College Logic

[Schtank]

I'm in a logic class in college, and I was wondering if there was a purpouse to determining the truth value of the statements similiar to the following: If the fact that neither Paris is in France nor Stockhold is in Sweden implies that Tuscaloosa is in Iowa, then there are no Democrats in Washington D.C

Thanks

[Jake_Ellison]

If we pretend that F=>F, why would that (the fact that we are pretending) imply that an unrelated fact (there's democrats in DC) is false?

I would say yes, it's a valid way of learning to identify logical fallacies. (such as starting out with a false premise, thinking it will lead to any conclusions)

[edit] I changed the whole post, after realizing that Tuscaloosa is in fact not in Iowa:) It's in Alabama.

Edited October 20, 2009 by Jake_Ellison

[DavidOdden]

I'm in a logic class in college, and I was wondering if there was a purpouse to determining the truth value of the statements similiar to the following: If the fact that neither Paris is in France nor Stockhold is in Sweden implies that Tuscaloosa is in Iowa, then there are no Democrats in Washington D.C

Well, there is a purpose behind developing the ability to determine the truth value of any statement. If you are incapable of determining the truth value of a statement, then there must be a reason. I believe there are only three reasons why you could not. First, the statement may have no truth value (as in the instant case). Second, you may lack the required knowledge of reality that enables you to validate the statement -- i.e. you may not know where Tuscaloosa is. Third, you may not understand the meaning of the statement, a problem which is likely to be true of this statement. In logical classes, certain words are redefined, especially the word "imply".

[Schtank]

Well, there is a purpose behind developing the ability to determine the truth value of any statement. If you are incapable of determining the truth value of a statement, then there must be a reason. I believe there are only three reasons why you could not. First, the statement may have no truth value (as in the instant case). Second, you may lack the required knowledge of reality that enables you to validate the statement -- i.e. you may not know where Tuscaloosa is. Third, you may not understand the meaning of the statement, a problem which is likely to be true of this statement. In logical classes, certain words are redefined, especially the word "imply".

Yah, I can see the purpouse of determining the truth value of statements, but the examples that the book gives seem much to unrealistic. Wouldn't it be better to use more realistic exampless? In hind-sight, I don't know why I decided to make this post, since any questions I have about my logic text book should be addressed to the publisher, not here on the forums lol. So sorry for wasting your times guys....

[woolcutt]

Yah, I can see the purpouse of determining the truth value of statements, but the examples that the book gives seem much to unrealistic. Wouldn't it be better to use more realistic exampless? In hind-sight, I don't know why I decided to make this post, since any questions I have about my logic text book should be addressed to the publisher, not here on the forums lol. So sorry for wasting your times guys....

The examples are often chosen to be bizarre intentionally so that you are forced to focus on the relevant material: the underlying LOGIC of the sentence at hand. That the logic should apply equally well to sensible situations should be obvious, but by masking out the possibility that you are using intuition, the instructor can have some guarantee that you have actually learned the material covered in the course.

[TLD]

I'm in a logic class in college, and I was wondering if there was a purpouse to determining the truth value of the statements similiar to the following: If the fact that neither Paris is in France nor Stockhold is in Sweden implies that Tuscaloosa is in Iowa, then there are no Democrats in Washington D.C

Thanks

The "Facts" are not facts, thus no truth value. Unless logic class logic has changed immensely since I was in school.

[Rudmer]

The "Facts" are not facts, thus no truth value. Unless logic class logic has changed immensely since I was in school.

Formal Logic classes aren't chiefly concerned with determining the truth value of a statement (as the given example demonstrates), but rather in determining the validity of the argument itself -- that is, if the conclusion necessarily follows from the premises. For this purpose, the premises are assumed to be true. For instance, a very basic valid argument form is: A, B, therefore A and B -- substitute any sentence you want for A or B, and the validity of the argument still remains, even if A or B are false in actuality.

[DavidOdden]

Formal Logic classes aren't chiefly concerned with determining the truth value of a statement (as the given example demonstrates), but rather in determining the validity of the argument itself -- that is, if the conclusion necessarily follows from the premises. For this purpose, the premises are assumed to be true. For instance, a very basic valid argument form is: A, B, therefore A and B -- substitute any sentence you want for A or B, and the validity of the argument still remains, even if A or B are false in actuality.

