Falsification

OHear: Chap. 3

Popperian Philosophy of Science

Inductive Comfirmation a Myth

as Hume's difficulty

that induction depends for its warrant on a uniformity of nature principle: that future (or unobserved) cases will be similar to past (or observed) cases.
that is itself unwarranted.

and Goodman's new riddle

if some uniformity of nature principle were warranted
we still would lack warrant for knowing how it's uniform

of all the many properties in respect of which the future (or observed) and past (or unobserved) cases might be similar
which similarities are projectable?

and sampling difficulties

laws cover a virtual infinity of cases
next to which the actually observed cases (no matter how numerous) virtually nothing
hopeless unless somehow the sample is representative
and this requires

a uniformity of nature principle (runs us into Hume's problem)
and a specific one at that (so Goodman's riddle perplexes us)

ray of hope:

while we can't observe enough positive instances to confirm a law:

Popperian Vision: a way around the difficulties about inductive confirmation

Scientific Method

Scientists make bold conjectures

predictively bold & hence highly falsifiable

due to their generality: the more it predicts the more falsifiable
and precision: the more precisely it predicts the more falsifiable

Science advances by kind of epistemological selection (compare: natural selection)

bold theoretical conjectures get made
and refuted
to be replaced by other bold conjectures

which can survive these refutations
which will succumb to other refutations\

onward & upward

toward ever truer
or better corroborated theories and laws

worries re:

degrees of truth or verisimilitude: truth seems an all or nothing matter (like pregnancy)
whether corroboration isn't just confirmation in diguise

Demarcation Problem

Prescient concern: the problem waxes

fueled by the pretenses of various narratives to the honorific name science

from Marxism and psychoanalysis (in Popper's heyday)
to Creation Science and Postmodern social analysis (nowadays)

together with increasing uncertainty and confusion about the objectivity of scientific knowledge

internal difficulties:

the problems about confirmation
lackluster progress in the social sciences

external difficulties: critiques of scientific objectivity

from the left: accusations of scientism

advocates of multiculturalism who see science as an imperialistic hegemonic imposition of a white European worldview.
feminists who see science as a paternalistic imposition of a male worldview on females

from the right: partisans of various "narratives" such as the Genesis creation story

claiming that the Genesis creation story is a competing theory on a par with evolutionary theory
claiming that belief in evolution is just a much a matter of faith as belief in creation

Popper's approach

scientific theories (or scienfically held theories) expose themselves to refutation

by making bold testable predictions: e.g., Einstein's
and testing them
facing the music -- admitting defeat -- if they fail the test.

unscientific (or unscientifically held) theories marked by

vagary and dubiour testability of their predictions
exclusive concern for piling up confirming instances
ignoring or explaining away counter-evidence

Corroboration & Verisimilitude

What's the problem?

The evolutionary comparison

Evolution -- common misconceptions to the contrary notwithstanding -- is not inherently progressive
humans aren't at the top of the evolutionary tree (as we like to think)
we're at the end of one branch
along with every other living species (each the end of it's own branch)

What makes the evolution of scientific theories epistemological? Not just historical.

a growth of knowledge.
not just a change of stories.
if we're not going to say that the successor theories are

more highly confirmed or
more probably true than other (as yet unrefuted) competitors

grue vs. green
Ptolemy v. Copernicus v. Kepler

Corroboration =±testability * success

testability or empircal content: how much it rules out: being more likely a priori to be false

more precise, more testable
more comprehensive, more testable

severe test

predictions highly improbable in the light of existing knowledge
e.g., Einstein's theory that light should bend due to the gravitational influence of the Sun

a theory is highly corroborated relative to competing theories to the extent that it

has survived severe testing better than the competing theories
due to competing theories

not having been so severely tested (perhaps due to being less testable)
or having failed such tests.

