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Some Remarks on Logical Form: Difference between revisions
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I have said elsewhere that a proposition "reaches up to reality", and by this I meant that the forms of the entities are contained in the form of the proposition which is about these entities. For the sentence, together with the mode of projection which projects reality into the sentence, determines the logical form of the entities, just as in our simile a picture on plane II, together with its mode of projection, determines the shape of the figure on plane I. This remark, I believe, gives us the key for the explanation of the mutual exclusion of {{nowrap|R P T}} and {{nowrap|B P T}}. For if the proposition contains the form of an entity which it is about, then it is possible that two propositions should collide in this very form. The propositions, "Brown now sits in this chair" and "Jones now sits in this chair" each, in a sense, try to set their subject term on the chair. But the logical product of these propositions will put them both there at once, and this leads to a collision, a mutual exclusion of these terms. How does this exclusion represent itself in symbolism? We can write the logical product of the two propositions, ''p'' and ''q'', in this way:—(170) | I have said elsewhere that a proposition "reaches up to reality", and by this I meant that the forms of the entities are contained in the form of the proposition which is about these entities. For the sentence, together with the mode of projection which projects reality into the sentence, determines the logical form of the entities, just as in our simile a picture on plane II, together with its mode of projection, determines the shape of the figure on plane I. This remark, I believe, gives us the key for the explanation of the mutual exclusion of {{nowrap|R P T}} and {{nowrap|B P T}}. For if the proposition contains the form of an entity which it is about, then it is possible that two propositions should collide in this very form. The propositions, "Brown now sits in this chair" and "Jones now sits in this chair" each, in a sense, try to set their subject term on the chair. But the logical product of these propositions will put them both there at once, and this leads to a collision, a mutual exclusion of these terms. How does this exclusion represent itself in symbolism? We can write the logical product of the two propositions, ''p'' and ''q'', in this way:—(170) | ||
{| style="border-collapse: collapse | {| class="table-centered-text" style="border-collapse: collapse; margin: 20px auto;" | ||
| style="width: 5em; height: 3em; border-right: 1px solid black; border-bottom: 1px solid black;" | p | | style="width: 5em; height: 3em; border-right: 1px solid black; border-bottom: 1px solid black;" | p | ||
| style="width: 5em; border-right: 1px solid black; border-bottom: 1px solid black;" | q | | style="width: 5em; border-right: 1px solid black; border-bottom: 1px solid black;" | q | ||
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What happens if these two propositions are {{nowrap|R P T}} and {{nowrap|B P T}}? In this case the top line {{nowrap|"T T T"}} must disappear, as it represents an impossible combination. The true possibilities here are— | What happens if these two propositions are {{nowrap|R P T}} and {{nowrap|B P T}}? In this case the top line {{nowrap|"T T T"}} must disappear, as it represents an impossible combination. The true possibilities here are— | ||
{| style="border-collapse: collapse | {| class="table-centered-text" style="border-collapse: collapse; margin: 20px auto;" | ||
| style="width: 5em; height: 3em; border-right: 1px solid black; border-bottom: 1px solid black;" |{{nowrap|R P T}} | | style="width: 5em; height: 3em; border-right: 1px solid black; border-bottom: 1px solid black;" |{{nowrap|R P T}} | ||
| style="width: 5em; border-bottom: 1px solid black;" |{{nowrap|B P T}} | | style="width: 5em; border-bottom: 1px solid black;" |{{nowrap|B P T}} | ||
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That is to say, there ''is'' no logical product of {{nowrap|R P T}} and {{nowrap|B P T}} in the first sense, and herein lies the exclusion as opposed to a contradiction. The contradiction, if it existed, would have to be written— | That is to say, there ''is'' no logical product of {{nowrap|R P T}} and {{nowrap|B P T}} in the first sense, and herein lies the exclusion as opposed to a contradiction. The contradiction, if it existed, would have to be written— | ||
{| style="border-collapse: collapse | {| class="table-centered-text" style="border-collapse: collapse; margin: 20px auto;" | ||
| style="width: 5em; height: 3em; border-right: 1px solid black; border-bottom: 1px solid black;" | {{nowrap|R P T}} | | style="width: 5em; height: 3em; border-right: 1px solid black; border-bottom: 1px solid black;" | {{nowrap|R P T}} | ||
| style="width: 5em; border-right: 1px solid black; border-bottom: 1px solid black;" | {{nowrap|B P T}} | | style="width: 5em; border-right: 1px solid black; border-bottom: 1px solid black;" | {{nowrap|B P T}} | ||