polyadic

Now we might expect this form of realism to appeal to anyone committed to realism without polyadic properties.

Medieval Theories of Relations Brower, Jeffrey 2009

Having ruled out the possibility of their being polyadic, however, the medievals don't leave themselves with many options.

Medieval Theories of Relations Brower, Jeffrey 2009

There is some disagreement as to the precise analysis of the situations that makes these sorts of predications true, but even here the medievals work out their views from within a common framework provided by Aristotle's Categories: relational situations do not include anything corresponding to the notion of a polyadic property, but instead include only substances and their monadic properties or accidents.

Medieval Theories of Relations Brower, Jeffrey 2009

As mentioned above, on the simplest or most ontologically parsimonious form of realism without polyadic properties, what we are calling ˜reductive realism™, paradigmatic relations are identified with ordinary, non-relational monadic properties or accidents.

Medieval Theories of Relations Brower, Jeffrey 2009

And if that by itself weren't enough, there is the fact that medievals habitually speak of relations in polyadic terms, explicitly comparing them to a road

Medieval Theories of Relations Brower, Jeffrey 2009

What recent advances in logic have made possible is not the concept of a polyadic property, but merely its representation within a formal system.

Medieval Theories of Relations Brower, Jeffrey 2009

According to Albert, the problem with arguments of the sort Auriol gives is that they rely on a questionable assumption, namely: if there are no real polyadic forms or properties, then there is nothing in extramental reality to correspond to our relational concepts.

Medieval Theories of Relations Brower, Jeffrey 2009

The result of these apparent limitations is that Kant's logic is significantly weaker than “elementary” logic (i.e., bivalent first-order propositional and polyadic predicate logic plus identity) and thus cannot be equivalent to a mathematical logic in the Frege-Russell sense, which includes both elementary logic and also quantification over properties, classes, or functions (a.k.a. “second-order logic”).

Kant's Theory of Judgment Hanna, Robert 2009

In particular, what do they say about arguments such as Auriol's, which in effect deny the coherence of realism without polyadic properties?

Medieval Theories of Relations Brower, Jeffrey 2009

Now in the case of substances, it is perhaps clear that they are not polyadic in nature.

Medieval Theories of Relations Brower, Jeffrey 2009