Worry about Corroboration

Stated as a dillema

Either corroboration = inductive confirmation in disguise

we're pretty much back where we came in: deja vu all over again
with perhaps a more plausible description of how we actually do go about it

stressing conjectures & refutations
in the context of competing theories

but no help with the problem of how highly corroborated theories

are more warranted or likely to be true
and more justifiably projectable

corroboration measures past projective success
Buty why should we regard that as increasing the likeliness of future projective success

pace Hume
pace Goodman

Note how the notion of severe testing seems to smuggle in induction

a severe test is one which predicts something highly improbable in the light of existing knowledge
how can we know what's improbable in the light of existing knowledge except inductively

by projecting future probabilities
on the basis of past similarities

Or if corrorboration is not inductive confirmation in disguise . . . just a matter of past success

this simply gives up on the problem of how highly corroborated theories are

more warranted or likely to be true
and more justifiably projectable

they're not: talk of truthlikeness or verisimilitude (that Popperian last resort) notwithstanding
problems about justifiability of induction don't go away

they just become the problem about "why we should be at all interested" in corroboration
if highly corroborated theories are not

more likely to be true
and more likely to be successfully projectable

A Bayesian Approach

Popper: Post Mortem

Scientific Advancement -- the growth of knowledge in science -- a basic premise
Basic difficulty

knowledge roughly characterizable (or, at least, has traditionally been characterized) as justified true belief
the past of science is seen by Popper is a progression of falsified theories

since these weren't true
these didn't constitute knowledge

today's science is viewed as a collection of as yet unfalsified (highly falsifiable) theories

which await falsification
and probably will be falsified eventually . . . if not sooner
so even in the improbable event some current theory is true (and never will be falsified)
we're still not warranted in believing it true
so it's still not knowledge

compare the so-called "dangerous induction":

except for a few not-yet-falsified theories, all scientific theories yet observed have proven to be false
therefore, probably, these not-yet-falsified theories will prove false
and ditto for all future scientific theories
so science at any time is a collection of false beliefs: which isn't knowledge
and over time a succession of false beliefs: which isn't growth of knowledge

Inductivism Reconsidered

Preliminary emphases & concessions to scepticism

emphasis: revisiting the evolutionary comparison

as evolutionary fitness is relative to circumstances or background conditions

survival depends on a relativly stable environment
and an degree of adaptaion between the environment and the organisms that live in it

so does scientific fitness -- crucially the projectibility of scientific laws -- depend on background conditions

a relatively stable environment
in relation to which the best theories are best adapted

conceding to skeptical doubts that there's no guarantee of environmental stability (in science as in evolution)

everything might change in the twinkling of an eye (pace Hume): compare cataclysmic environmental change
or (pace Goodman) similarities whose projection had served us well no longer do so given some alteration of circumstances

evolutionary examples:

some species who rely on earth's electromagnetic field to navigate & would become disoriented & die if the polarity of that field were suddenly reversed
frogs detect and snap at (or flick their tongues at) ambient black dots in their vicinity

in the laboratory, e.g., they'll eat BBs
works because these ambient black dots are almost always flies or other edible insects
would not work if their environment altered to include a significant proportion of

poisonous airborn particles (due to pollution, say)
of snapworthy size & shape

Remaining hope against these skeptical difficulties

given that there really are some projectable regularities in our environment
how can we go about discovering them?
beginning from the projections we undeniably (and in some cases unavoidably do make:

by nature including

evolutionarily built in predispositions

e.g., to identify and reidentify objects
through changes of light, place, angle of perception, etc.
enabling us to track

lions and tigers and bears,
friend, foes, foodstuffs, etc.

by natually occuring conditioning due to experience be come to expect

fire to burn
bread to nourish
water to quench or thirst if we drink it
to drown us if we breath it, etc.

