Dear all, The Serious Metaphysics Group will meet this Wednesday from 4.30 p.m. to 6.00 p.m. in the Faculty Board Room.
Our speaker is James Cargile (Virginia). His title and abstract are as follows. Title: Russell’s Paradox Abstract: It is generally agreed that Russell’s Paradox proves that there cannot be a set of all non-self-membered sets. There is no such general agreement about the significance of this point. A rough version of Russell’s own main moral is that there is no such property as being a non-self-membered set. A popular view in prominent first order set theories is that there is such a property, but it does not determine a set (though it is said to determine a “class” in NGB). The latter view is unsatisfactory because ~(xԑx), like every open wf of FOL, determines a subset of the domain in every interpretation. The set is not itself a member of the domain in ZF or NGB, but that evasion is bad philosophy. The rough version of Russell’s answer misrepresents him. His actual answer conflates there being no such property as being a non-self-member with there being no such predicate as “…is a non-self-member”. There is obviously such a predicate in English, so Russell’s move is that there is no such predicate in a logically proper language, which can be arranged in formulating the “language”. The truth is that “…is a non-self-member” is a meaningful predicate of English which does not express a property. “The set of dogs is a non-self-member” and “The set of cats is a non-self-member” are both true, but do not attribute a common property. The first says that every property which has as its extension the set of dogs is a property the set does not have, so the set is not a dog. In a similar way, the second attributes not being a cat. If I succeed in making this clear, then it can be seen that (Det) every property determines an extension and every extension (set) is determined by at least one property. Opposition to (Det) comes from a variety of sources. Some advocates of plural descriptions argue that “The non-self-members do not form a set” is consistent and true. This needs to be distinguished from the correct “The predicate ‘is a non-self-member’ does not express a property (and thus does not determine a set)”. Another major problem for (Det) is the Burali-Forti Paradox. Since I agree that there is such a property as being an ordinal number, (Det) requires there is a set of all ordinals, which conflicts with standard set theories. If time permits, I will attempt to answer this. Failure to recognize (Det) has caused great confusion in philosophy. Just one example is the idea that Socrates is ontologically prior to the set whose sole member is Socrates. This disastrous metaphysical view is the sort of thing that has arisen from logically incorrect responses to Russell’s Paradox. Not every predicate expresses a property and not every property is expressed by a predicate, but every set depends on some property or properties. So I will argue, hoping to persuade. Hope to see you there! The full termcard is available on the webpage <https://www.phil.cam.ac.uk/seminars-phil/SMG <https://www.phil.cam.ac.uk/seminars-phil/SMG> <https://www.phil.cam.ac.uk/seminars-phil/SMG <https://www.phil.cam.ac.uk/seminars-phil/SMG>>>. Best wishes, Alex Alexander Roberts Lecturer, Faculty of Philosophy University of Cambridge Website <http://users.ox.ac.uk/~magd4036/> _____________________________________________________ To unsubscribe from the CamPhilEvents mailing list, or change your membership options, please visit the list information page: http://bit.ly/CamPhilEvents List archive: https://lists.cam.ac.uk/pipermail/phil-events/ Please note that CamPhilEvents doesn't accept email attachments. See the list information page for further details and suggested alternatives.
