Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective Of or pertaining to a
polyad  adjective Comprising many elements
Etymologies
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Examples

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

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

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.

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, nonrelational monadic properties or accidents.

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

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

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.

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

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

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