Main Topics Notes
2. Two Kinds of Reasoning - arguments: premise (a reason for accepting conclusion) + conclusion
(M&P) - same statement can be premise/ conclusion, depends on function in argument
- unstated premises/ conclusions are just too obvious to be stated
deductive demonstrations - premises demonstrate conclusion, proof
- valid argument: when, if premises are true, so has to be the conclusion!
- sound argument: valid, + premises are true
inductive supporting - premises support conclusion, evidences
- strong/ weak: how much premises raise probability of conclusion being true
- unstated premises can make argument deductive or inductive, depends on being
universal ('always', 'never') or not → see content and context
- balance of considerations reasoning: weighting for & against (compares w/
alternative explanations); o en a mix of deduc. + induc.
IBE - inference to the best explanation: concludes true because it is the best supposition;
abduction; a type of inductive reasoning
what is NOT an argument - pictures, movies, gestures, threats, bribes, music (cannot be thought as true or false,
they only cause me to have an opinion, NOT a premise)
- 'if…. then….' sentences (not premise + conclusion)
- lists of facts: not offered as reasons for a conclusion
- 'A because B'(B is cause); only an argument if B is evidence/ reason
Aristotle's rhetorics - ethos: persuasion by personal attributes (reputation…)
- pathos: persuasion by emotional appeal
- logos: persuasion by information and arguments (usually least appealing)
- persuasiveness of an argument is subjective (psychological, not logical)
understanding an argument - find conclusion → find premises → look for reasons for premises → number &diagram
evaluating an argument - logic: is it deductively valid or inductively strong?
- truth: are premises true?
9. Deductive Arguments I:
categorical logic (M&P) = based on relations of inclusion or exclusion of classes, given categorical claims
categorical claims - A: all (S) are (P) → affirmative
- E: no (S) are (P) → negative
- I: some (S) are (P) → affirmative
- O: some (S) are not (P) → negative
- S: subject term; P: predicative term (only nouns are terms, indicate a class)
Venn diagram - all shaded areas = empty; X means 1+ subjects (some); blank means no info
translation to standard form - in the present tense, into equivalent claims = mean same thing
- 'only' introduces the predicate of an A-claim
- 'the only' introduces the subject of an A-claim
- 'whenever'/ 'wherever' usually introduces the subject of an A-claim about time/places
- claims w/ 1 individual is an A- or E-claim ('all people identical to Aristotle')
- mass nouns are treated as 'examples of' (boiled okra are → all examples of b.o.)
square of opposition - A- and E-claims are contraries (not both true)
- I- and O-claims are subcontraries (not both false)
- A- and O-claims, & E- and I-claims are contradictory (never both true together)
- following existential assumption (subject and predicate classes are not empty!)
- possible to make inferences of the other claims, given one of them, across the square
categorical syllogism = two-premise deductive argument; claims are standard form; 3 terms, each 2x
- major term (P): P of conclusion
- minor term (S): S of conclusion
- middle term (M): in both premise, but not in conclusion
All As are Bs. All Bs are Cs. → All As is Cs
testing validity: Venn - 3 classes fill in for 2 premises and check if it resembles conclusion
, - always color areas before placing Xs
- place X on line separating classes if still unclear
- existential assumption: for A/E premises + I/O conclusions, it's still valid when
putting an X in the remaining only uncolored area of that circle
- pay attention to unstated premises!
- TIP!: write down abbreviation letters for each premise
1. Science as knowledge - empiricists and logical positivism: based on experience, logic relation w/ theories
derived from the facts of - 1600s Galileo's Tower of Pisa: observable facts started being taken seriously
experience (Chalmers) - misconceptions:
a. Clear, unprejudiced observation
b. Facts are prior to theory
c. Facts are firm and reliable foundation for knowledge
- visual experiences not solely determined by object: learn to be competent observer
in science, inner state, prior knowledge, expectations
- knowledge is derived from factual statements about observation
a. Statements of facts are not determined in straightforward way by stimuli
b+c. Observation statements presuppose knowledge, an elaborate perpetual scheme
to exploit the world, a prerequisite to formulate them
- even though knowledge dependent, statements can still be established by
observations (by logic)
- fallibility of observation statements: subject to correction (improved knowledge and
technology); scientific knowledge and facts in which it is based on are interdependent
2. Observation as practical - active and public: range of things done to check authenticity of what is being
intervention (Chalmers) perceived, and can be checked by anyone skilled enough; the exact challenge in
science: making arrangements to minimize observer's expectations… for a valid obs.
