Monday, December 13, 2010

The CTT paper, final version

The writing process of the paper on the Church-Turing thesis, random processes and platonism has come to an end. The paper is forthcoming in Philosophia Mathematica. A more or less final version of the paper is available here. (wrt to earlier versions, I added a bunch of remarks and answers to possible counterarguments, explained what Church randomness is and why Church-random sequences are not Turing-computable and elaborated on the intuitive source of the conceptual conflation involved).

Many thanks to Leon Horsten, Liesbeth De Mol, Robert Thomas, Jeffrey Ketland, Gualtiero Piccinini, Stanisław Dercz and two anonymous referees for discussion and comments.

Friday, November 19, 2010

Possibility and the burden of proof

If I didn't run into this sort of arguments often enough, I wouldn't be writing about this. Some time ago, Gualtiero Piccinini (whose computability-related stuff I really enjoy reading) posted a question about known good arguments for the existence of afterlife. Joshua Carl Davis commented:
I make an argument in my book Metaphysics and the Meaning of Life that there is an afterlife. The argument goes as follows: 1) It is always valid to argue from actuality to possibility (a logical principle dating to Medieval times), 2) I exist now therefore it is possible for me to exist again. While this does not prove the immortality of the soul, it switches the burden of proof to the other side and, I believe it is an overwhelming burden. The argument is given on page 282. The book is available on Amazon. Good luck to you.
Eric Thomson gives a pretty straightforward explanation of what went wrong there.
  1. ET argues that equally well the fact that one didn't exist before they were born shifts the burden to the other side.
  2. ET points out that establishing possibility doesn't automatically shift the burden of the proof.
  3. ET indicates that the possibility of future existence doesn't follow from the actual existence by the principle that JCD refers to.
As for point 1, JCD responds:
As for your first point, which to you is more certain: "I exist now" or "I did not exist before I was born"? That should indicate which is the stronger argument.
The problem is, a reductio argument of this sort cannot be refuted by saying one of the premises is less certain than other. Suppose someone gives an argument: "P - therefore, by my magical strategy, Q", and someone else responds: "The magical strategy doesn't fly: I can equally well argue: Z - therefore, by the same magical strategy, not Q". Now, saying that Z is less certain than P doesn't help. As long as Z and P are both true, the reductio works and shows that the magical strategy (let's not hesitate to use the technical term) sucks.

What has to be done to defend the magical strategy? Well, once one is convinced it works and accepts P, plain modus tollens will force them to reject Z. This is a problem because if this is what happens, the magical strategy gives an argument: "P - therefore by my magical strategy, Q. But if Z were true, then by my magical strategy, Q would be false. Therefore, Z is false". Apply this to the case in question and it turns out that JCD can save his argument against this reductio only by denying Z. But to save an argument for life after death by assuming life before birth will not be a convincing strategy to many.

As for point 2, I wouldn't have much to add. It is perhaps metaphysically possible that BSG is true and JCD is a cylon travelling in time (and perhaps across possible worlds), but this doesn't shift the burden of the proof: he doesn't have to focus on proving that he isn't. I am still allowed to assume he isn't, unless proven otherwise. (In general, the burden shift JCD proposes would be pretty bad in court: innocent unless proven guilty would turn into guilty unless proven innocent given the possibility of guilt.)

JCD addresses ET's point 2 as follows:
As regards your second point, I do believe the burden of proof is switched. My existence is already a possibility based on the fact that I currently exist. The argument only illustrates that the burden is, was, has always been, on the other side. It's the difference between saying there will be another lion or there will be a unicorn.
Now,"I do believe the burden of proof is switched" and "The argument only illustrates that the burden is, was, has always been, on the other side." is not an adequate response, it is just a restatement of JCD's claim (actually, its strengthening). I'm not even sure if it's consistent to say that the burden is switched and that it has always been on the other side.

How about "My existence is already a possibility based on the fact that I currently exist"? Well, ET claims: mere possibility doesn't shift the burden. JCD's claim is consistent with this. I can say that existence is already based on the fact that I exist and yet maintain that this doesn't shift the burden. ET doesn't deny the possibility of JCD's existence, so stating it has nothing to do with ET's objection.

Perhaps, what JCD means is that we already know that our existence is possible (well, we do exist), whereas we don't have a compelling reason to believe that our non-existence is. If this was true, then indeed, the burden of proving the possibility of non-existence would be on JCD's opponents. Alas, the experience of the fragility of human existence is quite common, and so are prima facie consistent thoughts about death of the body as the end of life. If JCD claims human non-existence is impossible, an argument is needed.

