## Talk at Boğaziçi by Sanna Hirvonen (Oxford) on “The Challenges and Advantages of Contextualism for Predicates of Taste” (Friday, 14/10/2-16)

Sanna Hirvonen (Oxford) will give a talk at Boğaziçi University this Friday (14/10/2016) from 5-7pm in Tb130 on “”The Challenges and Advantages of Contextualism for Predicates of Taste”. Everybody welcome.

**Abstract**: An account of the semantics / pragmatics of predicates of taste must be able to explain two apparently conflicting features: How the truth of judgments of personal taste depend on the taste of the speaker, and how there can still be disagreements of taste. Michael Glanzberg’s [2007] “flexible” contextualist account holds that the context selects an experiencer class. If the experiencer class includes more people than the speaker, then a disagreement of taste may concern e.g. the average taste of the experiencer class. In this paper I show that the contextual mechanisms posited by Glanzberg lead to two kinds of undesirable predictions regarding entirely ordinary judgments of taste: (i) Some judgments of taste get highly unintuitive truth-values that the speaker / hearers are not able to track, and (ii) Some judgments of taste that fail to express propositions, but the speaker / hearers cannot tell when this happens.

## Talk at Boğaziçi by Frank Zenker (Lund): “Can Bayesian models have ‘normative pull’ on human reasoners?” (Thursday, 13/10/2016)

Frank Zenker (Lund) will give a talk at Boğaziçi University this Thursday (13/10/2016) from 5-7pm in Tb130 on “Can Bayesian models have ‘normative pull’ on human reasoners?”. Everyone welcome.

**Abstract**: Rejecting the claim that human reasoning can approximate generally NP-hard Bayesian models—in the sense that the mind’s actual “computations” come close to, or be like, the inferences that Bayesian models dictate—this paper addresses whether a Bayesian model can have normative pull on human reasoners. For such normative pull to arise, we argue, a well-defined and empirically supported approximation relation is required—but broadly absent—between (i) human reasoning on the ground and (ii) the behavior of a non-NP-hard model. We discuss a responsible stance on this issue.

A long abstract can be found here.

## Mini-Workshop at Boğaziçi on Logic and its Applications (30/09 – 01/10/2016)

**Friday, September 30**

**Saturday, October 1**- Berna Kılınç (Boğaziçi University, Turkey)

- Aybüke Özgün (LORIA, CNRS-University of Lorraine, France and ILLC, University of Amsterdam, the Netherlands

## Kant Reading Group at Boğaziçi (Fall 2016)

Ken Westphal and I will be continuing our Kant reading group at Boğaziçi this semester on Wednesdays from 5-7pm in TB365, starting on Wednesday, October 5th. Everyone welcome.

We will hold our first meeting of the semester, however, this coming TUESDAY (September 27th) from 5-7pm in TB130. In this meeting we will decide what to read in the coming semester (so, please come with suggestions). And, we will discuss the following article:

George, Rolf (1981). Kants Sensationism. *Synthese* 47 (2):229 – 255.

If you would like to be added to our mailing list, please email Melisa: melisakurtcan@gmail.com

This reading group is part of the joint Boğaziçi -Southampton Newton-Katip Çelebi project AF140071 “Agency and Autonomy: Kant and the Normative Foundations of Republican Self-Government” run by Lucas Thorpe (Boğaziçi) and Sasha Mudd (Southampton) and by Lucas Thorpe’s Bogazici University BAP project 9320

## Philosophy/Cog-Sci Reading Group at Boğaziçi (Fall 2016)

Our philosophy/cog-sci reading group will continue this semester on Mondays from 5-7pm in TB365. The topic for the start of the semester will be affordances. Everyone is welcome.

We will begin this coming Monday (26/09/2016) by discussing the following article:

Lorenzo Jamone, Emre Ugur, Angelo Cangelosi, Luciano Fadiga, Alexandre Bernardino, Justus Piater and Jose Santos-Victor, (2016) “Affordances in psychology, neuroscience and robotics: a survey” IEEE TRANSACTIONS ON COGNITIVE AND DEVELOPMENTAL SYSTEMS, VOL. XX, NO. XX, XXXX.

If you would like to be added to our mailing list, please send an email to Elif at: conceptsandbeliefs@gmail.com

This reading group is organised as part of Lucas Thorpe‘s TÜBİTAK project “Concepts and Beliefs: From Perception to Action” ( 114K348).

## Two Talks at Boğaziçi by Özge Ekin Gün on the Philosophy of Maths and Kant. (22&23/09/2016)

*Freie Universität Berlin*) at Boğaziçi this coming week:

**Thursday, September 22nd, 2016 (3pm -5pm, TB130): **

**Friday, September 23rd, 2016 (4pm-6pm, Venue TB130):**

Everyone welcome.