- objective but fallible: with advances in knowledge and technology, despite being
objective (publicly tested by straightforward procedures)
4. Deriving theories from - even if 'science derives logically from the facts', not temporarily, still not true:
the facts: induction - logical validity (deduction) cannot establish the truth alone, but is truth preserving
(Chalmers) given premises are true for sure
- scientific laws cannot be derived from the facts logically (they are generalizations,
goes beyond the premises): they are inductions only
- principles of induction: a legitimate inductive argument has:
a. Sufficiently large N of observations
b. Observations are repeated under variety of conditions
c. Derived law does not conflict with any accepted observation statement
problems with inductivism - 'large' is arbitrary; what counts as significant variation in conditions? (prior
knowledge of the situation → cannot be derived by facts without prior knowledge
already); there is almost always exceptions…
- how can exact laws (mathematically inducted) be justified by inexact evidence
(margin of error)??
- inductive inferences are not logical, and neither can be justified by experience
(would be an inductive reasoning itself, even if changing it to a probability statement)
- there will always be an infinite number of possible hypothesis for a finite number of
observations, making the probability of one of them being true equal to zero
appeal of inductivism - facts from observation → (induction) → laws & theories → (deduction) → predictions,
explanations
- 1. Laws and theories + 2. Initial conditions → predictions, explanations (deduction)
- induction seems to formally capture objectivity, reliability and usefulness
- BUT: need to be practically constructed, not straightforwardly given, dependent on
presuposed knowledge, and subject to improvement and replacement!
2. Two Kinds of Reasoning - arguments: premise (a reason for accepting conclusion) + conclusion
(M&P) - same statement can be premise/ conclusion, depends on function in argument
- unstated premises/ conclusions are just too obvious to be stated
deductive demonstrations - premises demonstrate conclusion, proof
- valid argument: when, if premises are true, so has to be the conclusion!
- sound argument: valid, + premises are true
inductive supporting - premises support conclusion, evidences
- strong/ weak: how much premises raise probability of conclusion being true
- unstated premises can make argument deductive or inductive, depends on being
universal ('always', 'never') or not → see content and context
- balance of considerations reasoning: weighting for & against (compares w/
alternative explanations); o en a mix of deduc. + induc.
IBE - inference to the best explanation: concludes true because it is the best supposition;
abduction; a type of inductive reasoning
what is NOT an argument - pictures, movies, gestures, threats, bribes, music (cannot be thought as true or false,
they only cause me to have an opinion, NOT a premise)
- 'if…. then….' sentences (not premise + conclusion)
- lists of facts: not offered as reasons for a conclusion
- 'A because B'(B is cause); only an argument if B is evidence/ reason
Aristotle's rhetorics - ethos: persuasion by personal attributes (reputation…)
- pathos: persuasion by emotional appeal
- logos: persuasion by information and arguments (usually least appealing)
- persuasiveness of an argument is subjective (psychological, not logical)
understanding an argument - find conclusion → find premises → look for reasons for premises → number &diagram
evaluating an argument - logic: is it deductively valid or inductively strong?
- truth: are premises true?
