Argument:

All As are Bs

All Bs are Cs

Thus All As are Cs

Imp and I use diffirent defenitions of both “Valid” and “Follows” Let me explain. My understanding of “Valid” is that it is in propper form. What is propper form?

Propper form is such a form in which the Conclusion must follow from the Premises. This is propper form. The above argument is in propper form. It is thus Valid. What does follow mean? I cannot give a concise defenition, but it probably has something to do with the rules of inference or something. But I can tell when an argument is valid. Most people can. Modes Ponens is valid. In that the conclusion follows from the premises.

Here is an example of a conclusion following from premises:

If A, Then B

A

Thus B

Heres an example of NOT following.

If A, Then B

A

Thus G

I understand “following” best in terms of the transitive property in Math.

X=Y

Y=5

Thus, X=5

Now, Imp on the other hand, has diffirent ideas:

For Imp, Modes Ponens:

If A, Then B

A

Thus B

would be INVALID if the premises were not true. He said that any argument with a logical fallicy can be considered invalid. And that false premises are a logical fallicy. For me, this is the popular usage of the word invalid. Talking to someone not schooled in logic, I may say, “No, thats an invalid argument” which for me means not good bassicly. But again, in my logic classes, I learned that validity has only to do with form. A form is valid if the conclusion follows from the premises. Now what is follows for Imp?

For Imp, “follows” apparently means that a conclusion must be true. For a conclusion to “follow” from its premises, the premises must be true, and thus the conclusion too is true.

What is the point of all this? We were arguing if a True Conclusion could follow from False Premises. Using Imps defenition, you can see why a True conclusion cannot follow from false premises:

All dogs are fish

All fish are mammals

Thus, all dogs are mammals.

The conclusion here is true, premises false. By Imps defenition of “Follows” the conclusion DOES NOT follow from the premises, because “following” is contingent on the Truth of the premises for Imp. By my defenition of “follows” this example is such that a true conclusion DOES follow from false premises. Just like the transitive property in math, if you replace the objects (dogs, fish, mammals) with numbers and variables (X,Y,5) than you can see how the transitive property would work for this form.

Now the question to the Logicians. Please tell me and Imp which of the defenitions of Valid and Follows, Imps or mine, is the more common one, or more generally accepted among… uh… the logical community?