Upload
dangdung
View
216
Download
0
Embed Size (px)
Citation preview
HPS 1653 / PHIL 1610Introduction to the Philosophy of Science
Evidence, confirmation & inductivism
Adam [email protected]
Wednesday 10 September 2014
HPS 1653 / PHIL 1610 Lecture 4
Induction is everywhere
I The nutritional value of bread
I The quick way to the lobby
I A key postulate of Einstein’s special theory of relativity: ‘The speedof light is independent of the speed of the source.’
I Why perform randomized controlled trials?
HPS 1653 / PHIL 1610 Lecture 4
Inductivism vs. Hypothetico-Deductivism
Inductivism: Scientific knowledge is derived from the observable facts byinduction (and deduction).
Hypothetico-deductivism: Scientific theories are not derived fromanything; they are hypothesized. Once hypothesized, they are thenconfirmed or disconfirmed by the observable facts.
I Reichenbach’s distinction between the context of discovery and thecontext of justification.
I For both accounts above, inductive confirmation plays afundamental role.
HPS 1653 / PHIL 1610 Lecture 4
Hempel’s account
Hempel’s account of “inductive confirmation” aimed to do justice to twomain ideas:
1. Nicod’s Criterion. Any positive instance of a universalgeneralization confirms it.
E.g. ‘Fa & Ga’ confirms ‘All F s are G s’.
2. Equivalence. If two hypotheses are logically equivalent, then thesame evidence confirms/disconfirms them equally.
This is to avoid confirmation being a matter of how a hypothesis ispresented. We want confirmation to rely only on the content of thehypothesis and evidence.
HPS 1653 / PHIL 1610 Lecture 4
Hempel’s account
Hempel observed that induction works in “the opposite direction” todeduction. . .
A central idea is the development of a hypothesis.
Let I be the class of individuals mentioned by the evidence statement E .
I E.g. E = ‘a and b are white swans’ ⇒ I = {a, b}.
Then the development of any hypothesis H for I , devI (H), is just Hrestricted to I .
I E.g. H = ‘All swans are white’ ⇒ devI (H) = ‘If a is a swan, then ais white; and if b is a swan, then b is white.’
I H = ‘There is a white swan’ ⇒ devI (H) = ‘a is a white swan or bis a white swan.’
HPS 1653 / PHIL 1610 Lecture 4
Hempel’s account
I E directly confirms H iff E deductively entails devI (H).
I E confirms H iff E directly confirms every member of some set ofsentences K such that K deductively entails H.
I E.g. ‘a and b are white swans’ directly confirms ‘All swans are white.’
I ‘a and b are white swans’ directly confirms ‘There is a white swan.’
I ‘a and b are white swans’ confirms ‘All swans in the US are white.’
I Inductive confirmation is defined here in terms of deductiverelationships between sentences. So Hempel makes induction asformal as deduction.
HPS 1653 / PHIL 1610 Lecture 4
Problems that Hempel’s account does solve
I Scientific hypotheses that aren’t universal generalizations
I Every sentence inductively confirms every other!?I Take any sentence S ,
e.g. ‘We are ruled by the flying spaghetti monster.’
I Take some humdrum evidence E , e.g. ‘This swan is white.’
I S&E deductively entails E .
I So, E inductively confirms S&E (?)
I But S&E deductively entails S .
I So, E inductively confirms S (?)
HPS 1653 / PHIL 1610 Lecture 4
The problems of induction
The justificatory problem: Why are inductively strong inferences betterthan inductively weak inferences?
The definitional problem: What characterizes inductively stronginferences?
I Hempel’s account is an attempt to solve the definitional problemonly!
I The justificatory problem is commonly taken to be Hume’s(1738)—but see Goodman’s (1955) take on the matter.
HPS 1653 / PHIL 1610 Lecture 4
Three challenges
The justificatory problem (Hume’s problem)
I Hume’s dilemma
The definitional problem (Hempel’s problem)
I The ravens “paradox”
I Goodman’s “new riddle”
HPS 1653 / PHIL 1610 Lecture 4
Hume’s dilemma
Found first in A Treatise of Human Nature (1738):
I Any argument to justify induction is going to use either deductiveinference or inductive inference (or both).
I Deductive inference is not ampliative, but the conclusion thatinduction is justified extends our available knowledge. So deductionon its own will not do it.
I Using inductive inference to justify induction assumes as justified thevery inferences that we are seeking to justify. So using induction iscircular.
I So, any justification for induction will be either inadequate orcircular, also inadequate.
I (Does it help if we add abductive inference to the mix?)
HPS 1653 / PHIL 1610 Lecture 4
Deduction not on its own
Object 1, which is F , is GObject 1, which is F , is G
...Object N, which is F , is G
Nature is uniform (e.g. the future is like the past)All F s are G
I But how do we justify the claim that nature is uniform?
I Hume’s dilemma again!