"Validity" here refers to something quite specialized, namely the ability to reduce a string of symbols to certain other special strings of symbols by symbol substitution. For example, if you can reduce your string to something of the form "( A⊃B ) &A" then you can derive "B". But arguments are not advanced using such symbol forms, and correctly translating from natural language to some symbolic system is non-trivial, indeed there is no general way to do it, and thus the "validity" of arguments can't necessarily be checked by appear to symbolic logic. In addition, truth is really outside the reach of symbolic logic, precisely because truth cannot be detached from reality, but the point of symbolic logic is to detach epistemology from reality. So it makes no sense for formal logic to "assume that the premises are true", since what it does isn't related to truth. It simply says what the allowed sequence of deductions are (depending, of course, on what the formal system is). Edited October 21, 2009 by DavidOdden

[TheEgoist]

As a mid-level philosophy undergrad, I'm not getting the hostility towards formal logic. All throughout the classes, professors are sure to remind you the class is about forms, not about actual truth values. Being a deductive system, it isn't improper simply to look at the basic forms of the arguments themselves and whether they necessarily follow. Certainly I think it should be more concrete-based, but I think it's also a necessity that deductive logic model itself very strictly. Removing truth values from premises makes that easier.

[Rudmer]

As a mid-level philosophy undergrad, I'm not getting the hostility towards formal logic. All throughout the classes, professors are sure to remind you the class is about forms, not about actual truth values. Being a deductive system, it isn't improper simply to look at the basic forms of the arguments themselves and whether they necessarily follow. Certainly I think it should be more concrete-based, but I think it's also a necessity that deductive logic model itself very strictly. Removing truth values from premises makes that easier.

I agree. I think that the hostility may come from not understanding what a formal logic course is like -- it bears 100 times more similarity to a math course than any other philosophy course, in my opinion. When I took my university's formal logic course, I didn't actually learn anything until about halfway through (beginning with predicate logic) because I had already learned the material in a Discrete Mathematics course.

Think of it this way: in math courses, sometimes the homework problems are ridiculous and have no relation to reality -- take the classic problem of Gabriel's horn, for instance, which has infinite surface area but a finite volume. The point of the problem is to teach/illustrate mathematical principles and techniques (solids-of-revolution, convergence, etc.) as a kind of thought experiment. That's what formal logic does. Where math says "pretend that this thing could actually exist, and tell me its volume," formal logic says "pretend that these premises are true, and determine if the conclusion necessarily follows."

And I would argue that formal logic can be very useful in advancing arguments. One common counterargument tactic that I use is to derive the symbolic representation of my opponent's argument (mostly in my head), come up with a ridiculous argument of identical form, and through it show that the form it shares with my opponent's argument is invalid. In this way, I oftentimes invalidate my opponent's argument without ever having to get into drawn out debates about contested premises -- if the argument form is invalid, it doesn't matter what the particulars of the argument are, the argument is still invalid.

EDIT: I just took a look at his profile, and saw that DavidOdden teaches at Ohio State, so I now assume that he is familiar with formal logic courses. The above was written without this knowledge.

Edited October 21, 2009 by Rudmer

[DavidOdden]

As a mid-level philosophy undergrad, I'm not getting the hostility towards formal logic.

You need to distinguish hostility from disregard. I find the value of formal logic (as it it, not as it might be) to be negligible, but I don't think it's evil. But you also have to distinguish reactions to formal logic itself, versus what people do with formal logic. One should have a hostile reaction if you encounter someone talking as though formal logic has to do with truth. If you understand the nature of truth (Metaphysics 1011b25), you will understand that systems of formal deduction do not deal with truth. Dealing with formal logic on its own terms is fine. Now, to return to the OP, I conclude that this particular course is not a pure class in formal logic, because it is using natural language "arguments", while not accepting the full truth about natural language.

Certainly I think it should be more concrete-based, but I think it's also a necessity that deductive logic model itself very strictly.

On the contrary, I think formal logic should be less concrete based and it should be strictly formal. Learning the deductive rule modus ponens and how to admit B given ( A⊃B ) & A is fine. Learning how to use the Kleene axioms is even better, albeit a bit tough for 150. The problem arises when you start making claims about "facts" and "implies", and when you start getting sloppy about the relationship between arguments advanced in natural language and any kind of symbolic system.

[aleph_0]

Well, formal logic doesn't deal with truth but with truth-preservation through deductions. So there is a use for it when you are concerned with truth. For example, it is at least useful for understanding how arguments in mathematics go, when they say "Here is a proof that ___ if and only if ____..." or "Here is a proof that if something is ___ then it is ___..." I've found that I am better equipped than most other students in my undergraduate math classes because I've had this formal logic training, and I am better at LSAT logic games. The material conditional might not be the English "if", but it is something. It's just a set theoretic relation of inclusion, for truth of propositions.