# Who Shaves the Barber?

## David Ripley: Curry’s Paradox and Substructural Logic | WSB #51

September 15, 2018

Consider the sentence C: "If this sentence is true, then David Ripley is a purple giraffe". Suppose the sentence is true. Then the antecedent of the sentence ("this sentence is true") is true. According to the inference rule modus ponens, if an if-then sentence (such as C) is true and its antecedent is true, then its consequent ("David Ripley is a purple giraffe") must be true. It follows that if C is true, then David Ripley is a purple giraffe. But this conclusion is C: in other words, by simply supposing how things might turn out if C were true, we have proved that C, in fact, is true. So C is true, and since C's antecedent is the claim that C is true, its antecedent is true as well. Now we can use modus ponens again to show that C's consequent must be true. In other words, David Ripley really is a purple giraffe. QED.

This argument is Curry's paradox. Obviously, the choice of "David Ripley is a purple giraffe" is arbitrary; a sentence of the form of "If this sentence is true, then X" can be used to prove any claim X. Now, in actual fact, David Ripley is not a purple giraffe, but a philosopher of language and logic. According to Ripley, solutions to paradoxes like Curry's (as well as the Liar and the Sorites) fall into two broad categories: those that solve the paradoxes by messing with the meanings of important concepts (such as the meaning of "if-then", truth, "not", etc.) and those that solve them by changing the structural rules of inference by appeal to substructural logics. The latter approach, says Ripley, is preferable because it allows us to keep the intuitive meanings of these important concepts. There are various structural rules that can be modified to avoid the paradoxes, but the one that Ripley prefers is the denial of transitivity. This would mean that even if we prove that a implies b and that b implies c, we have no guarantee that a implies c. Ripley tells a story about assertion and denial conditions to argue that, precisely because of the paradoxes, the denial of transitivity conforms to natural language inferential norms. We conclude with a discussion of "revenge" Curry paradoxes for Ripley's approach, and of frontiers for substructural logic.

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.

Sources:

David Ripley (website)
Curry's paradox (Stanford Encyclopedia of Philosophy)
"Comparing Substructural Theories of Truth" (David Ripley)
"Revising Up: Strengthening Classical Logic in the Face of Paradox" (David Ripley)

Topics discussed:

0:19 - Introduction to David Ripley
3:17 - Logic, reasoning, and ways to approach paradox
25:19 - The Liar as analogous to Curry
34:34 - Taxonomy of solutions: vocabulary-based vs. structural-based
45:35 - Logical connectives and natural language analogues
49:55 - Optimism vs. pessimism in responses
55:23 - Substructural solutions: non-contractive
59:42 - Substructural solutions: non-transitive
1:06:52 - Assertion and denial conditions
1:20:44 - Gaps and gluts and revenge
1:33:01 - History of and horizons for substructural logic

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## Jody Azzouni: Ontology without Borders | WSB #50

July 31, 2018

An old problem: I say, "Santa Claus is fat". I am saying something true about Santa Claus. But (content warning) Santa Claus doesn't exist. So what is it that I am correctly saying is fat? And what - if not its ostensive subject - makes the sentence true?

This problem is at the center of ontology. The most influential approach in the 20th century was offered by W. V. O. Quine, who argued that we're committed to the existence of any object that we must quantify over in order to state the truths of physics in first-order logic. At first, this seems rather arbitrary. Why first-order logic? What makes quantifiers so special? Why physics? And what does what we're "committed to" tell us about what actually exists? For roughly the first half of this interview, philosopher Jody Azzouni unpacks the thinking behind Quine's famous criterion. In the second half, he expounds his own view: he rejects Quine's criterion, and so sees no problem with referring to that which doesn't exist. This leaves Azzouni open to embrace a radical nominalism, in which almost none of the objects we typically think of as existing really do. This is because, as Azzouni explains, "ontological borders" are projected. There is nothing "out there" that separates one object from another. The fact that our language is built around distinct objects tells us plenty about our psychology, but nothing about the world itself, which comes with "features" but not individual objects.

