Friday, June 19, 2009

Non-Classical Mathematics 2009 (introductory remarks)

Finally, I can write something about what's going on now. I'm in Hejnice, lodged in a cell (it's quite comfortable though) in a monastery pretty much in the middle of Czech mountains. I was here two years ago, but this time I have wireless internet access. It's pretty cool.

So, what's going on? Well, it seems, Non-classical Mathematics (surprisingly??) attracted more mathematicians than philosophers and logicians. In fact, most of the people present here are rather mathematically-minded. This, of course, is not a complaint. For a philosopher (or a philosophically-minded logician, for that matter), dealing with mathematicians is a bit of a challenge though. They usually spend less time looking for philosophical motivations for their work and more time doing real mathematics. This means, if you're a philosopher, listening to mathematical talks will require more effort. You have to overcome the first impression that people sometimes get into extremally complicated technical issues without explaining why we should be interested in them. I mean, I'm pretty sure these people know what they're doing and why they're doing that, but the standards they employ for motivation of technical work are a bit different. Also, this stuff is often more complicated than most of more philosophically motivated work, so it's a bit more difficult to follow (which means, it's easy for me to feel slightly retarded when faced with all those technical results).

There are, however, also certain clearly positive aspects to this experience. For instance, a few brief conversations I had here confirm my view that doing mathematics doesn't require one to have a clear philosophical position about what mathematics is about (I mean, this is not deeply surprising, I've talked with mathematicians before). For instance, a guy who works on weak set theories, when asked about his view on what set theory is about, said cheerfully something like "I don't care, you know, it's a theory, I play around with it, prove stuff and that's it - what else would I need to know?". It's refreshing. This also means that philosophers of mathematics can still claim there's something for them to do.

This reminds me of P. F. Strawson's remark about analysis of concepts used by specific theorists:
The scientific specialist [...] is perfectly capable of explaining what he is doing with the special terms of his specialism. He has an explicit mastery, within the terms of his theory, of the special concepts of his theory [...] the specialist may know perfectly well how to handle these concepts inside his discipline, i.e. be able to use them perfectly correctly there, without being able to say, in general, how he does it. Just as we, in our ordinary relations with things, have mastered a pre-theoretical practice without being necessarily able to state the principles of the practice, so he, the scientific specialist, may have mastered what we may call a theoretical practice without being able to state the principles [...] a mathematician may discover and prove new mathematical truths without being able to say what are the distinctive characteristics of mathematical truth or of mathematical proof [...] even operating within his own specialism, a specialist was bound to employ concepts [...] from the fact that he there employs them quite correctly, it by no means follows that he can give a clear and general account or explanation of what is characteristic of their employment in his specialism. [Analysis and Metaphysics]
There is a downside to it. If you discuss philosophical aspects of mathematical concepts, mathematicians quite likely won't give a rat's ass about it. I mean, it's to be expected, just like you don't expect a competent kettle user to be interested in someone's specification of sufficient and necessary conditions for something to be a kettle (or an ink-spiller to be interested in philosophically interesting ways of spilling ink). Just like a mathematician might have a hard time convincing philosophers that the complex questions he's trying to answer actually matter, a philosopher might have a hard time convincing mathematicians that philosophical considerations about mathematics have some relevance.

Of course, there is no clear-cut distinction between the mathematicians and the philosophers. I presented a very simplified sketch of some aspects of the extremes of a very interesting and often fruitful tension.

