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Bas van Fraassen - The Scientific Image
Chapter Five: The Pragmatics of Explanation
The language of explanation
● A theory T can explain a fact E without being either true or empirically adequate
○ thus to say that T explains E does not commit us to either the realism or the empirical
adequacy of T
○ so the question of the acceptability of an explanation is separate
■ when we say we ‘have an explanation’ this implies that our explanation is
acceptable
● The grammar of explanation is such: fact E explains fact F relative to theory T
○ e
...
the gravitational pull of the moon explains the ebb and flow of the tides in Newton’s
theory
A biased history (of theories of explanation)
1
...
g
...
Red shift is a
consequence of the galaxy moving away from us, not the reason for the motion
○ unnecessary - we can explain without giving good grounds to believe that a phenomena
will occur - in cases of low probability
...
g
...
this means that we can warn
someone with untreated syphilis that they may contract paresis (explanation), but doesn’t
give them good grounds to believe that they will do so
● We would have to modify the account such that the explanatory information gives us good and
relevant grounds for believing the phenomena has, does or will occur
○ this invites us to the problem of what is meant by relevance
● Testability is met by all scientific theories, so can’t help ameliorate the difficulties with Hempel’s
account
2
...
5, Salmon’s is not - it allows for the probability of E given F
to be lower than that of E simpliciter
■ this can explain the paresis example
○ BUT statistical relevance cannot explain, for example, why an event happens at one
particular moment rather than another
Statistical relevance is neither necessary nor sufficient for explanation
○ insufficient - we can assemble the statistically relevant factors without always explaining
■ e
...
if we spray some ivy with a poison that is 90% effective, we can explain the
death of some ivy with the statistically relevant factor, but we can’t explain why
the 10% is still alive by saying ‘because it was sprayed with poison’
○ unnecessary - we can explain without reference to statistically relevant factors
■ e
...
if paresis can be contracted from either syphilis or epilepsy with a probability
of paresis given either equalling 0
...
John belongs to a family in which everyone
has either syphilis or epilepsy
...
This is an explanation, despite
the fact that extra knowledge that he had, say, syphilis, would not alter the
probability of him developing paresis at all
It seems that both Hempel and Salmon see explanatory power as nothing more than empirical
adequacy and empirical strength
○ thus explaining an event is indistinguishable from a) showing its occurrence to not
constitute an objection to the empirical adequacy of one’s theory, and b) providing
information entailed by the theory and relevant to the event’s occurrence

Global properties of theories
● Friedman views scientific explanation not as a question of explaining individual phenomena, but
of making sense of broader phenomena through global theories
○ hence we evaluate something as an explanation of P relative to an assumed background
theory, K
● Problems:
○ what is included in the background theory - just laws, or information as well?
■ if information, it can’t include all our information, because we know that P when
we ask for an explanation of P
○ an explanation relative to K implies that P is true - but of course, the point to explain
might be the non-occurrence of P: cf
...
why should explanation rest on this?
The difficulties: asymmetries and rejections
● Two cases that none of these theories of explanation can deal with:
○ where the request for explanation is rejected, despite the case lying within a theory’s
domain
■ e
...
Newton’s theory did not contain an explanation of gravity, only a description

○

■ not everything within a theory’s domain is a legitimate topic for why-questions
asymmetry: even if a theory implies that one condition obtains when and only when
another does, it may be that one condition is explained in terms of the other and not viceversa
■ redshift and flagpole examples

Causality: the conditio sine qua non
● In modern philosophy, causation is seen as a relation between events
...
hence if A and C then B’ cannot be translated into natural language
directly, because ‘If the match is struck it will light
...
This doesn’t seem like an explanation
■ here we must recognise that all these factors form a causal network, for which we
must identify the salient part
● which part is deemed salient is context dependent
○ in fact, the truth-conditions of the counterfactuals introduce further context-dependence
■ ‘if the plant had not been sprayed, and all else had been the same, then it would
not have died’ is only true where ‘all else’ that is kept ‘fixed’ rules out all other
ways for the plant to die
● but it is the speaker who keeps the situation fixed, in their own mind
● hence we can imagine two speakers, with different information,
contradicting each other’s counterfactual conditionals
○ but is this really a contradiction? isn’t it better modelled as two
different contexts for ‘everything else being equal’?
○ possible worlds doesn’t solve this problem, because there are so
many different relations of similarity: how are we to determine
the closest possible world? different from context to context