Want to hear a different take on the same questions? Check out my interview with Amie Thomasson.

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.

Sources:

Jody Azzouni (Tufts faculty page)
"On What There Is" (W. V. O. Quine)
Word and Object (W. V. O. Quine)
Ontology without Borders (Jody Azzouni)

Topics discussed:

0:19 - Trends in contemporary philosophy
5:37 - Contested objects and proposed principles
12:11 - Quine's criterion of ontological commitment
18:43 - Why quantifiers?
20:53 - Quine's Word and Object: "exercise in sophisticated paraphrase"
27:39 - Evaluating paraphrases
37:16 - Against Quine's criterion
42:07 - Other metaontological criteria
48:18 - Nominalism
51:02 - Reference failure and the aboutness illusion
57:49 - Object projectivism
1:02:42 - Does the world come with implicit boundaries?
1:10:02 - Truth about non-existent objects
1:11:51 - Stuff, features, and individuation conditions
1:20:45 -  Amie Thomasson's easy ontology
1:26:54 - The role of natural language

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## Michael Hicks: Fiction-Directed Thought | WSB #49

July 17, 2018

I have a (true) thought that Sherlock Holmes lives on Baker Street. But what is this thought about? Is it about Sherlock Holmes? If so, is it about something that doesn't exist? Can we really have thoughts about non-existent objects? What makes those thoughts true or false, if there is no object for the thought's content to correspond to?

Philosopher Michael Hicks distinguishes fiction-directed thought from world-directed thought. A fiction-directed thought is knowingly about fiction; it is a kind of pretense. It is crucial that thoughts about fictional entities be fiction-directed. If if I think my "thought" about Sherlock Holmes is about a real person - in other words, if it is world-directed - then I don't have a thought at all, because the ostensive object of my thought does not exist. According to Hicks, world-directed thought is "environment dependent". It takes the intentional state and the object of the intentional state to make a thought. If the latter is missing, then there is no thought. Thoughts about fictional entities, as well as about hallucinations and other non-existent objects, must be fiction-directed in order to qualify as thoughts. Put another way, thought about fiction only successfully happens when we play a game of pretense set up by the author.

Be sure to listen to part 1 of this interview first.

If you're interested in the metaphysics of thought, I discuss higher-order thoughts in this interview with David Rosenthal.

Next week: Jody Azzouni: Ontology without Borders

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.

Sources:

Michael Hicks (homepage)
"Pretense and fiction-directed thought" (Michael Hicks)
"A note on pretense and co-reference" (Michael Hicks)

Topics discussed:

0:51 - Environment dependence
4:11 - Shared hallucinations and optical illusions
15:25 - Russell and risk of error
23:24 - Thinking about Sherlock Holmes
46:24 - Difference in the content of fiction-directed thought?

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## Michael Hicks: What Is Thought? | WSB #48

July 10, 2018

What is a thought? There are two ways to approach the problem, says philosopher Michael Hicks. One is as a question about introspective experience. The other - favored by Hicks - is as asking about the nature of interpersonal understanding. We do understand each other; and this is what constitutes the existence of thoughts. With this approach established, Hicks explains to what extent it does or doesn't imply an "external" view of mind. We also compare this conception of thought to Gottlob Frege's, and discuss whether it involves a commitment to a "third realm" of abstract objects.

Next week: Michael Hicks: Fiction-Directed Thought

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.