As for point 3, JCD's reasoning goes from P to Possibly P and from Possibly P to Possibly P and Q: I exist. Therefore, it is possible that I exist. Therefore, it is possible that I exist after my body dies. Of course, the first move is valid (you don't have to conjure medievals to see that), but the second one isn't (just take Q to be not-P, for instance; or any sentence that metaphysically excludes P, if you prefer).

Tuesday, November 16, 2010

Evolutionary arguments do go astray (sometimes)

Norton (Why thought experiments do not transcend empiricism. In Hitchcock, C., editor, Contemporary Debates in the Philosophy of Science, pages 44–66, Blackwell) when talking about developing non-classical logics to model certain aspects of thought experiments gives the following, as he calls it, evolutionary argument:
I think there are some reasons to believe that no new, exotic logic is called for. In outlining the general notion of logic above, I recalled the evolutionary character of the logic literature in recent times. New inferential practices create new niches and new logics evolve to fill them. Now the activity of thought experimenting in science was identified and discussed prominently a century ago by Mach (1906) and thought experiments have been used in science actively for many centuries more. So logicians and philosophers interested in science have had ample opportunity to identify any new logic that may be introduced by thought experimentation in science. So my presumption is that any such logic has already been identified, in so far as it would be of use in the generation and justification of scientific results. I do not expect thought experiments to require logics not already in the standard repertoire. This is, of course, not a decisive argument. Perhaps the logicians have just been lazy or blind. It does suggest, however, that it will prove difficult to extract a new logic from thought experiments of relevance to their scientific outcomes – else it would already have been done! (pp. 54-55)

To gains some perspective on this argument, consider the following “evolutionary” argument. Norton, among other things, works on the philosophy of relativity. Now, relativity theory has been around, pretty much, since the same time when Mach wrote about thought experiments. So philosophers interested in science have had ample opportunity to identify and solve any philosophical issue that may be introduced by relativity theory. So, in this field, any philosophically interesting claim has already been made and any philosophically argument has been given, and Norton’s work in philosophy or relativity is redundant. Unless, of course, philosophers of science since the discovery of relativity theory have just been lazy or blind.

Tuesday, November 2, 2010

A geeky note about multilingual support for WinEdt 6.0

So WinEdt 6.0 has been out for a while now. It's a good piece of software, and I've been using various versions of WinEdt since 2003 (sometimes I use emacs with auctex, but for larger projects, I definitely prefer WinEdt).

Anyway, if you often switch between languages, you have to play around to get WinEdt to open your files with appropriate dictionaries. This is where modes kick in. It so happens that the explanation that WinEdt provides for this stuff isn't too clear, so here is a step-by-step procedure that will get you multilingual support for WinEdt 6.0.

  1. Download appropriate dictionaries. They are available here. Extract (if needed) and save the file(s) somewhere. It doesn't really matter where, just make sure you know where it is. Say you want to install Polish and download pl_huge.dic saving it at C:\Program Files\WinEdt Team\WinEdt\Dict\pl_huge.dic.
  2. Run WinEdt 6, go to Options. Under Editor: Mouse, Modes, Defaults you will find Modes. Open the file.
  3. Now, what I do, is I look at the submodes and add a line: MODE=":PL|*.pl.tex" This creates a submode PL which is assigned automatically to all files ending with .pl.tex
  4. I also replace corresponding lines for US and UK English, using: MODE=":UK|*.uk.tex" and MODE=":US|*.us.tex"
  5. That way, whenever I have a file in Polish I save it as name.pl.tex, if I have a file in American English, I save it as name.us.tex, and so on.
  6. This sets the modes right. Now dictionaries. In the Options tree go to Dictionary Manager and then to Word Lists.
  7. Then you add something like this to the list:
DICTIONARY="Polish"
FILE="C:\Program Files\WinEdt Team\WinEdt\Dict\pl_huge.dic"
ENABLED=1
MODE_FILTER="PL"
LOAD_ON_START=1
SAVE_ON_EXIT=1
ADD_NEW_WORDS=1
USE_FOR_COMPLETION=1
ALLOW_COMPOUNDED_WORDS=1

The first line just gives your setting a name. The second locates the dictionary file (that's why you need to remember where you saved it). The mode filter tells you for which modes this dictionary is active.

