Abstract
Segundo a objeção da Má Companhia, o fato de que a infame Lei Básica V de Frege proporciona o padrão de definição geral dos princípios de abstração superior é uma boa razão para duvidar da validade deste tipo de definições. Neste artigo, eu argumento contra esta objeção, mostrando que o padrão de definição dos princípios de abstração — como extrapolados a partir do §64 do Grunlagen de Frege — inclui um requisito adicional (que denomino como a condição de especificidade) que não é satisfeito pela Lei Básica V, embora seja satisfeito por outras abstrações de ordem superior, tal como o Princípio de Hume. Mostro também que a falha deste requisito adicional no caso da Lei Básica V é engendrada por uma característica essencial da concepção de Frege da lógica, e que, assim, o próprio Frege não deveria ter tomado a Lei Básica V como uma definição por abstração.
Highlights
Frege’s early attempt to provide logical foundations to arithmetic is based on a special sort of definitions which have been named abstraction principles
The main purpose of this paper is to show that the Basic Law V cannot be considered as a bad company of Hume’s Principle due to the fact that it does not satisfy the definitional pattern described in §64 of the Foundations
Basic Law V is an instance of the definitional pattern behind all abstraction principles
Summary
Frege’s early attempt to provide logical foundations to arithmetic is based on a special sort of definitions which have been named abstraction principles. A possible reply to the bad company objection is based on a deeper analysis of the definitional pattern that characterizes abstraction principles resulting in new requirements on the relation appearing in the left limb such that the Basic Law V may be shown to fail to satisfy these requirements that other reasonably consistent abstraction principles meet. This is the strategy that I pursue in this paper.
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