○

■

e
...
‘Danny is a man, Danny likes women
...
g
...
g
...
g
...
g
...
a son is not the same as a man, even if all sons are men, and every man is a son)
○ an explanation is an answer to a why-question
A theory of why-questions
● A why question ‘why P?’ presupposes that P, and asks for a reason
○ the proposition that P is the topic of the question
○ the question has a contrast-class, which is a class of propositions including that P
i
...
g
...
This claims:
○ that P is true
○ that the other members of the contrast class are not true
○ that A is true
○ that A is a reason (because)
● Does ‘because’ not signify a modal/counterfactual/other failed model?
○ no, it simply means that A is relevant to P in the causal process (Salmon), as the why
question is interpreted
Evaluation of answers
● How do we decide whether an answer is telling, good, or better?
○ is it acceptable/likely to be true?
○ does A favour the topic B as against the other members of the contrast-class?
■ cf
...
g
...
Kuhn and the image of science
● Two lines of attack on normal image of science:
○ Weak/boring attack - there is a special method and ideal mode of application but
scientific practice falls short of this
○ Strong/exciting attack - there is no such defensible ideal with which actual practice can
be compared (early Kuhn)
● Is Kuhn’s use of term ‘paradigm’ too vague? Components include:
○ Shared symbolic generalizations - theoretical assumptions that are deployed without
question
○ Models - agreement over particular analogies or that certain connections should be
treated as identities
○ Values - theories ought to be accurate, consistent, wide in scope, simple and fruitful
...
g
...
Demonstrated by textbooks
...
g
...
Revolutions
● Normal science includes agreement over problems and over what constitutes a solution
○ during normal science, if a test fails, the ability of the tester is questioned, not the theory
● Breakdown leads to competition between paradigms
...
In fact, given that
opposing paradigms are incommensurable, only propagandizing plays a role
● Kuhn assumes radical meaning variance (RMV), which holds that there is no logical
contradiction between Newton’s assertion that simultaneity is not relative and Einstein’s assertion
that simultaneity is relative
● RMV means that the problem of rational comparison of rival theories does not arise (what about
degrees of RMV?)
● Incommensurability of paradigms would surely rely on radical variance in what constitutes a

good explanation - incommensurability due to radical standard variance
○ Kuhn does not show that what constitutes a good explanation has varied in the history of
science
○ e
...
shift from gravity as innate (and hence inexplicable (dubious?)) to mechanical
explanation of gravity represents a change in beliefs as to what can be explained, not
what constitutes a good explanation
○ Kuhn claims that the question: ‘which problems is it more significant to have solved?’
cannot be resolved non-circularly or non-paradigmatically
○ But surely the solution to problem A could be shown to lead to x, y and z paths of fruitful
research, whereas B is a dead-end (isn’t this still paradigmatic?)
3
...
Kuhn does describe some of the characteristics good scientific
theory should have:
○ Accuracy within its domain; should be in agreement with results of existing
experiments/observations
○ Consistency, internally and with other accepted theories
○ Broad scope - consequences should extend far beyond the particular
observations/laws/sub theories it initially explains
○ Should be simple - bringing order to otherwise confused phenomena
○ Should be fruitful of new research findings - should disclose new phenomena
● Problem is different beliefs as to which theories are actually most simple, consistent, broad etc
● Kuhn says that these five factors can be used to persuade scientists to change their mind, but this
doesn’t show one theory to be better than another
○ these factors only have force because they are generally accepted, and there is no way of
justifying them
○ thus the recognised criteria doesn’t allow for justification (functional exp: is this the
accepted criteria because it doesn’t allow for justification?)
● If there is no justification for these or any other principles of comparison, the project of the
rationalist is doomed
○ Kuhn believes that if there could be justification for comparison, the principle of
induction would be solved, and it cannot be
■ which principle of induction? If Kuhn means that nothing can constitute
evidence that an empirical claim is more likely to be true than false, then his
historical study is pointless; it is a philosophical thesis
...
g
...
Duck-Rabbits
● Kuhn describes the change in world view upon adopting a new paradigm as akin to suddenly
seeing a duck-rabbit as a rabbit, rather than a duck
○ NS - this is an absurd example - none of us had such a dramatic shift of attitude when we
went from Newtonian mechanics to Einsteinian mechanics at school (but was Newtonian
mechanics science or history? Is Einsteinian mechanics, as taught through paradigmatic
exemplars, science? Maybe not in Kuhn’s view)
○ In this example, and in others like it, one cannot simultaneously see the duck-rabbit as a
duck and a rabbit, and nor is there a way in which it should be seen
...
Where is Truth?
● Kuhn’s controversial thesis is that different scientists looking at a swinging stone see different
things - pendulum/constrained body etc
○ the scientists are LOOKING at the same phenomenon, but SEE different things, and
relations between things
● Science’s existence and success can be explained without reference to some ‘full, objective, true
account of nature and that the proper measure of scientific achievement is the extent to which it
brings us closer to that ultimate goal’
○ the idea of matching the ontology of a theory and what is really there is illusory; there is
no theory-independent way of reconstructing phrases like ‘really there’
● If this means that truth is relative to theory, we have an idealist gloss
...
But if truth is
paradigm-relative and we can realize when truth-conditions are satisfied, then the
translation between paradigms implies a theory neutral notion of truth
Kuhn and the Rationalists
● Kuhn’s belief in the impossibility of justifying the ‘Five Ways’ means that the evolution of
science can only be explained externally, and not internally
...
We can understand which choices they will make and what problems
they will undertake, but there is no internal logic or narrative
...
Under this interpretation Kuhn
is still not a realist, for progress is not related to truth or verisimilitude

