Truth of scientific laws

Once we have a law, we have an explanation, but we need to trust the laws from which such explanation it’s provided in order to rely on them; otherwise data they provide aren’t reliable. In other words, why should we rely on the explanation they provide?

Two currents which face each other:

  • logical and prescriptive explanations
  • extra-logical and descriptive explanations

If a law expresses a regularity, what explains the regularity itself?

  • a matter of logic
  • a matter of portraying what goes on in the real world

Logic alone can’t succeed in defining laws.

More general laws

According to Hempel, we infer empirical regularities from laws of gradually broader scope. Such laws are general because they’re more comprehensive.

Example of Newton’s law of gravitation:
it can’t be observed, but several empirical instances are explained by inferring to a general law which, if accepted, makes sense of such phenomena. What does the explanation is the inference to a broader and more general law, not the law itself. If Newton’s law is true, then a certain correlations can be explained.

Different degrees of explanatory power are displayed by the same explanatory inference, which is both deductive and nomological. The ultimate value of a theory is dependent from the degree of generalization. From empirical data to laws always more abstract and general.


data simple account of individual fact or events
empirical laws non accidental correlations between relatively observable\/measurable magnitudes
first order theories sets of assumptions using comprehensive laws
second order theories still more penetrating explanation on the basis of more comprehensive laws


  1. The very idea of explanation
  2. The model of theory entailed in this idea of explanation
  3. The role of hypotheses

They start as separate problems, but they converge to a greater unique one.

First problem

The very idea of explanation:
how can we correlate, to trace back, an instance to a law?

The problem lies in “fitting” phenomena into observable regularities: it doesn’t count as an explanation; it goes beyond the discovering of co-occurences between types of events.

Newton’s example: two similar explanations with a critical difference:

  • Every object in the Universe attracts every other object with a force which is proportional to the product of the masses of the two objects and inversely proportional to the square of the separation between the centers of mass of the two objects
  • A “universal” force of gravitation F exists between any two masses m and M, directed from one to the other, proportional to each of them and inversely proportional to the square of their separation distance r

It is the very existence of the force which accounts for the observation. We are conjecturing the existence of theories and object well beyond logical boundaries (Feyerabend ???)

A different type of explanation: an entity which explains what we see. Postulated entities often can’t be observed. they seem to explain very well what goes on, but they haven’t enough empirical data in their support.

There is more to science than logic: sentences used to describe the world through laws are simpler than the actual structure of the world.

Theories are ontological maps of the inner constitution of the world, they should instead explain why phenomena behave in the way they do at the observable level. Laws postulate what’s actually out there in the universe, waiting for a experimentation to prove or reject it.

Second problem

The model of theory in this account. A theory is explanatory not simply by virtue of the logical inferences legitimized by the form of its laws.

if a body were free of forces, it would move at constant velocity

Logic isn’t enough: in the real world there are no object which can be free of forces!

So scientific theories are ontological maps of the inner constitution of the world; they should explain why phenomena behave the way they do at the observable level.

It follows that theories become very risky devices: they might discover entities that turn out not to exist

An alternative to scientific explanation beyond logic: [[ Scientific realism ]]

Third problem

Accounting for the discovery of the hypotheses.

Popper: we can only test our conjectures when we have them, by using a hypothetico-deductive method; the same goes with Hempel:

From Popper’s point of view, the procedure to follow is +++

The hypotetico-deductive model

  1. Observation (O)
  2. Hypothesis formulation (H)
  3. deduction of a consequence to the hypotheses (if H, then p)
  4. Empirically check the validity of the conclusion (p?)
  5. if the conclusion is proven to be not true, also the hypothesis will be not true. (!p, !H)

Logic doesn’t care about how the hypotheses is brought about, but they focus on the testing:

The initial stage, the act of conceiving or inventing a theory, seems to me neither to call for logical analysis nor to be susceptible of it. The question how it happens that a new idea occurs to a man… may be of great interest to empirical psychology; but it is irrelevant to the logical analysis of scientific knowledge.

Logic of Scientific Discovery, p.20

Hempel agrees with Popper on this

The transition from data to theory requires creative imagination. Scientific hypotheses and theories are not derived from observed facts, but invented in order to account for them. They constitute guesses at the connections that might obtain between phenomena […]. “Happy guesses” of this kind require great ingenuity, especially if they involve a radical departure from current modes of scientific thinking […]. Nevertheless, the ways in which fruitful scientific guesses are arrived at are very different from any process of systematic inference […] In his endeavour to find a solution to his problem, the scientist may give free rein to his imagination, and the course of his creative thinking may be influenced even by scientifically questionable notions. Yet scientific objectivity is safeguarded by the principle that while hypotheses and theories may be freely invented and proposed in science, they can be accepted into the body of scientific knowledge only if they pass critical scrutiny.

Guesses and the connection we might obtain from phenomena, invent hypotheses.

At this point, Hempel disagrees with Popper:
testing doesn’t mean falsification

  • if a hypothesis is not true, it’s not false, but disconfirmed
  • if an hypotheses is not (not falsified), it is not true, it is confirmed.

even extensive testing with entirely favourable results does not establish a hypotheses conclusively, but provides only more or less strong support for it. Hence, […] it [scientific enquiry] may be said to be inductive in a wider sense, inasmuch as it involves the acceptance of hypotheses on the basis of data that afford no deductively conclusive evidence, but lend it more or less strong ‘inductive support’ or confirmation

Hempel, Philosophy of Natural Science, p.18

Next topic: Testing the hypotheses



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