Anyway, all this seems to have some bearing on the Burgess-Rosen critique of nominalist reconstructions of mathematical theories. The gist of the critique is this: when you give a reconstruction, you either give something different from what mathematicians actually have in mind, and thus, you put forward a revolutionary view of mathematics (which is highly impractical, because you're suggesting new textbooks have to be written, mathematics in schools should be changed, etc.), or you are claiming that your theory is an actual analysis of what they're doing, and then you have to show that this really is what they have in mind. Now, it seems to me that mathematicians usually don't have anything philosophical in mind at all when they're doing mathematics, just like we don't have a correct analysis of our every-day concepts when we use them. Thus, giving a nominalistic reconstruction is neither a suggestion that mathematics should be revised (in fact, I believe, a correct nominalistic story about mathematics should rather suggest that everything's okay with mathematics and it shouldn't be changed), nor a theory of what mathematicians have in mind. It's rather a proposal as to how a philosopher can make sense of mathematical activity and mathematical truth without being commited to abstract objects. And what would making sense consist in? Well, telling a nominalistically acceptable story which would be consistent with one's philosophical views and which would allow one to understand on the philosophical level how mathematics can be true and yet applicable. Sort of.

Having said all this, I will switch back to the reporting mode now and post some more detailed remarks on the content of the talks some time soon.

FMER, Leuven, June 10-12, cont'd

Day 3, after lunch

Lara Buchak (joint with Branded Fitelson who couldn't make it to the conference) -Is it rational to have faith? - Lara was trying to cash out what having faith commits one to, and on the analysis she presented faith in X requires that one not actively look for further evidence for the truth or falsity of X. This move seems to collide with the expected utility theory of rationality. Then, she argued that the claim that expected utility maximisers should always perform cost-negligible experiments neglects the phenomenon of risk aversion. It turns out that for individuals who take risk into account in a certain way it is sometimes rational to refrain from gathering further evidence.

One issue was raised, if I remember well, by Joshua - namely, if this is the way you understand faith, Richard Swiburne doesn't have faith, for he actively looks for evidence pertaining to the truth of religion. Perhaps (now that I think of it) this can be circumvented by saying that faith in X would require one not to actively look for further evidence for the falsity of X (it depends how one construes Swiburne's thought, but one way to see this is to think that he does actively look for evidence in support of religion, but doesn't actively look for evidence against religion).

Another issue is that the notion of evidence in/against religion is quite elusive. Lara used an example of prayers: pray for something and see if you get it. But it seems that (at best) what you're testing this way is the conjunction of some of your religious beliefs and the claim that your will agrees with the will of God). Also, what counts as test or evidence for or against religion is highly theory-dependent. You can go Swinburnian about this and think that no actual event whatsoever is evidence against religion, because given certain considerations, everything that is happening should be happening if (his version of) theism is true. You can go more Tooleyan about this, and count every event that prima facie should not happen as evidence against the truth religion. Perhaps it's just me being confused, but I don't think we have a good understanding of a test that both a theist and an atheist would agree upon, so that the cost of its performing is negligible (given the negligibility requirement, for instance, Hick-style die-and-see-what-happens is out of the question).

The conference started with a slightly apologetic talk by Swinburne. It ended with a rather atheistic talk by Herman Philipse. He gave a series of short arguments against the claim that there is a C-inductive argument from the Big-bang to the existence of God. Briefly,i f h is theism, e is the occurence of big bang, and k is tautological background knowledge, Swinburne argues that Pr(e|h&k)>Pr(e|k). The first point that Philipse makes is that given that God would want to create humans and the fact that given the cosmic singularity, the probability that it will result in there being humans is quite low, it seems that Pr(e|h&k) is very low. Another point raises pertaining to Swinburne's claim that Pr(e|k) is very low. Since Pr(e|k)=Pr(e|h&k)Pr(h|k) + Pr(e|~h&k)P(~h|k) we need to know the prior probability Pr(e|~h&k) and Pr(~h|k). Philipse argued that Pr(e|~h&k)> Pr(e|h&k). He also attacked Swinburne's use of simplicity criterion. Since this was directed against Swinburne who was present, quite an interesting discussion followed.

