[bain] notes on philosophy o science

8/12/2019 [Bain] Notes on Philosophy o Science

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. Course Intro

wo main areas of philosophy of science:

) Methodology of Science

) Philosophical Foundations of Particular Theories in Science

) Methodology of Science

Is there a scientific method?

What characterizes the sort of knowledge produced by such a method?

exact/hard

physics

chemistry

biology

etc.

nonexact/soft

sociology

anthropology

psychology

etc.

physics

chemistry

biology

psychology

sociology

anthropology

geology

paleontology

oceanography

meterology

archeology

etc.

sample fields in sciencefied via

uction? unified

allegence to a

gle method?

t related at all?

Possible grouping. Other possibiliti

experimental vs. theoretical

life sciences vs. hard sciences

ample topics

) Explanation

Does science aim towards providing explanationsof phenomena? What is a scientific explanation, and how doe

it differ, if at all, from other types of explanations?

) ConfirmationWhat is the relation between theoryand evidence? What factors condition our belief in the claims made by

scientific theories?

Laws of Nature

What is a law of nature?

) Scientific Realism

What do scientifictheoriestell us about the world? What would the world be like if they were true? Should w

draw a line between claims a theory makes that we could be justified in believing and claims that we cannot bejustified in believing?

Science vs. Pseudoscience

The demarcation problem: Are there general characteristics we can use to distinguish science from

pseudoscience?

Scientific Change

What happens when one theory in science supplants another? Can science be said to progress?

) Unity of Science

Is there one science or many sciences? How are different fields in science related, if at all?


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) Philosophical Foundations of Particular Theories in Science

hilosophy of physics

) Nature of spacetime in general relativity

) Interpretations of quantum mechanics

Determinism in classical and quantum physics) Ontology of quantum field theory

hilosophy of biology

) Types of explanation in the theory of natural selection

) Demarcation: evolution vs. creationism

Reductionism in biology

ample Topics:

hilosophy of psychology

) Demarcation: psychoanalysis

) Realism vs. anti-realism: behaviorism vs. cognitive science

this course, well first become aquainted with the central issues in Area (1). To do this, we wi

ve to go back to their original formulations, which usually means going back to the group of

ilosophers in the 1920s-30s generally known as the logical positivists. All 20th century

ilosophy of science is either an extension of, or a reaction (usually violent) to this group. Thest 3/4s of the class will be spent on the following topics:

I. Explanation and Laws of Nature

II. Confirmation

III. Scientific Theories, Scientific Change, and Scientific Realism

the last quarter of the course, we'll look at some topics in Area (2).


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2. Explanation. Part 1. Topics: I. Introduction

II. Deductive-Nomological (DN) Mod

III. Laws: Preliminary SketchIntroduction

rst blush:

scientific explanationis an attempt to render understandableor intelligiblesome particular

ent, or some general fact, by appealing to other particular and/or general facts drawn from one

more branches of empirical science.

Salmon notes, this is pretty vague. Lets get a bit more precise.

erminology:

Explanandum- fact (particular or general) to be explained.

Explanans- that which does the explaining

Explanation- (2 hair-splitting views)(a) A linguistic object consisting of an explanandum-statement and an explanans statement

(b) A collection of facts consisting of explanandum-facts and explanans-facts.

ore Preliminaries: Arguments

nce DN views explanations as arguments, we should be clear about what arguments are.

ASIDE: Weve now introduced 2 distinct types of object:

(1) an explanation; and

(2) an argument.

These are notnecessarily the same type of object! One attempt to further define what an explanation

in science amounts to is the DN account. This particularaccount claims an explanation is a type of

argument. We will investigate the adequacy of this account in the following lectures. But at this point,

it is very importantto realize that, in general, explanationsand argumentsare differents sorts of things.

An argumentis a collection of statements, one of which is identified as a claim

(conclusion), and the others are identified as reasons given for the claim (premises).

(For our purposes, nothing too important rides on this distinction. Just be aware of it.)


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Two Main Types of Argument (not explanation!)

1. Ampliative: Conclusion contains information

beyond that expressed in premises.

2. Not necessarily truth preserving.

3. Not erosion-proof: Addition of premises may

strengthen/weaken argument.

1. Non-ampliative: Content of conclusion

is present in premises.

2. Truth-preserving: Ifpremises are

true, conclusion mustbe true.

3. Erosion-proof: Addition of new premises

does not affect strength of argument (as long

as original premises are left alone).

4. Deductive validity is all-or-nothing.

A deductive argument is either valid or

invalid.

4. Inductive strength comes in degrees. Some

inductive arguments are stronger/weaker than

others.

his is a valid deductive argument:

It is non-ampliative: the conclusion is already implicit in the premises.

It is truth-preserving: If it is true that all animals with wings can fly, and if it is true that pigs have wings, then

must also be true that pigs can fly.

It is erosion-proof: If we added the premise Wilbur has butterfly wings, the conclusion would still follow in th

required truth-preserving way.

ASIDE: Of course, pigs donthave wings, and notall animals with wings can fly (penguins, for example). Note,however, that the truth-preserving property simply requires that it can never be the case that allthe premises are true

and the conclusion false. So long as this holds, the argument is valid. This does allow any other combination of truth-

values for the premises and conclusion. For instance, a valid argument could have all false premises and a true

conclusion; or all false premises and a false conclusion; or some combination of false/true premises together with a

false/true conclusion. Again, the onlycombination that is prohibited by property (2) is the combination of all true

premises and a false conclusion.

ASIDE: If we explicitly added Pigs dont have wings as a third premise, then the conclusion Pigs can fly

would stillbe true if all the premises were true. To see this, note that this new third premise contradicts the

second premise Pigs have wings -- they cant both be true at the same time (or false at the same time). So

adding Pigs dont have wings prevents the argument from ever having all true premises and a false conclusion;

and this is just the truth-preserving property (2). Similarly, adding Pigs cant fly as a third premise would

contradict the conclusion, which is already implicit in the first two premises. So again, we could never have a

situation in which all the premises were true and the conclusion false. So again, property (2) would be upheld.

Finally, as weve seen, its validity is all-or-nothing. Weve established that it is valid, and shown that nothing w

can do to it (short of destroying it) obviscates this fact.

x1: All animals with wings can fly.

Pigs have wings.

Pigs can fly.

Deductive Inductive


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x2: 95% of observed smokers developed lung cancer.

Smoking causes lung cancer.

his is an inductive argument.

It is ampliative: The conclusion contains information not already present in the premise.

It is not necessarily truth-preserving: If it is true that a certain survey found that 95% of smokers surveyed went

to develop lung cancer, then it does not necessarily follow that smoking was to blame. There could have been oth

usal factors that influenced the development of cancer in those 95%.

It is not erosion-proof. Suppose we added a second premise that states 100, 000 smokers were surveyed. This

uld strengthen the conclusion, all things remaining equal. It would establish that the sample size of the survey wa

y big. However, if we then added a fourth premise that states All smokers surveyed lived in coal mines, this

uld weaken the conclusion. It would establish that the sample was pretty biased; in this case, it would lead us to

nk that perhaps the large incidence of cancer was due to inhaling coal dust, as opposed to smoking.

Finally, (3) shows how inductive strength comes in degrees.

. Deductive-Nomological (DN) Model of Scientific Explanation

N explanation - an account of the explanandum that indicates how it follows deductively from a

w of nature (covering-law account).

ey characteristics are given by:

he conditions of adequacy define what a DN explanation is. In other words, an explanation is a

N explanation if and only if it satisfies conditions 1-4.

Conditions of Adequacy

1. Must be a valid-deductive argument with premises stating the explanansand the

conclusion stating the explanandum.

2. Premises (explanans) must contain a law.

3. Explanansmust have empirical content.

4. Explanansmust be true.

CLAIM: Scientific explanations are DN explanations.

mpel & Oppenheim (1948) Studies in the Logic of Explanation


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eneral form of DN explanations

x1: Why do skaters spin faster as they bring their arms in towards their bodies?

(reducing rotational intertia).

DN explanation:

1. Angular momentum is conserved.

2. Skater doesnt interact with external objects.

3. Skater has non-zero initial angular momentum.

4. Skater brings arms in towards body

! Skater spins faster.

law

conditions

observed phenomena

bsumption of particular fact (skater spinning faster) under a law (conservation of angular

omentum).

x2: Why did Jans bracelet melt when it was heated to 1063 C?

DN explanation:

1. Gold melts at 1063 C. law

2. Jans bracelet is made of gold. condition! Jans bracelet melted at 1063 C. observation

ASIDE: Ex1satisfies the 4 conditions of adequacy. In particular, it is a valid-deductive argument-- If thepremises are all true, then the conclusion must be true. To see this concretely, note that the argument can be

formulated mathematically in the following manner (where the angular momentumLof a spinning object is

defined as L= I!, where Iis the objects moment of inertia(its rotational inertia, which is roughly a measure

of the objects tendancy to continue spinning in the absernce of external forces), and !is its rotational velocity

(which measures how fast it is rotating)):

1. Li= Lf2. Li= Ii!i and Lf= If!f

3. Li= 0

4. If < Ii

! !f> !i

(nothing contributes to Lother than the skaters Iand !)

