KNOWLEDGE EVOLUTION

arguments, rather than their content (Haack 1978). In linguistics, the main concern is the
internal structure of the concept.

Instead of their differences, both of the schools share the same underlying
Cartesian design of ‘mathesis universalia’ (Gk. mathesis = science, Lat. universalia =
universals), since the assimilation of ‘common notions’, within the Cartesian framework,
opens the way to the principles of logic. But the development of linguistic semantics is
not directly related with the foundation of logic, rather there exists an interlude of formal
semantics (fig. 3). ‘Common notions’, as the principles of logic, along with the
epistemological concerns, constitute the background of the formal semantics. Formal
semantics differs from the logic, by the virtue of its interest. In logic, the basic concern is
the performable computing operations (= reasoning), not the propositional form
associated with a particular ‘idea’; whereas formal semantics is motivated by the exactly
opposite interest, namely the propositional form, being associated with an ‘idea’. As a
result, it now becomes quite tough to remain topic-neutral. On the other hand, the basic
concern of the formal semantics is not to produce natural language semantics, but to clear
the imperfections of logic, with the help of natural language evidences (Katz 1997).
Following example will elaborate this claim. Both the sentences, namely John found a
unicorn and John painted a unicorn, have the same underlying logical form, which is
(λQ(λP∃x(Q(x) ∧ P(John, x))). Being specified, the λ-operator gives rise to the following
two representations:

(1) John found a unicorn = ∃x(UNICORN(x) ∧ find(John, x))

(2) John painted a unicorn = ∃x(UNICORN(x) ∧ paint(John, x))

Both of these two translations admit the inference ∃x(UNICORN(x)) - that means
both of them imply the existence of a unicorn, while sentence (1) presupposes the
existence of a UNICORN and in sentence (2) UNICORN is a representation. So, how to
solve this puzzle? - In formal semantics, the most obvious way out is as follows:

(3) John found a unicorn

⇒ (∃x: Thing)(unicorn(x) ∧ find(John, x))

⇒ (∃x: Thing)(unicorn(x))

(4) John painted a unicorn

⇒ (∃x: Representation)(unicorn(x) ∧ paint(John, x))

⇒ (∃x: Representation)(unicorn(x))

Whether the concept unicorn will be specified as a thing or as a representation,
will be strictly determined by the meaning of the predicate associated with it, not by the
concept internal structure of the unicorn itself. Furthermore, the name ‘John’ should
also be specified, since the acts of finding and painting are directly related with the
concept of rational agency. So a fuller interpretation would be as follows:

(3')    (λQ(λP( ∃x∕Γlιing)(Q(x) ∧ P(John: Rational, x)))( FIND)( UNICORN)

(4')   (λQ(λP(∃x^epresentation)(Q(x) ∧ P(John: Rational, x)))( PAINT)( UNICORN)

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