 

Nagel - The Structure of Science
The Logical Character of Scientific Laws
●

Laws have the form of generalized conditions: ‘For any x, if x is A then x is B’
○ fulfilment of this schema is not sufficient for something to be classed as a law
○ thus the difference between lawlike universal statements and non-lawlike universal
statements will underpin much of any explanation

Accidental and Nomic (i
...
lawlike) Universality
●

●

●

●

Scientists characterise many statements as laws, but there are divergent opinions
○ is it a law if it refers to a particular object e
...
the sun?
○ are statistical generalizations laws?
○ can we ever make laws of uniform human behaviour e
...
economics?
If we use the schema ‘For any x, if x is A then x is B’ then we do not discriminate between
accidental and nomic universality
○ because of the rules of logic, if the antecedent is false, then the universal conditional is
true irrespective of the content of its consequent - ‘vacuously true’
This is inadequate; laws express more than coincidental concomitance between objects
○ in the case of nomic universality, we want to say that there is not, never has been, and
never will be an x such that it is A but not B; that it is physically impossible
...
g
...
’
So how can we support subjunctive conditionals, given that they are not formalizable?

Are Laws Logically Necessary?
●

●

It seems that laws are necessary
...

1
...

● but some seeming laws do refer to particular objects e
...
the sun
○ also there may be laws that properly formulated must contain a specific temporal
restriction
● one way around this is to distinguish between ‘purely qualitative’ and other types of
predicate
...
Another distinction can be made between
fundamental and derivative lawlike statements, whereby universal conditions are
fundamental if they contain no individual names and all its predicates are purely
qualitative, and derivative statements are logical consequence of some set of fundamental
statements
...

● Problem: most extrapolations from fundamental statements that contain references to
particular objects rely on more premises (i
...
facts about the world) than simply
deduction from fundamental laws
● Alternatively, we may require simply that laws be universals that are not restricted to
a specific volume of space or interval of time
2
...
e
...

unrestricted universal may be true if vacuously true
● The vacuous truth of an unrestricted universal is not sufficient for counting it as a law; ‘it
counts as a law only if there is a set of other assumed laws from which the universal
is logically derivable’
3
...
No analogous assumption is made in the case of nomic universals
...
There is usually a strong disinclination to consider something to be a law of nature if the only
evidence
available for it is direct evidence (ie observation)
● thus a statement is only accepted as a law when there is ‘quite overwhelming evidence’
needed to dislocate it
● hence for many supposed laws we may be disposed to reinterpret apparently negative
evidence in order to retain the statement as part of out knowledge
Contrary-to-fact Universals (Counterfactuals)
●

The conditions laid out above are not sufficient for a statement to be considered a law
...
One criticism of Humean analysis is that de facto universals cannot support subjunctive
conditionals
○ for example, ‘All ravens are black’ does not support the subjunctive conditional ‘for all x,
if x were a raven then x would be black’, and specifically ‘if inhabitants of polar regions
were ravens they would be black’ because we do not know if certain conditions e
...
polar
conditions would affect ravens’ plumages
...
But more interestingly
we could argue that the law is in a position to support some conditionals, but not this
particular one, because we do believe that environmental factors can affect things like
plumage
...
The problem of counterfactuals is how to make explicit the logical structure of counterfactual
statements (‘If a were P, then b would b Q’), which cannot be translated straightforwardly into
non-modal logic in the indicative mood
○ If we try to do so, we end up with an antecedent-consequent for which the antecedent is
false, and thus the consequent is vacuously true
○ To get around this, we can say that the indicative form of the consequent follows
logically from the indicative form of the antecedent (though they no longer take the form
of if-then) when the antecedent is conjoined with the relevant laws and initial conditions
for the law - the counterfactual is asserted within some context of assumptions and
special suppositions
■ it may be very difficult in some counterfactuals e
...
sociohistorical ones, to set
out the context of assumptions and special suppositions