(Intuitively, to preserve the equation Ii!i= If!fwhen Ifis less

than Ii, the quantity !fmust be greater than !ito compensate)

L1, L2, ...

C1, C2, ...

O1, O2, ...

law(s)

conditions underwhich laws are applicable

observed phenomena

explanans

explanandum


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itial Problem for DN model: What is a law of nature?

reliminary Sketch

laim: Laws must

) Describe regularities that hold universally at all times and places.

) Be capable of supporting counterfactual statements.

Be capable of supporting modal statements.

unterfactual statement= An if-then statement with a false if-clause.

Ex: IfAbe Lincoln were alive today, thenhed be clawing at the lid of his coffin.

odal statement= A statement that asserts a physical necessity or (im)possibility.

Ex: It is impossible to construct an enriched uranium sphere with mass > 100,000 kg.

hree examples of candidate laws:

) All the apples in my refrigerator are yellow.

) No gold sphere has a mass greater than 100,000 kg.

) No enriched uranium sphere has a mass greater than 100,000 kg.

(1) lawlike? (Does it satisfy (a), (b), (c)?)

It doesnt satisfy (a). It refers to a particular place (and time).

To say that a law supportsa counterfactual/modal statement is to say that the law makes

the counterfactual/modal statement true.

Hempel & Oppenheim (1948) Studies in the Logic of Explanation

(2) lawlike?

It satisfies (a). (It's reasonable to suppose that in our universe there will never be enough goldto assemble such a massive sphere.)

It doesnt satisfy (b). It doesnt support the following true counterfactual statement:

If two gold spheres with masses of 50,001 kgeach were put together, then they would form a sphere with mass

100,001 kg.

It doesnt satisfy (c). It doesnt support the following true modal statement:

It is possible to construct a gold sphere with mass greater than 100,000 kg.


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ccidental generalization= A true generalization that satisfies (a) but not (b) or (c).

ircularity Problem with this preliminary account of laws

his account says a law of nature is a true generalizationthat statisfies conditions (a), (b) and (c

particular, laws differ from accidental generalizations solelyon the basis of the ability of laws t

pport counterfactualsand modal statements.

awlike generalization= A true generalization that satisfies (a), (b) and (c).

UT: Why do we think certain counterfactuals and modal statements are true in the first place

If its because we think there are laws of nature that underlie them, then we cant use

them to define what we mean by a law, on pain of circularity.

O: This preliminary account works only if we alreadyhave a theory of counterfactuals and

modal statements that is independentof the notion of a law and which can be used to

determine which counterfactuals/modal statements are true and which are false. Such a

theory is hard to envision. (And note that it cant simply be based on our intution; i.e.,

we can say that, intuitively, we think that the modal statement Its physically possible t

construct a 100,000 kg gold sphere is true. The question is, What underlies thisintuition?)

(3) lawlike?

It satisfies (a).

It satisfies (b). It supports the following true counterfactual statement:

If 100,000 kgof enriched uranium were assembled, then we would no longer have any uranium.

It satisfies (c). It supports the following true modal statement:

It is impossible to construct a sphere of enriched uranium with mass greater than 100,000 kg.


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3. Laws of Nature: Three AccountsTopics:

I. Regularity Account

II. Best System Account

III. Necessitarian AccounRegularity Account

laim: Laws are regularites.

ASIDE: Lets make this a bit more concrete. Think of Fand Gas properties. In particular, let Fbe the

property of being in free fall near the surface of the earth, and let Gbe the property of experiencing an

acceleration of 9.8 m/s2 (which is the acceleration due to gravity). Then Newtons Law of Gravity,

which, in this context, claims that all objects in free fall near the surface of the earth experience an

acceleration of 9.8m/s2 is, on the SRT account, nothing more than the collection of all instances of objects

displaying both Fand G. A law, on the SRT account, is just a report of a bunch of observations.

roblems

) Not all regularities are laws. In particular, accidental generalizations are not laws.

Hence being a regularity is not sufficientfor being a law.

ASIDE: Bird also considers the possibility of "single-instance" laws, which

(obviously) are not regularities. His example is the Big Bang as a single

instance of the law encoded by Einstein's field equations in general

relativity (with relevant initial/boundary conditions). The idea is that the

Einstein equations are supposed to describe the (large scale) structure of

our universe, hence there can only be one instance of them; namely, that

instance that in fact does describe our universe.

mple Regularity Theory (SRT)

is a law that Fs are Gs if and only ifall Fs are Gs.

) Not all laws are regularities(which means being a regularity is not necessaryfor being law). Purported examples:

) No-instance laws

(i) The ideal gas law: P= kT/V

(ii) Newtons 2nd law: F= ma

The claim here is that (i) and (ii) both are applicable onlyunder ideal conditions, and in

nature such ideal conditions never occur. So there are no realinstances of (i) or (ii).

Nevertheless, we still want to think of them as laws.


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) Functional laws

Laws expressible as functions that can take on a continuum of values, more than the finite

number of instances that can be physically observed in nature.

P

V/T

A functional law is more than the mere sum of all

of its instances. Think of the instances as a finite

number of data points on a graph. These data

points dont pick out a unique function (curve on

the graph). There are a number of different curves

that can be made to fit to the data points.

Ex1: The ideal gas law

ASIDE: Functional laws indicate why the distinction between accidental generalizationsand

lawlike generalizationsbased on the ability to support counterfactuals (and modal statements)

seems initially plausible. A functional law gives us information about instances that have not yet

been observed. Such a law allows us to infer what wouldbe the case ifcertain conditions were met.

Probabilistic laws

A law that states that Fs have a certain probabilityof being Gs.

Ex2. All nuclei of Type Ahave a half-life of 100,000 years (i.e., in 100,000 years, half of a population of Type

nuclei will have decayed).

F= being a nucleus of type A

G= decaying after 100,000 years

Claim: A probabilistic law cannot be consideredjusta summary of its instances.

Why? A probabilistic law describes an averagedistribution of a property over a populatio

of individuals. So an individual might not have the property but stillbe governed b

the law.

P= pressure, T = temperature, V= volume, k= const.

Gives Pas a function of T/V.

Allows Pto take on a continuumof values; more than those values that actually occur as regularities

displayed by actual gases (under conditions approaching ideal conditions).

Hence this functional law is more than just a summary of its actually occurring instances.

P=kT

V

Any individual Type Anucleus may nothave decayed after 100,000 years (the law says that on

average, half the population will have decayed after 100,000 years, which will be true if some decay

before and some after 100,000 years). But we still want to say that allType Anuclei are governed the probabilistic law.


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To say that an individual Type Anucleus has a probability of 1/2 of decaying after 100,000 years is to say that

the nucleus has an intrinsic indeterministic property-- there is nodeterminant fact of the matter about the

nucleus that we could ever knowthat would allow us to predict if it will have decayed after 100,000. All we can

say now (or at any time) is that the nucleus has a probability of 1/2 of decaying after 100,000 years.

laim: Under the ontic view, there canbe instances of probabilistic laws, these instances being

individuals with intrinsic indeterministic properties.

ut: This assumes a particular interpretationof probability.

Espistemic Interpretation of Probability= Probabilities are a measure of our ignorance.

To say that an individual Type Anucleus has a probability of 1/2 of decaying after 100,000 years is to say that,

at the present, we dont have enough information about it to predict with certainty whether it will decay after

100,000 years. But there isa determinant fact of the matter whether it will or will not decay. All we can do

with our present state of knowledge is to predict what will happen to a large ensemble of such nuclei: we can

predict that, on the average, 1/2 will have decayed after 100,000 years.

Ontic Interpretation of Probability= Probabilities refer to probabilitistic properties.

o: An STRer can respond to the probabilistic law objection by adopting an ontic view of

probabilities.

ASIDE: But there doseem to be epistemic probabilities in physics. Probabilities in Statistical Mechanics are

epistemic, for instance. The STRer will thus have to claim that there are no laws in Statistical Mechanics!

The reallaws are those of Newtonian Mechanics to which Statistical Mechanics reduces. Note, also, that in

Quantum Mechanics, probabilities are not given for ensembles, but for individual states. The view of

probabilities thus is the ontic, as opposed to the epistemic, view (at least for most interpretations of QM).


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. Best System Account (BSA): Modified Regularity Account

SA: A regularity is a law if and only ifit appears as a theoremor axiomin that true

deductive systemwhich achieves a best combination of simplicityand strength.

least numberof axioms

info-content

Motivations

) Laws systematizefacts; they dontjustreport them.

