Nick Fletcher PF303

What is a Scientific Explanation?

What exactly constitutes a scientific explanation has been the subject of

philosophical debate since pre-Socratic times (Woodward, 2003). However, a

turning point in debate over the subject occurred when Hempel postulated his

deductive-nomological and inductive-statistical models of scientific explanation

and most modern debate has followed on from Hempel’s work (Woodward,

2003). This essay aims to explain these two models, and, by analysis of some

counter-arguments to the model, hopes to show that if a broad view of causation

is taken and applied to Hempel's models, the two models are together able to

describe well what a scientific explanation is.

Hempel postulated his ‘covering law’ model of scientific explanation in

1965, which states that any scientific explanation must start with a law from

which the explanation can be deduced (Papineau, 2005). This model is often

referred to as the ‘deductive-nomological’ (DN) model of scientific explanation

due to this deductive element1. For particular events, the DN model ascribes to

the following schema (Papineau, 2005):

Initial conditions: I1, I2, …, In

Laws: L1, L2, …, Ln

Explanandum: E

This schema rests on four premises; the explanans only provides a scientific

explanation of the explanandum iff:

(i) E is a logical consequence of the conjunction of the explanans

(ii) E does not follow from any proper subset2 of the explanans

sentences

(iii) The explanans sentences must have empirical content3

(iv) The explanans sentences must all be true. (Taken from Ruben,

1990)

For example, a scientific explanation of an event where an apple falls to the

ground from its tree has as initial conditions the position of the apple before its

decent (I1), the fact that the apple has mass (I2) and that the apple has just

become detached from the tree (I3). The relevant law here is the law of gravity

(L), which states that any object of mass unsuspended in the air will fall to the

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Nick Fletcher PF303

earth4. Thus, after consideration of the initial conditions of the event and the

application of a relevant law a scientific explanation can be reached deductively;

that the apple fell to the ground because of the law of gravity.

The DN model is also able to accommodate explanations of laws in terms

of other laws through the following schema (Papineau, 2005):

Laws: L1, L2, …, Ln (Explanans)

Explanandum: L.

To take an example from Papineau (2005), a scientific explanation of rainbows

has as explanans the laws that sunlight is a mixture of all wavelengths of light

(L1), different wavelengths of light refract differently when passing from air into

water (L2) and the shape of a raindrop causes internal reflection off the back of

the raindrop (L3). The explanans can thus be deductively used to explain why we

see rainbows when sunlight shines through rain (L.).

In addition to the DN model, Hempel also postulated the inductive-

statistical model of scientific explanation, which relaxes the requirements of the

laws to allow probabilistic laws to be used as explanans as well as exceptionless

laws (Papineau, 2005). This model follows the following schema (Papineau,

2005):

Initial Conditions: I1, I2, …, In

Probabilistic Laws: L, to the effect that most I1, …, Ins are Es

Explanandum: E.

For example, a scientific explanation of why the Wasps beat Bristol Rugby

recently could have as initial conditions that that the Wasps have a stronger and

heavier pack (I1) and faster and more skilled backs (I2). Statistically, as it is more

likely that the team with a stronger, heavier pack and faster, more skilled backs

tend to win in rugby, this probabilistic law can be used to provide a scientific

explanation of the win. The probabilistic nature of this law is highlighted by the

fact that the score was 32-30, with the winning try being made in the 80th

minute; the law is clearly probabilistic rather than exceptionless as things may

well have actually gone the other way.

These models suggest that there is a strong symmetry between

explanation and prediction Indeed, if the model holds then the only difference

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Nick Fletcher PF303

between the two is that prediction occurs before the event has occurred and

explanation afterwards (Papineau, 2005). In this way, the model appears to

subscribe to the symmetry thesis, that (a) ‘every successful prediction is a

potential explanation’ and (b) ‘every successful explanation is a potential

prediction’ (Ruben, 1990; pp.146). However, whilst it is clear that (a) is sound, it

is not clear that (b) is. The most widely used counter-example to (b) is that of

Koplic spots, spots which appear as a precedent to the manifestation of measles.

These spots can be used to accurately predict later manifestation of measles

(albeit with some exceptions) but the spots cannot be used to explain why the

manifestation occurs. Hempel is vague on this point, arguing that (b) is ‘open to

question’ (quoted by Ruben, 1990; pp.146) but it could be argued that (b) is not

refuted by this example.

This problem can be solved by a distinction between scientific and non-

scientific predictions. A scientific prediction will satisfy the symmetry thesis, for

example after observation of a patients blood and discovery of the measles virus

a scientific prediction can be made that the person is likely to develop measles if

they have not already. However, Koplic spots cannot be used to scientifically

predict development of measles because the Koplic spots cannot form part of a

scientific explanation due to premise (ii). A prediction can be made on the basis

of such spots, but the spots are an intermittent result of the measles virus, so

this must also be included in a full scientific explanation. After this inclusion, the

explanandum (prediction of the symptoms of measles), follows from a proper

subset of the explanans statements, i.e. the development of measles becomes

predicted, scientifically, by the presence of the measles virus in blood, not by the

Koplic spots. This distinction is essentially made through an appeal to causation,

and as such is able to solve the problem for instances of causal scientific

explanation. However, it is clear that there are instances of scientific explanation

that do not involve causation, explanations that appeal to laws of coexistence

rather than laws of succession (Ruben, 1990).