9. Deductive Arguments I:
categorical logic (M&P) = based on relations of inclusion or exclusion of classes, given categorical claims
categorical claims - A: all (S) are (P) → affirmative
- E: no (S) are (P) → negative
- I: some (S) are (P) → affirmative
- O: some (S) are not (P) → negative
- S: subject term; P: predicative term (only nouns are terms, indicate a class)
Venn diagram - all shaded areas = empty; X means 1+ subjects (some); blank means no info
translation to standard form - in the present tense, into equivalent claims = mean same thing
- 'only' introduces the predicate of an A-claim
- 'the only' introduces the subject of an A-claim
- 'whenever'/ 'wherever' usually introduces the subject of an A-claim about time/places
- claims w/ 1 individual is an A- or E-claim ('all people identical to Aristotle')
- mass nouns are treated as 'examples of' (boiled okra are → all examples of b.o.)
square of opposition - A- and E-claims are contraries (not both true)
- I- and O-claims are subcontraries (not both false)
- A- and O-claims, & E- and I-claims are contradictory (never both true together)
- following existential assumption (subject and predicate classes are not empty!)
- possible to make inferences of the other claims, given one of them, across the square
categorical syllogism = two-premise deductive argument; claims are standard form; 3 terms, each 2x
- major term (P): P of conclusion
- minor term (S): S of conclusion
- middle term (M): in both premise, but not in conclusion
All As are Bs. All Bs are Cs. → All As is Cs
testing validity: Venn - 3 classes fill in for 2 premises and check if it resembles conclusion
, - always color areas before placing Xs
- place X on line separating classes if still unclear
- existential assumption: for A/E premises + I/O conclusions, it's still valid when
putting an X in the remaining only uncolored area of that circle
- pay attention to unstated premises!
- TIP!: write down abbreviation letters for each premise
1. Science as knowledge - empiricists and logical positivism: based on experience, logic relation w/ theories
derived from the facts of - 1600s Galileo's Tower of Pisa: observable facts started being taken seriously
experience (Chalmers) - misconceptions:
a. Clear, unprejudiced observation
b. Facts are prior to theory
c. Facts are firm and reliable foundation for knowledge
- visual experiences not solely determined by object: learn to be competent observer
in science, inner state, prior knowledge, expectations
- knowledge is derived from factual statements about observation
a. Statements of facts are not determined in straightforward way by stimuli
b+c. Observation statements presuppose knowledge, an elaborate perpetual scheme
to exploit the world, a prerequisite to formulate them
- even though knowledge dependent, statements can still be established by
observations (by logic)
- fallibility of observation statements: subject to correction (improved knowledge and
technology); scientific knowledge and facts in which it is based on are interdependent
2. Observation as practical - active and public: range of things done to check authenticity of what is being
intervention (Chalmers) perceived, and can be checked by anyone skilled enough; the exact challenge in
science: making arrangements to minimize observer's expectations… for a valid obs.
- objective but fallible: with advances in knowledge and technology, despite being
objective (publicly tested by straightforward procedures)
4. Deriving theories from - even if 'science derives logically from the facts', not temporarily, still not true:
the facts: induction - logical validity (deduction) cannot establish the truth alone, but is truth preserving
(Chalmers) given premises are true for sure
- scientific laws cannot be derived from the facts logically (they are generalizations,
goes beyond the premises): they are inductions only
- principles of induction: a legitimate inductive argument has:
a. Sufficiently large N of observations
b. Observations are repeated under variety of conditions
c. Derived law does not conflict with any accepted observation statement
problems with inductivism - 'large' is arbitrary; what counts as significant variation in conditions? (prior
knowledge of the situation → cannot be derived by facts without prior knowledge
already); there is almost always exceptions…
- how can exact laws (mathematically inducted) be justified by inexact evidence
(margin of error)??
- inductive inferences are not logical, and neither can be justified by experience
(would be an inductive reasoning itself, even if changing it to a probability statement)
- there will always be an infinite number of possible hypothesis for a finite number of
observations, making the probability of one of them being true equal to zero
appeal of inductivism - facts from observation → (induction) → laws & theories → (deduction) → predictions,
explanations
- 1. Laws and theories + 2. Initial conditions → predictions, explanations (deduction)
- induction seems to formally capture objectivity, reliability and usefulness
- BUT: need to be practically constructed, not straightforwardly given, dependent on
presuposed knowledge, and subject to improvement and replacement!
