The covering laws are normally different for different explananda.

But if each particular explanation would involve a separate quest of a covering law, these laws would likewise be multiplied without necessity and without reason.

This is similar with a sophism. Why is a law a covering law? Why such a model is subsumptionist? Not because many different initial conditions and explanandums are subsumed under a covering law? What explains different explanandum under the same covering law are different initial conditions.

In actual scientific practice, an explanation does not consist in deriving the explanandum from a covering law plus suitable initial conditions.

The actual scientific explanations from the domain of natural sciences many times are very weak or imperfect from a logical criterion of consideration. That is, they are not a model for the philosopher or the logician of scientific explanation. Many times when we subsume a special case under a general one we can talk of deduction or derivation, but if the covering law or background theory has a causal form, if the covering law or background theory has not a pure logical structure (only with logical relations and operations etc.), then their deduction or derivation is not a genuine one, is not a logical deduction or derivation, but the representation of a causal or physical consequence.

Furthermore, of the covering laws relied on in explanations have the

same logical form as universal syllogistic premises, how do covering law explanations differ from syllogistic explanations?

By content and aim. The valide explanation should have a valide logical structure. Why there can be no scientific explanations that have a syllogistic logical structure?


Instead, Hertz started from something that is not typically emphasized or even mentioned in covering law accounts of explanation.

It is what we have called the background theory.

In Hertz’s case, it consists of Maxwell’s equations.

From them Hertz deduced

how wave-like electromagnetic disturbances are propagated.

You see, somebody deduced something from equations. Equations contains equalities quantities, addings, subtractings, fractions, multiplications etc. of quantities, NOT TRUTH VALUES. The mathematical equality is a quantitative equality. A pure equation has a pure mathematical structure, not a logical one. Having a mathematical structure it cannot substantiate a deduction, cause the deduction has logical nature.

Conclusion: The mathematical consequences should be distinguished from the logical ones.

'nu ma lasa saplec'

Scientific laws, but alone theories, are rarely of the form of a general implication.

Scientific theories are rarely in a pure logical form. That is why, together with the ad explanandum and explanandum they do not form a valide logical structure.

However, the gist of Hertz’s explanation did not consist in the deduction of the explanandum from the propagation law (plus initial conditions).

Philosophy of science is not history of science. Philosophers of science are not interested of the individuality of a scientific explanation. An individual scientific explanation can be a very wrong model. We are interested by the most intelligent, rational,

adaptable, economic, pure,

and perfect (necessary and suficient) model of the scientific explanation.

A Regulative Ideal. We are not slavers of science We should something to lead. We should propose the most rational, valide, economic, and intelligible model. Economic and intelligible to be very practicable.



The explanatoriness of an explanation does not come from the background theory, but from the connection between A, T and D that the explanatory interpolation theorem brings out.

The authors' T is a background theory. That is, T can be a physical theory, a physical conditional, a causal generality. For instance, if salt is put in water, then it will undergo dissolvation or W(s) D(s).

Now, this consequence can be necessary but is not a logical consequence. That is, it is not a necessary consequence of a logical structure as a is a logical consequence of the logical structure (a&b). That is, the authors mixes the logic with physics, they do not observed that if T is physical conditional and A would be the antecendent condition, then D would be a causal consequence, not a logical consequence. T should transformed and reconstructed until will become a logical truth or a logical implication and only then, if A constitute the antecedent of the logical implication, D will follow as a logical consequence. The authors suposse logical dependencies between T, A, and D, but if T is not transformed, if T is only a causal conditional, then the relations between T, A, and D represent only causal or universal physical dependencies not logical implications.


A suitable interpolation formula I explains why G follows

from F by showing how the structures specified by F interact with the structures specified by G

so as to make the consequence inevitable.

In the general theory of explanation the interpolation theorem can thus be used insofar as the explanation of an event, say one described by E, can be thought of as depending on two different things,

on the one hand on some given background theory and on the other hand on contingent ad hoc facts concerning the circumstances of E.