) How do you systematize facts? Construct a theoryin which they can be embedded. Hence,

to get at laws, write down the simpliest and strongest theory that accounts for the

phenomena. The laws will be the basic principles(theorems or axioms) of this theory.

theory

Kepler's Laws

Law #1: The orbits of the planets are in the forms of ellipses.

Law #2: The orbits of the planets sweep out equal areas in equal time intervals.

Law #3: The ratio D3/T2is constant for all planets (D= ave. distance from sun, T= period).

dvantages

Allows a distinction between accidental generalizationsand laws. Accidentalgeneralizations will not figure into the simpliest and strongest systematization of the facts.

) Allows a distinction between basiclawsand derivedlaws.

Ex. Keplers 3 Laws of planetary motion are derived from Newtons law of gravity. The BSA will claim tha

under the best system, Newtons law of gravity will appear at a lower level (maybe as one of the axioms

of the system), while Keplers laws will appear at a higher level. Note that the Simple Regularity Theo

cannot make this distinction. Under SRT a law is simply a regularity, and no provision is given for

distinguishing more fundamental regularities from less-fundamental ones.

The account of laws (most) scientists take for granted. Ask a physicist what a law of nature

is and she will probably recite a law (like Newtons Law of Gravity) that appears as the

foundation of a given theory in physics (Newtons Theory of Gravity). But: What about

fields like biology or psychology?

) Accounts for the link between laws and counterfactuals/modalstatements. What we take to

be true counterfactuals is based on what we know about the world. And what we know

about the world is given to us by our best theories. So both laws and counterfactuals have

their bases in our best theories.


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roblems

) Refers to standards of simplicity and strength. Shouldnt laws be independent of such

standards? Laws are supposed to be objectivefeatures of nature.

) What if there is more than one best system?

One response: Insist that nature is simple and uniform and will yield to our probing in a

nice well-ordered manner (uniformity of nature assumption). This may be appealing in the

more abstract sciences (theoretical physics, for instance); but a biologist will quickly tell you

how complex and redundant some aspects of nature are (biological systems for the most part

usually make use of what they are given and usually in highly redundant, complex ways).

One response: This assumes a pre-theoretic intuition concerning what a law is. The BSA

says, Let our theories decide for us what the laws of nature are. Whatever they decide will b

a law by definition, and notan accidental generalization. (What Bird might be getting at is

the worry that we will never have available to us an ideal best system of the world, and thus

may never know what the true laws of nature really are. But this is really a different issue

than the one the BSA is intended to address. All the BSA is giving us is a definition of what

a law of nature is. Theres nothing about a law of nature that requires that, for something to

be a law, we have to have epistemic access to it.)

One response: Then there is no fact of the matter as to what the true laws of nature are.

) Birds objection: It may be possible for the best system to have accidental generalizations as

its axioms and theorems.


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I. Necessitarian Account

is a law that Fs are Gs if and only if Fness necessitatesGness.

universal universal relation of necessitationbetween universals

ssumes the following metaphysical distinctions:

universals

particular

Fness, Gness

necessitation

he necessitarian account says: A law is a relation of necessitationbetween two universals

xample:

t Fness = being in free fall near the surface of the earth

Gness = having an acceleration of 9.8m/s2

individual = a piece of chalk that I just dropped

he piece of chalk (the individual) has both the properties of Fness and Gness.

individual

general property

property of general property

r, according to the diagram, a law is a particular propertythat holds of two general properties

hat hold of an individual(i.e., a law is a particular relation(a 2-place property) that holds

etween two general properties of an individual). This particular relation is called necessitation.

ASIDE: Think of necessitationlike youd think of the 1st-order relation taller than. Two individual

objects can stand in the relation taller than(the Empire State Building and a grass hut, forinstance). Similarly, two general properties of an object can stand in the relation of necessitation.

he necessitarian says: These properties alsostand in the relation of necessitationto each

her: Fness necessitatesGness. This is a manifestation of Newtons Law of Gravity. The law i

st the relation of necessitation between being in free fall near the surface of the earth and

aving an acceleration of 9.8m/s2.


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dvantages

) Allows the distinction between accidental regularities and laws. All instantiations of laws are

regularities; but a regularity need not be an instantiation of a law. (Only those regularities

that are characterized by the necessitation relation are instantiations of laws.)

) Provides a basis for induction. Bird claims that the SRT and the BSA do not. Well comeback to the problem of induction later in the course. The idea is that the necessitation

relation provides the metaphysical connectivity that justifies causal inductive inferences.

we dont allow for some form of connectivity, we cant justify such inferences. And the SRT

and the BSA dont give us this. Big Problem: What justifies the claim that such connectivi

exists? In other words, How can we ever be sure when the relation of necessitation is presen

and when it is not? This is probably the central problem facing this accout...

) Provides an explanation for lawlike regularities. The intuition is that the necessitation

relation explainsthe presence of those regularities that are instantiations of laws: Why do

pieces of chalk in free fall near the earths surface fall with an acceleration of 9.8m/s2?

Because those pieces of chalk also have the 2nd-order property of necessitation. This

additional property explains this regularity.

ASIDE: Bird claims that the SRT and BSA cannot explain regularities in the same way. The SRT

cannot: you cant explain a regularity by refering back to the regularity. But arguably the BSA does

provide an explanation for lawlike regularities; in particular, it provides what is called a unifyingexplanation(which well look at in more detail later): it explains lawlike regularities by demonstrating

how they are embedded in a unifying systematization of the facts. In any event, we cant really view

(2) as an advantage until we have a grasp of what the notion of explanation is. (Recall, we are

looking at different accounts of laws in orderto get a grasp of what an explanation is.)


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roblems

) What is the necessitation relation? Any description of it fails to distinguish it from the BSA

acocunt.

To see the problem that (2) presents, consider two worlds W1, W2that agree on all

observable regularities. The necessitarian must claim that they could stilldisagree on what

the laws of nature are. (Note that the BSAer must claim that W1and W2mustagree on

what the laws of nature are (as long as their standards of simplicity and strength are the

same).)

) How is the necessitation relation known? It has to go beyond observable regularities (if we

stop at observable regularities, we have the BSA). It is an in-principle unobservablepropert

(unlike, say, the property being in free fall near the surface of the earth).

The question for the necessitarian is, if the laws of W1and W2are different, how could we

ever come to know this? If our only access to laws is through empirical observations of

regularitiesin nature, then we could never come to know this.

One response: We have a built-in intuition that lets us directly grasp what the laws

of nature are.

Reply: Dont fortune-tellers make similar claims?


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4. Explanation. Part 2.Topics:

I. Problems with DN

II. DN Variants

General Characteristics

(a) Argument Thesis: DN explanations are arguments.

(b) Nomic Expectability Thesis: DN explanations demonstrate how the explanandumis

nomically expected; i.e., how it follows necessarily from a law.

(c) Explanation/Prediction Symmetry Thesis: Any DN explanation of a particular fact

could have been used to predictthe fact if the explananshad been available prior to

the facts occurrance. So:

(i) Every DN explanation is a potential prediction.

(ii) Every prediction is a potential DN explanation.

Note that (c) seems problematic right offthe bat: Predictions can be based on merecorrelations, whereas DN explanationscannot: they have to based on real laws

What this entails:

) Anything that satisfies the Adequacy Conditions is a scientific explanation.

(Conditions 1-4 are sufficient conditionsfor something to count as a scientific explanation.)

) All scientific explanations satisfy Adequacy Conditions.

(Conditions 1-4 are necessary conditionsfor something to count as a scientific explanation.)

DN Adequacy Conditions

(1) Valid deductive argument.

(2) Explanansmust contain law(s).

(3) Explanansmust have empirical content.

(4) Explanansmust be true.

he general opinion is that this Claim is false. There are purported counterexamples to both

aim (A) and Claim (B). Lets look at some of them.

ecall:

N explanations that satisfy these conditions have 3 general characteristics:

laim: Scientific explanations are DN explanations.


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ounterexamples to Claim (A)

onsider the following DN explanation of the length of the shadow of a flagpole:

) Flagpole and Shadow

Explains the length lof the flagpoles shadow by showing how lfollows from a law and the

conditions that make the law applicable. Satisfies Adequacy Conditions 1-4, so it's DN.

Explains the height hof the flagpole by showing how hfollows from a law and the condition

that make the law applicable. Satisfies Conditions 1-4, so it's a DN explanation.

Problems with DN

(1) Light propagates rectilinearly.

(2) Sun is at certain elevation e.

(3)

(4) Flagpole has height h.

! Shadow has length l.

law

conditions

observed fact

amples that attempt to demonstrate that the Adequacy Conditions are not sufficentfor something to count as a

entific explanation. They are examples of things that satisfy the Adequacy Conditions but should notbe considere

itimate scientific explanations.

ut: We can also construct the following DN explanation that alsosatsifies Conditions 1-4:

(1) Light propagates rectilinearly.

(2) Sun is at certain elevation e.

(3)

(4) Shadow has length l.

