By Kennington A.
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An outline of the geometry of space-time with the entire questions and matters defined with out the necessity for formulation. As such, the writer indicates that this can be certainly geometry, with real structures everyday from Euclidean geometry, and which permit designated demonstrations and proofs. The formal arithmetic at the back of those structures is supplied within the appendices.
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6 Remark: Mathematical activity may be perceived internally. 4) in saying that all meaning must be connected to “sensible experience” unless one includes internal perception as a kind of sensory experience. Pure mathematical language refers to activities which are perceived within the human brain. 7 Remark: The intellectual content of mathematics lies in human ideas. Lakoﬀ/N´ un ˜ez , page xi, makes the following comment on the lack of intellectual content in mathematical symbols. Mathematics is seen as the epitome of precision, manifested in the use of symbols in calculation and in formal proofs.
Lakoﬀ/N´ un ˜ez , page 49, has the following comment on where the ultimate meaning of mathematics comes from when mathematical symbols are recursively interpreted. To understand a mathematical symbol is to associate it with a concept—something meaningful in human cognition that is ultimately grounded in experience and created via neural mechanisms. [. . ] The meaning of mathematical symbols is not in the symbols alone and how they can be manipulated by rule. Nor is the meaning of symbols in the interpretation of the symbols in terms of settheoretical models that are themselves uninterpreted.
So when you copy something, it must go through your mind! It is also important to develop an awareness of whether you do or do not really understand something. It is important to remove the mental blind spots which can hide the diﬃcult things. When copying material, it is important to determine which is the first word where it becomes diﬃcult. Read a diﬃcult sentence until you ﬁnd the ﬁrst incomprehensible word. Focus on that word. If a mathematical expression is too diﬃcult to understand, read each symbol one by one and ask yourself if you really know what each symbol means.