But the gory details objection goes philosophically deeper because it implies that even if the explanatory principles of classical genetics could be derived from the explanatory principles of molecular genetics, the derivations would not be explanatory.
Now contrast such derivations with retrodictive derivations in which the present motions of the planets are derived from information about their future velocities and positions at $t$, the forces operative at $t$, and so on.
He hypothesised the existence of residues and derivations in social life; the underlying identifiable psychic tendencies promoting people to act in the way they do and the justifications they cloaked their decisions in.
There were also letters to scientists and other scholars, pages of derivations of mathematics and physics formulae, and copious writings on alchemy and religion.
The mapping associates syntactic derivations with semantic readings, expressed as terms of the simply typed linear lambda calculus.
In line with the Curry-Howard 'formulas-as-types, proofs-as-programs' method, derivations in the various categorial calculi are associated with terms of suitable fragments of the lambda calculus.
But as we saw in the discussion of the syntax-semantics interface, we can restrict attention to the sublanguage of LP that forms the image of derivations in syntactic calculi making interesting claims about word order and phrase structure.
This issue of 'spurious' ambiguity can be tackled by the introduction of normal form derivations (as in Hepple 1990, Hendriks 1993), compare focused proof search regimes in linear logic), combined with the use of chart-based parsing methods, as in Hepple 1999, Capelletti 2007.
In this way we can assign Gödel numbers to formulas, sequences of formulas (once a method for distinguishing when one formula ends and another begins has been adopted), and most notably, proofs, or derivations.
This contextual definition governing cardinal numbers is the basic principle upon which Frege forged his development of the theory of natural numbers.[5] In Gl, Frege sketched the derivations of the basic laws of number theory from Hume's Principle; these sketches were developed into more rigorous proofs in Gg I. We will examine these derivations in the following sections.
These two pieces are combined together into a derivation of B that does not have the detour formula A ⊃ B. In Gentzen's thesis, all assumptions are in the end closed by implication introductions, but nowadays one considers also derivations that leave a collection of formulas as open assumptions.