! Flagpole has height h.

law

conditions

observed fact

ut: Is it a legitimateexplanation? It explains a cause(the heighth of the flagpole) by means o

its effect(the length lof the shadow). Effects are normally explained in terms of their

causes, and not vice-versa.

ASIDE: Explaining why a flagpole has a certain height by refering to the length of its shadow is analogous to explainingwhy you approached an automatic sliding door (in a grocery store, say) by refering to the door sliding open. Your approachto the door caused it to slide open; its sliding open is the effect of your approaching it. You dontnormally say Why did Iapproach the door? Because it slid open. You donormally say Why did the door slide open? Because I approached it.

Moral: The DN model does not account for causal factorsin explanations.


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) Man & Birth-Control Pill

onsider the following DN explanation of why the man Wes failed to become pregnant during the

st year:

(1) If a human takes pill Yconsistently over the course of a year, then that

human will fail to become pregnant during that year.

(2) Wes is a human and Wes took pill Yconsistently over the past year.

! Wes failed to become pregnant during the past year.

Satisfies Conditions 1-4. So it's a DN explanation.

ounterexamples to Claim (B)

k Stain

nsider the following explanation for why there is an ink stain in the carpet in Wes office:

cause Wes knocked over a bottle of ink.

his explains the ink stain by referring to its immediate cause. Note that it is nota DN

planation (it doesnt satisfy Adequacy Conditions 1-4).

ut: Is it a legitimatescientific explanation? Taking birth-control pills is irrelevantto whethe

or not a man becomes pregnant. Hence premise (2) is irrelevant to the fact (that Wes did

not become pregnant) being explained.

Moral: In scientific explanations, the explanansshould be relevantto the explanandum.

ASIDE: Note that the law in (1) might be questioned. If it does not count as a law, then the

example does not count as a DN explanation. However, under the regularityaccount, it is a legitimate

law (it simply states a regularity). And under the BSA, it might be considered a derived law; a more

fundamental law being something like: Chemical Xin pill Yinhibits the production of human egg cells.

amples that attempt to demonstrate that The Adequacy Conditions are not necessaryfor something to be a

itimate scientific explanation. They are examples of legitimate scientific explanatoins that do not satisfy the

equacy Conditions.

Claim: Causal explanations that do not appeal to laws are legitimate scientific explanations.

SIDE: We couldconstruct a detailed, complicated DN explanation of the ink stain. It might appeal to laws in

ewtonian dynamics that would describe Wes's elbow knocking over the ink bottle; and to Newtons law of gravity to

scribe the bottle falling to the carpet; and to laws of diffusion in chemistry to describe how the ink spread into the

rpet; and possibly even to laws in chaos theory to describe the pattern of the ink stain. (Moreover, it would also have

appeal to laws in psychology and/or neuro-physiology to describe the mental processes that caused Wes to move his

bow in a certain way.) The assumption underlying the causal explanation approach is, Do scientists really always

ppeal to such complex, convoluted DN explanations? Or are they willing to use much more simple causal explanations?


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. DN Variants

) DS - Deductive Statistical: Explains a statistical regularity by subsuming it under a

statistical law.

) IS - Inductive Statistical: Explains a particular fact by subsuming it under a statistical

law.

mportant distinction:

Universal generalization: All Fs are Gs

tatistical generalilzation: X% of Fs are Gs

he laws that appear in DN explanations are in the form of universalgeneralizations.

he laws that appear in DS and IS explanations are in the form of statisticalgeneralizations.

explanandum

law

universal

statistical

DN

DS

DN

IS

particular

fact

general

regularity

roblem of Irrelevant Conjunctions: A general regularity (law) can be derived from the

conjunctionof that law with any other (true, empirical) law. This conjunction is itself a law an

can be used in the law premise of DN-type explanations. But this conjunction doesnt alway

explain the original law/general relgularity.

Ex: Keplers Laws Kcan be derived from the conjunction (K& B), where Bis Boyles Law (which is a true,

empirical law). But the conjunction (K& B) doesnt explain Keplers Laws. In particular, the following DN

explanation of Keplers Laws isnt a legitimate scientific explanation (note that it does satisfy all 4 DN conditions)

(1) (K& B)

! K

law

N-type explanations of general regularities(DN and DS) face...

generalregularity

ASIDE: Note that DN-type explanations of particular facts(DN and IS) dontface this

irrelevant conjunction problem. If you conjoin a particular fact to a law, the result is nota

law that could be used in the Law Premise of a DN-type explanation. (Intuitively, the

particular fact refers to a specific time and place, so the conjunction would, too; hence it would

not count as a law.) Note, also, that this Problem may only be a problem for the regularity

account of laws, underwhich it seems legitimate to consider (K& B) a law if Kand Bare laws

separately. Under the BSA, (K& B) will probably not be considered a legitimate law.


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ven that DN-type explanations of general regularities face serious problems, we can still ask, do

N-type explanations of particular facts work? Weve seen some problems with the original DN

planation of particular facts. Lets now look at the IS model.

ductive Statistical (IS) model of explanation

IS Adequacy Conditions

(1) Strong inductive arugment.

(2) Explanansmust contain statistical law(s).



(5) Explanansmust satisfy the Requirement of Maximal Specificity(RMS).

ASIDE: Why is RMS needed in addition to Condition 1? Consider the following two strong inductive

arguments:(1) Almost all cases of strep-throat clear up quickly after penicillin treatment.

(2) Jane Jones had strep-throat.

(3) Jane Jones recieved penicillin.

! Jane Jones recovered quickly.

(A)

(1) Almost all cases of penicillin-resistent strep-throat do not clear up quickly after

penicillin treatment.

(2) Jane Jones had penicillin-resistent strep-throat.

(3) Jane Jones recieved penicillin.

! Jane Jones did not recover quickly.

(B)

Both (A) and (B) are strong inductive arguments: Their premises give high probabilities to their conclusions.

But their conclusions are contradictory. If we only knew the premises of both, which conclusion are we

warranted in believing? Intuitively, we are more warranted in believing the conclusion of (B), since its premises

contain information that is more relevantto its conclusion than do the premises in (A) to its conclusion. In

other words, while (A) and (B) both satisfy (1) above, (B) also satisfies RMS, whereas (A) does not.

strong inductive argumentis one in which the premises give a high probability to the conclusio

RMS: All relevant information must be present in the explanansthat would

have an effect on the explanandum.


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he IS conditions can be combined with the DN conditions into the following:

DN/IS Adequacy Conditions

(1) Must be either a valid-deductiveargument, or a strong inductiveargument.

(2) Explanansmust contain a law(s) (universal or statistical).



(5) Explanansmust satisfy the Requirement of Maximal Specificity(RMS).

Modified Claim: The DN/IS Adequacy Conditions are necessaryand sufficientconditions

for scientific explanations of particular facts.

other words: All scientific explanations, and only scientific explanations, of particular facts

are either DN explanations or IS explanations.

eve seen that the DN leg of this modified claim is problematic. Lets look at the IS leg. The

neral opinion is that it fails, too.

ote: BothIS and DN are characterized by the Argument Thesis, the Nomic Expectibility Thesi

and the Explanation/Prediction Symmetry Thesis. (In the IS model the argument is

inductive instead of deductive, and the law is statistical instead of universal.)

ASIDE: DN explanations automatically satisfy RMS: Characteristics

(3) and (4) of valid-deductive arguments indicate that the premises of a

valid-deductive argument are maximally relevant to the conclusion.

ounterexamples to IS

amples that attempt to demonstrate that the IS conditions are neither necessarynor sufficientfor scientific

planations of particular facts.

) Vitamin C and the Common Cold

onsider the following IS explanation for why Wes recovered quickly from his cold.


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(1) 85% of people with common colds who take massive doses of Vitamin C recover quickly.

(2) Wes is a person with a cold who took massive doses of Vitamin C.[0.85]

! Wes recovered quickly.

Satisfies IS Conditions 1-5. So it's an IS explanation.

Moral: The argument thesis plus RMS stillallows irrelevant information to be included in

the premises of an IS explanation.

) Syphilis and Paresis

is example is supposed to show that there are legitimate scientific explanations of particular facts that are not IS

planations (or DN explanations).

(1) 25% of all victims of untreated latent syphilis develop paresis.

(2) The only way to get paresis is if you had untreated latent syphilis.(3) Smith had untreated latent syphilis.

[.25]

! Smith developed paresis.

Legitimatescientific explanation of why Smith developed paresis.

ut: Is it a legitimatescientific explanation of why Wes recovered quickly? Fails to take intoconsideration that people tend to recover quickly from colds regardless of whether or not

they take massive doses of Vitamin C. Question left unanswered: Is Vitamin C

consumption statistically relevantto cold recovery? If it isnt, then Premise (2) is irrelevan

to the conclusion.

ut It's not a strong inductive argument: The premises give a very lowprobability to the

conclusion.

