Logic, Reasoning, and Persuasion

deductive argument

• intended to provide logically conclusive support

  • logical structure that guarantees the truth of the conclusion

• if premises are true, conclusion must be true

  • if true, then said to be “truth preserving”

  • premises are intended to guarantee the conclusion

• ABSOLUTE —> conclusion is either true or not

• 
  

valid argument

• an argument that succeeds

• about the structure/form of the argument and not if it’s actually true

• valid = correct logical structure

• can be valid even if the premises are false

invalid argument

• an argument that fails

• conclusion does not follow from the premises

• invalid = conclusion does not follow

• any argument that is invalid is automatically an induction

inductive argument

• intended to provide probable support

  • more flexible

• if premises are true, conclusion is probably or likely to be true

  • can make it worthy of acceptance

• “some”, “few”, “many”, “most”

strong argument

• an argument that succeeds in providing probable, but not conclusive, logical support

• makes the conclusion highly probable

• strong = conclusion is likely

weak argument

• provides evidence that doesn’t make the conclusion probable

• weak = conclusion likely is not based on the evidence/premises

sound argument

has 2 main conditions:

1. it is valid

2. all of its premises are true

3. must be written in a natural language

necessary conditions

• conditions a thing must have in order to be that thing

• necessary = must have

sufficient conditions

• conditions that are enough to guarantee that something exists or is a certain kind of thing

• sufficient = enough

good argument

• successfully supports the conclusion

• can be deductive or inductive

• deductive —> valid + true premises = sound

• inductive —> strong + true premises

bad argument

• reasoning does not support the conclusion

• EX: invalid deductive argument, weak inductive argument, argument with false premises

deduction

• an inference

• conclusion is supposed to follow

• any argument where an author intends to reach a conclusion that is guaranteed to be true —> absolute

induction

• not absolute

• “this is probably true”

cogent induction

• all premises are true

• invalid argument

• has strong inductive reasoning

non-cogent induction

• false premises

• invalid

• weak, has one or more false premises

informal argument

• in english or any super popular language

• makes it stuffy

• very casual

formal argument

• written in variables and symbols

• use "P”, “Q”, etc.

affirming the antecedent —> modus ponens

• deductive

• valid argument

• affirm P —> get Q

• If it rains, the ground gets wet.
  It is raining.
  Therefore, the ground is wet.

denying the consequent —> modus tollens

• valid

• deny Q —> deny P

• If it is raining, the ground is wet.
  The ground is not wet.
  Therefore, it is not raining.

hypothetical syllogism

• all 3 statements are conditional (will have 2 premises and 1 consequent)

• argument is always valid

• P —> Q —> R, therefore P —> R

• If I study, I will pass the test.
  If I pass the test, I will pass the course.
  Therefore, if I study, I will pass the course.

denying the antecedent

• not valid

• P —> Q, not P, therefore not Q

• If it rains, the ground gets wet.
  It is not raining.
  Therefore, the ground is not wet.

  
  

affirming the consequent

• invalid

• P —> Q, Q, therefore P is present

• If it rains, the ground gets wet.
  The ground is wet.
  Therefore, it rained.

disjunctive syllogism

• valid

• deny a disjunct to affirm the other (P and Q are disjuncts)

independent premise

• offers support to the conclusion without the help of other premises

• each premise can stand on its own to support the conclusion

• You should bring an umbrella.
  The weather forecast predicts rain.
  The clouds are dark.

  
  

dependent premise

• premises work together to provide support for the conclusion

• premises cannot stand on their own

• All humans are mortal.
  Socrates is human.
  Therefore, Socrates is mortal.

formal fallacies

• invalid

• do not know that it is invalid, therefore it’s formally invalid

• EX: denying the antecedent and affirming the consequent

conversion

• switches subject and predicate

• can or can’t mean the same thing

• All S is P —> universal affirmative

  • not logically equivalent

• No s is P —> universal negative

  • same when converge

• Some S is P —> particular affirmative

  • same when converge

• Some S is not P —> particular negative

  • not logically equivalent

obversion

• make affirmative —> negative

• make negative —> affirmative

• ALL 4 ARE VALID

contraposition

1. switch the subject and predicate

2. make both negative

3. All S is P —> universal affirmative

   • logically equivalent

4. No s is P —> universal negative

   • not logically equivalent

5. Some S is P —> particular affirmative

   • not logically equivalent

6. Some S is not P —> particular negative

   • logically equivalent ??? maybe

3 rules

square of opposition

boole square of opposition

• diagonals

aristotle

• 1st systematic physician

• 1st to write about logic and its rules

• first natural scientist —> created species/genus

• 1st to do psychology —> why animals and plants do things

• 1st systematic political scientist

• 1st for aesthetics

socrates

• main person

• students were Plato and Aristotle

sub - alternities