Sources:

Michael Hicks (homepage)
"The Thought" (Gottlob Frege)
"The Extended Mind" (Andy Clark, David Chalmers)

Topics discussed:

0:20 - Introduction to Michael Hicks
2:42 - What are thoughts?
14:15 - Internal or extended thinking
23:46 - Meta-ontology
35:03 - Frege and abstract objects

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## Left Market Anarchism | WSB #47

July 3, 2018

Political philosophy begins with the question: who should have political authority and why? Anarchism answers: no one. Popular mythology tells us this is synonymous with chaos and disorder, but there are many reasons to doubt this must be so. In this episode, I argue that anarchism - properly understood - is in fact the correct answer to the problem of political authority; it is the only answer that avoids unjust hierarchies, provides for individual and social freedom, and optimizes for general welfare. This is because, in a word, society is best seen (and run) as a web, not as a pyramid.

Much of my focus is on specifying what I mean by anarchism, and which version of anarchism I'm arguing for. Specifically, I argue that the notion of a free market - again, properly understood - is at the heart of anarchism. At the same time, I argue against "capitalism" as being a confused and rather unhelpful notion, quite removed from the notion of a free market. I also argue against popular libertarian approaches to free markets and anarchism, such as the so-called "non-aggression principle" and property rights. Instead, I zero in on a notion of free market defined as a cultural norm in which monopolies are viewed as unacceptable. This definition, I argue, properly communicates what a free market really is and it provides the necessary conditions for a free and prosperous society. It is, at the same time, a maximally permissive definition: it requires no particular views on interpersonal ethics or lifestyle, and is as compatible with (for example) communism as it is with more familiar notions of "free markets".

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.

Sources:

"'Capitalism' and 'socialism' are anti-concepts" (Roderick Long, video)
"Market Anarchism as Constitutionalism" (Roderick Long)
Pressing the Button (website)

Topics discussed:

0:20 - Intro and disclaimers
5:09 - The question of political authority
7:49 - "The will of the people" justification
12:19 - Resource allocation and "a web, not a pyramid"
14:49 - Unjust hierarchies: the state, capitalism, and others
21:48 - What is capitalism?
26:33 - What is a free market?
31:05 - Against free markets as non-aggression
36:23 - Against free markets as property rights
40:04 - Free markets as anti-monopoly cultural norm
42:35 - Competition as the source of regulation
48:18 - Property rights compatible tyranny
52:44 - Cultural norms
56:12 - Scale, weakness, communism
1:01:50 - More on monopoly, hierarchy, and coordination
1:07:32 - Objections: social order, market regulation, collusion
1:12:44 - Objections: public goods, externalities, defense
1:20:46 - Objections: rent & interest, natural monopolies, epistemic conservatism
1:25:01 - Objections: utopian, people are evil
1:26:26 - Competition as cooperation

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## Kit Fine: Metaphysical Ground | WSB #46

June 26, 2018

Some things are true in virtue of other things. For example, the fact that it is either raining or snowing today is true in virtue of the fact that it is raining today (if, indeed, it is). Or consider another example, put in different terms: the fact that my cat Irene exists is sufficient to account for the fact that at least one cat exists. We might then ask: what is this being in virtue of, or accounting for?

Philosophers call this metaphysical ground. Thus, the existence of my cat Irene grounds the fact that at least one cat exists. But how does this grounding relation work? How is it related to logical entailment? To cause? To essence? Is it possible for there to be partial grounding? Can a fact ground itself? If not, does a vicious regress emerge? What is the role of ground in metaphysics? In this interview, metaphysician Kit Fine covers these questions and more before zeroing in on a logical puzzle of ground, related to the paradoxes of self-reference such as the Liar.

Next week: Left Market Anarchism

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.

