Philosophers' Carnival # 145

Welcome one and all to the 145th edition of the Philosophers' Carnival! You may notice that this edition is a bit shorter than most previous ones. This is because, in deference to the new carnival policies, I've decided to include only what I believe to be the best of the best submissions.

And so, without further ado, I present to you the Philosophers' Carnival's main attractions:

　
Chad McIntosh of Appeared-To-Blogly examines the link between theism and the multiverse hypothesis, and concludes that the multiverse hypothesis is 'metaphysically laden'.

　
Richard Brown of Philosophy Sucks! shares some notes and thoughts on Giulio Tononi's inaugural lecture at NYU's Center for Mind and Brain.

　
Over at M-Phi, Catarina reviews Stephen Read's exposition of Thomas Bradwardine's solution to the Liar Paradox.

In his blog post "A Response to an Anti-Naturalist" at Larval Subjects, Levi Bryant replies to a critique of his defense of naturalism and materialism.

At Philosophy, et cetera, Richard Chappell critiques M. Oreste Fiocco's paper "Consequentialism and the World in Time", in which Fiocco gives arguments against consequentialism based on the philosophy of time.

Do you have infinitely many beliefs about the number of planets? Apparently not. Eric Schwitzgebel argues that if that's true it shows that "...it seems problematic to think of belief either in terms of discretely stored language-like style representations (perhaps plus swift derivability allowing implicit beliefs), or in terms of map-like representations."

　
In a post at the hanged man Matthew J. Brown argues, in opposition to some recent papers by Heather Douglas, that "...value judgments do have legitimate direct roles to play in the internal processes of scientific inquiry"--three roles, to be precise.

Finally, Mark Lance presents an interesting problem for the semantics and epistemology of mathematics in the first part of his post on domains of quantification over at New APPS. To be specific,

"...one knows what one is saying with such a sentence only if one knows what domain one is quantifying over. If we are discussing anything as complex as the reals - equivalently second order arithmetic - and mean to quantify over the "intended model" - that is, do not specify some constructable model as our domain - then we do not know what we are quantifying over. Thus, we do not know what we are saying when we make claims with second order arithmetic quantifiers."


That's all for this edition. The next Carnival will open at Talking Philosophy on December 10th.

A Dilemma for Dialetheism

I've just published a revised version of my article "A Dilemma for Dialetheism" on Scholardarity.com, which was originally published in the Spring 2010 edition of the Stanford undergraduate philosophy journal The Dualist (vol. 15). In the article I argue that dialetheists, who believe that some sentences are both true and false, either cannot express the notion that some sentences are not both true and false, or else that their accounts suffer from "revenge" liar paradoxes that not even they can regard as being both true and false. If you like logic and paradoxes as much as I do, please check it out and let me know what you think.

Another new variant of the liar paradox?

I've thought of another variant of the liar to add to my collection--I'll leave it to my readers to tell me if someone has already thought of it.

Consider the following statement:

(*): Nothing entails that (*) is true.

Suppose (*) is false. In that case, it is false that nothing entails that (*) is true. So something entails that (*) is true. But if something entails that (*) is true, then (*) is true. But then what (*) says must be the case, and hence it follows that nothing entails that (*) is true. So if (*) is false, it is true both that something entails that (*) is true and that nothing entails that (*) is true, which is a contradiction. (*) must, in consequence, be true. So it is true that noting entails that (*) is true. (*), however, is not only true, it is necessarily true, for its falsity would entail a contradiction. However, if (*) is necessarily true, its truth is entailed by every statement whatever. So if (*) is true, it is true both that nothing entails that (*) is true and that everything entails that (*) is true. This too is a contradiction. So no matter whether (*) is true or false, it must be both true and false.

A new variant of the liar paradox?

A few weeks ago I thought of the following variant of the liar paradox. I won't pretend that this post advances our understanding of the liar in any way, I'm just wondering if anyone else has thought of it before.

Consider the following statement:

(1) If there are elephants, then (1) is false.

If there were no elephants this statement would not be problematic. But there are. So let's assume that (1) is true. Given that there are elephants and that (1) is true, it follows by Modus Ponens that the consequent of (1) is true, and hence that (1) is false. So if (1) is true, and there are elephants, then (1) is false.

Let's now assume that (1) is false, granting once more that there are elephants. If (1) is false, the falsity of the consequent of (1), and hence (1) itself, cannot follow from the fact that there elephants. On this supposition (1) and its consequent are false, to be sure, but their falsity must not be entailed by the fact that there are elephants. But if the fact that there are elephants does not entail the falsity of the consequent of (1), and hence (1) itself, it must be possible for there to be elephants while they are both true. But we have already seen that if (1) is true, and there are elephants, then (1) is false. Thus it is not possible for there to be elephants while (1) and the consequent of (1) are both true. So the fact that there are elephants does entail the falsity of (1) and its consequent. But then what (1) says is true: If there are elephants, it must be false! Hence if (1) is false, it is also true.

Consequently, if there are elephants and (1) is true then (1) is false, and if there are elephants and (1) is false then (1) is true. Unless we're prepared to deny the existence of elephants, we have a paradox.