Causal Laws
●

●

 

A law is said to be causal apparently because the relation it formulates satisfies the four
conditions above
○ many understandings of causal laws state necessary but not sufficient conditions for
cause-effect relations e
...
if you strike a match it will burst into flame neglects need for
oxygen, dry match etc
Most types of law in science are not causal
...
Why? Because there
are more ways for a stick to be horizontal than vertical
...
Hence insofar as we
explain we must accept the existence of such entities
● Baker’s indispensability argument claims that ‘Mathematics is indispensable for our best science
...
’
○ this view is supported by the idea that postulating mathematical entities might result in an
increase of ‘theoretical virtues’ including explanatory power (Melia, Colyvan)
● So the argument so far is:
○ there are genuinely mathematical explanations of empirical phenomena
○ we ought to be committed to the theoretical posits of these explanations
○ therefore we ought to be committed to the mathematical entities postulated by these
explanations
● Are we committed to the real existence, or the fictional existence, of the posits of such
explanations?
From mathematical explanations of scientific facts to mathematical explanations of mathematical facts
● Is the indispensability argument question begging?
○ we cannot use the existence of genuine explanations to imply mathematical entities,
because ‘genuine’ explanation implies true explanans
● (IF we assume the existence of some basic mathematical entities) we can argue via explanatory
power for the existence of other, more abstract entities, in a different indispensability argument:
○ there are scattered results in one branch of mathematics which call for an explanation

●
●

○ such an explanation could refer to more abstract entities e
...
ideals, analytic functions
○ therefore we have good reason to believe in the existence of such abstract entities
Such an argument, as the previous one did, requires an element of realism (in this case over the
existence of natural numbers, for example)
Although Quine and others have used indispensability arguments to post the existence of abstract
entities - sets, numbers etc - via empirical science, we may try to explain the existence of
mathematical entities through solely mathematical explanations

Mathematical explanations of mathematical facts
● In the history of maths there has been a preference for theories that convince AND show why
they are true, rather than theories that convince but do not explain
○ however, mathematical explanations do not only come in the form of proofs
...
f
...
e
...
Steiner sort of rejects this - explanatoriness
cannot be accounted for in terms of generality BUT explanatory proofs must be
generalizable

 

 

David Lewis - The Metalinguistic Theory: Laws of Nature
●

●

●

●

●

Laws of nature are often understood such that if an antecedent of a counterfactual is taken
together with some laws, and the antecedent is consistent with all laws, then the counterfactual is
true
...

This view of laws could be incorporated into Lewis’ metaphysics by claiming that there exist
possible world ‘spheres’ around world i such that those worlds do not violate the laws prevailing
in world i, and that worlds are more distant insofar as more (qualitatively or quantitatively?) laws
of i are violated in them
...
However, the status that they do have is not arbitrary
...
e
...
P
...
These virtues tend to conflict - pure logic is simple but not
strong
○ We value a balance of simplicity and strength
○ Thus a restatement of the theory of lawhood is: a contingent generalization is a law of
nature if and only if it appears as a theorem/axiom in each of the true deductive
systems that achieves a best combination of simplicity and strength
○ A generalization is a law at a world i, if and only if it appears as a theorem in each of the
best deductive systems true at i
...
If we knew everything truth would not
be a consideration, though strength/simplicity still would
This theory succeeds in explaining six facts about laws of nature:
1
...
Lawhood is contingent
...
It explains how we can know by exhausting instances that a generalization is true, but
not that it is a law
4
...
Duh
...

5
...
Lawhood seems a vague concept, because our notions of strength and simplicity are
only roughly fixed

●
●

 

Laws, so defined, are important, and make a big different to the character of a world
...
In the
second the facts up to the event are the same, and the laws would be almost identical but
a small miracle occurs and the wheel lands on red
○ which is closer? the latter
...

○ therefore the preeminence of laws of nature among cotenable factual premises is a matter
only of degree

 

Thomas Kuhn - The Structure of Scientific Revolutions
Chapter 9: The Nature and Necessity of Scientific Revolutions
●

●

●
●

●

●

●

Why call a change of paradigm a revolution?
○ in the case of politics, revolutions are necessitated when the existing institutions have
ceased to adequately meet the problems posed by their environment
...
When debating paradigm choice, a paradigms is defended with the
use of the very same paradigm - necessarily circular
○ Paradigm conflict cannot be resolved by logical or probabilistic argument, because there
are insufficient common premises/values between paradigms
...
These are examples of cumulative scientific development, but it is rare in practice
Yet historically scientific development has demanded the destruction of prior paradigms
In order for new discoveries to emerge, paradigms must be destroyed - they can only emerge to
the extent that previous anticipations about nature and instruments have been wrong
...

