Intro to Logic

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For those who do not know, it is a philosophical, yet highly structured class. I like to think of it as mathematical (which is why I put it here instead of the philosophy section), because the rules used (especially in symbolic logic) are so set in stone. Most of the kids in my class are having a really hard time with it. I realize that most people just don't think this way, but to me, it is so natural. I don't even have to think.

For me, the hardest part of the class is remembering the names of the rules and matching them wit the correct form. For example, I know:
p v q
p-->r
q-->s
-------
r v s

is a rule of implication. it makes perfect logical sense to me, and I know when this is to be used in proofs. My problem is remembering the names of them. This one is Constructive Dilemma (I had to look up the name just now). There are others. I am frustrated because next week, we have our final, and we do not get to use our little crib sheets with the names of these on it. Even though I know exactly what I am doing, I may still end up with half points off on this section because of this. It is very frustrating.

I have the same problem with his true and false problems. He words them strangely, and I don't understand the question. I had three points knocked off of my test last week because I had no clue what he was talking about.

Does anyone else have a problem with memorizing things? I have the same problem with Calc Two and the formulas. I know the names, and I know the forms, but putting them together is hit or miss. It is very annoying.

I can relate. I've also taken logic and calc, and I share your strengths and weaknesses. I use flashcards to help with the memorization--connecting the rules and formulas with their names. Like it does for you, the logical/mathematical part comes pretty naturally for me.

You're right. Logic is a branch of mathematics.


I don't really have a good suggestion here, but you have my sympathy. I can't see why you would need to memorize arbitrarily assigned names for these things.


I also found Calc II really annoying. Memorizing the crap out of something is no way to learn math, but that's how they do Calc II for some reason. That class was probably my least favorite math class of all time.

Point of clarification.

There is a difference between Logic studied in a philosophy course and Logic studied in a mathematics class.

Mathematical Logic consists, but not limited to, four main sub-branches known as Set Theory, Model Theory, Recursion Theory, and Proof Theory.
Others may include Decidability (differ from Decision Theory), Computability, Category Theory, and Topos Theory.

The Logic covered in a Philosophy course is usually Propositional or Predicate Calculus, depending on the level of depth the course explores. Other courses include Modal Logic, Deontic Logic, Quantum Logic, Second-Order Predication Calculus, or multi-valued Logic.

Propositional Logic and Predicate Calculus, also known as Symbolic Logic, are mathematical in appearance and in how both involve symbols representing concepts or objects.

Since the late 1890s, Logic has become more foundational to mathematics, principally, Set Theory.

The primary difference between the logic studied in a philosophy course and the logic studied in mathematics is Philosophy courses Logic focus on truth-value: propositions having truth-value, how to determine truth-value, finding truth-value of propositions, proving consequences of assumed truth of propositions, etc..

Mathematical Logic courses' concerns are about constructing the mathematical universe beginning with ZF Axioms (and sometimes C)* and demonstrating the consistency of mathematics.
When taking a course in Mathematical Logic, presumed to know Predicate Calculus. In fact, rudimentary Predicate Calculus is applied in advanced mathematics courses such as real analysis or topology.


*ZF = Zemlo-Frenkle, two mathematicians who formalized the fundamental axioms that all mathematics may be provably reduced to.
The 'C' in ZFC refers to the disputed Axiom of Choice.

@sheldon: Exactly. This course is the very basics. I have also taken Descrete math, where we got into some mathematical logic, so when we did truth tables and symbolic logic (and the types of valid arguments) I already knew most of it. The symbolic language is very slightly different though.

I will say that even in the philosophical class, the logic is used for the sake of argument evaluation, it is very mathematical in how it is done.

I want to find out if there is an advanced logic class. This one is too easy. I only have three days left. My lowest test was a 93 because I did not understand how he asked some of his questions. If not for that, I would have had a high A at least.

I took Logic 106, which goes over this stuff. I loved it. Unfortunately at the time I was working on two contracts doing programming and trying to get through community college.

would it be?

r-->t
s-->u

t v u...? So on and so forth?

t-->v
u-->w

v v w

v-->x
w-->z



x v z Can you go this far?

I took a logic class, and I enjoyed learning about contradictions and such. I feel it helps me spot contradictions in social situation, and hence allows me to assess if something is not right about the people I am interacting with.

Show by truth table that (p v q) ^ (p -> r) ^ (q -> s) -> (r v s) is a tautology.

ruveyn

I would, but I already know it is true because it is a classic form.

Have you tried proving it by Natural Deduction or in Gentzen's formalism?

How do you know its a classic form. That has to be proven.

ruveyn

I have proven it using a truth table in class. It is called "Constructive Dilemma." It is a classic form that is used when proving something valid or not. It is a famous form because so many logicians (and mathematicians) use it. It is just as valid as Modes Ponens (p-->q, p therefore q) or Modes Tollens (~p-->~q, ~p therefore ~p). Earlier in logic class, we did go and prove it. It was not mathematically based though (you used the '^' symbol which is not part of the symbolic language I was using, but I think you meant 'and' which would give the same results).

I *could* do a truth table for it. To me, doing truth tables is like eating candy. I love doing them, but setting one up so I could do it on the forum and have it look pretty (I am a perfectionist too) would take some work. I am lazy too.

The way we know the "classic forms" are kosher is because their truth tables are all tautologies.

A truth table that gives all "true" values cannot have an instance where the premises are true and the conclusion false.

ruveyn

Yep. I know. That's why I didn't want to do a truth table. I already knew (and had seen the truth tables) that they were tautologies. I am picky with format, and I think if I did a truth table on the net, I would be bugged with the spacing. It was bad enough to do it in my notes on the computer.