By Guillermo E. Rosado Haddock
Gottlob Frege is likely one of the maximum logicians ever and likewise a thinker of significant importance. during this publication Rosado Haddock deals a severe presentation of the most subject matters of Frege's philosophy, together with, between others, his philosophy of mathematics, his sense-referent contrast, his contrast among functionality and item, and his criticisms of formalism and psychologism. greater than simply an creation to Frege's philosophy this e-book can also be a hugely severe and mature overview of it as a complete during which the constraints, confusions and different weaknesses of Frege's idea are heavily tested. the writer can also be a Husserlian pupil and this ebook comprises worthy discussions of Husserl's overlooked perspectives and comparisons among the 2 nice philosophers.
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Additional resources for A Critical Introduction to the Philosophy of Gottlob Frege
Secondly,36 it is true that the sequence of prime numbers, as well as the sequence of even numbers, that of odd numbers, and many others are also ωsequences and, as ω-sequences, have the same structure as that of the natural numbers (they are all order-isomorphic). However, if we take into account the additive and multiplicative properties of the natural numbers, as well as the properties of being prime, or of being odd, they get lost or have to be redefined when we consider other ω-sequences. Thus, for example, in the ω-sequence of even numbers, none has the property of being equal to its own product.
Thus, we could try to define number as follows:17 (1) (2) (3) To a concept F corresponds the number 0, if in general, regardless of what b is, the statement that b does not fall under F is true. To a concept F corresponds the number 1, if the statement that b does not fall under F is not true in general, regardless of what b is, and if from the pair of statements ‘b falls under F’ and ‘c falls under F’ follows that b and c are the same thing. To the concept F corresponds the number n+1, if there is an object b such that to the concept ‘falls under F but is different from b’ corresponds the number n.
Section 51, p. 64. , section 53, p. 64. 13 Ibid. For a more detailed discussion of this issue, see Frege’s ‘Dialog mit Pünjer über Existenz’, in Nachgelassene Schriften, pp. 60-75. 14 See Die Grundlagen der Arithmetik, p. 64. 12 Grundlagen der Arithmetik: Second Part (§§46-109) 39 On the other hand, it would be clearly mistaken to conclude that existence or uniqueness can never be traits of concepts. What Frege sustains is that they are not traits of concepts under which objects can fall, that is, of first order concepts.
A Critical Introduction to the Philosophy of Gottlob Frege by Guillermo E. Rosado Haddock