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    Premise P2—that forms are as many as the predicates truly... — Carmelics
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    Challenges→Each form in the infinite hierarchy of forms of largeness is infinitely many.

    Premise P2—that forms are as many as the predicates truly applied to them—thus conflates intensional predication with mereological composition, invalidating the inference to infinite many-ness.

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    Key Terms

    Infinite many-ness(in metaphysics and mathematics)
    The quality or state of being endless in quantity—having infinitely many of something, with no upper limit to the count.
    Intensional predication(in logic and metaphysics)
    A way of describing something based on its internal qualities or meanings, rather than just listing the physical things that compose it. For example, describing a painting by its artistic meaning rather than by naming every brushstroke.
    Mereological composition(in metaphysics)
    The way parts combine together to form a whole object. 'Mereology' is the study of how parts relate to wholes, so this phrase is about how smaller things build up into bigger things.
    Predicates(in logic and philosophy of language)
    Words or phrases that describe properties or characteristics of something—like 'is red' or 'is tall' in the sentence 'The ball is red.'

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    Premise
    A premise is a statement or fact that you assume to be true as a starting point for reasoning or making an argument. Think of it as the foundation or building block you use to reach a conclusion—for example, "All dogs are animals" and "My pet is a dog" are premises that lead to the conclusion "My pet is an animal." Premises are essentially the evidence or claims you offer before drawing a final conclusion.
    forms(Timaeus metaphysical scheme)
    The eternal and unchanging entities that serve as the 'model' or 'father' in Plato's tripartite metaphysical scheme in the Timaeus.
    inference(Nyāya epistemology)
    A component of epistemology in Nyāya philosophy; a veritable inference yields knowledge about the world and must have premises that are themselves known

    Connections

    1 linked claim · 2 topics

    Modality & Possibility1 linkedPhilosophy of Language1 linked
    Each form in the infinite hierarchy of forms of largeness is infinitely many.

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    Each form in the infinite hierarchy of forms of largeness is infinitely many.

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