Such scientific explanations have only laws of coexistence as explanans

rather than laws of succession; taking example from Bromberger (taken from

Ruben, 1990; pp.148), the length of a shadow cast by a pole can be both

predicted and explained by the height of the pole and the angle of elevation of

the sun. However, it is clear that the height of the pole can be predicted by the

length of the shadow and the angle of elevation of the sun, but not explained.

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Nick Fletcher PF303

Here again I would argue that the length of the shadow does not scientifically

predict the height of the pole, and therefore its inability to explain it is irrelevant.

The height of the pole can be used to scientifically predict the length of the

shadow, and therefore can also be used to scientifically explain it. This is because

there is a sort of causality to such coexistences. If the shadow did not exist in the

example, perhaps due to someone shining a torch where the shadow should be,

it would not affect the existence of the pole; however, if the pole were to cease

existing, the shadow would cease existing also. The existence of the shadow

depends entirely on the existence of the pole, in a way it is caused by it, whilst

the existence of the pole depends in no way upon the existence of the shadow.

Whilst this idea does not fit with Hempel's beliefs about causation, that causation

must involve a succession in time, using this different view of causation does not

cause problems in the DN model. Thus, (b) holds and the symmetry thesis can be

used as a gage as to whether an explanation is truly scientific.

It could be argued that the addition of causality to scientific explanation

causes problems in terms of constitutive explanations and teleological

explanations. A constitutive explanation could take the form of:

L: Water is H20,

I: The liquid in the glass is H20

E: Therefore the liquid is water5

This is indeed a truly scientific explanation of why the liquid in the glass is water,

but it is not clear where the notion of causality comes into it. However, it could be

argued that the fact that the liquid in the glass is constituted by H20 causes it to

be water, and whilst this requires a slightly broader view of causation6 than is

held by most philosophers, it has intuitive value and serves to allow such

explanations to rightfully be called scientific.

Teleological explanations concern why a certain purpose has been

achieved or end has come about, for example ‘why are polar bears white?’,

‘because it helps them to hunt with more success.’ Whilst this is clearly a

scientific explanation, it is not clear how the polar bears improved hunting skills

can have caused them to be white. However, the explanation can be re-phrased

thus:

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Nick Fletcher PF303

L: Evolution means that animals with the best characteristics for survival are

more likely to survive longer an thus produce more offspring,

I: Polar bears live in snow-covered lands,

E: Polar bears have evolved white fur to help them hunt

All that has occurred here is a law has been introduced that, in conjunction with I,

truly explains E scientifically by creating a causal link between I and E. E is shown

to be, in a way, caused by both L and I, and causation remains valid as a

component of scientific explanation.

Thus, from his covering-law model of explanation, Hempel has been able

to produce two models of scientific explanation, DN and IS. One of these models

is deductive and the other inductive as, just like any argument, scientific

explanation can occur either deductively or inductively. Between them these

models seem able to cover all instances of scientific explanation, albeit after

taking a broad and quite intuitive view of causation; including those that involve

coexistent laws and successive laws, as well as straightforward, constitutive or

teleological explanations. Furthermore, mere explanations can be distinguished

from truly scientific explanations via the symmetry thesis. To conclude, a

scientific explanation is7 one that takes the form of either a deductive or

inductive argument involving laws or initial conditions that both entail and are

causally related to the explanandum.

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Nick Fletcher PF303

1There is also a more relaxed version of the covering-law model that does not insist on this deductive element, the statistical-relevance model, which shall be discussed later in this essay. 2i.e. there are no surplus explanans that are not necessary for the explanation.3As noted by Ruben (1990), this point is fairly redundant as the explanandum is necessarily an empirical fact, meaning that (i) ensures (iii) is necessarily fulfilled.4This is not an exact definition, but serves the purposes of this essay.5The terms ‘H20’ and ‘water’ can be interchanged according to the information one holds over what is in the glass.6A subject too vast to be considered here in much detail.7Arguably; there is much left to develop but not enough room here.

Bibliography:

Papineau, D. (2005). ‘Methodology: The Elements of the Philosophy of Science’. In Grayling, A. (ed.) (2005). Philosophy 1: A Guide Through the Subject, pp.123-180. Oxford University Press. Ruben, D. (1990). Explaining Explanation. Routledge, London & New York.Woodward, J. (2003). ‘Scientific Explanation’. The Stanford Encyclopedia of Philosophy.

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