Juval said:
I see now. I established that Bruce is going paragliding, but I did not establish the condition that Bruce is in fact a person.
What I meant when I said that the standardized symbols are the syntax, or more aptly, the "rules" that govern the structure of the given semantics is as follows: As I understand, like natural languages, formal languages also have syntax. For example, there are both atomic and molecular sentences, and of course, connectives such as conjunction, disjunction and negation. I know that in logic, negation is expressed by the symbol \neg. So what I mean is that I must personally provide the non-standardized semantics for my argument (whatever they may be), and upon having defined them, I may then structure them with the standardized rules such as \wedge (and), or \neg (not).
In the elementary study of mathematical logic, examples like Bruce going paragliding, are presented as textbook exercises and to solve them, a student must specific a semantic interpretation. I have never seen any "serious" use of such verbal examples by mathematicians. So I'll say that it is true that one must personally provide the semantics in order to express verbal arguments in symbolic logic, but I don't want to give yo the impression that this is an important application of symbolic logic.
There may be people who have studied symbolic logic and attempt to apply it to problems stated in natural language. As far as I know, these are isolated cases and have not developed into any kind of intellectual discipline.
Some texts on logic use an informal syntax. The more advanced ones have rigorous syntax rules. If you are familiar with the syntax rules used by computer languages, that is an example of rigorous syntax. Natural languages don't have a rigorous syntax. Specifying the meaning of various symbols in terms of natural language isn't enough to define a rigorous syntax.
Concerning the math encoding, if I go to a philosophy forum for help with logic, it will have something such as Latex right? And also, is there any way that such language can be written out on non-math related forums?
I haven't joined any philosophy forums, so I don't know about them. I haven't tried writing equations on non-math related forums. Based on some directions for writing equations that I once saw on bautforum.com, you may be able to embed an html reference to a latex interpreter site in your message and have it display your LaTex. I don't recall the details of how to do this.
I did notice that in the example you gave me, you did not express the condition making it necessary that anybody going paragliding dies... i.e the simple action of paragliding equals death.
Correct me is I'm wrong, but I think that you could well have written a counterexample for it. I imagine you could have done so by expressing a case in which bruce does go paragliding, but then simply negating the apparently necessary outcome of death... which is by all means possible within the laws of physics. What do you think?[
First, let's make sure the goal of logic is clear. Logic is the study of reliable methods of reasoning, not the study of objective facts about the real world. To critique an argument from the "logical" point of view, we must ignore the semantics of the real world. A typical argument asserts that if some premise (which may be a complicated statement, consisting of several component statements) is true then some other statement is true. To test if an argument is valid or invalid, we may arbitrarily assigns the values "T" or "F" to any statement in he argument. If we discover an instance where the premise is 'T" and the conclusion is 'F' then the argument is invalid.
My remarks about a counterexample may be misleading since I used phrases such as "Bruce goes paragliding". That is merely an illustration of the fact that one may arbitrarily assign a "T" value to a statement in a argument while testing it's validity. So the "semantics" of evaluating an argument are no more than assigning a specific value ("T" or "F") to the statements in it.
For example, the argument:
Premise: (A implies B) and B is true
Conclusion: A is true
is invalid.
It can be presented verbally as:
Premise: (If a person has nonzero mass then that person has nonzero weight on the surface of the earth) and (The person Bruce had nonzero weight on the surface of the earth)
Conclusion: The person Bruce has nonzero mass
To show it is invalid, one may specify that case where "The person Bruce has nonzero mass" is "F". The real world semantics of such a specification contradict physical facts about people but it is permitted. (If the physical facts are to be taken into account, they would have to be added as premises to the argument.)
(Edit: In the above symbolism, I should have used quantifiers, and made something like
Premises: (For each x, (P(x) and M(x)) implies W(x)) and W(b)
Conclusion M(b)
but I hope you get the idea anyway.)
It's relatively pointless to appeal to symbolic logic in debates about real world issues such as politics or economics. A complete statement of the premises needed for an argument with a significant conclusion would be too vast. Although commentators enjoy criticizing each others "logic", it is a trivial game to play. No commentator can write a readable essay and state all the necessary premises. Most criticisms of "logic" in political debates are (correctly) criticisms about unstated assumptions being made. But there is always going to be debate about what assumptions to make and nobody can write an readable essay about a complicated real world problem that lists all the necessary assumptions. That's why all commentators need a somewhat "like minded" audience.
