Consequently, mathematical statements
have to be interpreted in a non-realist way:
How can we know that mathematical statements
are true through purely a priori means?
Equations, statistics, and other kinds of mathematical statements
are fundamentally inapposite to human experience and cannot in any way assert the truths of human experience.
The Gordon hypothesis is that complex mathematical statements
are less likely to be operational relative to other economic statements: We offer evidence on this proposition.
Vector graphics is the creation of digital images through a sequence of draw commands or mathematical statements
that place lines and shapes in a given two-dimensional or three-dimensional space.
He devised a way to construct self referencing mathematical statements
on the order of:
For example, compared to all of the other countries, a greater percentage of mathematics problems per lesson in Japan involved proving or verifying mathematical statements
, and a smaller percentage of mathematics problems per lesson were repetitions of previous problems.
So it would seem that there is no way to interpret mathematical statements
at face value and vindicate our claim to mathematical knowledge.
There is a great deal of similarity between Resnik's and Shapiro's views, so many of the above questions are answered along similar lines: both Resnik and Shapiro are mathematical realists - they both believe that mathematical entities exist independently of our knowledge of them and that mathematical statements
are mind-independently true or false; they both agree that structuralism and realism are independent of one another; and they both provide essentially the same account of sameness of structure.
Teaching students to read aloud symbolic mathematical statements
is an important part of developing their symbolic, and hence, mathematical literacy.
The authors begin with brief mathematical statements
of models, procedures, and notation, and present data examples to illustrate the models.