ASIDE: This is not only a criticism of the Argument Thesis, but also of the Nomic Expectibility Thesis. The

example does not show how the explanandumis expected from a statistical law. It shows the opposite: that

the explanandumis very unlikely, given the statistical law. Nevertheless, the example is a legitimate scientific

explanation. Note that one could uphold the Nomic Expectability Thesisby claiming that the explanation is

incomplete; that the statistical law in (1) is reducible to an as yet undiscovered universal law, and this law

would show how the explanandumis expected nomically. Note that to claim this is the case for all such

counterexamples is essentially to claim that all statistical laws are ultimately reducibleto universal laws (hence

all IS explanations are just incomplete DN explanations). This entails that there are no fundamentally

probabilistic facts. This is a bit hasty: this is denied under the accepted interpretation of quantum mechanics.


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5. Explanation. Part 3: Alternatives to DN.Topics:

I. Unification Accoun

II. Causal Account

III. Pragmatics Accou

Unification Account

scientific explanation of a fact (particular or general) is a demonstrationof how the fact can be

rivedfrom a unifyingset of argument patterns.

Scope: The greater the scopeof T, the greater the number of conclusionsthat can be drawn

from T.

Simplicity: The greater the simplicityof T, the smaller the number of argument patternsin

Stringency: The greater the stringencyof T, the smaller the range of applicabilityof T.

t of argument patterns= basic principles(axioms, theorems, etc) that (may) underlie a

theory.

Ex. General relativitycan be thought of as a unifying set of argument patternsthat can be used to describe a

certain class of phenomena. Arguably, the set has great scope, great simplicity, and great stringency(it only

applies to certain phenomena; namely, phenomena that experience the gravitational force; and it prescribes the

behavior of such phenomenon in very restricted ways). Astrology, on the other hand, is not stringent: you can

apply its descriptions to almost any phenomenon you experience. (Any event you experience in the course of a

day is bound to have been predicted by your daily horoscope, given a flexible enough interpretation.)

eneral Idea: To scientifically explain a fact, you have to demonstrate how it can be embedde

a unifying theory. This explains the fact by showing how it is related to other facts.

our Characteristics:

) Unification explanations are derivations.

Friedman (1974) Explanation and Scientific UnderstandingKitcher (1981) Explanatory Unification

nifying power: a set of argument patterns Tis unifyingif it scores high on the following

properties:

A derivation= A sequence of justified steps; each step being explicitly shown to follow fro

the preceding ones.

Note: Contrast with DN-type explanations, which are arguments(recall, arguments are

sets of setences with one being a claim and the others reasons given for the claim).

In an argument, you dont have to explicitly show how each sentence follows directly from the last.

This allows irrelevant premisesto crop up; in a derivation, there can be nostep which is not

relevant to the other steps.


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) The unification account is committed to an Expectibility Thesis: A unifying

explanation must show how the explanandumis to be expectedfrom the explanans.

roblems with the Unification Account

) Problem of subjective standards: How are we to judge which explanations are more

unifying than others?

) Unifying explanations are not necessarily reductionistic. One might think that to

provide a unifying explanation of a fact is to show how that fact can be reducedto the

fundamental facts that underlie the ultimate grand-unifying theory of everything. In

particular, to provide a unifying explanation of a biological fact, you have to show how it ca

be reduced to facts in chemistry, say, or physics.

) The unification account is global: A unifying explanation embeds a localfact in a

larger, globaltheory.

Note: This is not necessarily nomicexpectibility, as with DN. In comparison to DN, one

might say that unification replaces law with unifying systematization (i.e., theory").

But note the other main difference with DN given in Characteristic 1.

But: The unification account iscompatible with the possibility that biology, say, ultimatel

can never be reduced to physics. If this is so, you can still construct unifying explanations obiological facts; theyll just refer to unifying theories in biology and make no reference to

physics.

(same problem that the BSA account of laws faces)

ASIDE: Our text claims that the unification account also suffers from the Problem of

Irrelevant Conjunctions(just as it claims the general regularity DN & DS accounts do). The

claim here is that (K& B) can be thought of as a set of argument patterns (K= Keplers Laws, B= Boyles Law); and Kcan be derived from (K& B). But Kisnt explained by (K& B). This is

aimed at Friedmans original account of unification. The account given above is due to Kitcher

and it has a ready response to this criticism. According to it, one can say that Kcan also be

derived from N(Newtons theory of gravity), and Nis a betterexplanation of Kthan (K& B)

because Nis moreunifyingthan (K& B). One might claim that (K& B) in fact isnta unifying

explanation of Kat all: (K& B) has poor simplicity. But this response in turn faces the problem

of subjective standards: Can we say that Nis objectively more unifying than (K& B)?


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) Problem of probabilistic explanations: Some legitimate explanations give a low

probability to their explananda, hence their explanandaare notexpectedfrom their explanan

(recall the syphilis and paresis example). Since the unification account is commited to an

Expectability Thesis, it faces this problem.

To see how this folds out, consider the following distinction:

Two Types of Probabilistic Explanations:

(a) reducible: Given enough information, these reduce to explanations in which the

explanandumcan be logically deduced from the explanans.

(b) irreducible: The explanandumcannot be logically deduced from the explanans,

regardless of how much further information is provided.

Deductive chauvinism claims: All probabilistic explanations can be reduced to

deductive explanations. There are nolegitimate irreducibleprobabilisticexplanations.

Ex1: Suppose an electron beam impinges on a potential barrier (think of a beam of electrons focused on a wal

The Schrdinger equation in quantum mechanics gives the probability for each electron in the beam to be

reflected or to tunnel through. Suppose a given electron, e1, tunnels through the barrier. We can ask:Why did e1tunnel through the barrier?

We cannot construct a derivationwith the conclusion e1tunneled through the barrier. All the Schrdinger

equation gives us is the probabilitythat e1will tunnel through (say its 0.80). The Schrdinger equation does n

predict with certainty whether e1will or will not tunnel through.

What this means: We cannot construct a unifying explanation of why e1tunneled through.

e1

prob of 0.2ofbeing reflected

prob of 0.8oftunneling through

barrier

One response: Deductive Chauvinism-- Claim that there are nolegitimate explanations

of inherantly probabilistic facts.

In other words: While there may be inherantly probabilistic events, Deductive Chauvinism claims such even

cannot be explained (to the extent that inherantly probabilistic events cannot be predicted with certainty).

But: The unificationist who is also a Deductive Chauvinistwill respond that this is fine, since there are no

legitimate explanations of inherantlyprobabilisitic events, and the actual event of e1tunneling through the

barrier is just such an inherantly probabilistic event.

ASIDE: Such a unificationist can explain why e1had an 80% chance of tunneling through the

barrier (instead of, say, a 50% chance). This is entailed by the Schrdinger equation. But

such a unificationist, again, says there is noexplanation for why e1did in fact tunnel through.


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So: A unificationist can claim that there are noexplanations of inherantly probabilistic event

A physicistmight be satisfied with the claim that there is no explanation for why a particular

electron tunnelled through a barrier.

But: Does this work for explanations in the social sciences?

Ex2: Suppose an anthropologist studying the Yanomami indians of Brazil seeks an explanation

of why the Yanomami attacked village A. The anthropologist has determined the following:

(a) The Yanomami tendto attack when resources are scarce;(b) The Yanommami tendto attack when the military advantage is theirs; and

(c) The Yanomami tendto attack when their social influence is threatened.

Note: There are nofactors that determine with certaintywhen the Yanomami will attack.

So: The event of such an attack is an inherantly probabilisticevent.

So: A unificationist who is a deductive chauvinist must claim that there is noexplanation for why the Yanomam

didin fact attack village A.

But: The anthropologist certainly will not be satisfied with this and will indeed claim that someform of

explanation for the attack can be constructed.

Moral: Deductive chauvinism is a high price to pay as a response to the problem of

probabilistic explanations. But if the unificationist does not adopt it, she is faced with the

same sorts of problems that afflict the IS account.

. Causal Account

o explain an event is to provide information about what caused it.

wo Characteristics

) The causal account is local.

) Basic causal account claim: Causal structure underlies laws and theories. This is

what gives them explanatory power. So all DN-type and unification explanations are causal

explanations, but not all causal explanations can be viewed as DN-type or unification

explanations.

roblems with the Causal Account

) Problem of the nature of causality: How are legitimate causal explanations

distinguished from illegitimate explanations based on mere statistical correlations?

Salmon (1984) Scientific Explanation and the Causal Structure of the WorldLewis (1986) Causal Explanation

ASIDE: The above example comes from: Steel, D. (1998) Warfare and Western Manufactures:A Case Study of Explanation in Anthropology, Philosophy of Science65, pp. 649-671.


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) Problem of purely theoretical explanations: Some theoretical explanations do not

explicitly refer to causes.

Ex: Why cant you fit a left-handed glove on your right hand?

Theoretical explanation: Due to the topological properties of the left-handed glove and the right hand.

Causal explanation: Due to the resistance of the inner surface of the left-handed glove with your right hand

Claim: Purely theoretical explanations count as legitimate scientific explanations. So the

causal account cannot be a complete account of scientific explanation.

