As Chomsky suggests, if mathematics does not play a genuine role in biolinguis-
tics, as it does in physics, in what sense does mathematics work for biolinguistics,
as stated in the Galilean Style? It is important to note that, as we saw in sec-
tion 2.3, Wisan (1978: 3) argues that Galileo uses it “in order to achieve the
logical certainty of mathematics” in reasoning. Thus, in Galileo’s science of
motion, mathematics was used at least partly to attain “rigorous demonstrations
from evident principles.”
As Chomsky (1979: 125) states, similarly in biolinguistic s, “a certain quasi-
mathematical mode of expression is presupposed in the overall program” and
a formal system, such as “some variety of recursive function theory,” is used
“to formulate precise principles and precise rules within a formalized system,”
although “it would not be correct to consider that as mathematics.” Thus, the
role of mathematics in the Galilean Style should be interpreted in a broader
sense, taking into consideration the role of mathematics in early modern science.
3.3 Shift to mechanisms
Chomsky (2000: 6) states that in the cognitive revolut ion of the 1950s, “there
was an important change of perspective: from the study of behavior and its
products (such as texts) to the inner mechanisms that enter into thought and
action.” In light of the Scientifi c Revolution, it is obvious that this “change of
perspective” corresponds to the replacement of Aristotelianism by mechanical
philosophy in the Scientifi c Revolution.^7
Freidin (2012: 893) characterizes this change of persp ective as “the first step
towards the current perspective” involving “a shift in focus from the external
forms of a language to the grammatical system that generates it, a system that
is assumed to exist in the mind of the speaker, constituting the core part of a
speaker’s knowledge of his or her language.”
Under this perspective, as Freidin (2012: 893) states, “in its initial concep-
tion, the grammar consists of two distinct formal mechanisms for generating
the sentences of a language: phrase structure rules and transformations. The
former constructs initial syntactic structures which the latter could modify in
certain ways, including the combination of pairs of initial structures – yielding
complex and compound sentences.”
Now, it is interesting to note that Chomsky (1965:9) states that the model
of grammar consis ting of these formal mechanisms is a neutral characterization
of “the knowledge of the language that provides the basis for actual use of
language by a speaker-hearer” as follows:
... a generative grammar is not a model for a speaker or a hearer. It
attempts to characterize in the most neutral possible terms the knowledge
of the language that provides the basis for actual use of language by a
speaker-hearer. When we say that a sentence has a certain derivation with
respect to a particular generative grammar, we say nothing about how the
speaker or hearer might proceed, in some practical or effi cient way, to
construct a derivation.
On the current status of biolinguistics 179