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This theory of judgment dominated logic for centuries, but it has some obvious difficulties: it only considers proposition of the form " All A are B.
", a form logicians call universal.
It does not allow propositions of the form " Some A are B ", a form logicians call existential.
If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.
( Indeed Arnauld's contemporary Descartes famously argued so, regarding the concept " God " ( discourse 4, Meditation 5 )).
Arnauld's theory was current until the middle of the nineteenth century.

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