) Problem of irreducible probabilistic explanations: What caused the Yanomami to

attack village A? What caused e1to tunnel? To provide causal explanations of irreducibly

probabilistic events, we need a theory of probabilistic causation (and a theory of simple

causation is hard to come by).

I. Pragmatics Account

Motivation: Explanations are context-sensitive.

van Fraassen (1980) The Scientific Image

ragmatic Features of Explanations

) Clarification of explanation-seeking question

What is the explanandumfor which an explanation is being sought?

Ex1: In the glove example, is the relevant question What prevents me right now from putting this left-handed

glove on my right-hand?or is it In general what prevents objects with opposite handedness from matching

up? The causal explanation is a more appropriate answer to the first question; the theoretical explanation is

more appropriate to the second question.

Ex2: The question Why did Adam eat the apple?will be responded to in different ways, depending on how it

interpreted:

(a) Why did Adam eat the apple? (As opposed to a grape or an orange.)(b) Why did Adameat the apple? (As opposed to Eve or the snake.)

(c) Why did Adam eatthe apple? (As opposed to throwing it at the snake, etc.)

In the glove example, you would offer the causal explanation to someone unfamiliar with topology, whereas youmight offer the theoretical explanation to a mathematician.

) Knowledge-context of the explanation-seeker

The information content of the explanans of an adequate explanation will depend on the

knowledge of the questioner.


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Suppose a congressional committee is seeking an explanation for a plane crash in order to modify existing safet

regulations. It will be more interested in explanations that refer to the procedures the crew went through (or

failed to go through), as opposed to explanations that refer to principles in Newtonian dynamics.

elevant Distinction

) Ideal Explanatory Text: a complete description (nomic, systematic, causal) of the

explanandum. The full, gory details. (Non-pragmatic aspect.)

Claim: Scientific explanations are almost always requests for explanationinformation, and notfor the ideal explanatory text.

) Explanation Information: Accounts of particular aspects of the ideal explanatory text.

(Pragmatic aspect.)

) Interests of the explanation-seeker

The content of the explanans of an adeuate explanation will depend on the purpose for which

the explanation is being sought.


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6. Confirmation

Relation between theoryand evidence

Fundamental question: How does evidence contribute to the credibility of a theory?

eneral Considerations (epistemological)

otion of justification (reasons for belief)

) Whatjustifiesa scientific claim?

) Cansuch claims be justified? (Hume)

) What is the senseof justification involved?

articular Considerations

) What is a hypothesis H?

) What is evidence E?

) Can a general relation between Eand Hbe defined that describes how Esupports/lends

credence to H?

Econfirms H means __________.

ossible Claims

) Econfirms Hjust when Eis entailed by H. Symbolically: H!E

bject matter of confirmation theory: Analysis and assessement of such claims.

Well come back to these

considerations later

Introduction

Topics:

I. Introduction

II. Hypothetico-Deductive Method

III. Instance Confirmation

) Evidence can never confirm single, isolated Hs; evidence can only confirm theories-as-a-

whole/belief systems/conceptual schemes. (strong holism)

) Econfirms Honly relative to background knowledge K. (weak holism)

) Some types of evidence confirm a given Hmore directly than other types.

c...


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seful distinctions

2Parts to Language in which claims about objects are made1. Observationalvocabulary- terms in language that refer to objects

of types (1) and (2).

2. Theoreticalvocabulary- terms in language that refer to objects of

type (3).

2Types of Inference

I. Inferences from evidence to observational claims.

II. Inferences from evidence to theoretical claims.

2Types of Claims about Objects

(i) Observational Claims All swans are white. Electron A has momentum p.

(ii) Theoretical Claims Quarks come in 3 flavors.

3Types of Objects

(1) Directly observable objects swan

(2) Indirectly observable objects dinosaur electron

(3) In-principle unobservable objects quark

Aside: An anti-realist answers yes to (A) and no to (B).

A realist answers yes to both (A) and (B).

Questions for Confirmation Theory

(A) Are inferences of Type I justified? If so, how?

(B) Are inferences of Type II justified? If so, how?


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ep 2: Conduct an experiment to see if our prediction O holds true. Take a sample of gas at t

stated initial volume and pressure (in a compression chamber, say), and then vary thepressure to its final value (by either compressing the gas or allowing it to expand), whil

keeping its temperature constant. Now measure its final volume and see if it is identica

(within the appropriate error analysis) of the predicted value O.

Hypothetico-Deductive (HD) Method of Confirmation

ep 3: Suppose Ois true. This constitutes a positive outcome, and HD requires us to say O

confirms H.

Steps to HD Method:

Given hypothesis H, deducean observational consequence O(i.e., an observational claim).

Test O(i.e., check to see if it is true or false).

If Ois true, then His confirmed. If Ois false, then His disconfirmed.

This is required to be a valid-deductive argument; i.e., if the premises are true (if H and I and A areall true), then the conclusion must be true (the prediction must follow). The D in HD refers to

this deductive inference described in Step 1. (The H in HD refers to the H being tested.)

Form of deduction in Step 1:

H hypothesis

I initialconditions

A auxiliary hypotheses

! O observational prediction

hypothesis to be tested

required to deduce O from H

H: PiVi= PfVf (Boyles Law: PV = constant, at constant temperature)

I: values for Vi= initial volume, Pi=initial pressure, Pf=final pressure

constant value for temperature

A: principles underlying instruments used to measure gas

principles underlying composition of gas chamber

etc...

! O: predicted value for final volume Vf=PiVi/Pf

xample 1: HD Test of Boyles Law

ep 1:


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neral argument pattern of HD method (all 3 steps) for positive outcomes:

Not H is true. Note that even saying H is confirmed i

misleading. The truth of O lends support not just to H, bu

to the conjunction (H &I &A). So the postive outcome

case of HD testing is ambiguous -- it doesnt really tell us

how the evidence O lends credibility to H by itself.

An inductive argument!

neral argument pattern of HD method (all 3 steps) for negative outcomes:

xample 2: HD Test of Corpuscular Theory of Light

ep 3: Ois false! A small bright spot will appear in the center of the disk ("Poissons Bright

Spot"). A negative outcome, so HD requires us to say O disconfirms H.

ep 1: H: Corpuscular Theory of Light (claim: light consists of corpuscles traveling in straight lines)

I: Cicular disk is lit from behind

A: Assumptions about composition of disk, medium between light source and disk, etc.

! O: Cicular disk lit from behind will cast uniform shadowep 2: Perform experiment!

ut, again: Whatis disconfirmed? Not just H, but (H& I& A)!

It has the valid form

of modus tollens:

(p "q)

#q

!#p

Valid-Deductiveargument!

If (H& I& A) are all true, then Ois true.

Ois true.

His confirmed.

If (H& I& A) are true, then Ois true.

Ois not true.

! (H& I& A) are not true.

OI& A

H

uestion: To what extentdoes a positive outcome Oconfirm H? Absolutely?

o!: We cant infer that His true solelyon the basis of a singlecorrect prediction. But the

single correct prediction doeslend some support to H.

hus: While the inference in step 1 from Hto Ois deductive, the completeHD inference from O

back to His inductive:


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aim (Falsificationism):

ence progresses deductively byfalsification. We are not warranted in believing hypotheses th

ve been HD-confirmed, because they are based on inductiveinference. Rather, we are only

rranted in believing hypotheses that have withstood attempts to HD-disconfirmthem. Such

soning is based on valid-deductiveinferences.

uhem-Quine Problem:

the light of a disconfirming prediction O, which of (H& I& A) is to blame? Which gets

alsified by disconfirming evidence?

Popper (1959) The Logic of Scientific Discovery

uhem-Quine Thesis

ypotheses are never tested in isolation. They are always tested in the context of background

sumptions.

Popper: Believe only in Hs that have withstood severe tests.

But: What if the reason for a passing grade rests not in the H, but in the Iand/or the A?

Duhem (1906) The Aim and Structure of Scientific TheoriesQuine (1953) "Two Dogmas of Empiricism"

Note: This is a major problem for the HD method, which assumes that confirmation can be localized;i.e., that hypotheses can, at least to some extent, be tested in isolation from other hypotheses.

ASIDE: Popper has been extremely influential, and typically if a scientist knows anything about the

philosophy of science, she will have heard of Popper and Falsificationism. Unfortunantly, many scientistsonlyknow about Popper and falsificationism. But confirmation theory did not stop in the 1950's...

he HD notion of confirmation essentially is the following (the first possible claim from page 1 of

ese lecture notes):

HD: Econfirms Hjust when Eis entailedby H(symbolically: H!E).

he 3 Steps of the HD method just indicate how to apply this definition of confirmation in actual

uations.

part from the Duhem-Quine Problem, the HD method faces two other problems:


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wo Further Problems with HD Method

Problem of Alternative Hypotheses (Underdetermination of Theory by Evidence)

For any prediction O, there are any number of incompatible Hs that can be constructed that

all entail O. So if Ois true, which Hdoes it confirm?