by nurture including

categories built into our language
accumulated wisdom of common sense and cultural lore

and these make a hopeful starting point

because they've stood the test of time

generalizing on these bases has hitherto been conducive to survival
so "given that our environment doesn't radically change" (pace Hume & Goodman, again)
"we have good reason to accept them as a starting-point" (p.45)

besides which . . . we've no choice: it's an offer we can't refuse

we can't begin to think or even perceive without employing some categorial expectations
even some specific categorial expectations are wired in: e.g. the LM illusion

but these preliminary prescientific categorial expectations are only a starting point

regularities postulated by our sensory apparatus, language, and cultural lore often fail us

as in the LM illusion or following a mirage in the desert
as with the BBs (in the frogs case)
medeival campaign to wipe out cats (those minions of Satan)

thereby ridding themselves of supposedly bad things (which, you'd suppose, would make things better)
causing really bad things: the proliferation of plague carrying rats

failures of projectability of common-sense categories indicative of their

failure to mirror the basic underlying structures of the world

to pick out natural kinds
to mirror real objective similarities and differences
to "carve nature at the joints"

causes of failure

categories may mirror appearances

distinctions of appearance that don't signal real underlying differences
resemblances in appearance that don't signal real underlying similarities: e.g. "ornamental marble"

other factors in & features of such categorial limitations

things behaving similarly only in certain special conditions
may only work in a limited area of space & time

The challenge: how to get from

this starting point (these preliminary categorial expectations) to
"regularities at some more fundamental level of nature" which

"have a better of applying beyond our region of space & time"
and in a broader range of circumstances: compare

Gallileo's law of free fall: freely falling bodies accelerate at a fixed rate (32ft/sec/sec)

only applies on Earth
due to specific characteristics of Earth (it's mass)

vs. Newtons theory of Universal Gravitation

in sum: "to arrive at theories of a greater depth and breadth than are given in our initial predispositions," i.e.,

"to find genuine natural kinds, united by similarity of deep structure,"
"which would lead them to behave similarly in all sorts of yet unencountered situations" (p. 45)

note a global natural-epistemological predisposition -- to atomistic materialism -- in O'Hear's forumlation

predisposition: the way to more universal theories (of greater breadth) is through theories describing similarities of deep structure or microstructure (of greater depth)
natural (if not warranted) induction from scientific endeavors so far: levels of scientific generality

laws of physics: broadest application: roughly everywhere
laws of chemistry: less broadly applicable: fail under extreme conditions (centers of stars, etc.)
laws of biology: still less broadly applicable: wouldn't expect laws of earth-biology to project well to ETs.
laws of psychology: still less? Specific to societies, classes, sexes, ages?

Bayesian Methodology

What can be gleaned from the preceding reconsideration?

Popper is right in

in emphasizing severe tests

under widely varied and
as yet unencountered circumstances

and deemphasizing the piling up of confirming instances

resulting from familiar sorts of observational tests
under the usual limited range of conditions

why he's right: this conduces to broader laws

Popper is wrong in according no probative weight to preexisting conceptions

all conjectures start out equal except for

the boldness of their conjectures
or their inherent falsifiability

but they shouldn't all start out equal (n.b. the shift from theoretical to practial mode)

past success should count for something (n.b. this is to say, in effect, some have accrued confirmation?)
given that some categorial expectations are inescapable
and these have worked -- sort of -- so far

if everything changes in the twinkling of an eye, of course, then we're screwed

but a hopeful strategem (Bayesian)
is better than no strategem

Bayes's Theorem

Informal description

follows from the probability calculus, given certain assumptions
describes the probablity of theory after certain test evidence has favored it
the upshot of the theorem is that such probability is increased both

by the severity of the test evidence
and the initial probability of the hypothesis being tested

Formal description

P(h/e.k) = the Probability of the hypothesis on the evidence (provided by the test) given our background knowledge
Bayes's Theorem

