Logic

This is a brief list of some basic definitions used in logic. These definitions come from "An Introduction to Probability and Inductive Logic" by Ian Hacking.

-Premises and conclusions are Propositions, statements that can either be true or false. AKA T/F statements.

-A logical argument is defined as "a point or series of reasons presented to support a proposition which is the conclusion of the argument."

-A Fallacy is an error in reasoning that is so common that logicians have noted it. An example is 'Affirming the Consequent'.
If A, then B
B
So:
A.
This is a very common fallacy in arguments where the consequent [B] is a premise and the arguer mistakenly assumes that it proves the andecedent [A]. To put it simply, only A would prove B, B can be proved through other means. An example is if A meant 'Jon wants a job' and B meant 'Will get his hair cut'.
If Jon wants a job, then he will get his hair cut
He will get his haircut
So Jon wants a job.
the reason this is false is that it could also be that Jon is going on a hot date that likes guys with nice orderly hair. so that means that it is incorrect to assume the andecedent based off the consequent.

-There are 2 ways to criticize an argument:
1) Challenge the premise - show that at least one of the premises are false
2) challenge the reasoning - show that the premises are not a good reason for the conclusion

-Validity has to do with the logical connections between the premises and the conclusion, it is not a statement about the truth value of them. A valid argument could have false premises and a true conclusion. Likewise, an invalid argument could have true premises and a true conclusion. A general idea is that the conclusion has to follow from the premises in order for the argument to be valid.
ex: If A, then C
A
So:
C
That is an example of a valid argument. What A and C are don't have to be true, it just has to follow that if you have A in a conditional statement then you have to have C.

-A Sound argument is an argument where all the premises are true and the argument is valid. Likewise, an unsound argument either has a false premise and/or the argument is invalid.

-A rough definition of inductive logic is "Inductive logic analyzes risky arguments using probablity ideas."

-There are deductive probabilities though: Using a 6 sided die
The probability of rolling any side is equal
There are 6 possibilities
So
Rolling a 4 is 1/6 probability.
That is a valid and deductive argument using probability.

These are just some rough definitions and ideas so that when you are analyzing/criticizing an argument you can use the logically correct definitions [such as validity and soundness].