How involved do you want to be in a non-symmetric relationship?

Fraser MacBride
University of Manchester
There are three different degrees to which we may allow a systematic theory of the world to embrace the idea of relatedness?supposing realism about non-symmetric relations as a background requirement. (First Degree) There are multiple ways in which a non-symmetric relation may apply to the things it relates?for the binary case, aRb ? bRa. (Second Degree) Every such relation has a distinct converse?for every R such that aRb there is another relation R* such that bR*a. (Third Degree) Each one of them applies in an order to the things it relates?with regard to the state that results from R's applying to a and b, either R applies to a first and b second, or it applies to b first and a second. Whereas the first degree is near-indubitable, embracing the second or third generates unwholesome consequences. The second degree embodies a commitment to the existence of a superfluity of distinct converses and states to which such relations give rise. The third degree embodies commitment to recherché facts of the matter about how the states that arise from the application of one non-symmetric relation compare to any other. It is argued that accounts that purport to offer an analysis of the first degree generate unwelcome second or third degree consequences. This speaks in favour of our adopting an account of the application of relations that's not an analysis at all, an account that takes the first degree as primitive.
Keywords Relations  Order  Converses  Realism  Fine
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Reprint years 2014
DOI 10.1080/00048402.2013.788046
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New Work for a Theory of Universals.David Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
Principles of Mathematics.Bertrand Russell - 1903 - Cambridge University Press.

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