(no subject)
In the history of philosophy an important question is the question of origins. If, objectivly, there was an origin to what we call 'western thinking', its objectivity makes it possible to find. Whatever the answer, it must be of a sort that anyone might notice. Philosophy starts with the obvious. Ordinal numbers are obvious. We usually think of ordinal numbers as being like first, second, third... which is not incorrect, just too limiting. Ordinal numbers are estimated measures made before we convert them into cardinal numbers that measure exactly. Part of my argument is that the difference between an ordinal and cardinal number is the difference of exactness. Since ordinal numbers are based on perception, in a sense they are subjective. Thales was the first to notice that the perception of 'firstness' could be the cause of the abstract 'one'. The time was around six hundred B,C, and everywhere that was relatively civilized both ordinal and cardinal numbers were in use. There are two descriptions of Thales that pertain to this question. 1., he is said to have estabished the equinoxes with exactness, a feat that requires knowledge of the integration of incommensurables and, 2., he is said to have discovered a way to prove the truth or falsity of geometrical figures without reference to anything other than logic and reason: god was superfluous. The first is related to induction, the second to deduction.
It was obvious to Thales that 'first' and 'one' are related causally, ie, every time you experience an event that qualifies as a first, by implication there is only one way to explain it. He saw that 'one' is a generalization abstracted from experience. In the case of 'one', the experiences are all instances of 'first'. Every change presents us with a new 'first' and more content for our generalizations. When the Pythagoreans discovered the value of pi they didn't know that abstracting the general direction of pi was enough to establish its identity. There is evidence to say that Thales understood ordinal/cardinal integration. An experienced number is an ordinal number like 'first, second, bigger, smaller, etc. These 'numbers ' exist' in the sense that the relations exist that give them content. There exists a relation between Indiana and Ohio that says that Ohio is larger than Indiana. "Larger' is an ordinal term that describes a measurable difference between the two states. Most people don't carry a large supply of measuring tools with them all the time. That means that the majority of the common measurments we make, each time our mind makes a comparison, are done using ordinal numbers. An ordinal number allows one to quantify differences without using cardinal numbers.
It was obvious to Thales that 'first' and 'one' are related causally, ie, every time you experience an event that qualifies as a first, by implication there is only one way to explain it. He saw that 'one' is a generalization abstracted from experience. In the case of 'one', the experiences are all instances of 'first'. Every change presents us with a new 'first' and more content for our generalizations. When the Pythagoreans discovered the value of pi they didn't know that abstracting the general direction of pi was enough to establish its identity. There is evidence to say that Thales understood ordinal/cardinal integration. An experienced number is an ordinal number like 'first, second, bigger, smaller, etc. These 'numbers ' exist' in the sense that the relations exist that give them content. There exists a relation between Indiana and Ohio that says that Ohio is larger than Indiana. "Larger' is an ordinal term that describes a measurable difference between the two states. Most people don't carry a large supply of measuring tools with them all the time. That means that the majority of the common measurments we make, each time our mind makes a comparison, are done using ordinal numbers. An ordinal number allows one to quantify differences without using cardinal numbers.