8. Now you also have to turn off your English dictionaries for the Polish file and switch them on for US and UK submodes. That is, you look at all English dictionaries listed and make sure their mode filter contains appropriate submode. Thus, for example:


DICTIONARY="English (common)"
FILE="%B\Dict\English\eng_com.dic"
ENABLED=1
MODE_FILTER="US"
LOAD_ON_START=1
SAVE_ON_EXIT=1
ADD_NEW_WORDS=0
USE_FOR_COMPLETION=1
ALLOW_COMPOUNDED_WORDS=1

Then, you save all the changes you've made in the options sections, restart WinEdt to make sure it loads its settings anew and check if language selection works properly. Make sure the files you use have appropriate extensions.

If you think something's still off, feel free to include mode declaration in the beginning of each file. Just include % -*- TeX:US -*- (or % -*- TeX:PL -*- or...) in your preamble.

Tuesday, October 19, 2010

Applications of Logic in Philosophy and Foundations of Mathematics CFP

If structural completeness is your thing, Janusz Czelakowski, Tomasz Połacik and Marcin Selinger are organizing a conference focusing on such issues. It will take place in a nice small mountain town in Poland (Szklarska Poręba) 9-13 may, 2011. The conference is about to be bilingual, so feel free to take a look at the CFP and maybe drop them a line.


Monday, October 11, 2010

Second Entia et Nomina Workshop CFP

This is the second time Gdansk University is organizing Entia et Nomina, a logico-philosophical workshop. Most likely, it is also the last time the language is Polish. Next time, we plan to switch to English. So, English speakers - stay tuned. Polish speakers - CFP below:




EntiaEtNomina2011CFP

Friday, October 8, 2010

PhDs in Logic, CFP

17-18 February 2011, PhDs in Logic III, Brussels, Belgium (deadline: 15 November 2010)

PhDs in Logic is an annual two-day graduate conference and winter school in logic. Each year we invite four established professors to do a tutorial on their work in two one-hour sessions. We also give about ten PhD students the opportunity to do a thirty-minute presentation on (a) their own work or (b) an overview of some topic in their field.

The current conference will feature the tutorials by Eric Pacuit (*Epistemic Logic*), Sonja Smets (*Quantum Logic*), Mai Gehrke (*Algebraic Logic*) and Peter Koepke (*Set Theory*). PhD students in logic with a background in philosophy, computer science, or mathematics are the intended audience for these tutorials. They are also the type of students we have in mind for our thirty-minute student sessions.

Students interested in doing a talk should send a 500-1000 word abstract to phdsinlogic+abstracts at gmail.com by November 15th, 2010.

For more information, visit our website at http://www.vub.ac.be/phdsinlogic2011/.

Saturday, October 2, 2010

Busting a myth about Lesniewski and definitions

Some time ago I run into a few logicians chatting at a conference about how Lesniewski formulated the standard theory of definitions. For some reason I felt obliged to say a few words about this. One thing let to another, and this ended up in a footnote to Gupta's entry on definitions at the Stanford Encyclopedia (see footnote three). A few more coincidences and I started writing a paper about this with Severi Hamari. After a freakish number of revisions (around 20) we finally agreed on a version, and I posted it on academia.

Many thanks for their comments to John MacFarlane, Nuel Belnap, Wilfrid Hodges, Paolo Mancosu, Oystein Linnebo and Jan von Plato (I hope I didn't forget anyone).

Abstract:

A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to S. Lesniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Lesniewski’s published orunpublished work is known where the standard conditions are discussed. Second, Lesniewski’s own logical theories allow for creative definitions. Third, Lesniewski’s celebrated ‘rules of definition’ lay merely syntactical restrictions on the form of definitions: they do not provide definitions with such meta-theoretical requirements as eliminability or conservativeness. On the positive side, we point out that among the Polish logicians, in the 1920s and 30s, a study of these meta-theoretical conditions is more readily found in the works of J. Lukasiewicz and K. Ajdukiewicz.

History and Philosophy of Computing, Ghent, Nov 7-10, 2011

From 7-10 November 2011 the Centre for Logic and Philosophy of Science organizes an International Conference on the History and Philosophy of Computing.


AIMS AND SCOPE

The computing sciences collect the most diverse complex of experts: philosophers, logicians, historians, mathematicians, computer scientists, programmers, engineers. The number of involved subjects grows accordingly: from foundational issues to their applications; from philosophical questions to problems of realizability and design of specifications; from theoretical studies of computational barriers to the relevance of machines for educational purposes.

