introduction to logic

logic

• logic: the systematic study of valid rules of inference, i.e. the relations that lead to the acceptance of one proposition (the conclusion) on the basis of a set of other propositions (premises)
  • uses the premises/conclusion format to come to new knowledge
  • can be used to make/evaluate various arguments
• argument: a discourse in which certain things being said (the premises) imply something else (the conclusion)
  • arguments in the realm of logic are not fights or squabbles, they are necessary and good
• validity: if the conclusion of an argument is logically connected to (or entailed by) the premises; it has the right logical form
  • when the conclusion logically follows from the premises, the argument is said to be VALID.  When it does not, the argument is said to be INVALID.
• soundness: if the conclusion of an argument is logically connected to the premises (right logical form) AND all of the premises are true statements

disagreeing with an argument

• to disagree with an argument, one must either:
• disagree with (one or more of) the premises or
• prove the argument does not have a valid form
  • it is not OK merely to disagree with a conclusion.
  • validity has nothing to with how you feel about the argument

logic in real life

• rarely are arguments found ready-made in logical form
• we must locate arguments, isolate them, reconstruct them in logical form, and analyze them
• this requires close, careful reading and attention to what others are saying—critical thinking

logical indicators

• finding arguments is made easier by locating logical indicators, words that draw attention to premises and conclusions
  • some PREMISE indicators: because, as, for the reason that, for, given that, since, assuming that, etc.
  • some CONCLUSION indicators: therefore, thus, ergo, follows that, so, consequently, hence, that is why, etc.
• arguments usually aren’t found ready-made in logical form with premises and conclusions identified
  •  usually found  in paragraph form/in the comment sections online where all happiness/reason go to die
• we must locate arguments, reconstruct them in logical form, and analyze them to see if they actually are valid, or just sound nice while actually being illogical/invalid
• informal fallacy: an argument which appears to be valid and convincing but is actually not