As for Bayesian-style arguments for/against God's existence, I'm rather sceptical. The problem is, even if the math adds up, they all rest on primitive assessment of probability of things like "big bang occurs" relative to the existence of God, or relative to the negation of his existence, and many other probabilities of this sort. When asked questions like "what's the probability that intelligent beings like humans exist given the hypothesis that there is no god and no multiverse?" or "What's the probability that Big Bang occurs given the hypothesis that God exists", I'm just inclined do say: I have no idea. I would love it if (a) someone explained to me the notion of probability at play, and (b) showed me how on this notion of probability, the probability claims involved can be assessed without hand-wavy and practically untestable extra assumptions. Perhaps I'm just a frequentist and haven't seen too many worlds being created. My bad.

FMER, Leuven, June 10-12, cont'd

Day 3, before lunch

Edward Wierenga talk titled Developing Molinism employed fairly complex modal stuff (you know, actuality, counterfactuals and all that) to help formulate Molinism, the view that God has a knowledge of propositions that are intermediate between being necessarily true and independent of God's will or creative ativity, and contingently true propositions dependent on God's will. These are contingent true propsitions not dependent upon God's will (in the intended interpretations: propositions about future but free actions of men).

This knowledge is often taken to be a knowledge about certain counterfactuals (like "If Adam were placed in the Garden of Eden, he would freely eat the forbidden fruit"). This knowledge would assist God in devising the world so that it is the best world possible without interfering with human free decisions. The technical problem is that it's difficult to find right truth-conditions for counterfactuals of this sort which satisfy all the desiderata. Wierenga first discussed his original view (that Plantinga's conditionals of world actualizations can do the job) and criticized it, and then presented another suggestion, employing tense considerations.

Paul Bartha talking about Many gods, many wagers, discussed in detail the many-gods objection against Pascal's wager. He then argued that given the evolutionary stability condition on probabilistic reasoning (roughly, the condition is that after making a bet, no further probability considerations of the state of affairs after making the bet will make you change your mind) the many-god objection doesn't raise any difficulties that the classical version of Pascal's argument already encounters.

David Glass - Can evidence for design be explained away? - An obvious way to counter a design argument is to provide an alternative explanation. For instance, evolution theory is taken to render inconvincing certain design arguments. The problem is, certain version of design arguments are compatible with alternative explanations - why accept both? Well, don't if there's no need to do that! The technical question, however, is when one explanation is good enough to render the other redundant. Are there cases where it is better to accept both explanations than only one of them?

David addresses these issues within the Bayesian framework. Even if two explanations are marginally independent they typically become negatively dependent when one conditions on the evidence they explain. So, if one explanation is found to be true, this lowers the probability of the other explanation. There are, however, two important possible outcomes. Say a design hypothesis D has a certain prior probability Pr(D). Next, suppose it receives confirmation from evidence E so that Pr(D|E)>Pr(D). Then, we find out that an alternative explanation A is true. This undermines Pr(D|E&A). In the first case, Pr(D|A&E) is not higher than Pr(D), and so the initial confirmation of D by E has been completely negated. In the second, Pr(D|E&A) is higher than Pr(D) but lower than Pr(D|E). Given than only the first kind of outcome counts as explaining away, it turns out that it is very difficult to come up with an alternative theory that completely explains away the evidence for design.

FMER, Leuven, June 10-12, cont'd

This is getting overwhelming. I haven't finished posting about FMER and I'm already at another conference (Non-classical mathematics) that I also would love to blog about. I'll do my best to complete the FMER mini-series as soon as possible.

Day 2, after lunch

Alan Hajek talked about Blaise and Bayes. He first surveyed a few variants of arguments usually given as reconstructions of Pascal's wager in terms of "dominance" and "expected utility". It was fun, especially since he also showed that they're invalid, for some slightly surprising but equally obvious reasons. He discussed certain emendations that can be made to salvage the wager.

Joshua Thurow's talk was titled Does religious disagreement actually aid the case for theism? Disagreement trailblazing for the miraculous. He pointed out that disagreement about an inferentially-based belief may not automatically force one to suspend judgment en block. Divide the evidence for and against religions into two sets: A - the testimony to the occurrence of miracles, B - everything else. Suppose there is enough disagreement about the evidence in B that considered alone B supports suspending judgment in all religious belief. Then, using Bayes's theorem, Joshua argued that if A includes even moderate testimonial evidence for the occurrence of a miracle, then A and B together support whatever theositic religion is most supported by the testimony in A.

