The deductive-nomological model of explanation

We can explain many sorts of things in terms of scientific theory. Mendel's theory explains particular events (this cross produced pur­ple offspring) or general regularities (all the offspring of a red-white cross will be red or pink).

Let's take, as our example, Mendel's explanation of the outcome of a particular cross.

EXPLANANDUM: We crossed a pink pea with a (homozygous) red one and the cross produced red and pink offspring.

(It's worth pointing out that this isn't an observation sentence, because “homozygous” is a theoretical term. To find out if a pea plant is homozygous red we'll have to see if it breeds true.)

The explanans will contain two sorts of sentences. One sort will state antecedent conditions, which describe the setup in which the explanandum occurred. In this case, the antecedent conditions are just:

C: We crossed a pink pea with a homozygous red one.

The other sentences in the explanans represent general laws. I shall return to the issue of what makes a generalization into a law in a later section. For the moment, let's work with the definition that a law is a generalization that the theory says must be true. Thus, we have

Roman">L₁: A pea has pink flowers if and only if it has genotype RW.

L₂: A homozygous pea has red flowers if and only if it has geno­type RR.

along with MG and the laws of segregation and independent assort­ment.

L₃: A cross between RR and RW must produce some offspring that are RR and some that are RW.

Together C, L₁, L₂, and L₃ allow us to deduce

E: The cross must produce red and pink offspring.

And from C and E we can deduce

EXPLANANDUM: We crossed a pink pea with a (homozygous) red one and the cross produced both red and pink offspring.

(In this deduction we first draw from E the consequence

E': The cross produced red and pink offspring,

using the law of modal logic that says that if something must be so, it is so, and then draw the explanandum as a consequence by using the elementary law of sentential logic that says from two sentences (C and E) you can deduce their conjunction.)

Hempel says that this explanation is sound if it satisfies three con­ditions:

I.    Logical conditions of adequacy

(R1) The explanandum must be a logical consequence of the explanans.

(R2) The explanans must contain general laws.

II.  Empirical condition of adequacy

The sentences constituting the explanans must be true.

We can summarize Hempel's view like this. There's an explanans:

C₁, C₂,...

L₁, L₂,... L_r General laws

from which we derive by logical deduction the explanandum:

E                      Description of the empirical phenomenon to be

explained.

Now you can see why this is called the deductive-nomological model. “Nomological” comes from the Greek word “nomos,” mean­ing law. Hempel thinks that the explanation is correct if you can deduce the explanandum from the laws of the theory and the antecedent conditions.

It's important that Hempel needed not only the logical conditions of adequacy but the empirical condition as well. To see why, let's suppose we tried to do without it. Now consider Mendel's explana­tion of some crosses that involve just two alleles of one gene. Remember, Mendel didn't know about chromosomes. So his expla­nation simply says that there are factors in the organism (genes) that are handed down from the parents to the offspring. Now, suppose that Mendel had a colleague—call him Wilhelm—who thought these factors were little spherical objects inside the plant's cells. If Mendel's explanation meets the logical conditions of adequacy, then Wilhelm's theory does, too. But surely the explanation in terms of little spherical objects is just wrong. Someone who thinks that this is why the crosses turned out the way that they did is just mistaken.

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