## What is Wrong with Cantor’s Diagonal Argument?

Cantor gave two proofs that the cardinality of the set of real numbers is greater than that of the set of natural numbers. In the better known of these proofs, his diagonal argument, Cantor randomly tabulates the real numbers in the interval [0, 1) in a square array. He asks us to assume for *reductio* purposes that this table is “complete” in the sense that it contains the totality of real numbers in that interval. He then constructs a new number from the diagonal of the table. He asserts that this constructed number is a new real number in [0, 1) which cannot be found in the putatively complete list. His famous conclusion is that no table that lists real numbers in that fashion will have the items in it being enumerable by natural numbers. Since no such list will manage to include all of the real numbers in [0, 1), it follows, according to Cantor, that there have to be more real numbers than natural numbers. Hence the size, or cardinality, of the set of real numbers is greater than that of natural numbers.

I will use a binary version of Cantor’s table for ease of exposition:

1 0.**1**01110110001…

2 0.1**1**0101110000…

3 0.11**0**100011101…

4 0.011**0**11100011…

5 0.1000**0**1000110…

6 0.00111**1**111110…

7 0.001011**1**00010…

8 0.1100011**0**1001…

9 0.11101100**1**010…

10 0.011110111**0**01…

11 0.0101010101**0**0…

** .**

** .**

** .**

** ***d* = 0.11000110100…

* i* = 0.00111001011…

Thus we begin with the Cantorian assumption that this infinitely long and random list includes all the real numbers in the interval [0, 1). The numbers on the diagonal of the list (boldfaced in the table) give us the infinitely long number *d*. From *d*, Cantor would obtain the number *i*, by substituting every 0 after the decimal point in *d* by 1, and every 1 in *d* by 0. Now, the number *i* couldn’t be found in the list, according to Cantor, because *i* is guaranteed to differ from each binary number in the list since the number’s digit that falls on the diagonal is changed. Therefore, no list of real numbers (in this example the reals in [0, 1)) can be enumerated by natural numbers, which entails that there are more real numbers than natural numbers.

The problem I see with Cantor’s argument is the following. I will call two binary numbers in [0, 1) “inverses” of each other if one number has 1 in a certain location after the decimal point, the other number has 0 in the corresponding location; and if it has 0 in that location, the other number has 1. Thus the numbers on lines 3 and 7, for instance, are inverses of each other. So are the numbers on lines 5 and 10. Crucially, *d* and *i* are also inverses of each other. If we are to assume this list is complete, every number in the list must have its inverse also included in the list. Cantor says *i* is not included in the list. But how come? The number *i*’s inverse, namely *d*, *is* in the list—it is on line 8. Since its inverse is in there *i* must also be in there, like every other pair of inverses.[*] Suppose *d*’s inverse *was* in the list, say it was on line 17. Cantor would say his diagonal trick would change the 17th digit of the number on line 17, and therefore *i* could not be in the list.

So we have a contradiction: (a) The number *i* has to be in the list, say in line 17, because its inverse *d* is. (This is my claim, not Cantor’s.) (b) Yet *i* cannot be in the list, because it differs from the number on the 17th line in its 17th digit. (This is Cantor’s claim.) If one thinks (a) and (b) both sound plausible, as they might, one would find himself facing this paradox:

(i) We can make a random list of real numbers in [0, 1).

(ii) This list can be assumed to be exhaustive.

(iii) The diagonal *d* of the list and *i* can be fully formed.

(iv) The number *i* has to be in the list, if the list is to be exhaustive, since its inverse is.

(v) The number *i* cannot be in the list, since it is different from every number in the list in some *n*-th digit.

Since (iv) is impeccable, Cantor’s diagonal procedure which derives (v) can be faulted with leading to paradox, and consequently his denial of (ii) can be claimed unjustified. Hence his entire diagonalization procedure must be flawed. Therefore his claim that there are more real numbers than natural numbers is unwarranted.

As for the flaw in Cantor’s diagonalization procedure, I think it arises from the following phenomenon. The diagonal and its inverse clash at some digit. Suppose the 17th digit of the diagonal is 1; then the 17th digit of its inverse would have to be 0. But, since the two digits overlap, the diagonal’s 17th digit being 1 rules out the would-be inverse’s 17th digit being 0. Thus the diagonal disallows its inverse (with the correct 17th digit 0) from being a member of the table.

Hence, we need not get impressed when Cantor comes up with a number *i* which is not in the table. We know that *i* *would have been* in the table if it had not been censored by the very diagonal of the table.

It should now be obvious that the problem of missing *i* arises from the fact that Cantor lists real numbers in the form of a *table*. That turns out to be a deceptively misleading way of displaying real numbers.[**]

_______________________

[*] If *i* were not to be in the list although its inverse is, we could not assume the list was complete to begin with.

[**] My more detailed criticisms of Cantor’s arguments and my way of showing that reals cannot be more numerous than naturals can be found at: https://www.academia.edu/26887641/CONTRA_CANTOR_HOW_TO_COUNT_THE_UNCOUNTABLY_INFINITE_