argument false, and my professor jumped all over me. I had no opportunity to simply apaologize for the mistake, and I made no attempt to debate the issue, but after I thought about it, the more I thought I ought to have argued the matter.

I would contend that it is possible to make an argument a statement. That is, we can easily say "if it is true that P -> Q, P, then it is also true that Q." To restate: if the premises are true, then the conclusion is true. Therefore an argument is really just an elaborate statement.

Do I have a case?

The logic is fine:
1. P->Q
2. P
3. Therefore Q

Watch for fallacies though and be sure in your premise it really is true that "If P then Q".

 

[NavyGuy7]

The answer that counts is that even if you are right, it's a dumb reason to antagonize your professor. Let it go.

Perhaps, you could pull your professor aside, and explain calmly your view on the matter, and ask that he hear you out. After all, if you are to learn, you must ask questions. You can ask without antagonizing.

 

[Sequim]

I would contend that it is possible to make an argument a statement. That is, we can easily say "if it is true that P -> Q, P, then it is also true that Q." To restate: if the premises are true, then the conclusion is true. Therefore an argument is really just an elaborate statement.

Do I have a case?

In a sense yes. Just as an explanation of political policy can be considered to be a policy statement. But in logic, "statement" is generally taken to be synonymous with "premise." Moreover, not all arguments with true premises have true conclusions. Take the following argument in which both premises are true.

All buses have wheels​

All buses are conveyances that carry passengers​

______________​

All conveyances that carry passengers have wheels​

Which is false; Boats don't have wheels. (This is an example of the fallacy of illicit minor.)

 

[Wiccan_Child]

In a sense yes. Just as an explanation of political policy can be considered to be a policy statement. But in logic, "statement" is generally taken to be synonymous with "premise." Moreover, not all arguments with true premises have true conclusions. Take the following argument in which both premises are true.

All buses have wheels​

All buses are conveyances that carry passengers​

______________​

All conveyances that carry passengers have wheels​

Which is false; Boats don't have wheels. (This is an example of the fallacy of illicit minor.)

While this is indeed an example of the illicit minor fallacy, strictly speaking this is not an example of true premises leading to a false conclusion: the second premise is false, since it equivocates 'buses' with 'conveyances that carry passengers'.

 

[Sequim]

While this is indeed an example of the illicit minor fallacy, strictly speaking this is not an example of true premises leading to a false conclusion: the second premise is false, since it equivocates 'buses' with 'conveyances that carry passengers'.

A bus isn't a conveyance for transporting passengers?

Conveyance: 2: a means or way of conveying: as a: an instrument by which title to property is conveyed b: a means of transport : vehicle ​

Bus: 1 a: a large motor vehicle designed to carry passengers usually along a fixed route according to a schedule​

(Merriam-Webster)​

And, to carry passengers along a fixed route certainly certainly qualifies as transporting.

 

[Robbie_James_Francis]

While this is indeed an example of the illicit minor fallacy, strictly speaking this is not an example of true premises leading to a false conclusion: the second premise is false, since it equivocates 'buses' with 'conveyances that carry passengers'.

That depends on how the statement is written in the logical calculus. To make 'bus' and 'conveyance that carries passengers' logically equivalent using the biconditional would make the premise false. But it is possible using the predicate calculus (and even the propositional calculus I believe) to make this mean 'all buses belong to the category of conveyances for passengers'.

I'm not sure exactly how, because I rarely turn up to logic lectures.

 

[Wiccan_Child]

A bus isn't a conveyance for transporting passengers?

Strictly speaking, the statement "A bus is a conveyance for transporting passengers" is false.

It is the statement "A bus is a member of the set of conveyances for transporting passengers" that is true.

Similarily, the statement "A dog is an animal" is, strictly speaking, false: dogs are not animals, but rather are members of the set of animals.

"a ϵ A" ≠ "a = A"

Colloquially, however, the statement "a is b" can mean either "a is in b" or "a & b are the same thing". And probably some other things as well. Damn our contextual language!

EDIT: RJF, I think we're talking about the same thing here. Hurrah!

 

[StrugglingSceptic]

In propositional, categorical and predicate logics, premises are either true or false, and arguments are either valid or invalid. All arguments are valid unless true premises give rise to false conclusions. A simple example of a valid form would be P -> Q, P Therefore Q. An invalid form would be P -> Q, ~P Therefore Q. The premises represent truth values, and the conclusion is either valid or not.

The argument is either valid or not. The conclusion and premises may be true or false, excepting that, if the argument is valid, and the premises true, the conclusion must be true.

Now for my question. In class the other day, I inadvertantly called a conclusion to an argument false, and my professor jumped all over me. I had no opportunity to simply apaologize for the mistake, and I made no attempt to debate the issue, but after I thought about it, the more I thought I ought to have argued the matter.

The guy sounds like a d*ck. Don't worry about it.

I would contend that it is possible to make an argument a statement. That is, we can easily say "if it is true that P -> Q, P, then it is also true that Q." To restate: if the premises are true, then the conclusion is true. Therefore an argument is really just an elaborate statement.

It isn't, but the reason is subtle. When you study logic formally, it is a good idea to keep a self-conscious distinction between the well-formed formulas that you take to stand for propositions, and the statements that you make about those well-formed formulas. You can make this distinction by considering the metalanguage versus the formal language, and the metatheory versus the formal theory. The metalanguage is the language (presumably English) which you use to talk about the formal language (the well-formed formulas of the relevant logic). The metatheory is the assumed theory you use to reason about the formal theory.

Keeping this distinction, you would say that Modus Ponens -- the ability to deduce Q from P and P->Q -- is defined in the metalanguage as an inference rule for most logics, while the statement "P & (P->Q) -> Q" is just a statement in the formal language. The two are therefore completely distinct.

I've tried to be very brief here: firstly, since it's very late, and secondly, since I can't assume much about your knowledge of formal logic. Please don't hesitate to ask any questions, and I'll do my best to clarify.

 

[MarionetteDarner]

I've tried to be very brief here: firstly, since it's very late, and secondly, since I can't assume much about your knowledge of formal logic. Please don't hesitate to ask any questions, and I'll do my best to clarify.

Actually, that made perfect sense to me. Thank you.