Sources:

Kit Fine (homepage)
"Vagueness, truth, and logic" (Kit Fine)
"A Guide to Ground" (Kit Fine)
"Some Puzzles of Ground" (Kit Fine)

Topics discussed:

0:20 - Intro to Kit Fine
2:50 - Vagueness
6:44 - What is ground?
10:40 - Realism
16:15 - Two notions of necessary ground
19:10 - Relevance and ground
24:35 - Ground and philosophy, cause and science
28:00 - Ground and ontological reduction
35:18 - Regress, circularity, and weak ground
44:55 - Types of ground and the "source" of logic
52:50 - Ground of ground
1:03:02 - Essence and ground
1:09:10 - A puzzle of ground

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## Nicolas Langlitz: Psychedelics and Philosophy | WSB #45

June 19, 2018

Psychedelic substances, such as psilocybin mushrooms, LSD, and ayahuasca, do much more than generate sensory hallucinations. Users often come away with a sense of having gained deep insight into the nature of reality - even if what that insight is, and what is so special about it, can be hard to communicate. Anthropologist Nicolas Langlitz associates it with the "perennial philosophy" - an old idea, popularized by Aldous Huxley, that all world religions communicate the same basic truth. Years after writing the book The Perennial Philosophy, Huxley tried mescaline and LSD and became convinced that psychedelics provide a shortcut to the kinds of mystical experiences that would put us in touch with that basic reality - what he called the "world mind". Langlitz is skeptical that psychedelics really do communicate some kind of metaphysical truth. In this interview, we discuss what psychedelics do reveal, if anything, and what the relationship is between experience and knowledge.

Next week: Kit Fine: Metaphysical Grounding

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.

Sources:

Topics discussed:

0:20 - Intro to Nicolas Langlitz
1:05 - Anthropology and philosophy
10:06 - Nick's research on psychedelics
22:23 - Perennial philosophy (Huxley)
29:20 - Indescribable?
33:09 - Materialism and mysticism
41:14 - Diversity v. unity of psychedelic experience
47:40 - Validity and expression of the psychedelic experience
59:50 - Place of psychedelics in society

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## Jc Beall: Logic of Christ | WSB #44

June 12, 2018

Christ is a walking contradiction. He is both fully human and fully divine. Indeed, he is both mutable and immutable. According to classical logic, the existence of a true contradiction would imply that everything is the case, no matter how absurd. And so, theologians and Christian metaphysicians have worked for centuries to conceptually make sense of Christ's dual nature in a way that avoids contradiction.

Philosopher and logician Jc Beall argues that these efforts have been motivated by a naive understanding of logic. There are "subclassical" logics - that is, logics weaker than classical logic - in which contradictions do not entail every arbitrary conclusion. And these aren't ad-hoc constructions. Beall argues that one subclassical logic - called First Degree Entailment (FDE) - is, in fact, the correct account of logical consequence, for reasons independent of the Christian problem. Beall covers the basics of how FDE works and why it is the universal or "basement-level" consequence relation. This allows us to have our cake and eat it too: we may take Christ to be, quite literally, both mutable and not mutable, at the same time and in the same respect. This isn't just appealing for its simplicity. Beall suspects that it is essential to Christ's role that he be literally contradictory.

If you're interested in Jc Beall's work and non-classical logic, check out my interview with Greg Restall (part 1 and part 2) on the book Logical Pluralism, co-authored by Beall and Restall.

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.

Sources:

Jc Beall (homepage)
"Christ - A Contradiction" (Jc Beall; forthcoming)
"Theological Axioms and the Bounds of Logic: Christ as the Fundamental Problem" (Jc Beall)
Spandrels of Truth (Jc Beall)

Topics discussed:

0:20 - Intro to Jc Beall
1:20 - Spandrels of Truth
5:35 - Fundamental problem of Christology
16:23 - Explosion and disjunctive syllogism
25:06 - Other solutions to the fundamental problem
28:57 - Trinity and identity
31:37 - Logic, logical pluralism, and entailment
42:55 - Closure
46:08 - Consequence as "basement level" closure relation
53:19 - First Degree Entailment
1:03:50 - Are truth and falsity mutually exclusive?
1:10:01 - How weak can you go?
1:22:00 - Relevance to Christian practice

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## Jason Lee Byas: Against Criminal Justice | WSB #43

June 5, 2018

What gives some people the right to put others in prison? Is prison - and the criminal justice system generally - an ethically permissible method for dealing with criminality?