Thus the two paradigms are logically incompatible
○ It is not logically impossible that science could proceed in a cumulative manner, but
insofar as science proceeds through paradigms, it is historically implausible
Objection from early logical positivist school: any theory that has been accepted must be correct
(in some sense)
...
Thus Einstein’s
relativity did not prove Newtonian dynamics incorrect, but rather science supposedly never
demanded that Newton’s laws should be applied to certain scale problems, or to a certain level of
precision
...
Science would be static around what could be
explained by theories - there would be no anomalies and without anomalies there cannot
be progress
...
g
...
g
...
g
...
Arguments are relevant to explanations
because ‘p’ bears an appropriate relation to a particular argument
● There is a set of arguments available for explanatory purposes, and these can be referred to as the
explanatory store
...
g
...
g
...
g
...
The explanatory store may be
extended by the addition of approximately true, approximately similar arguments that are simpler
(i
...
refuted theories that are still pretty good)
● We can posit the existence of a generating set, which describes all of the patterns of argument of
in a set of arguments
● The we determine which of the generating sets of all the possible sets of arguments is most
complete with respect to K
● Unifying power is achieved by generating a large number of accepted conclusions from a few,
stringent patterns
...
Generalized solution seems to be that explanatory unification wins the day because it
requires that explanations apply to many cases, and unify our beliefs
...
This is impossible, in
both history (social sciences) and the natural sciences
● The use of universal empirical hypotheses distinguish genuine from pseudo-explanations, which
rely upon metaphor , vague analogies and intuitive ‘plausibility’
● For any scientific explanation, the original conditions, the universal statements and the
relationship between the two can all be checked empirically
● The logical structure of scientific prediction is very similar to that of scientific explanation:
○ a statement about a future event is derived from
■ statements about known past or present conditions
■ statements of applicable general laws
● It may be said that an explanation is not complete unless it could have functioned as a prediction
○ However, explanations are rarely stated so completely as to exhibit a predictive character;
often most or many universal generalizations AND original/determining conditions are
omitted entirely
● Historical explanation, as well as explanation in empirical sciences, aims to show that events
were to be expected in the light of certain conditions - rests on assumption of universal laws
● Explanations offered in history often fail to explicitly state the general regularities they
presuppose, for two possible reasons:
○ The regularities relate to individual psychology, which is supposed to be familiar to all
and hence taken for granted
○ It would be difficult to state the purported regularities in such a way as they would be
consistent with all empirical observation e
...
people tend to migrate to areas with better
living conditions; or explanations in terms of class struggle etc
● We could suggest that the phenomena are of a statistical character, and thus the generalizations
only need to be probabilistic (isn’t this just ignorance of all conditions and all generalizations?)
● Clearly explanatory analysis of historical events can only offer an explanatory sketch, which does
not admit so readily of an empirical test
○ however, in contrast to nonempirical explanations or sketches, empirical explanations
will at least indicate what kind of evidence might tend to confirm them
● In order to test a given explanation, we should try to reconstruct the conditions of the argument as

far as is possible, identifying the words ‘thus’ ‘therefore’ ‘because’ etc
○ in this manner we will see that many ‘explanations’ are very broad sketches e
...

geography and economics determine art
○ If we test the claim that a theory successfully predicted a future event, we must examine
the extent to which this prediction was borne out of the theory as opposed to an
individual’s lucky guess
●

●

●

●
●
●

 

This view of historical explanation contrasts with the ‘empathetic understanding’ of history,
whereby a historian tries to imagine how an agent would have acted, without reference to general
laws
○ this relies on intuitive plausibility and what appeals to our imaginations
Some ‘interpretations of historical phenomena’ rely on interpretation by means of some particular
approach or theory (e
...
Marxism???)
○ this means subsuming evidence under a general idea which is not susceptible to empirical
tests - bad
‘Development of institutions’ type enquiries rely upon descriptions of ‘relevant’ conditions and
facts, but for them to be relevant they must be causal, and thus we arrive at explanation as we
have already conceived it
Claims about determination and dependence similarly rely upon testable universal empirical laws
There may or may not be any specifically historical laws
...
’

 

Carl Hempel - Studies in the Logic of Explanation
Intro
●

To explain a phenomena is to answer a ‘why?’ question rather than a ‘what?’ question
○ i
...
explanation stands in contrast to description