Ex. H= Boyles Law: PV= ! or V(P) = !/P, for constant !.

H: V(P) = !/P

H': V(P) = AP2+ BP+ C

O: P1V1= !

P1 P2

V2

P

V1

V

Moral: The confirmation relation cant be simple entailment (H!E).

Problem of Statistical Hypotheses

If His a statistical hypothesis, then noOcan be deducedfrom it to test it. At most, we have

If His true, then Ois highly-probable.

Ois true.

Moral: The confirmation relation needs to account for probabilistic inductions.

Ois entailed by bothHand H'(and any other curve that intersects the point (P1, V1)).

So: If Ois true, which Hshould we believe?

In fact, in the graph above, Hand H'also both entail the prediction P2V2= !. Its not hard

imagine a curve H''that differs from Hbut agrees with Hon any indefinite number of

predictions.

His _______?


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. Instance Confirmation.

ecall: The task is to define a relation between Eand H. In other words, to fill in the following

blank: Econfirms H means ________.

stance Confirmation fills it in thusly: Econfirms H means Eis an instanceof H.

x: H= All ravens are black

n instance of H, according to Nicods Criterion, is a black raven.

Econfirms Hjust when E= a black raven.

hat does Eis an instance of H mean? One definition is known as Nicods Criterion:

Nicods Criterion: For a hypothesis Hof the form All Sare P, an

instanceof His an individual that is both an Sand a P.

ne initial problem with Nicods version of Instance Confirmation:

s applicable only to hypotheses of the general form All Sare P (i.e., universal hypotheses).

ASIDE: Technically, a hypothesis of the form All Rare B is a universal affirmativesentence, which

can be written in 1st order predicate logic as (x)(Rx"Bx) (For all individuals x, if xis Rthen xis B).

A Nicod-instance of Hthen is an individual athat satisfies boththe antecedent andthe consequent of the

conditional being quantified over. Such an instance would be written as the singular sentence Ra& Ba.

ASIDE: Note that Instance Confirmation is different from HD Confirmation. HD bases confirmation on the

entailment relation (it says Econfirms Hjust when Hentails E). Instance Confirmation bases confirmation on

the notion of an instance of a hypothesis. Instances need not be entailed by their hypotheses. For example,

the Nicod-instance above of a black raven is technically not entailed by the statement All ravens are black.

For those familiar with predicate logic, the universal sentence (x)(Rx"Bx) (which says All ravens are black)

does not entail the singular sentence Ra& Ba(which says Individual ais a raven, and individual ais black).

me hypotheses in science are existential (i.e., Quarks exist); or a combination of universal an

istential (i.e., Every human dies a finite number of years after his/her birth). Hempel

dressed this problem with a more complex definition of instance. In general, however, there

e three problems that all versions of instance confirmation face (Hempels as well as Nicods):


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Problems with Instance Confirmation

) Ravens Paradox

laim: Instance confirmation allows evidence that is seemingly irrelevant to a given Hto

confirm H.

H1 = All ravens are black

H2= All non-black things are non-ravens

E1 = a black raven

E2= a piece of white chalk

ote: H1and H2are logically equivalent-- whenever H1is true, so is H2and vice-versa.

Hempel (1945) Studies in the Logic of Confirmation

Equivalence condition:

If Econfirms H, and His logically equivalent to H', then Econfirms H'.

hen: E2(a piece of white chalk) confirms H1(all ravens are black)! "Armchair ornithology"!

Moral: Instance-confirmation does not take relevancy into consideration.

(E1seems more relevant to H1than does E2.)

) Goodmans Paradox

laim: A piece of evidence Ecan be a positive instance of two incompatible hypotheses

(depending on how Eis interpreted).

Goodman (1955) Fact, Fiction and Forecast

et:

ow: Suppose we adopt the

Def. 1: Individual ais blitejust when ais blackif observed before 12/31/2006

and whiteif observed thereafter.

H1= All ravens are black

H2= All ravens are blite

et:

ow: Suppose we observe a blackraven on 11/31/2006. Does it instance-confirm H1or H2?

esponse #1: Wait until 12/31/2006 to determine what the evidence is whether it instance-

confirms H1or H2.


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eply: Time-dependence of a property is a relative characterisitic. Blitecan be viewed as time-

independent by defining blackin the following explicitly time-dependent manner:

eply: Consider H3= All ravens are blite3000. After 12/31/2006, the evidence fails to distinguis

H1from H3.

Def. 2: Individual ais blite3000just when ais blackif observed before 12/31/3000

and whiteif observed thereafter.

general: For any time t, we can define a property blitetthat is identical to blackup till tand

whitethereafter.

o: There are an infinitenumberof hypotheses that are instance-confirmed by what appears now

or at any time in the past or future, as a blackraven. Given the purely formalnotion of

evidence under Instance Confirmation, there is never a point at which we know for certain

what any given piece of evidence isand what hypothesis it instance-confirms.

esponse#2: The property blite(and its variants) is illegitimate because it is explicitly time-

dependent.

Def. 3: Individual ais blackjust when ais bliteif observed before 12/31/2006

and whackif observed thereafter.

Def. 4: Individual ais whackjust when ais whiteif observed before 12/31/2006

and blackif observed thereafter.

Note: The issue is what appearsformallyin the definition of a property. The claim is simply that whether or

not time-dependence appears in the definition is a purely formal matter. Of course what we really are concerned

with is whether or not the property we call blackistime-independent: is it really "projectible" into the future?

ASIDE: Hume's Problem of Induction(as we shall see) claims: There is no justification for projecting pastuniformities into the future (how do we know that all ravens will continue to be black in the future?).

Goodman's New Problem of Inductionclaims: Even if we allow that there areprojectable uniformities (ravens

do have some projectable property), there is no way to establish whatthey are (but is it blackor blite?).

Moral: A purely syntactic(i.e., formal) description of Econfirms H is

problematic. We need to take semantic(i.e., interpretational)

considerations into account in defining the confirmation relation.


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) Theoretical Hypotheses

laim: Instance confirmation cannot by itselfexplain how purely theoreticalhypotheses can be

confirmed.

purely theoretical hypothesis is a theoretical claim; i.e., a claim about an in-principle

observable object. An instance of such a claim will apparently be an in-principle unobservable

ject. Hence we can never have evidence Efor a purely theoretical hypothesis Hif our Eisstricted to instances of H.


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7. Probability and Confirmation

Motivation: Confirmation is an epistemicnotion; cant be described in purely syntactic (formal

logical) terms. Fundamental Question: How does evidence contribute to the credibilityof a

theory?

HD describes the confirmation relation as deductive entailment(syntactic relation).

Instance Confirmation describes the confirmation relation in terms of the formal notion of

an instance of a universal sentence(syntactic notion).

The Bayesian Accountdescribes the confirmation relation in terms of the notions of

probabilityand degrees of belief.

obability (Pr) function: A function that assigns a number between 0 and 1 to events.

Pr(B/A) means the probability of event Bgiven event A

Topics:I. Probability AxiomsII. Interpretations of ProbabilityIII. Bayesian Confirmation Theor

A1: 0 !Pr(B/A) !1. Every probability is a unique real number between 0 and 1.

A2: If A!B("Aentails B"), then Pr(B/A) = 1.

A3: Special Addition Rule. If Band Care mutually exclusive(cant both occur

simultaneously), then Pr(Bor C/A) = Pr(B/A) + Pr(C/A).

A4: General Multiplication Rule. Pr(B& C/A) = Pr(B/A)Pr(C/A& B)

Probability Axioms

) Negation Rule. Pr("B/A) = 1 #Pr(B/A) Proof: Pr(Bor "B/A) = 1 = Pr(B/A) + Pr("B/A)

) Rule of Total Probability. Pr(C/A) = Pr(B/A)Pr(C/A& B) + Pr("B/A)Pr(C/A& "B)

Proof: Pr(C/A) = Pr((B&C) or ("B&C)/A)

= Pr(B&C/A) + Pr("B&C/A) (A3)

= Pr(B/A)Pr(C/A&B) + Pr("B/A)Pr(C/A&"B) (A4)

C is logically equivalentto (B & C)or(!B& C)

Theorems (Consequences of Axioms):


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) Bayes' Theorem

Proof: Pr(B&C/A) = Pr(B/A)Pr(C/A&B) (A4)

Pr(C&B/A) = Pr(C/A)Pr(B/A&C) (A4)

Pr(B/A&C)=Pr(B/A)Pr(C/A&B)

Pr(C/A), Pr(C/A)! 0

=Pr(B/A)Pr(C/A&B)

Pr(B/A)Pr(C/A&B)+Pr(" B/A)Pr(C/A& " B)

ample: Frisbee Factory. Part 1.

achine #1 (M1): produces 800 frisbees/day, 1% of which are defective.

achine #2 (M2): produces 200 frisbees/day, 2% of which are defective.