Individualist anarchist and prison abolitionist Jason Lee Byas goes over the common justifications for the prison system and explains why none of them succeed. Specifically, he covers the doctrines of retributivism (specifically desert retributivism and expressive retributivism), deterrence, rehabilitation, and rights forfeiture, arguing against each. In place of prison, Byas proposes a tort system of restitution. Monetary restitution may not be sufficient to right the wrong of a crime, says Byas; but it is all that the law should mandate, leaving other desired correction or compensation up to community-based initiatives (Byas cites restorative justice as an example of the sort of institutions that can take the place of those corrective aspects of criminal justice that retribution does not address). Byas also explains how a system of monetary restitution can get around problems of class-based inequality (for example, if someone is so rich that they don't mind having to pay to commit a crime, or if someone is so far in debt that another dent wouldn't matter). Finally, he explains how violent offenders who pose an "ongoing threat" might be handled in his preferred system.

Next week: Jc Beall: Logic of Christ

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.

Sources:

Jason Lee Byas (articles at the Center for a Stateless Society)
"Against the Criminal Justice System" (Jason Lee Byas; Part I, Part II, Part III, Part IV, Part V)
"Prisons without Punishment?" (Jason Lee Byas)
"The Irrelevance of Responsibility" (Roderick Long)
The Apology Ritual: A Philosophical Theory of Punishment (Christopher Bennett)
Locked In: The True Causes of Mass Incarceration and How to Achieve Real Reform (John Pfaff)

Topics discussed:

0:20 - Intro to Jason Lee Byas
2:11 - What is prison abolitionism?
11:50 - Retributivism
15:00 - Desert retributivism
17:58 - Expressive retributivism
28:36 - Rights forfeiture and self-defense
40:44 - Differences in moral intuition
49:47 - Restitution and class difference
1:08:17 - Intention
1:13:47 - Restorative justice and social pressure
1:27:51 - Due process in communities
1:32:36 - Involuntary containment of ongoing threats
1:42:38 - Prospects

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May 29, 2018

For much of the 20th century, the Liar paradox has stood as an elusive and stubborn puzzle. The main solutions to it have significant drawbacks, such as blocking meaningful cases of self-reference or abandoning bivalence (the principle that all propositions are either true or false and not both). In recent decades, Stephen Read has rediscovered and defended a solution by the medieval thinker Thomas Bradwardine. If Bradwardine's argument is correct, the liar sentence is simply false. When properly examined, its falsity does not imply its truth. Bradwardine shows this with a clever argument that does not require us to abandon classical logic or block self-reference. It does rely on a controversial principle, "closure": any statement implicitly says (or means) everything that follows from what it says. Arguably, whether the Bradwardine solution succeeds or fails to conclusively solve the Liar depends on whether one accepts closure. In this interview, Stephen Read runs through Bradwardine's argument in some detail, then defends it against a few objections.

Bradwardine's argument is rather subtle and abstract and can be hard to follow verbally. Here's a short written version of Bradwardine's argument, with minimum symbolism, that shows each step and notes where logical principles are invoked.

Be sure to listen to the first half of this interview, where Stephen explains the Liar and its significance and solutions in the 20th century.

Next week: Jason Lee Byas: Against Criminal Justice

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.

Sources:

Thomas Bradwardine's Insolubilia (Stanford Encyclopedia of Philosophy)
"Lessons on truth from medieval solutions to the Liar paradox" (C. Dutilh Novaes)

Topics discussed:

2:20 - Intro on medieval logic
5:17 - Restriction and cassation
9:55 - Possibility of self-reference
14:38 - Intro to Bradwardine's solution
22:19 - Running through Bradwardine's argument
28:39 - Bradwardine's theory of truth v. Tarski's
32:29 - Objection to Bradwardine's closure principle
55:16 - Do sentences say they are true?
1:00:59 - Priest's Principle of Uniform Solution

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