Elementary survey of scientific explanation
● An explanation has two main constituents:
○ explanandum - the sentence describing the phenomena to be explained (rather than the
phenomenon itself)
○ explanans - the group of sentences that are adduced to account for the phenomenon
...
g
...
covering law models would at best grant external understanding
○ Covering law logicians respond to this by claiming it is a method and psychological
description, but that alone it suggests that ostensible empathy is equivalent to
understanding/explanation

Explaining and Justifying Actions
● When we ask for an explanation of a historical action, often we want a reconstruction of the
agent’s calculation
○ but the agent may not have calculated deductively, or with propositions, or even
deliberately
■ in these cases there may be nothing for the historian to do, but in any case, an
action is purposive insofar as there is a calculation which could be attributed to it
● There is an element of appraisal when we attempt explanations of social actions; we are interested
in what was seen to be appropriate; whether it was justified or excusable
○ of course, rational means more than the right/proper/intelligent thing to do - we must
investigate value norms/social context/individual psychology/extent of information
available to agent in ascertaining justification
■ the investigator must bring in foreign data to piece together the calculation
● ‘What the historian declares to have been the agent’s reasons must really be reasons (from the
agent’s point of view)
...
If Newtonian mechanics can be derived from Einstein’s
mechanics, then meaning must be fixed
...

● Problem weighting
○ Theories should be assessed not by their empirical or observational consequences, but by
seeing how good they are at solving problems
○ Fitting theories to agree with observation is easy, if you don’t care what the theory looks
like
○ Thus problem solving is the unit of scientific achievement
○ But no paradigm can solve all problems, so we are left to choose which puzzles are most
important to solve
● Shifting standards
○ Paradigms include standards for assessing theories, and these vary
■ e
...
novel predictions, unified explanations
● The ambiguity of shared standards
○ The standards we do agree upon may be open to interpretation e
...
simplicity,
consistency
● The collective inconsistency of rules
○ Accepted standards may conflict
McMullin’s Criticisms of Kuhn
● Post Structure, Kuhn seems to have moderated his relativism
○ paradigm debate can be rational insofar as it is based on shared values
● Yet he still claims that no objective notion of progress can be applied across revolutionary divides
○ it is impossible to show that the values that act as a criteria are connected in any
necessary way with truth or verisimilitude
● Shared values
○ Kuhn allows that revolutions can shake all of science e
...
Newton, or else a small

●

●

backwater e
...
X-rays
○ For the less consequential revolutions, maybe shared values are unaffected, but surely big
revolutions involve debates about standards
○ Kuhn rejects the idea that science has a fixed essence, or set of necessary and sufficient
conditions to distinguish it from other disciplines, identifying it instead as Wittgenstein
does cluster concepts
○ But if this is the case, why shouldn’t the ‘shared values’ of science change over time?
The justification of values
○ Although we cannot prove the connection between epistemic values and truth, we can
demonstrate the connection between simplicity, fertility and predictive reliability and
explanatory success
■ prior to Copernicus, it was believed that theories couldn’t give both reliable
predictions and good explanations
■ thus maybe we can justify our use of these values by appealing to lessons of
history and experience (question begging regarding induction?)
Rationality and Realism
○ McMullin disputes Kuhn’s rejection of scientific realism
■ Kuhn claims that the Ptolemaic and Copernican theories had about the same
predictive accuracy
■ McMullin suggests that whilst predictive accuracy is similar, Copernican could
explain far more phenomena (surely Kuhn acknowledges this, but claims
explanation is paradigmatic - Ptolemaic theory could have ‘explained’ the same
things with any collection of sentences)
■ ‘Kuhn’s instrumentalism makes him unwilling to recognize the important
distinction between prediction and explanation’ - McMullin argues that
explanatory power is an indicator of truth
■ Copernican theory’s fertility in important lines of research can be valued on
epistemic grounds, as an indicator of truth
...
’

Laudan’s Criticisms of Kuhn
● Laudan is not a scientific realist, so he evaluates Kuhn’s claims at the level of problem solving
● Cites two distinct models of scientific rationality:
○ Hierarchical model - paradigms have three components: the factual, the methodological
and the axiological
...
g
...
Factual disagreement is resolved by
appeal to methods, methodological disagreement resolved by appeal to axioms
...
Paradigms can be divided into
components and accepted or rejected piecemeal
...
There can
be rational discussion about the aims and goals of science, and has been e
...

