MS 455-456 (1903) - Lowell Lecture II

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If you bear in mind these characteristics of proper names, you will perceive that when lawyers and others use the letters A, B, C as a sort of improved relative pronouns, saying for example that if A owes B money and C owes A money, then B may “trustee” C for the debt (as you say in Massachusetts) these letters differ from new proper names only in the accidental circumstance that they are first introduced in the antecedent of a conditional proposition while proper names are first introduced in positive assertions. I call such improvised proper names selectives.

There is nothing in the world to prevent our using the capital letters as such individual names, provided we distinguish the first replica by scribing it heavily or otherwise. I cannot say that this is a bad way; it serves the purpose of putting out of view confusing [trifles?]. But I do say that it is inferior requires rather complicated rules, and from every other point of view except that of putting unimportant circumstances [out of view and convenience in printing?,] is usually inferior to another way of accomplishing fulfilling the same purpose, which I proceed to describe.

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Since the blackboard, or the sheet of assertion, represents the universe of discourse, and since this universe is a collection of individuals, it is natural seems reasonable that any heavily decidedly marked point of the sheet, should stand for a single individual; so that • should mean “something exists.” We cannot make this • • to mean that two things exist, since this would conflict with our convention that graphs on different parts of the sheet shall have each the same meaning as if each stood alone, so that consequently the second point merely reiterates that something exists.

You will ask me what use I propose to make of this sign that something exists, a fact that graphist and interpreter took for granted at the outset. I will show you that the sign will be useful as long as we agree that although different points on the sheet may denote the same individual, yet different individuals cannot be denoted by the same point on the sheet.

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If we take any proposition, say

A sinner kills a saint

and if we erase portions of it, so as to leave it a blank form of proposition, the blanks being such that if they are all every one of them is filled with a proper name, a proposition will result, such as

______ kills a saint A sinner kills ______ ______ kills ______

where Cain and Abel might for example fill the blanks, then such a blank form, as well as the complete proposition, is called a rheme provided it be neither logical necessity true of everything nor true of nothing, but this limitation may be disregarded. If it has one blank it is called a monad rheme, if two a dyad, if three a triad, if none a medad (from μηδέν).

Now such a rheme being neither logically necessary nor logically impossible, and representive as a [part of ?] a graph without being represented as compounded as a combination by any of the signs of the system is called a lexis and each replica of the lexis is called a spot. Such

[A lexis is therefore an incomplex contingent graph. ?]

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Lexis is the Greek for a single word and a lexis in this system corresponds to a single verb in speech.

The plural of lexis is preferably lexeis rather than lexises.

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a spot has a particular point on its periphery appropriated to each and every one of its blanks. Those points, which, you will observe, are mere places, and are not marked, are called the hooks of the spot. But if a marked point, which we have agreed shall assert the existence of an individual, be put in that place which is a hook of a graph, it must assert that some thing is the corresponding individual whose name might fill the blank of the rheme. Thus

• gives • to • in exchange for •

will mean “something gives something to something i n exchange for something.”

Now let us further agree that a heavily marked line , all whose points are ipso facto heavily marked and therefore denote individuals, shall be a graph asserting the identity of all the individuals denoted by its points. Then

will mean that there is a ripe pear, that is, something is a pear and that very same thing is ripe.

Last edit over 6 years ago by gnox
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