A historical awareness of the evolution of computing not only helps to clarify the complex structure of the computing sciences, but it also provides an insight in what computing was, is and maybe could be in the future. Philosophy, on the other hand, helps to tackle some of the fundamental problems of computing, going from the limits of the “mathematicizing power of homo sapiens”to the design of feasible and concrete models of interactive processes.

The aim of this conference is to bring together these two streams: we are strongly convinced that an interplay between the researchers with an interest in the history and philosophy of computing can crucially add to the maturity of the field.

We plan to have up to 30 contributed papers to be presented at the conference. We welcome contributions from logicians and philosophers or historians of science as well as from philosophically and/or historically aware computer scientists and mathematicians.

Topics of the conference include:

  • The birth, evolution and future of computation

  • Philosophical, foundational and practical issues of computability in logic, mathematics and computer science

  • Computation in the sciences

More details on deadlines and submissions can be found at:

http://www.computing-conference.ugent.be
computing.conference@ugent.be


INVITED SPEAKERS:

Bill Aspray (University of Texas)

Martin Davis (New York University)

Fairouz Kamareddine (Heriot-Watt University Edinburgh)

Sybille Krämer (Freie Universität Berlin)

Giovanni Sambin (Universita' di Padova)

Raymond Turner (University of Essex)


CONFERENCE CHAIRS:

Liesbeth De Mol and Giuseppe Primiero


PROGRAMME COMMITTEE:

G. Alberts (Amsterdam)

S. Artemov (New York)

M. Campbell-Kelly (Warwick)

A. Eden (Essex)

L. Floridi (Oxford & Hertfordshire)

R. Kahle (Lisbon)

B. Loewe (Amsterdam)

J. Meheus (Ghent)

E. Myin (Antwerp)

S. Negri (Helsinki)

V. de Paiva (Palo Alto)

S. Smets (Groningen)

G. Sundholm (Leiden)

C. Toffalori (Camerino)

J.P. van Bendegem (Brussels)

M. van Dyck (Ghent)

B. van Kerkhove (Brussels & Hasselt)

E. Weber (Ghent)

SUPPORT

A number of Students Grants will be available through our Sponsor and Supporting Associations. More details to come on the webpage of the conference.

Friday, September 24, 2010

Church-Turing against Platonism - extensive revision

The note I mentioned a while ago went through serious revisions and extensions. The main points stand, but I added extra content, explanations and arguments to turn this into something more resembling a paper. Here is THE NEW VERSION. (HT to Leon Horsten for his comments)

Friday, August 27, 2010

My top ten pieces of software

And now for something completely different. A brief list of neat pieces of software I've been using (widely understood to include online services).
  1. WinEdt (6.0) - my favorite LaTeX editor. I've been trying to use quite a few different editors, but this one really works for me. It's not freeware, it's not Linux-compatible (as you could figure out from its name). But I like how you can set up your own macros, how it uses bookmarks, and how it handles large multi-file projects.
  2. Allway Sync - a neat program (freeware in its moderate version) that helps you to synchronize your files across different units. If you switch between computers more than a few times a week, this one's really cool. What I've done is I configured it to check my flash disk automatically once I plug it in on any computer I'm using and to automatically update the files. Saves lots of time and helps to avoid file version mix-ups.
  3. PDFX-Change - a nice PDF viewer with convenient commenting options - quite useful for on-screen proofreading and grading, if you care about saving paper or if you work with people over the Internet.
  4. FreeMind - a java-based mind-mapping software. I use it to organize papers I've read (you can include local or external links). It is kinda cool to draw arrows between papers, add comments, group them according to topic and so on. Sometimes I also use it to outline papers.
  5. TimeGT - For a long time I was looking for a nice task management software. I tried quite a few different ones, but eventually settled on this one. It is complicated enough to handle my task groupings, but sufficiently user friendly to allow me spend less time organizing my tasks than actually performing them. Also, it is GTD-compatible.
  6. Speaking of GTD, GTD for gmail is a nice add-on that helps one to survive email storms. It works quite well for Firefox. The Chrome version is still a bit shaky, but things are looking bright.
  7. GoogleReader really helps me to keep track of all those interesting blog posts on all those neat blogs I'm following (only now I have 572 unread items). It's also an excellent procrastinating tool when you don't feel like really working, but don't wanna feel guilty about not doing anything useful. You can also find your friends and follow their recommendations.
  8. StyleWriter (4.0) - only recently I started using this interesting piece of proofreading software. What's quite nice about it is that it focuses on avoiding pompous and wordy phrases, lengthy sentences and such. It actually helps me to keep my writing simple(r). Alas, it's not freeware. Another problem is, it doesn't handle LaTeX too well, so I have to play around with my text before I run it by StyleWriter.
  9. JabRef reference manager. It works quite well with bibtex databases, and it is not too bad as a pdf manager.
  10. Speaking of references, Mendeley certainly deserves a honorable mention (I wrote about it some time ago). Come to think of it, I'm quite disappointed by how it can't handle switching between computers and changing local folders, so I'm waiting for a better version before I start using it seriously.