HPS 1653 / PHIL 1610 Lecture 4
Justifying induction by induction
In case 1, inductive inference workedIn case 2, inductive inference worked
...In case N, inductive inference worked
In case N + 1, inductive inference will work
I N.B. the associated universal generalization is too strong!
I Induction doesn’t have an unbroken record (black swans, albinoravens, . . . )
HPS 1653 / PHIL 1610 Lecture 4
Counter-induction
Swan 1 is whiteSwan 2 is white
...Swan N is white
Swan N + 1 won’t be white
HPS 1653 / PHIL 1610 Lecture 4
Justifying counter-induction by counter-induction
In case 1, inductive inference workedIn case 2, inductive inference worked
...In case N, inductive inference worked
In case N + 1, inductive inference won’t work
I See also Earman & Salmon’s (1992) crystal gazer (pp. 58-9).
HPS 1653 / PHIL 1610 Lecture 4
Responses to Hume’s dilemma
I “Dissolution”, e.g. Goodman (1955): the justificatory problemcollapses into the definitional problem.
I Reichenbach’s “pragmatic” justification
I Give up! ⇒ Falsificationism (next week)
I Probabilism (later weeks)
HPS 1653 / PHIL 1610 Lecture 4
The ravens “paradox”
I According to Hempel’s criterion, ‘This piece of paper is white’directly confirms ‘All non-black things are non-ravens’.
I But ‘All non-black things are non-ravens’ is logically equivalent to‘All ravens are black’.
I So ‘This piece of paper is white’ also confirms ‘All ravens are black’.
I Indoor ornithology!
I N.B. the implication is that Hempel’s characterization of stronginductive inference is wrong, not that any such characterization isimpossible.
HPS 1653 / PHIL 1610 Lecture 4
Responses to the ravens “paradox”
I Bite the bullet (Hempel).
I Relativity to order of information? (Given our hypothesis, non-blackX s vs. non-raven X s.)
I Confirmation as a three-place relation (between hypothesis, evidenceand background knowledge)?
I Recourse to degrees of confirmation? (N.B. ‘This piece of paper iswhite’ must still confirm ‘All ravens are black’ to the same degree asit confirms ‘All non-black things are non-ravens’.)
I Restriction to “projectible” predicates? (I’ll come back to this.)
HPS 1653 / PHIL 1610 Lecture 4
Goodman’s “new riddle”
I The target: Hempel’s general claim that it is possible to provide alogical (purely formal) characterization of strong inductive inference.
I Goodman was not an inductive skeptic! His aim was to show thatinduction is not (like deduction) a purely formal inference.
I Define a strange predicate ‘grue’:
I x is grue iff x is first observed before time t and green or otherwiseblue.
I Let t = December 31, 2014.
I BEWARE: grue things do not change colour!
HPS 1653 / PHIL 1610 Lecture 4
Strong inductive inferences?
O: This emerald (observed before t) is green
H: All emeralds are green
O: This emerald (observed before t) is grue
H ′: All emeralds are grue
Both inferences are of the form:
Ea &Ga
All E s are G
HPS 1653 / PHIL 1610 Lecture 4
Strong inductive inferences?
I Now assume that there are some emeralds that won’t be observeduntil after t.
I Take one such emerald, b.
I What colour ought we expect b to be?I According to the first strong inductive inference:
H: All emeralds are green.I So we ought to expect b to be green.
I According to the second strong inductive inference:H ′: All emeralds are grue.
I So we ought to expect b to be grue.I But b won’t be observed until after t, so (by the definition of ‘grue’):I We ought to expect b to be blue.
HPS 1653 / PHIL 1610 Lecture 4
Goodman’s “new riddle”
I The same evidence (a green emerald observed before t) equallysupports mutually incompatible hypotheses (assuming there areemeralds that won’t be observed until after t).
I The form of both inductive inferences is the same.
I One inference is better than the other (H > H ′).
I So inductive strength cannot be a matter of form alone: there’ssomething special about the content of ‘green’ that ‘grue’ doesn’thave.
I ‘Green’ is a projectible predicate.
HPS 1653 / PHIL 1610 Lecture 4
Why is ‘green’ projectible?
I ‘Green’ is projectible because it is entrenched in our historiclinguistic usage (Goodman).
I So which inductions are justified is relative to a linguistic heritage?
I ‘Green’ is projectible (or at least: more projectible than ‘grue’)because it is simple (or at least: simpler).
I Simpler how?I Define ‘bleen’ := blue and observed before t or otherwise green.
I Then ‘green’ = grue and observed before t or otherwise bleen,and ‘blue’ = bleen and observed before t or otherwise grue.
I ‘Green’ is projectible (or at least: more projectible than ‘grue’)because it picks out a natural kind (or at least: a more natural kindthan ‘grue’ picks out).
HPS 1653 / PHIL 1610 Lecture 4