Skip to content

Episode 55: Branden Fitelson discusses paradoxes of consistency

This month we are delighted to have Branden Fitelson back for his second appearance on the program.  The topic was some recent work he has been doing with Rachel Briggs, Fabrizio Cariani, and Kenny Easwaran on paradoxes of consistency.  Click here to listen to our conversation.

Branden Fitelson

Imagine you’re a scientist, and you publish a huge book presenting the results of your research over the past decade. You are exact in your methods, and to the best of your knowledge, everything you claim in the book is true. Nonetheless, you write the following in the preface: ‘Any mistakes in this book are mine and mine alone.’ Why think that it contains mistakes? Well, it almost certainly does; human beings are fallible, and every scientific book ever written contains some mistake or other. These things are difficult to write! But this raises an interesting paradox. On the one hand, if I were to list all the claims in the book, one by one, for each one, you would say that it was true. On the other, you readily acknowledge that there must be a mistake in there somewhere. It’s impossible for both of these things to be true: either every claim in the book is true, or at least one of the claims in the book is false. So what gives? Are you contradicting yourself?


Posted in Podcast.

Further reading on Frege and logicism

Interested in following up on our discussion with Patricia Blanchette? Take a look at the following material on the debate between Gottlob Frege and David Hilbert:

The Frege-Hilbert Controversy,’ Patricia Blanchette
Frege and Hilbert on Consistency,’ Patricia Blanchette

If you’re curious to take a look at what Frege wrote about the logicist project, his Foundations of Arithmetic is a wonderful read and readily accessible to those without a background in mathematics:

Foundations of Arithmetic, Gottlob Frege

Happy reading!

Matt Teichman

Posted in Further Reading.

Episode 54: Patricia Blanchette discusses Frege’s logicism

This month, we sit down with Patricia Blanchette to discuss the work of Gottlob Frege, one of the most influential philosophers of the 20th century.  Click here to listen to our conversation.

Patricia BlanchetteWe saw in our episode on the philosophy of mathematics how difficult it was to say what numbers are.  What is the number three, and how do I come to know things about it?  (Like that it’s odd, that it’s prime, that it’s the lowest number that’s both odd and prime, that it’s a factor of 135, and so on for all the things a mathematician might teach you about it.)  Frege thought we could make some headway on these questions if we could show that arithmetic was really just complicated logic.  And one way of demonstrating that arithmetic is just complicated logic is by showing that you can translate any statement about arithmetic into a statement about logic without changing its meaning.


Posted in Podcast.

Further reading on Wittgenstein and formal semantics

For those of you interested in following up on our previous episode, Martin Stokhof has a number of papers on the topics we discussed.

On Wittgenstein and formal semantics, you can check out:

The Architecture of Meaning: Wittgenstein’s Tractatus and Formal Semantics,’ Martin Stokhof
Formal Semantics and Wittgenstein: An Alternative,’ Martin Stokhof

On the distinction between abstraction and idealization, see:

Abstractions and Idealisations: The Construction of Modern Linguistics,’ Martin Stokhof & Michiel van Lambalgen

And on the philosophical import of formal languages, take a look at:

Hand or Hammer?  On Formal and Natural Languages in Semantics,’ Martin Stokhof

Posted in Further Reading.

Episode 53: Martin Stokhof discusses formal semantics and Wittgenstein

This month, we talk semantics with Martin Stokhof, Professor of Philosophy of Language at the Institute for Logic, Language, and Computation in Amsterdam.  Click here to listen to our conversation.

Martin StokhofFormal semanticists are in the business of spelling out the rules by which the meaning of a sentence in English (or French, or Spanish, or some other human language) are derived from the words in it and the way they’re put together.  You might think this is pretty straightforward, but see our interview with Hans Kamp for some nice examples of how the enterprise gets tricky rather quickly.  Basically, the issue is that it’s very complicated, in practice, to model the messiness of human language in a super precise way–in a way that, for example, a computer could understand.


Posted in Podcast.

Elucidations is now on Twitter!

Check out our new Twitter feed at @ElucidationsPod. We’d love to hear your comments/thoughts/suggestions.

Posted in Announcements.

Episode 52: Rafeeq Hasan discusses Rousseau on freedom and happiness

This month, we talk political philosophy with Rafeeq Hasan, Harper-Schmidt Fellow and Collegiate Assistant Professor in the Division of the Humanities at the University of Chicago. Click here to listen to our conversation.

RAFEEQIn today’s political discussions, we tend to assume that there are two ways a person can lean. Either you place a premium on your own personal freedom and property, or you place a premium on harmonizing your needs with the needs of others in your community. We think of these two ideals as mutually exclusive.  Of course it’s impossible to lean both ways!


Posted in Podcast.

Conditional Questions: A Problem for a ‘Classical’ Semantic Approach

In Elucidations Episode 51, Groenendijk and Roelofsen sketch out some of the merits of the inquisitive semantics approach to questions in contrast to the ‘classical’ semantic approach. One stark area of contrast is with respect to conditional questions—questions like: “If Matt drinks coffee, does Phil drink coffee?” Groenedijk and Roelofsen observe that the classic semantic approach to questions cannot easily accommodate these conditional questions. In this post, I’d like to flesh out this observation just a bit more.

The ‘classical’ semantic approach that we are working with takes the proposition the primary unit of analysis. That is, we start by laying out the truth conditions of propositions, and then build the rest of our semantic framework around this bedrock.  Remember that ‘proposition’ is jargon for the content of a sentence. For example, we say that the proposition expressed by the sentence “Julie got an A on her philosophy paper” is that Julie got an A on her paper; we say that the sentence is true when Julie in fact gets an A on her paper. Our classical semantics picture fleshes this out a bit more by introducing the idea of ‘possible worlds:’ formally entities meant to represent logically coherent states of affairs (i.e.: they contain no logical contradictions). We then say that a proposition is the set of worlds in which the sentence is true—the set of possible words in which Julie in fact got an A on her paper. For more on possible world semantics, see Matt’s post here: Possible Worlds Semantics.


Posted in Supplements.

Inquisitive Semantics Website

There really is a lot of exciting work being done right now using the framework of inquisitive semantics.  If you’d like to browse through it all, a great place to start is the inquisitive semantics website.

Matt Teichman

Posted in Uncategorized.

Background reading on inquisitive semantics

If you’d like to take a look how the inquisitive semantic framework is set up, this is an up-to-date overview:

Ciardelli, Groenendijk, and Roelofsen, ‘Inquisitive Semantics: a New Notion of Meaning

And if you’d like to examine the framework in a little more detail, this paper will probably answer all of your burning questions:

Ciardelli, Groenendijk, and Roelofsen, ‘Inquisitive Semantics: NASSLI 2012 Lecture Notes

Posted in Further Reading.