C. S. Peirce Manuscripts

Pages That Need Review

MS 455-456 (1903) - Lowell Lecture II

21
Needs Review

21

3rd. If it would be permissible to transform one graph, a, into another, b, it is permissible to scribe 4th. Whenever it is permissible to scribe

{{tex: \vscroll { \ a\ }{b} :tex}}

it is would be permissible were a scribed, to scribe b. 5th. A vacant enclosure may be called a blot is not permissively scriptible, and as such is [called a blot?] 6th. Any enclosure having a blot in its area may be cancelled or erased.

Here we have the three signs defined purely in terms of [what?] the logical transformations from them and to them without one word being said about what the signs really mean. They are left to be applied to whatever there may be that corresponds to them. This is the Pure Mathematical point of view, a point of view far from easy to a person as imbued with logical notions as I am.

These 6 rules are not quite so convenient, as are 3 rules, each double, which can without difficulty be proved to follow from these 6. These three double rules are what I call the three fundamental alpha rules of existential graphs.

They are as follows: I proceed to state them [Go to middle of p. 15] 1st, Rule of Erasure or Insertion 2nd, Rule of Iteration or Deiteration 3rd, Rule of Double Enclosure the Double Cut.

Last edit over 6 years ago by gnox
22
Needs Review

22

16

then if H were scribed on the bottom of a cut, it could be transformed into G without fear danger of introducing falsity. For if G is transformable into H, it is that we know that it cannot be that G is true while H is false. But if If then is on the sheet of assertion, that is, if H is on the bottom of a cut, G cannot be true and therefore we may scribe That is H on the bottom of a cut can be transformed into G. This is called the principle of contraposition. From all this it follows that

Any graph on the sheet of assertion or within an even number of cuts can be erased. While within an odd number of cuts already made, any graph can be inserted. This does not justify us in making any new cut within an even number of cuts. That, then is the first rule, called the rule of erasure and insertion.

[note here: Skip to p. 17]

The second is that a pair of cuts one within the other with no graph between them [????]

Last edit over 6 years ago by gnox
23
Needs Review

23

17

can anywhere be made or anywhere be destroyed. This is called the rule of two cuts. The third second rule is that any graph scribed on any area can be iterated, that is, scribed in a new replica, on the same area or within any additional cuts; and if a graph is already so iterated, it can be deiterated by erasing the inner replica. This is called the rule of iteration and deiteration. It follows by means of the principle of contraposition from the fact that if we have on the sheet of assertion

It rains

we can write

It rains It rains.

The ordinary logics give a form of inference called the modus ponens. The premisses are: If A is true, B is true and A is true. The conclusion is that B is true. Our system analyzes this into three inferential steps.

Last edit over 6 years ago by gnox
24
Needs Review

24

18

We have

a The rule of iteration and deiteration gives us a right to

a

The rule of two cuts gives a b

Finally, the rule of erasure and insertion gives b

I now pass to the beta part of the system of existential graphs. It is far more interesting and important than the alpha part but incomparably less so than the gamma part.

When one hears a proper name mentioned for the first time, one generally learns of the individual person or thing denoted by that name that it exists. It may, of course, be identified with a subject of force already well-known; but that will be exceptional. It will frequently be obvious apparent that it is a thing quite different from any hitherto

Last edit over 6 years ago by gnox
26
Needs Review

26

20

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.

Last edit over 6 years ago by gnox
27
Needs Review

27

21

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.

Last edit over 6 years ago by gnox
28
Needs Review

28

22

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. ?]

Last edit over 6 years ago by gnox
30
Needs Review

30

23

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
31
Needs Review

31

24

We call such a heavy line a line of identity. A point from which three lines of identity proceed has the force of the conjunction ‘and.’

There is no need of a point from which four lines of identity proceed; for two triple points answer the same purpose.

Therefore a figure like this is to be understood as two distinct lines of identity crossing one another. Nevertheless, in order to avoid possible mistake a bridge may be represented thus: One line passes under the bridge, the other upon it.

The more you scribe on the bottom of a cut, the less you assert. Thus means: It is not true that somebody returns to earth nor is it true that somebody is translated. But

Last edit over 6 years ago by gnox
32
Needs Review

32

25

merely says that both are not true. That is one or [the] other is false. Either nobody returns to earth or else nobody is translated.

Add to this a line of identity joining the two and still less is asserted. Either nobody is translated or if anybody is translated, that person does not return to earth.

Now take this That means somebody is a prophet but nobody is translated. If we continue the outer line to the cut, it will make no difference for no significance attaches to the shape of the line. If, however, the

Last edit over 6 years ago by guest_user
Displaying pages 281 - 290 of 392 in total