Michael Tooley discussed The probability that God exists. He employed Canapian-style structure-description approach to inductive logic to arrive at an upper bound on the probablitiy that God exists given only the information that the world contains n events each of which is such that in the light of the totality of known rightmaking and wronkmaking properties, it would be morally wrong to allow the event in question.

Given that there are n such events and that there are k unknow morally significant properties, the probability that none of those n actions is wrong all things considered, argues Tooley, is less than (k/k+1)(1/n+1). So, he argued, the probability that God exists must be less than 1/n+1.

One idealizing assumption that Tooley seems to take is that the total moral status of an action is assessed in terms of the number of morally relevant properties (rightmaking vs. wrongmaking), known or unknown. I think it's unlikely a theist would buy into this: they might insist that some (especially unknown) properties are more important and mere counting them (especially since it's not really obvious how you individuate properties so that counting makes sense) won't help to assess the moral status of an action.

Monday, June 15, 2009

Time Travel paper online

At FMER I had an opportunity to chat with Michael Tooley about time travel. Two years ago I had this paper about Tooley's example of loopless time travels and conditional logics. Michael put forward this example to indicate that if Lewis-Stalnaker semantics for conditional logics is adequate, then there are impossible cases of backward causation even without causal loops. Later on the argument was interpreted as an argument against the adequacy of conditional logics from the possibility of time travel (I recall that seemed to be the interpretation of Charles Cross, I was commenting on his talk at WCPA 2006 in Vancouver).

My point was that the impossibility of the situation described not only follows from basic assumptions of LS semantics, not only can be proven syntactically as holding in many conditional logics (that was Charles' observation), but also can be proven using fairly weak assumptions, weaker that those of Charles, and that the possibility of the situation is not very intuitive to start with (thus I rather sided with Michael, emphasizing that even without causal loops time travel can be tricky).

The chat reminded me about this paper, so I dug it up and posted to my academia profile. It's here.

FMER, news from the trenches (cont'd)

Here's Day 2, before lunch. *

The day started with a talk by Benjamin Jantzen titled Peirce on Miracles: The Failure of Bayesian Analysis. Benjamin started with a brief explanation of Hume’s criticism, according to which no testimony could be sufficient to justify belief in a miracle, given that the probability of fraudulent or mistaken testimony is always greater than the probability of the miracle occurring. He then considered Hume’s argument as an instance of Bayesian probabilistic inference. The basic idea is that the probability of a miracle having occurred given various testimonies to that effect is computed from the probability that each witness would report accurately given the occurrence of the miracle, the joint probability of the occurrence of such a collection of testimonies, and the antecedent probability of the miracle. Finally, Ben argued that given the Peircean criticism of the Bayesian approach, the probabilistic analysis of this sort is seriously flawed. The main gist of the criticism is that:
  • There is no such a thing as the objective veracity of a witness. To apply the Bayesian method we need to know the probability that a witness judged accurately and told the truth in a particular instance. The details of that instance cannot be replicated even in principle, so we have no class of sufficiently similar events to build a sample space (this objection hinges on Peirce’s frequentist account of probability).
  • Even if we grant such a thing exists, it doesn’t satisfy the independencies required by the method of balancing likelihoods employed in the argument. What leads one witness into error tends to lead others into the same error.
  • History tends to preserve only the positive assertions of the extraordinary and biases the computed posterior probability. When we hypothetize the occurrence of a miracle on the basis of some set of testimonies, we are not rational in using those same testimonies to determine the probability that this hypothesis is true.
The main positive lesson is that after constructing an abductively valid hypothesis we should gather independent data for an inductive phase.

