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de inesse asserts is true, and therefore it is true, no matter how it may be with A. If however the antecedent, A, is true, while the consequent, B, is false, then, and then only is the conditional proposition de inesse false. This sort of conditional says nothing at all about any real connection between antecedent and consequent; but limits itself to saying “If you should find that A is true, then you may know that B is true,” never mind the why or wherefore.
The question of the proper way of expressing a conditional proposition de inesse in a system of existential graphs has formed the subject of an elaborate investigation with the reasoning of which I will not trouble you. Suffice it to say that it is found that there is essentially but one proper mode of representing it. Namely, in order to assert of the universe of discourse that if it
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rains then a pear is ripe I must put on the blackboard this:
(letter??)
I draw the two ovals which I call a scroll in blue because I do not want you to m to regard them as ordinary lines. I want you to join me in making believe that they are cuts through the surface, and that inside the outer one the surface skin of the board has been stripped off disclosing another surface below. This I call the area bottom or area. Therefore “It rains” is not scribed on the blackboard or, as I say, is not scribed on the sheet of assertion. For what is scribed on that sheet is asserted to be true of the universe
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of discourse; while the statement “It rains” is a mere supposition. Let us say that that bottom inside the outer cut represents another universe, a universe of supposition, and that it is only in that universe that it is said to rain. Besides this graph, “It rains” the bottom of the outer cut contains the inner cut which interrupts its surface; and inside the inner we will make believe that a patch is put on with a surface like that of the blackboard, although cut off from it. I use the word area for any part of the surface [unbounded?] or bounded by cuts, never extending [through??] a cut.
The outer cut is itself on the sheet the sheet of assertion although the whole of its interior is severed from that sheet. Now this outer cut by being on the sheet of assertion, represents the conditional proposition de inesse to be true of the universe of discourse.
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In order to get an insight into how the scroll represents the conditional proposition de inesse, we must make a little
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A fixed terminology is a great comfort. Let us term the area on which a cut stands the place of the cut, while the area or bottom of the cut is the area within the cut. The cut itself is not a graph nor the replica of a graph. No more is the scroll. But the scroll with the two graphs scribed in its two closes or areas makes up a graph, or graph-replica; and this I call an enclosure. The term may be used indifferently to mean the graph or the replica.
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experimental research.
At present Thus far, we have no means of expressing an absurdity. Let us invent a sign which shall assert that everything is true. Nothing could be more absurd illogical than that statement, inasmuch as it would annihilate render logic false as well as needless. Were every graph asserted to be true, there would be nothing that could be added to that assertion. Accordingly, our expression for it may very appropriately consist in completely filling up the area on which it is asserted. Such filling up of an area, may be termed a blot.
Take the conditional proposition de inesse, “If it rains then everything is true
That amounts to denying that it rains. But there is no need of making the inner cut so large. Let us write