that mathematical existence
is a precondition of mathematical knowledge, a new source of possible disagreement emerges from the consideration of the nature of the mathematical entities that supposedly exist.
From the point of view of proof-theoretic semantics, we examine the logical background invoked by Neil Tennant's abstractionist realist account of mathematical existence
In intuitionistic mathematics, mathematical existence becomes inseparably fused with subjective construction, and mathematical veracity becomes one with the demonstrative trajectory of the intuitionist subject.
This title is better reserved for the Brouwerian subject, the 'creative subject' of intuitionistic mathematics, who, as we will see, generates the medium of mathematical existence in a process reminiscent of the Pythagorean cosmogony, where the 'Indefinite Dyad', in a dialectic with the One, gives rise to the entire universe of Number.
What the intuitionist mission of distilling mathematical existence down to what is subjectively constructible gains for mathematics in clarity, it looses in scope, and 'full of pain, the mathematician sees the greatest part of his towering edifice dissolve in fog'.
What is at stake in this dispute is, again, the centrality of the subject in the field of mathematical existence.
The intuitionist identification of mathematical existence with construction, and of truth with demonstration, has consequences that penetrate through to the logical structure of mathematical reason itself.
At least she's an economist interested in the real world, not in some silly mathematical existence
The author of the book under review denies that we have any clear sense of what it would be like for prime numbers to exist or not to exist, thus agreeing with Carnap as far as he goes, but then going beyond him to deny not only that there are clear supra-scientific standards of warrant, but also that scientific standards of warrant are sufficient to give mathematical existence assertions a clear sense, either.
It would imply what the author ultimately wants to deny, that questions of mathematical existence do have a clear sense, or at any rate, as clear a sense as questions of consistency.
As long as certain presuppositions are made, the formulation in terms of mathematical truth (which I will give below) will be equivalent to the one in terms of mathematical existence
It also contains papers on such topics as the phenomenology of mathematical truth, mathematical beauty, and mathematical proof, as well as discussions of identity, computer science, mathematical existence
, meaning, and Kant and Husserl.