Lydia and Tim McGrew talked about The Reliability of Witnesses and Testimony to the Miraculous. They started with Condorcet’s formula for the probability of an event:
where p is the antecedent probability of the event and t is the reliability of truthfulness of the witness. Then, they tracked subsequent changes that led to the formation of Bayes’s Theorem. Indeed, Condorcet’s account seems like a particular instance of B’s theorem, given the similarity between his formula and:
In particular, Condorcet’s formula is a special case resulting from three limiting assumptions.

  • The witness is equireliable – he is equally likely to tell the truth about H regardless of whether it occurs.
  • The witness is forthcoming – he would not be silent on the subject of H had it not occurred.
  • Testimony regarding H is restricted to YES or NO.
Lydia and Tim followed the history of the debate surrounding testimony and miracles (Babbage, Reid, Bentham, Hume, Campbell, Venn, Holder, Earman) , showing how it led to the rejection of these assumptions.

Finally, they argued that the move from Condorcet’s formula to Bayesian factors is correct and that the factors should not be construed as modeling witness’ reliability, but rather a function of a wider range of epistemically relevant factors.

* If you're one of the speakers and think your view is misrepresented, drop me a line.

Sunday, June 14, 2009

FMER, Leuven, June 10-12, News from the Trenches

Formal Methods in the Epistemology of Religion took place in Leuven, June 10-12 2009. The conference was amazing, I really had a blast. I was transiting from Ghent every day, and the schedule was quite intense, so only now I have a few moments to write about it.

Jake Chandler (of the choice & inference fame) and Victoria Harrison, with the financial support of the Centre for Logic and Analytical Philosophy have pulled off an excellent event, gathering together many prominent scholars working on formal stuff and philosophy of religion.

Most of the talks were related to Bayesian epistemology and its applications. It’s not the framework I usually deal with, so I've learned a lot. Also, after Prof. Swinburne’s talk I had the opportunity to give a talk about his modal argument in his presence, criticize his views, and see how he responds. That was pretty cool.

Anyway, here are some general remarks about the conference. I’ll start with Day 1 (the conference started in the afternoon, so there were only three talks), and comment about the other two days in near future.


The day hit off with a lecture given by Richard Swinburne, Bayes, God, and multiverse. Swinburne, employing Bayes’s theorem, explicated a probabilistic argument for God’s existence, arguing that given the empirical evidence we have, the relative assessment of the posterior probability of God’s existence is higher than the probability of godless multiverse and than the probability of a unique (and godless) universe (he referred to fine-tuning etc. here).

The second talk was delivered by me (on behalf of Agnieszka Rostalska and myself, it’s a joint paper but Agnieszka couldn't make it). I presented a formalization of Swinburne’s modal argument for the existence of the soul, and suggested another variant that avoids the main objection directed against it (it can be viewed as a weakening of one of the premises - thanks to Lara Buchak for this observation). I also argued that even this weakened version is epistemically too strong to convince anyone who allows the mere possibility of material conscious beings.
Some time ago, an anonymous referee of this paper said that the new version of the argument is not “much of an addition to the literature, since the modification which the author offers to Swinburne is one which it would be most implausible to suppose that he would wish to make”. In response to that: Swinburne was there when I was giving the talk and agreed that the modification which we offer is the one he would like to make for the same reasons for which we say it’s better (our further discussion pertained to our assessment of the revised argument, and Prof. Swinburne eventually suggested that he has a different argument which he will send in my direction some time soon - I'm looking forward to seeing it). The bottom line, if you want to state a conditional without any possibility of falsification, make sure your antecedent cannot be made true.
Graham Oppy talked about the Epistemological foundations of Koons’ cosmological argument. Koons argued that any exception to the principle of general causation that is narrow enough to avoid a collapse into global scepticism about empirical knowledge is also narrow enough to permit the construction of a successful proof of God’s existence. Oppy analyzed Koons’ arguments. Specifically, he took issue with Koons’ claim that in order to be justified in believing that one’s belief that p and the grounds for one’s belief that p are caused, one needs to be justified in believing that it is highly likely that any of the situations in one’s knowledge net is caused. Oppy discussed related epistemogical issues involved in Koons argument for the claim that we are in position to accept a priori a (defeasible) principle of causality.