abandonment of Aristotelian ideal
According to Laudan, Kuhn’s picture of scientific rationality is misleading because he mistakenly
accepts the hierarchical model uncritically
...
Similarly the holism of the hierarchical
theory leads Kuhn to misunderstand the nature of paradigms
...
He refers to it as the thesis of local
underdetermination, because it refers to choices over the few paradigms that have actually been
put forward; global underdetermination would claim that methodological rules and standards
could not determine choices between any possible paradigms
Laudan claims that:
○ standards do not always change from one paradigm to another
○ some shared standards e
...
consistency, novel predictions are not ambiguous
○ not all sets of methodological rules give conflicting advice
○ hence Kuhn’s argument is unsound
Laudan makes a distinction between two types of ‘importance’ of scientific problems
○ personal, social or economic significance (nonepistemic)
○ significance in proving or disproving a theory, which is not necessarily subjective and is
epistemic

 

A
...
Ayer - What is a Law of Nature?
●

●

●

●

●

What does ‘law’ mean in this context?
○ Not imperative (though Hobbes included imperatives in his laws of nature)
○ Rather the commands issued by nature are so powerful that they cannot be disobeyed
○ To disobey the commands would represent a contravention of the laws of logic (??)
To think of the laws of nature in this way may suggest some form of logical necessity or
necessary relation between events
...

○ Hume refutes this suggestion by claiming there is no intrinsic relation between cause and
effect, thus we can only understand the ‘laws’ of nature through experience
○ But what if Hume is wrong? If we examine statements/laws of the form ‘All Xs are Y’
then when we come to accept the law we change our understanding of X
...
But if the ultimate goal of physics (and maybe even biology, social
sciences) is a unified theory in which everything is axiomatized, then surely all generalizations
would be logically necessary
...
Conversely, the more easily applicable it is, the looser it would have to be
logically (i
...
fewer analytic truths)
■ the more we put into our definitions, the more uncertain it becomes when
anything satisfies them e
...
if we say hydrogen has
303,000,000,000,000,000,000,000 molecules then we restrict what we can call
hydrogen
○ We may claim that it is a property of ‘laws of nature’ that they are not analytically true;
hence such an axiomatic system of science would be qualitatively different to current
science
○ Thus to object to Hume that cause and effect are necessarily distinct is simply to say that
there may be necessary, axiomatic systems that can take the place of natural laws
...
We cannot describe empirical laws of
nature as logically necessary
...
Thus ‘necessity’ on this view
is the simple lack of exceptions
○ this can be extended to statistical laws without problem
One problem: if we formalise ‘All S is P’ as ‘for all X, if X is S then X is P’ and the antecedent is

●

●

●

false, i
...
X is not S, then X will be P but also A, F, H, U, Z
...

■ Is this too strong? There are cases e
...
‘the Newtonian law that a body on which
no forces are acting continues at rest or in uniform motion along a straight line’
in which the set is empty; there are no bodies without forces acting upon them,
but we still believe the generalization is true and would be demonstrated if there
were such a body; we want to extend the laws of nature to hypotheticals
■ one way to do this would be to claim that such generalizations are hypothetical
conclusions of instantial laws
Another reason to bring in possibilities is that there seems to be no other way of differentiating
between generalizations of fact e
...
all the cigarettes in my cigarette case are made of Virginia
tobacco, and generalizations of law e
...
all the planets in the solar system orbit the sun
○ There is no obvious difference in logical formulation; each takes the form ‘All S is P’
○ We want to say that generalizations of law cover possible instances, whereas
generalizations of fact only cover actual instances, but this is difficult to express clearly
○ One way we can express this is that if generalizations of law cover possible as well as
actual cases, their range must be infinite, and thus they cannot possible be formulated
as conjunctions in the way that generalizations of fact can
...

○ Whilst this is illuminating, it may be too strong
...
The difference is that no number of positive
instances will entail the generalization of law, whereas they may the generalization of
fact
To say that generalizations of law cover possible as well as actual events is to say that they entail
subjunctive conditionals
○ Generalizations of fact also can cover subjunctive conditionals, but these will only be
restricted to the objects recognized in the set i
...
the specific cigarettes in the above
example
...
’
○ We could treat generalizations of law in the following way: A treats an expression for the
form ‘for all x, if Px then Qx’ as a law of nature if and only if there is no property R such
that x having property R as well as property P would weaken A’s belief that x had
property Q
...
g
...
g
...
In these cases
counterexamples do not falisify, but rather qualify, the law
○ Thus a generalization as formulated above will in one respect be destroyed if the
qualified formulation is considered a more exact statement of the law

 

Alexander Bird - Philosophy of Science
Chapter One: Laws of Nature
●

●

Aims of science including explaining, categorizing, detecting causes, measuring and predicting
all rely upon ‘the existence of laws’
○ separate claim: these aims also rely upon the concept, theory of a law
Laws of nature are things in the world which we try to discover - they are separate from our
theories or statements of laws