Both the background theory and the contingent “initial conditions” specify a kind of structure.

An explanation is an account of the interplay:interdependenta

between these two structures.

In explaining some particular event, say that P(b), we have

available to us some background theory T and certain facts A about the circumstances of the


The process of explanation will then consist of deducing the explanandum from T & A.

We see the authors pretend that to explain D is to deduce it from T&A:

(T&A) has as a logical necessary consequence D. But T is not infrastructured. Now, this is

the form of the actual scientific explanations or their ideal? Consider the explanation of aging in gerontology. Is there applied the authors' model of explanation. They require only one background theory, but for the explanation of aging were proposed hundreds of theories (see Medvede's An attempt at a rational clasification of theories of aging, Biol. Rev., 65, 375-398, 1990).

Most scientists consider that aging is,

not as phenomenon, a result of a multiple caused process. Most of the theories of aging, if not all, have a causal form.

Idealized a causal theory can have the form: A causes B. But the things are very complex in the explanation of aging. There are there long causal chains in wich an effect can become a cause for other effect. Moreovere, syncronicaly can act many causes. The evolution of the process that result in aging is very complex. Not an animal, but even the changes of the life of a single cell were not described and interpreted by the serious scientists. To explain the advancement of the aging process or time is a very hard thing which cannot be reduced at the simple deduction of a D from (T&A). But, however, if we separe from the whole process only an atomic gerontological

explanation, but what in gerontology is 'atomic' in physics can be very 'molecular', then we will have there only a theory T and maybe some conditions A, then this atomic explanation will have the form of authors' explanation. Suposse that T has the form A causes B (e.g., If the cell's telomeres undergo the changing x, then the cell loss its replicative capacity). Is this logic? Suposse another exemple, Salt decomposes in liquid water, that is, if salt is put in liquit water, then it will undergo decomposition. The consequence is necessary, but is this logic? The consequence is logical or causal, physical? The consequence is in thanks to the logical structure? Can F(x) be logicaly true or false? No. We saw a causal conditional or consequence. There can be

physical or causal necessary concesequences and necessary consequences of certain logical structure (eg., if (a&b), then a).

Now, the authors writed that (T&A) has as a logical consequence D, but their T can be a causal background theory or a physical theory, not a logical truth. But if T is a causal or physical conditional then the addition of A will substantiate only a causal or physical consequence not a logical one. The authors left T in its physical structure, but if T is not transformed or reconstructed

in a logical truth or logical implication, then (T&A) has not as logical consequence D. And indeed their T is not infrastructured logicaly. The authors confuse a physical (causal)necessary consequence with a logical necessary consequence. Moreover, they apply the Craig's theorem to the first-order of logic of predicate, but F(x) or G(x) cannot be neither true nor false logicaly.


It is ultra clear that, the author of Explanation as Interpolation relies or at least start form Craig's interpolation theorem, but is this theorem perfect?

The author reproduces Craig's theorem in the following way:

Assume that F and G are (ordinary) first-rder formulas, and assume that

(i) F_G

(ii) not _~F

(iii) not _ G

Then there exists a formula I (called interpolation formula) such that

(a) F _ I

(b) I _ G

(c) The nonlogical constants and free individual variables of I occur both in F and in G.

Now, consider the following case:

F = (a & b). G = (a V b). It is clear that F _ G, but what is the interpolation FORMULA here? Is ~(~a V ~b) or other equivalent transformation of F different from F? This transformations are equivalents because, finaly, they, though that are different descriptions, have the same sense. If 'I' should be realy different from F, then we can deduce from F either a or b, that is, parts of F. And, then, indeed, by extension, a implies (a V b), that is, G. But neither a nor b are formulas, but are constants.

Conclusion: interpolation should not be necessarily a FORMULA, though that the theorem says that there exists a formula I

The theorem was not perfect. F(x) cannot be neither true nor false logicaly, that is due its logical structure.

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