Wednesday, August 4, 2010

How not to use the Church-Turing thesis against platonism

Recently, I've written up a quick note explaining why an argument against platonism, based on the Church-Turing thesis and deployed by Olszewski (1999) doesn't work. It's here. Abstract below.
Olszewski [1999] claims that the Church-Turing thesis can be used in an argument against platonism in philosophy of mathematics. I argue that the argument relies on the illegitimate conflation of effective computability with computability by any means, and that even if it worked, it would not be an argument against platonism, but rather against any realism about truth-value of mathematical sentences.

Some Polish classics online

The Polish Virtual Library of Science made quite a few classical volumes available. Among them, some historical volumes of Acta Arithmetica, Annales Polonici Mathematici, Fundamenta Mathematicae, Mathematical Monographs series, Mathematical Dissertations and Studia Mathematica. Here. Of special interest, Kuratowski's and Sierpinski's works in the Mathematical Monographs series. Here. Alas, some of the stuff is in French and some is in Polish.

Thursday, July 15, 2010

Watch out in Kirchberg

Soon, some of you might be headed to Kirchberg for the yearly Wittgenstein Symposium organized by the Austrian Ludwig Wittgenstein Society.

What you might know is that if you want to, you might bring your tent and camp for free near the swimming pool in this lovely village during the event.

What you might not know is that if you do, this involves some risk. In 2008 when I was there, our rather international camp was attacked by a bunch of young nationalists yelling scheissen Polaken raus and such (even though, only some of us were actually Polish). So, my advice, enjoy the event, it's definitely worth it, but be careful and don't walk around alone at night.

Saturday, June 12, 2010

Gender gap in class

Having read about final gaps at Oxford, I got a tad self-consciouss and run the stats for the two largest classes I taught this year. It turns out that in Logic women are 1.17 points (out of 100) ahead of men, and in a course where we do stuff on theories of truth men are 2.14 points (also out of 100) ahead. I feel relieved.

Friday, May 28, 2010

Befriending numbers nominalistically

I probably should've posted this sooner. On Monday I'm giving a talk at Oxford, criticizing Nathan Salmon's argument against nominalism, to be found in his recent paper in Analysis titled Numbers versus Nominalists. Feel free to pop in if you're around. Details below.

Rafal Urbaniak (Ghent University/ Gdansk University) 'Yellow card for Salmon'
Monday, 31 May, 16:30 - 18:30, Ryle Room, Faculty of Philosophy,10 Merton Street, Oxford.


Nathan Salmon (Numbers versus nominalists, Analysis 68.3:177-182,2008) argues that nominalists cannot plausibly deny the inference from(A) `there are exactly two Martian moons' to (B) `something is such that it is number two and there are exactly that many Martian moons'.He insists that the latter claim commits one to the existence ofnumbers. Salmon in effect argues that nominalism faces a rather serious challenge, for (as he claims) the inference can be denied only at the expense of giving up on higher-order logic, which is very unlikely to be an independently motivated strategy. After briefly describing Salmon's argument I will sketch a variant ofthe nominalist position on which the troublesome and apparently committing sentence is ambiguous between a statement that is derivable from (A) but non-committing, and another, which is committing but (onthe nominalist's view) not derivable from (A), even if the nominalistfinds higher-order logic a reliable source of legitimate inferences

Tuesday, May 18, 2010

Boredom in philosophy

In Florida Philosophical Review David McNaughton has an amusing and somewhat to the point paper about why philosophy tends to be tedious and boring. Here.
Why is so much philosophy so tedious? Not, or not simply, because it is technical and complex, but because—too often—it displays mere cleverness. Implausible theories are defended against objections by ever more sophisticated technical fiddling with the details. Originality and creativity are in short supply. I argue that this is bad for philosophy, bad for philosophers, and almost inevitable given various structural features of the profession which require early and prolific publication. As a profession we are autonomous—we could change our structures if we chose.