Friday, June 5, 2009

Philosophy Journal Information

Before submitting a paper, it's good to check out what experience with that journal other people had: how long you're likely to wait, or whether you're about to get any feedback in case of rejection. Philosophy Journal Information is devoted to these things. Check it out, and don't forget to post your info!

Tuesday, June 2, 2009

A category theory book online.

A nice book on category theory, Toposes Triples and Theories (by Michael Barr and Charles Wells) is available here.

Philosophers' Rally, Cracow 2009 (Poland)

After having spent an intensive weekend in Cracow, I'm on a plane back to Brussells (well, actually, after I just got on it, all passengers were asked to disembark and identify their own luggage because we had one suitcase extra that didn’t seem to belong to anyone…) Anyway, although I was slightly frustrated with the previous large philosophical conference in Poland I went to (see more details here), I was quite delighted to attend this one (also, I like the fact that I could catch up with some of the Gdańsk students, who decided to take the trip and participate). Hence a few general comments about what Philosophers' Rally is and about philosophy in Poland in general.

As far as I know, there are two fairly regular, large and general philosophical events in Poland. One is the Philosophical Congress (the 2008 edition took place last September in Warsaw). In a way, it’s similar to large general conferences like CPA in Canada or APA in the States. What’s similar is a huge number of participants, and a wide spectrum of topics being discussed. What’s different about PC? Acceptance is based on semi-blind review of abstracts only (I’m quite positive the rejection rate is WAY lower, and what their review procedure is remains quite unclear to me), there are no pre-prepared comments after the talks, and there are no jobs interviews (philosophy job market in Poland is a topic for a whole different story). It’s usually organized by notable members of Polish philosophical community and most of the participants are faculty members from around the country (I recall, there were around 20 parallel sessions and chairs didn’t always pay attention to timing, so navigating between talks you wanted to make to was quite a complex task).

The other one is Philosophers’ Rally. It is more like a graduate conference (only, it’s really nation-wide). Apart from a bunch of invited speakers, who are faculty members, most of the participants are undergraduates, graduates and young PhDs. Most of the organizers are young and dynamic people. Acceptance is based on abstracts (I recall from a conversation with one of the organizers that the rejection ratio was around 20% and that the abstracts were sent for review to faculty members deemed competent in their respective fields; I think there were around 120 talks this year). [note: PR was on hiatus for a few years, and this is the first time it took place after its revival; also, it’s the first time they did require abstracts and did the reviewing; I think it’s a big step forward.]

From my observation, the atmosphere at a Polish philosophical conference can get quite weird (this doesn’t apply, or almost doesn’t apply to logic conferences in Poland though). The reason is, some philosophers behave as if they treated a conference like a rap battle (a lame one, too): you gotta get there, make noise, diss everyone else and show how smart you are. This on one hand leads to ad personam arguments and unjustified condescending remarks - you can actually sometimes hear a prof. telling a student something to the effect that they are wrong because they’re students, or arguments like “only an idiot would believe this”; also, certain groups whose members admire only each other (borrowing the phrase from Geach ;)) can be observed. An interesting phenomenon is that sometimes when a prof is considered important, some of their students will often follow them around, listening to what they have to say with awe even if it’s rude or utter crap, and imitating their style… weird stuff, I must say. On the other hand, this makes people take critical comments more personally, even if the comments are given with no vicious attitude and in good faith. Long story short: people often don’t make a distinction between persons and their views, and the overall culture of discussion leaves something to wish for.

Another thing which makes Polish philosophy quite different from what you usually see at an English-speaking University is the high level of continental deliberations. Approximately ½ or 2/3 of the conference topics were related to something that I don’t feel competent to describe.

