Hesperus is Bosphorus

A group blog by philosophers in and from Turkey

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

leave a comment »

Talks will take place in TB130 at Boğaziçi  University. Everybody welcome.
Friday, September 30
 
13.45 – 14.00  Welcome
14.00 – 15.00  Hans van Ditmarsch: The Moore Sentence and the Fitch Paradox in Dynamic Epistemic Logic
15.00 – 16.00  Philippe Balbiani: An Introduction to Subset Space Logics
16.00 – 16.30  Coffee Break
16.30 – 17.30  Aybüke Özgün: Justified Belief, Knowledge and the Topology of Evidence
17.30 – 18.30  Zafer Özdemir: Tableaux-based decision procedures for region based theories of space
19.30 –          Dinner
Saturday, October 1
10.00 – 11.00  Sebastian Speitel: Carnap-Categoricity and the Question of Logicality
11.00 – 12.00  Ahmet Çevik: Defining computability through the Church-Turing Thesis
12.00 – 14.00  Lunch and Coffee Break
14.00 – 15.00  Ali Karatay: Is Thales the first philosopher of mathematics?
15.00 – 16.00  Philippe Balbiani: Formal concept analysis: from formal contexts to modal logics and return
16.00 – 16.30  Coffee Break
16.30 – 17.30  Hans van Ditmarsch: Epistemic Gossip Protocols
19.00 –          Dinner
Further details can be found here:
https://sites.google.com/site/miniworkshoponlogic2016/home
Organised by

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

Written by Lucas Thorpe

September 26, 2016 at 11:43 pm

Posted in Uncategorized

Kant Reading Group at Boğaziçi (Fall 2016)

leave a comment »

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

 

 

Written by Lucas Thorpe

September 24, 2016 at 1:21 pm

Posted in Uncategorized

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

leave a comment »

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).

 

Written by Lucas Thorpe

September 23, 2016 at 1:24 pm

Posted in Uncategorized

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

leave a comment »

Two talks by Özge Ekin Gün (Freie Universität Berlin) at Boğaziçi this coming week:

 

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

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

math talk (1).jpg

Everyone welcome.

Written by Lucas Thorpe

September 18, 2016 at 2:48 pm

Posted in Uncategorized

What is Wrong with Cantor’s Diagonal Argument?

with 13 comments

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    0.101110110001…

2    0.110101110000…

3    0.110100011101…

4    0.011011100011…

5    0.100001000110…

6    0.001111111110…

7    0.001011100010…

8    0.110001101001…

9    0.111011001010…

10  0.011110111001…

11   0.010101010100…

                  .
                  .
                  .

   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_

Written by Erdinç Sayan

July 31, 2016 at 1:55 pm

Talk at Bogazici, Jonathan Cohen (UCSD), “On the Presuppositional Behavior of Coherence-Driven Pragmatic Enrichments”

leave a comment »

Please join us for this talk.

Monday, June 27, 5-7pm in TB 130:
Jonathan Cohen (UCSD), “On the Presuppositional Behavior of Coherence-Driven Pragmatic Enrichments” (joint work with Andrew Kehler)
abstract:
Consider (1) and (2):
(1) Every time the company fires an employee who comes in
late, a union complaint is lodged.
(2) If the company fires an employee who comes in late, a
union complaint will be lodged.
Now suppose there is an employee, Snodgrass, who is fired because he
was discovered to have been embezzling, and that the firing occurred
on a day on which he had happened to come in late. And suppose the
union does nothing about it. In this situation, it seems that (1) and
(2) can still be true.If so, there must be an enrichment at play that affects truth
conditions: even though Snodgrass came in late and was fired, the fact
that Snodgrass wasn’t fired *because* he was late causes the
event to sit outside of the domain restriction of (1), and, likewise,
not to satisfy the antecedent of the conditional in (2). Importantly,
this enrichment has no linguistic mandate, and therefore is clearly
pragmatic. So why does it intrude upon the truth conditions of (1) and
(2)?

We argue that this behavior arises as a result of the way in which the
enrichments interact with pragmatic presupposition. In particular, in
producing examples (1)-(2) with the intention to communicate the
enrichment, a speaker presupposes that a causal relation necessary to
make the inference is part of the common ground, and intends that
presupposition to restrict the interpretation of the
quantifier/antecedent in (1)/(2).

The analysis connects the associative inferences that underlie the
establishment of coherence relations between sentences in a discourse,
a class of intrasentential enrichments that result from the same
principles, and the manner in which presuppositions constrain the
interpretation of quantified expressions and conditionals.

If you have any questions, please email mark[DOT]steen[at-symbol]boun.edu.tr

Written by markedwardsteen

June 20, 2016 at 9:50 am

Posted in Uncategorized

MA Philosophy at Bilkent – Round 2

leave a comment »

Applications for Masters in Philosophy (Round 2)

BilkentPHILMAPoster

We are now accepting the second round of applications for the M.A. in Philosophy (for those starting the degree in Fall 2016).

Up to five successful applicants will have the opportunity to spend a semester at Australian National University.  In addition successful applicants will receive a comprehensive scholarship (tuition waiver, accommodation and monthly stipend including private health insurance).

This is a two year masters that includes coursework and a thesis. The language of instruction for all courses is English.

Admission requirements and online application can be found here.

Philosophy and non-philosophy majors are encouraged to apply. We also warmly welcome applications from international students.

 

Application deadline (Round 2): 18 July 2016
Written exam (Round 2): 25 July 2016**
Interview (Round 2): 27 July 2016**

Contact:  phil@bilkent.edu.tr

http://www.phil.bilkent.edu.tr

*Those planning to take the COPE exam on June 28-30 should contact us at the above email address by June 22 to reserve a place.

** International students may take the written exam remotely and complete the interview via skype.

 

 

Written by Sandrine Berges

June 20, 2016 at 9:07 am

Posted in Uncategorized