Marks and Remarks
Food for the Mind and Eye

No. 0008, January 28, 2015


DEPT. OF MATHEMATICAL LOGIC

No, A does NOT Equal B

Left does not equal right


      It is self-evident that A does not even resemble B so how can "A=B" be true? The problem is that the meaning of "=", the "equals" sign, is misunderstood because of an unwarranted assumption.

      For "A=B" to be true the symbol "=" cannot be a sign of identity. A is obviously not identical with B. If A=B is true, then the "=" sign must mean this: there is a recognizable individual "item X" to which people refer, without distinction, both as "A" and as "B". If the "item X" remains unchanged in its properties and location when it is referred to as "A" and as "B", then "A" and "B" refer to the one and the same individual "item X".

      What about the apparent identities "A=A" or, better yet, "2=2"? After all "2" is identical with "2", or is it? Well, actually there are two different "2"s here, each in a different location (one on the left side of the "=" sign, one on the right) so they cannot be identical. Again, the "=" symbol cannot be the sign of identity. Instead, it must mean this: the two "2"s are two labels both referring to the one and the same individual item (which, in this case, happens to look like, but is not identical with either of its labels).

      So it turns out the "=" sign does not mean that the two items on either side of it are exactly the same. Rather it means: "the two items on either side both refer to the one and the same unique third item".

      "And the consequences of this common misunderstanding are...?" prompts practical Prickles. Oh, immense. Consider the motto of the French Republic: "Liberté, Égalité, Fraternité". How it is implemented depends on the understanding of "Égalité". Just think of the consequences... "I'm trying, I'm trying," says Prickles.



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