Yet another observation: many of the talks, even if they are really clear and well-organized, are not devoted to making a point, claiming something, or arguing for or against anything. Rather, they focus on saying things like “A famous philosopher X said Y about Z”, or “A famous philosopher X said Y about Z, but another well-known philosopher V disagreed, but I won’t try to evaluate their arguments, I’m only presenting their views”. Although not too creative, this kind of work is useful in Poland, where accessibility to current literature (esp. books, for most of the universities have access to main journal databases) is slightly restricted for technical and pecuniary reasons. Also, if an undergraduate or a master’s student can do a good job presenting/comparing other people’s view, it’s a good exercise for them anyway.

Having said all this, I must stress that there are many young and intelligent Polish philosophers (some of them even undergraduates), who are doing sensible work on interesting topics. For instance:

Magda Kamińska (from Gdansk, yay!) presented the knowability paradox, described Williamson’s response to it, presented a few counterintuitive weakened paradoxes that you can run even if you switch to intuitionistic logic, and argued that a re-construal of non-omniscience claims in intuitionstic logic is not a successful strategy for dealing with the problem because it violates very basic intuitions that we have about quantification in natural language.
Bartosz Wcisło mounted a few arguments to the effect that the modality involved in the knowability paradox is uninteresting: that some Fitch-style unknowable sentences at a certain time may become knowable at a later time if you juggle around with temporary indices, and that in certain context sentences that are effectively decidable may come out Fitch-style unknowable. I don’t think the arguments worked, but fairly technical details were involved, and they are quite clever – it takes a while to figure out why this doesn’t fly.
• One of my favorites was Marta Ewa Romaneczko’s discussion of psychoanalysis. It is often claimed that it’s highly unfalsifiable and unscientific. Romaneczko in a clear and engaging manner argued to the contrary: that given certain fairly sensible approach to inter-theoretical falsification, falsifiability is available for many psychoanalytical claims, and that in fact there have been claims in the history of psychoanalysis that have been considered falsified and withdrawn when faced with data.

Many other familiar topics have been also discussed: metaphysical issues surrounding counting objects and constitution (Łukasz Krawiranda), availability of contingent identity with rigid designators (Błażej Skrzypulec), criteria of identity (Adam Andrzejewski), the relation between predicates and properties (Krzystof Posłajko, who also asked a wonderful question about deduction theorems in paraconsistent logics in my workshop), Frege’s notion of truth (Tomasz Pawlik), counterfactuals as the source of modal knowledge (Katarzyna Kuś), technical issues pertaining to probabilistic reasoning about causality (Leszek Wroński), empty names and their behavior within the framework of causal theory of reference (Rafał Ciok), the epistemology of thought experiments (Katarzyna Kobos), the physical acceptability (or its lack) of Lewis’ modal realism (Krzysztof Adamek), neo-Ryleanism about knowing-how (Bolesław Czarnecki), game-theoretic analysis of Kant’s imperative (Piotr Wilkin), Kai Nielsen’s critism of Malcom’s variant of the Ontological Argument (Jak Cieślar), semantic space hypothesis and AI programming (Krzysztof Hanusz), biological plausibility of Chomsky’s concept of linguistic competence (Piotr Wołkowski), a criticism of Dennett’s heterophenomenology from a Peircean perspective (Adrianna Smurzyńska), the question of intentionality of emotions (Paweł Bankiewicz) and the relation between epiphenomenalism and Davidson’s anomalism (Jarosław Ziółkowski).

Overall, despite certain particularities of Polish philosophical discourse (which were quite rare at Philosophers' Rally anyway), I’m quite optimistic: many young philosophers work hard on things currently discussed in the English-speaking world.

Another thing worth mentioning: apart from a few really minor glitches (which happen everywhere), the conference was really well-organized, and in this respect it stands second to none of those conferences that I’ve seen anywhere else (in fact, there even was an English-speaking section!). I would like to express my gratitude to the organizers: thanks guys for having me!