Color MS 462

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as [...ender?] them reversible.

The rule method given is such a comprehensive routine that is would be easy to devise a machine that would perform it. But [ofhen?] [?] have to be taken into account The immense diversity and complexity of the case renders any such procedure quite impracticable. Thus, from these three premises, which are certainly not of more than ordinary complexity, yield

no less than ninety entirely independent con cousins without iterating the premises with ite ration these would be strictly antecedent[less?] multitude, of which would have several hundred of some inte rest.These I say this without very careful examination, but I believe it is correct.

Last edit over 6 years ago by hniehus1
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The beta-part of the system of existential graphs is distinguished by its taking cognizance of individual identity and individuality. Perhaps, therefore, we ought to consider the following statement as beta- impossible:

A certain institution will pay every dollar it has borrowed or shall borrow with a borrowed dollar; and the payment of a dollar cannot balance debts of more than one dollar. Nevertheless, there are [?] will be some dollars borrowed that never will be repaid.

I have, however, introduced no rule into this part of the exposition which would stamp that statement as imposbible (illegible) the institution in question had an

Last edit almost 4 years ago by Lilith27
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eternal existence it might ,conceivably as far as my rules take cognizance of impossibilities, go on forever borrowing more and more dollars each year and after paying up all its old last year's debts have an ever increasing surplus of borrowed money in hand. But this possibility does not consist in anything state of things that ever will be an accomplished fact. It consists in a predicted endless future that never can come to pass become positive fact.

However, rightly or wrongly, I postpone all consideration of the distinction between esse in futuro and positive individual existence to the gamma part of the subject; and as long as I do this, there is no impossibility in the beta part of the development which differs does

Last edit almost 4 years ago by Lilith27
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is not essentially of the same nature as the absurdity of the following proposition graph not consist in a violation of the principle of contradiction, like an alpha-impossibility. There is, however, a difference with approach. As a simple example of the kind of impossibility

which my rules do condemn, we use, take this graph, which may be read as follows:

Arthur likes everything exhibited by a certain dealer who exhibits a picture painted by an artist who paints nothing that Arthur likes.

An impossibility like that of this second graph appears to have a different character.

You should have no difficulty in reading it. The heavy lines assert identity. The oval cuts assert the otherness of each the identity of an individual,

Last edit over 5 years ago by noamsol
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The oval cuts with lines running into through them assert the otherness of the individuals on the two sides. The oval cuts with lines running into themit and and these joining An oval cut with two lines running into it and these joining any graph assert that the individuals denoted by those lines are not in the relation signified by that graph. All these things were explained in the last lecture. They are perfectly simple. Yet if any of you is able without difficulty to see the meaning of that graph, if his mind is not rendered dizzy by the multiplicity of signs exactly alike, let me tell him that he has the making of an excellent mathematician in him.

The absurdity which this graph expresses asserts is that there is a certain triplet of different individuals and there is a pair of individuals; and each

Last edit almost 4 years ago by Lilith27
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