Minimalism about laws - the simple regularity theory
● Laws are just regularities
○ laws are nothing more than the collection of their instances
○ this is an expression of empiricism - concepts should be explicable in terms of our
experiences
● Simple regularity theory (SRT): it is a law that Fs are Gs if and only if all Fs are Gs
○ but this is neither a sufficient nor a necessary account of laws - there are regularities that
are not laws and laws that are not regularities
Regularities that are not laws
● There are many regularities that are accidental, not law-like
○ e
...
‘All persisting lumps of pure gold-195 have a mass less that 1000kg’ is contingent
○ whereas ‘All persisting lumps of pure uranium-235 have a mass of less than 1000kg’ is
not contingent, it is a law of chemistry
■ SRT cannot distinguish between genuine laws and mere coincidences
● We can create a contrived example e
...
describe Jane perfectly (such that only she fits the
description) and then claim that all people matching that description play the oboe
○ retort of the SRT minimalist:
■ is it right to bundle a collection of properties together as one property?
● well, this is done by some things that we consider laws e
...
gas laws
relate the pressure of a gas to the compound of its temperature and
volume
■ can one instance be regarded as a regularity?
● and there are presumably laws that cover e
...
the Big Bang, for which it
is the only instance, or else the properties of transuranium elements with
very short half lives, for which there is not observable regularity at all
● Another problem for the SRT minimalist: how to account for laws without instances
○ the statement ‘All Fs are Gs’, if there are no Fs, is trivially true (according to logic)
■ so how are we to distinguish the trivially true regularities that are laws from the
trivially true regularities that aren’t
● we can’t, using SRT anyway
● Another problem for the SRT minimalist: how do we account for functional regularities?
○ where a law refers to a continuum - e
...
the pressure of a gas, there are infinitely many
points on the continuum, so such a law cannot be modelled on observed regularities-

there will inevitable be gaps
■ hence if we are to model such a law, we need to go beyond observed instances
Laws and counterfactuals
● Laws support counterfactuals - what would have happened in a possible but not actual situation
● On the SRT model, every empty regularity is true
...
g
...
e
...
this means that the law is consistent with every particle (i
...
the whole
nucleus) decaying after time t
● this is a problem for the minimalist because the law is equivalent to its
instances, and here is a radical divergence between the law and its
instances
● BUT this argument commits the fallacy of assuming that what is possible
for any individual particle is possible for a collection of particles
○ this argument is only valid if there is a logical gap between a law
and its instances, which is precisely what the minimalist denies
■ hence it begs the questions against the minimalist
The systematic account of laws of nature
● So, if we consider the argument that regularities are an unnecessary feature of laws to be invalid,
then perhaps the minimalist simply needs to add conditions to regularities to ensure that
regularities only capture laws
● In summarizing a set of facts we could, rather than mentioning every regularity they exhibit, only
record a sufficient number to capture all the facts we are interested in - a systematic summary;
simple and strong
○ this would allow us to distinguish between accidental regularities and laws - insofar as
generalizations capture many, disparate examples, they are lawlike
■ so ‘All emeralds are green’ is more informative and hence stronger than ‘all
emeralds are coloured’ or ‘all South American emeralds are green’
● This is the systematic account:
○ ‘a regularity is a law of nature if and only if it appears as a theorem or axiom in that true
deductive system which achieves a best combination of simplicity and strength’
■ insofar as we are ignorant of the best axiomatization, we are ignorant of the laws
of nature
● Problem: what does simplicity mean?
○ the fact that we can replace a simply law like ‘X is green’ with the complex law that ‘X is
grue’ (Goodman) suggests that we cannot trust linguistic simplicity
● Problem: systematic account assumes that there is precisely one system that optimally combines
strength and superiority
...

● The systematic account is an improvement on the simple regularity theory because under it,
accidental regularities are likely to have alternative explanations in terms of other laws
○ but we can imagine a world with many laws, each with few instances
...
g
...
g
...
g
...
g
...
if Fness necessitates Gness then this entails that everything which is F is also G
b
...
Instances of Fness may only coincidentally also
be instances of Gness, without there being any necessitation
c
...
Furthermore, since necessitation is a
relation among universals, it is a second-order universal
d
...
Its instances are cases of, for example,
a’s being G because a is F (a’s being F necessitates a’s being G)
● But actually this doesn’t distinguish nomic necessitation from Ramsey-Lewis’ systematic
account
...
all Fs are Gs
b
...
a law explains its instances
b
...
it is possible for systematic regularities to diverge from the laws that there are (there can

be systematic regularities which are not laws)
■ this may be what a law is, but it gives us no insight into what the relation of
necessitation is - in fact it skits over it, when it is itself metaphysically dubious



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