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