= getting a frisbee produced on May Day "B= getting a frisbees produced by M2

= getting a frisbee produced by M1 C= getting a defective frisbee

ote: Pr(C/A) = Pr(B/A) $Pr(C/A& B) + Pr("B/A) $Pr(C/A& "B)

$ $+=

Prob of getting adefective frisbee,given it's a MayDay frisbee

Prob of gettingan M1 frisbee,given it's a MayDay frisbee

Prob of getting adefective frisbee,given it's an M1May Day frisbee

Prob of gettingan M2 frisbee,given it's a MayDay frisbee

Prob of getting adefective frisbee,given it's an M2May Day frisbee

= 0.8 $0.01 + 0.2 $0.02 = 0.012

ote: Bayes' Theorem lets us calculate "inverse" probabilities; i.e., probabilities of past events,

based on present events.

uestion: What is the probability of getting a defective May Day frisbee? What is Pr(C/A)?

ample: Frisbee Factory. Part 2.

uestion: Given a defective frisbee, what is the probability that it's an M1 frisbee? What is Pr(B/A& C)?

Pr(B/A &C) =Pr(B/A)Pr(C/A & B)

Pr(B/A)Pr(C/A & B)+ Pr(! B/A)Pr(C/A& ! B)

=0.8"0.01

0.8"0.001+ 0.2"0.02= 2/3

Prediction: Given a cause, what is the effect?

"Retrodiction": Given an effect, what is the cause?


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. Interpretations of Probability

Classical Interpretation Laplace 1814 A Philosophical Essay on Probabilities

Ex1. A= getting an even number on roll of standard die

favorable cases of A= {2, 4, 6}

equally possible cases of A's type= {1, 2, 3, 4, 5, 6} Pr(A) =

3

6

Ex2. A= getting two heads on the flip of two non-biased coins

favorable cases of A= {HH}

possible cases of A's type= {HH, HT, TT}equally possible cases of A's type= {HH, HT, TH, TT}

hy "equally" possible?

Pr(A) =1

4

Pr(A) =# of favorable cases of A

# of equally possible cases of A's type

Principle of Indifference (PI):

Two outcomes are equally possibleif we have no reason to prefer one to the other.

roblem: PI may lead to violations of the Probability Axioms!

Ex3. Joe the Sloppy BartenderJoe's sloppy mix for a 3:1martini: Anywhere from 2:1to 4:1

Two properties associated with Joe's sloppy martini:

(1) Ratio of gin to vermouth: From 2:1 to 4:1

(2) Proportion of vermouth: From 1/3 = 20/60 to 1/5 = 12/60

3:1martini = 3parts gin, 1part vermouth

Now: Consider the two following outcomes for Property (1):

Next martini will have a ratio of gin to vermouth of 2:1to 3:1.

Next martini will have a ratio of gin to vermouth of 3:1to 4:1.

PI: Both outcomes are equally possible!

Now: Consider two outcomes for Property (2):

Next martini will have a proportion of vermouth of20/60 to 16/60.

Next martini will have a proportion of vermouth of16/60 to 12/60.

PI: Both outcomes are equally possible!

But! The PI has now given us contradictory predictions!

(a) According to the PI applied to Property (1), there's a 50% chance that Joe's next

martini will have a proportion of vermouth between 20/60 and 15/60 (=1/4).

(b) According to the PI applied to Property (2), there's a 50% chance that Joe's next

martini will have a proportion of vermouth between 20/60 and 16/60.

Two differentprobabilties for th

same outcome:Violation ofAxiom 1

2 non-linearlyrelated properties!


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Frequency Interpretation

Pr(A) = the limit of the sequence of relative frequenciesof A.

Ex1. A= getting a head on flip of non-biased coin

Actual flips: H T H T T T H H T T H T T T H ....

Relative frequencies of A: 1/1, 1/2, 2/3, 2/4, 2/5, 2/6, 3/7, ...

Pr(A) = limit of the sequence {1/1, 1/2, 2/3, 2/4, 2/5, 2/6, 3/7, ...} = 1/2.

Relative frequency of A =#of actual occurances of A

#of actual occurances of events of A's type

What this means: As the members of the sequence go to infinity, ifthere is a member afterwhich all other

members are very close to some number L, then Pr(A) = L. If not, then Pr(A) is not defined. (And we

believe, in this case, that the limit exists and is 1/2.)

o: A sequence of relative frequencies = sequence of real numbers!

ef. A sequence of real numbers has a limitLjust when there is a member of the sequence

afterwhich all other members are very close to L. If there is no such member, then the

sequence has no limit.

wo Problems

finite data

(behavior of finiteinitial sequence)

limit

(behavior ofinfinite sequence)

extrapolate

How? And what justifies this process?

ASIDE: Mathematically, theproblem is to determine a uniq

formula that describes a givensequence of relative frequencieOnce we have such a formula,

determining if it has a limit, anwhat it is, is not difficult. Butan infinite number of formulasare compatible with any finiteinitial sequence of real number

Claim: Anylimit Lis compatible with anyfinite initial data sequence

How are limiting frequencies determined?


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Propensity Interpretation

Ex. Coin flips

Let

m

n

!

"##

$##

%

#

'##

=

#heads

#totalflips

!

"##

$##

%

#

'##

be a finite sequence of relative frequencies.

Suppose limiting frequency = 1/2.

Then the sequence

m+ a

n+ b

!

"##

$

##

%

#

'

##

also has limiting frequence = 1/2, where a!b.

What this means:

(a) Add any sequence of bflips, aof which are heads, to {m/n} and limiting frequency remains unchanged.

(b) Chop off any sequence of bflips, aof which are heads, from {m+a/n+b} and limiting frequency remains

unchanged.

So:

Strong Claim: The observed relative frequencies in any finite sample are irrelevant towhether a limiting frequency exists and what it is.

) How are Single Case Probabilities Explained?

How does the Frequentist explain the probability of a single occurance?

Pr(A) = a measure of the causal tendancy(propensity) to produce A.

Ex. A= getting a 6 on roll of a standard die

Pr(A) = 1/2 = measure of the propensity in the die to produce 6 upon oneroll

Ex. Outcome of 2008 election. What does it mean to say "The probability of a democrat winning is 85%"?

explains single case probability

roblem: How are "Inverse" Probabilities Explained?

ote: The Propensity Interpretation explains the probability of an outcomein terms of its cause

ut: Bayes' Theorem lets us calculate the probability of a causein terms of its outcome/effect!

o: The Propensity Interpretation cannot explain alltypes of probabilities.


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Personalist Interpretation

Pr(A) = the degree of beliefin Aof an ideal rational person whose set of beliefs

conform to the Probability Axioms.

ef1. An incoherent set of beliefsis a set that does not conform to the ProbabilityAxioms.

laim: A person is subject to a Dutch Bookif and only if that person holds an incoherent

set of beliefs.

ef2. A Dutch Bookis a set of bets such that the subject loses no matter what the

outcome of the event wagered on.

Example

Let A= getting heads on next flip of coin.

"A= getting tails on next flip of coin.

Suppose: Joe's degree of belief in A= 2/3. %2:1 odds for heads

Joe's degree of belief in "A= 2/3. %2:1 odds for heads

"2:1 odds" means"Joe is willing torisk $2 to gain $1"

(A) Heads

Heads bet pays off: +$1

Tails bet fails: #$2

#$1 net

(B) Tails

Heads bet fails: #$2

Tails bet pays off: +$1

#$1 net

Only 2 possible outcomes:

Joe loses no matter what! Joe has succumbed to a Dutch Book!

Why Did Joe Succumb To a Dutch Book?

Because his set of beliefs did not conform to the Probability Axioms. In particular, he failed to abide by

the Negation Rule: Pr(A/K) + Pr("A/K) = 1, where K= "background knowledge".

mportant Distinction

ropensity Interp: Probabilities measure the tendancy of a mechanism to produce a

single outcome.

requency Interp: Probabilities are properties of sequences of outcomes.

Both agree that probabilities are objective features of physical systems.


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Logical Interpretation

roblem: Too "subjective"?

nyset of beliefs will be judged rational so long as it conforms to the Probability Axioms.

ntuition: You can subscribe to really strange, WEIRDbeliefs, so long as your belief system is

nsistent!)

This means that the Personalist Interpretation does not explain or prescribe how the values of

probabilities are to be set/determined (a problem similar to one faced by the Frequency Interpretation).

Pr(A) = a weightedsum of all state descriptionsof the universe in which Ais true.

state description= a description of a possible way the universe could be ordered.

xample: Simple universe with 3 individuals and one property

dividuals: a, b, c

operty: F

ow to assign weights? Carnap's Method:

) Group state descriptions according to similar structure.

) Assign equal weights to structure descriptions.

Assign equal weights to all state descriptions with same structure.

State Description Weight Structural

[bain] notes on philosophy o science

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