1. Frege and Counting
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1. Frege's statement concerns the nature of number and the fact that number is not a property of the thing being numbered. The act of counting is imposed by an external mind and is not inherent in the thing itself. When we count 1000 leaves, as Frege states, we are not selecting leaves in any order that would correspond with the number of the count, and even in the aggregate the leaves cannot be said to possess a characteristic that is "1000." If the 1000 leaves of the demonstration were tossed out on a lawn and picked up again, an entirely different set of 1000 might be selected and would still constitute 1000 leaves. The leaves themselves do not possess the characteristic of number; number is imposed by the mind doing the counting.In explaining how he has arrived at this truism, Frege cites Baumann to the effect that we should reject the idea that numbers are concepts extracted from external things. Baumann states that external things do not present us with any strict units but rather with isolated groups or sensible points, "but we are at liberty to treat each one of these itself again as a many" (Frege (22). Frege and Baumann are both considering a characteristic of an object as something that is inherent in that object, that is in effect a defining element of the object. Frege refers to such things as color or hardness and notes that it is true that simply by thinking, he is not able to change the color of an object or its degree of hardness. He can change its
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is a reality in that counting is always the same process and number is always the same conception.
Number has an objective meaning that derives from the collision of the internal and external worlds. The mind seeks to order the external world, and number is one way of ordering that world. Number is neither strictly a characteristic of objects as discussed here or a subjective conception as it might seem from its description. It has elements of both in that it is a conception that has a reality in the external world even though number is not an inherent characteristic of an object. It is, though, an inherent characteristic of our perception of objects--to perceive objects is to count them, to know that there are this many and not that many. We count the leaves, but even if we do not count them out one by one, we know that there is a larger number of leaves in pile A than in pile B because pile A is larger. We know when we see two leaves that this is more than one leaf, and less than three leaves--the act of naming the number does not affect this basic realization. Number is inherent in our perceptions.
3. Frege first considers defining directions by giving a "criterion of identity" for them so that the statement
"the d
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Some common words found in the essay are:
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Approximate Word count = 2086
Approximate Pages = 8 (250 words per page)
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