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Within the last 24 hours, this page has been literally flooded by tens of people, most of them following a friendly link at Brian Weatherson's weblog. What's more, I'm now the world's leading authority on higher-order mereological contradictions! Seid umschlungen, Millionen.
There are many ways to update a belief system. For example, 1) believe every proposition that comes to your mind; 2) believe everything that makes you feel good; 3) believe everything Reverend Moon says. In "A Priority as an Evaluative Notion", Hartry Field argues that there is no fact of the matter as to which way is best.
In one sense, this is trivial. Of course the normative question which way you should choose does not have a purely factual answer. Which way you should choose depends on what you want from your belief system.
A sentence is context-dependent if different utterances of it in different contexts have different truth values. A common kind of context-dependence is contingency. For instance, 'there are unicorns' is true when uttered in a world that contains unicorns, and false otherwise. Now look at Convention T:
'p' is true iff p.
When 'p' is context-dependent, it doesn't really make sense just to call it true. However, Convention T certainly isn't meant to apply only to non-contingent (and otherwise non-context-dependent) sentences. So what shall we make of it? Two possibilites come to mind:
1) 'p', uttered in the present context, is true iff p.
Let S be the sentence "S contains a quantifier that does not range over everything".
S (and every utterance of S) is contradictory. Interestingly, it is so even if the quantifier in S really does not range over everything. From which it follows that either there are true contradictions, or "S contains a quantifier that does not range over everything" is not true iff S contains a quantifier that does not range over everything.
First: Are fundamental particles mereological atoms?
Fundamental particles are 'the ultimate constituents of the world', those upon whose properties and relations everything else supervenes. Many of us believe that the instrinsic properties of complex things supervene upon the properties and relations of their consituents. Then maybe the fundamental particles can be identified with the ultimate constituents of the world, if there are any. In fact, when we find that some things are composed out of smaller things, we will usually not call the complex things 'fundamental particles'. I think it is in this sense that fundamental particles are supposed to be indivisible -- not because we lack the means to break them into parts, nor because it is impossible 'in principle' to break them, but simply because they lack (proper) parts.
Okay, as promised here comes the third and last part of my little series on Rieger's paradox. I will first describe a general version of Russell's paradox, of which Rieger's is a special case. Then I'll discuss whether Frege is already prey to the paradox by his admission of too many concepts. Whether he is will depend on whether it makes sense to say that there are entities which are not first-order entities. I'm sorry that there is probably nothing new in all this.
First, the general version of Russell's paradox.
Yesterday, I argued that Frege can escape Rieger's Paradox if it is allowed that the thought that Fb might equal the thought that Gb (briefly, [Fb]=[Gb]) even if F and G are not coextensive.
In particular, to escape the paradox there has to be a concept F, such that [Fb]=[Ob] even though O([Ob]) and 
F([Ob]). O, recall, is defined thus:
O(x) iff 
F(x=[Fb]
Fx)
I did not say how this F might look like. Here is a good candidate:
In the October issue of Analysis, Adam Rieger presents the following paradox in Frege's ontology.
For any object b and first order concept F, there is the thought [Fb] that b falls under F. Let Con and Obj be functions that yield the (referents of the) constituents of such thoughts: Con([Fb])=F, and Obj([Fb])=b. We stipulate moreover that 'b' shall denote the mountain Ben Lomond, and define O ("ordinary") as follows:
As you maybe already noticed, I've redesigned my weblog. Now I can blog without cluttering the news column of umsu.de.
Over the past 20 minutes I've been searching for philosophy weblogs, as my link list is still rather short. Unfortunately, I could find nothing meeting the standards set by Brian Weatherson's brilliant blog. Any suggestions?
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