97) This identification between the construction required by a mathematical statement
and the (constructive) proof of the same statement is wrong, as I show in my paper (2000).
The essential features of the content are listed in one of two ways: either a series of mathematical statements
following a strict, logical hierarchy, or as categories of knowledge based on the logic apparent in the mathematical ideas.
From a realist perspective, mathematical statements
can be regarded as objectively true if there are some mathematical posits that make them true.
How can we know that mathematical statements
are true through purely a priori means?
Such mathematical statements
can never approach the reality of aesthetic experience, and the attempt to offer them as an explanation for that phenomenon would be recognizable by all minimally rational persons as inane.
What computers can do is think in code, a series of simple, mathematical statements
. Human beings, on the other hand, can imagine and dream, hope and despair, hate and love with all their hearts.
He introduces the foundations of mathematics as conceptualized by Russell and Whitehead, Hilbert, and Bourbaki: the tools for mathematical reasoning, a formal methodology, and the interplay between the written structures of mathematical statements
and their meaning.
It should be noted that Quantitative Trading Systems focuses expressly upon trading strategies that derive from unambiguous mathematical statements
, not any system that relies on subjective judgments (i.e.
This paper argues for the assimilation of this thesis to Wittgenstein's "no-conjecture thesis" concerning mathematical statements
. Both flow from a strong verificationist view of mathematics held by Wittgenstein in his middle period, and this also explains his views on the law of excluded middle and consistency.
It is true that physicists are often sloppy with mathematical formulations and usage of language, but it is also true that mathematicians often read physics papers superficially and see misconceptions, "errors", erroneous mathematical statements
, etc., instead of trying to figure out the true content behind an informal (and therefore necessarily imprecise) description, whose emphasis is on physics and not mathematics.
Algebra and calculus students have difficulties to express themselves in a statement of mathematical symbols and to comment on written mathematical statements
to end with equivalent mathematical symbols statement.
Gordon (1955) that complex mathematical statements
are less operational than other economic statements.