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Extra resources for Bolzano’s Theoretical Philosophy: An Introduction
Sample text
As Bolzano sees it, on the one hand, the content of an idea can be increased without implying that the extension decreases. Bolzano explains: [. ] It is only required that we add a component [. ] from which no new property of the object represented follows [. ] Thus the content of the concept of a round sphere is greater than the concept of a sphere in general though the extension of both concepts is the same. (1837, §120, 569) 28 Bolzano’s Theoretical Philosophy Conversely, the content of an idea can be decreased without implying that the extension increases: But as we have already seen in §64 the objects that fall under a given idea A can have properties whose idea do not appear as components in the idea of an A.
The main obstacle to Bolzano’s program was the limitation of the theory of logic that was available at the time. In order to provide an account of deductive knowledge that would not resort to extra-conceptual resources, Bolzano had to show that logic can effectively reflect the structure of deductive knowledge. The first step was to do away with the decompositional conception of analysis that provided the paradigm explanation of conceptual knowledge at the time. The idea that in order to understand a concept one needs to decompose it is most eminently associated with Kant’s views on analyticity.
According to him: • There are simple and complex object-ideas. Simple ideas are treated as unstructured. (Cf. e. of the form ‘Something which has b’ where ‘which has’ is a name-forming operator (cf. ). If, for instance, the subject-idea ‘A’ of a proposition ‘A has b’ is complex, Bolzano proposes that we analyse it according to the following pattern: ‘Something which has a, has b’, and so forth. (Cf. ) • A property-idea, if it is complex, is typically “conjunctive”. Such is the predicate-idea ‘b, b , b ’ in ‘A which has b, b , b ’.