HPS 1653 / PHIL 1610 Introduction to the Philosophy of Science - Evidence ... · 2014-09-15 · HPS 1653 / PHIL 1610 Introduction to the Philosophy of Science Evidence, ... E.g. ‘Fa

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?


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.


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.


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.’


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.


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 (?)


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.


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”


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?)


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!


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, . . . )


Counter-induction

Swan 1 is whiteSwan 2 is white

...Swan N is white

Swan N + 1 won’t be white


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).


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)


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.


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.)


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!


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


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.


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.


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).


Why this matters


Documents

HPS 1653 / PHIL 1610 Introduction to the Philosophy of Science - Evidence ... · 2014-09-15 · HPS 1653 / PHIL 1610 Introduction to the Philosophy of Science Evidence, ... E.g. ‘Fa