P(h/e.k) = P(e/h.k) * P(h/k) / P(e/k)
the probability of the hypothesis on the evidence given our background knowledge equals

the probabilty of the evidence on the hypothesis given our background knowledge
times the probability of the hypothesis given the knowledge alone
divided by the probability of the evidence given the knowledge alone

in the case of a universal hypothesis: P(h/e.k)=1:

so the probability of the hypothesis on the evidence

will increase as a function of P(h/k): i.e. the prior probability of the hypothesis
and increase inversely as a function of P(h/e): i.e., the prior improbability or the evidence

Discussion

Summary: Implications of Bayes's Theorem

Popper was right that it's fruitless to pile up comfirmations in familiar conditions
Popper was wrong in discounting prior probabilty as a plus factor (even going to the opposite extreme)
We should select theories that have a high probability based on what we already know then test them severely.

Objection: Where do the initial probability assignments come from?

concerns P(h/k) & P(e/k):

our worries about induction apply

determining P(h/k): involves projecting a general hypothesis h from a limited data set k
determining P(e/k): involves projecting a future event e from knowledge of past events.

and there are practical difficulties besides

"To work out degrees of probability or confirmation . . . for actual scientific theories is well nigh impossible." (49)
"Those who have studied such matters have tended to restrict their efforts to simple formal languages . . . ." (49)

charge: "There will thus be an inerradicable subjectivity in calculating the posterior probability [P(h/e.k)] of a theory after the evidence is in owing to various personal estimates of prior probability.
Reply (de Finetti & Savage)

different prior probability assessments tend to converge with increasing amounts of relevant evidence
i.e., initial differences in probability estimates will come out in the wash
so use of Bayes theorem

as it firms up our initially subjective probability estimates on the face of the evidence
and will bring about intersubjective convergence of estimates

O'Hear's Conclusion: Skeptical Doubts (of Hume & Goodman) Cannot Be Refuted

yet on (hopeful & natural) assumption:

(pace Goodman) that we have some projectible categories
and (pace Hume) that it won't all change in the twinkling of an eye

Bayes's theorem

formulates an approach to inductive confirmation
that is "emminently reasonable" (50)
skeptical doubts aside

My misgiving

isn't the "skeptical doubts aside" still the expression of a hope
and again "the critic will say that he had hoped for more than hope"

looking forward to criticisms: isn't hope perilously close to faith
faith in science & evolution vs. faith in Genesis & creation on a par

Issues: Loose talk so far eliding:

methodology & metaphysics and hence fictionalism & realism

epistemological or methodological claim: the reasonableness of severe testing and of relying on theories which survive severe tests.
the metaphysical claim that what we are thus led to postulate about the world is shown to be true: Scientific realism.

alternative: fictionalism or antirealism: scientific theories are warranted as useful ways of talking about phenomena
but we are not liscensed on this account to infer the real existence of the posited mechanisms and entities

(Humean) Inessentialism and (Aristotelean) Essentialism

Humean talk of "the discovery of far-reaching regularities"
Aristotelean talk of "the discovery of natural kinds"

Essentialism vs. Inessentialism

Essentialism: Science aims to discover of natural kinds or essential natures of things which make them act in certain ways

and would have behaved similarly in different (counter-factual) circumstances
there's a fundamental difference between

accidental regularites: all humans are less than 10' tall; copper is the stuff all Lincoln pennies are made of
causal regularies: F=MA; copper conducts electricity.

Inessentialism: Science reveals groups of things with certain kinds of underlying structures which happen to act in certain (thus far) predictable ways

there's no rational basis for inferring the future from the past or the particular from the general: conterfactuals are not rationally warranted (induction is a topic for psychology not logic)
there's no fundamental difference between accidental generalizations and causal regularities: Humeans are skeptical also about causation.

Methodological Reconciliation

if there are causal necessities not just empirical regularities

whether we would ever be warranted in asserting
remains a further question (subject to Humean doubt)

nevertheless

if there are essences and causal necessities to be discovered the search for far-reaching regularities seems most apt to lead us to them.
though "we cannot be sure our theories and concepts are discovering them or describing them correctly.