Now we might expect this form of realism to appeal to anyone committed to realism without polyadic properties. ❋ Brower, Jeffrey (2009)
Moreover, as we have already seen, the notion of a polyadic predicate, from which our own concept of a polyadic property is derived, corresponds exactly to the medieval notion of a relative term. ❋ 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. ❋ 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. ❋ Brower, Jeffrey (2009)
As this passage helps to make clear, the root of the medieval objection to polyadic properties is ontological in nature, stemming from a particular conception of subjects and attributes. ❋ 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. ❋ Brower, Jeffrey (2009)
Having ruled out the possibility of their being polyadic, however, the medievals don't leave themselves with many options. ❋ 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”). ❋ Hanna, Robert (2009)
Although the medievals 'objection to polyadic properties stems in large part from ontological considerations, they also offer other reasons for rejecting them. ❋ 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 ❋ 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. ❋ Brower, Jeffrey (2009)
How is it that medieval philosophers maintain a form of realism about relations while at the time rejecting the existence of polyadic properties? ❋ Brower, Jeffrey (2009)
In particular, what do they say about arguments such as Auriol's, which in effect deny the coherence of realism without polyadic properties? ❋ Brower, Jeffrey (2009)
Now in the case of substances, it is perhaps clear that they are not polyadic in nature. ❋ Brower, Jeffrey (2009)
Although plural quantification provides a fairly natural interpretation of quantification over (monadic) concepts, it provides no natural interpretation of quantification over (polyadic) relations. ❋ Linnebo, Øystein (2008)
Relations generate a few special problems of their own, but for the most part properties and relations raise the same philosophical issues and, except where otherwise noted, I will use ˜property™ as a generic term to cover both monadic (one-place, nonrelational) properties and (polyadic, multi-place) relations. ❋ Swoyer, Chris (2000)
Chimpanzees can obtain about the same efficiency as humans in terms of quantity of social interactions because their grooming is often mutual and polyadic [involving three or more individuals]. ❋ EMJ [email protected] (2010)
Equality in polyadic algebras,” Transactions of the American Mathematical Society, 86: 1 “ 27. ❋ Burris, Stanley (2009)
Homogeneous locally finite polyadic Boolean algebras of infinite degree,” Fundamenta Mathematica, 43: 255 “ 325. ❋ Burris, Stanley (2009)
Historians of philosophy sometimes speak as if the medievals could not have possessed the concept of a polyadic property ” as if conceiving of relations in this way only became possible in the nineteenth and twentieth centuries, with the advent of a formal logic of relations and multiple quantification (Cf. Weinberg 1965, esp. ❋ Brower, Jeffrey (2009)
