18) Psychologism as a doctrine or 'school' was not only rejected by the phenomenologists (Husserl) and Logicists
(Frege), but also by critical vitalists like Driesch who, only a few years after Leib und Seele, dedicated a whole book (not merely an essay) to The Crisis in Psychology (1925).
This reasoning is pretty compelling, even in advance of the logicist
reduction, provided one agrees with Frege that the numbers are objects.
Given the intuitionistic logical apparatus on which these statements are built, it should be clear to the classicist as well as the constructivist why these statements cannot be constructive theorems, despite the fact that, read classically, they are easily demonstrable from logicist
constructions and could even be taken as axiomatic in a structuralist system.
Presentations seeking to answer the question ranged across fascinating attempts to model forms of deception by harnessing: analogical processing; formal, logicist
methods; cognitive architectures; and sophisticated NLP techniques.
A great mediator, Popper sought an approach to mathematics that navigated between logicism (formalism) and intuitionism in a way that both avoided excessive Platonism of the logicist
and the "subjective" constructive foundationalism of intuitionism.
His honours thesis in mathematical philosophy used the logical resources of Russell and Whitehead's Principia Mathematica, resulting in Quine's early commitment to the logicist
position that mathematics is reducible to logic.
Peirce's synthetic reading resulted in an original view of the relationship between logic and mathematics, very different from the logicist
For instance, consider an analysis from the logicist
project of Russell and Frege: Whenever a number is present so is a set (more specifically, the set of all sets similar to that set).
More positively, he interprets those remarks as arguments against the logicist
reduction of mathematics to logic.
If basic arithmetic propositions are logically true--as the logicist
contends--then there is tension between this conservation requirement and the ontological commitments of arithmetic.
1991]: `Against Logicist
Cognitive Science', Mind & Language, 6, pp.
Margaret Boden, in a chapter on the impact of computational theories on philosophy, draws attention to the fact that, whether you are a logicist
or a connectionist, the tools of your trade may be equally inappropriate in philosophical debate.
As well as giving the discipline its name, McCarthy made fundamental contributions of lasting importance to computer science in general and artificial intelligence in particular, including time-sharing operating systems, the LISP programming languages, knowledge representation, common-sense reasoning, and the logicist
paradigm in artificial intelligence.
12) The logicist
approach to the foundation of mathematics led to the formulation of several paradoxes, which exposed the internal limits of logical theories.
What is strikingly absent in a volume on one of the founders of modern logic is a more comprehensive treatment of Frege's formal systems (that in the book Begriffsschrift [Bs] and that in the book Grundgesetze der Arithmetik [GgA]) and his logicist
treatment of arithmetic.