Friday, May 7, 2010

Łukasiewicz at Harvard, 1926

I was browsing a volume of a Polish philosophical journal (Ruch Filozoficzny) dating back to 1928, looking for something quite unrelated when I came across Łukasiewicz's report about the Sixth International Congress of Philosophy, Harvard, Sept 13-17, 1926, which, as it turns out, he attended. I did find his report slightly unusual, so here's a juicy bit, in my rough translation:
Almost everything made the worst impression on me. Perhaps this was only bad luck. I wasn't present and the most interesting talks by Driesch, Weyl and Whitehead, which took place before my arrival. Although, having seen the content in print, I infer that perhaps I wouldn't have gained much had I actually heard them. From what I've experienced, a few details.

In the plenary session, Bougle from Sorbonne was talking about philosophy and peace movement, and E. Becher from Munich about darwinism and international relations. Both talks were on the level of newspaper articles; and the topics were more propagandistic than scientific. Becher said that Darwin's theory cannot be applied to human societies, because at war it is the bravest who perish, and the weak hide behind the lines. It came across my mind that had the Germans won, one could find a philosopher who'd say that according to Darwin's theory the bravest have the right to live and the weakest have to die. In the logic session Schiller from Oxford was trying to eradicate the difference between facts and values saying that facts become values and values become facts. I didn't understand anything and even now I think he was only playing with words. J. E. Heyde from Gryfia [not sure what place Ł meant, RU] was teaching in Rehmke's spirit how to solve the "ultimate" "problem of knowledge". He emphasized that what is not extended cannot occupy space. I reminded him that mathematicians don't take points to be extended and yet they locate them in space. He seemed surprised, opposed softly, and eventually said that he'd like to correspond with me about this. I gave him my address. So far, no message. Other talks weren't any better, maybe except for an interesting talk about the meaning of the concept of probability by C. J. Ducasse from Providence, Rhode Island.

On the last day, in the logic section, after five boring talks a short discussion took place. I spoke, giving critical remarks about the talks and expressed the view that the level of philosophical conferences is way lower than the level of other scientific conventions. A few people nodded, in general my impression was they didn't get it.

My only profit from the congress is that it supported my conviction that philosophy, as it is nowadays practiced, and as it has always been practiced, can have various values, can be uplifting, can satisfy your heart's needs, but is devoid of the most important value I think it should have: scientific value.



Monday, April 26, 2010

J. H. Sobel (1929-2010)

Only now I have learned that Jordan Howard Sobel has passed away. A brilliant philosopher of religion, epistemologist and logician. I had the pleasure of attending his talk in 2007 in Vancouver (SEPA annual meeting) and chatting with him at dinner. His Logic and Theism is definitely to be recommended. Rest in peace...

Friday, April 16, 2010

Frege's slingshot, a minor fix (in case you care about details)

In one of the classes, I'm talking about slingshot arguments, and I was thinking about a possibly clear way of laying out Frege's argument that (if sentences have denotations) propositions aren't in general denotations of sentences, showing why the conclusion technically speaking doesn't follow, and how once an extra assumption is added the argument flies. Here's the result. (If you know and understand Frege, this probably won't surprise you, but I'm only concerned with a way of presenting this to students here).

Frege in On Sense and Nominatum argues:
Thus far we have considered sense and nominatum only of such expressions, words, and signs which we called proper names. We are now going to inquire into the sense and the nominatum of a whole declarative sentence. [...] Is this thought to be regarded as the sense or the nominatum of the sentence? Let us for the moment assume that the sentence has a nominatum! If we then substitute a word in it by another word with the same nominatum but a different sense, then this substitution cannot affect the nominatum of the sentence. But we realize that in such cases the proposition is changed; e.g., the proposition of the sentence "the morning star is a body illuminated by the sun" is different from that of "the evening star is a body illuminated by the sun''. Someone who did not know that the evening star is the same as the morning star could consider the one proposition true and the other false. The proposition can therefore not be the nominatum of the sentence; it will instead have to be regarded as its sense.
To put this in a step-wise manner: consider two sentences:

[A] The morning star is a body illuminated by the sun.
[B] The evening star is a body illuminated by the sun.

The assumptions are:

[F1] If one can accept a sentence p but deny a sentence q simultaneously (in a given context), p and q do not express the same proposition.

[F2] Substitution of co-referential designators in larger expressions preserves the denotation of whole expressions.

[F3] In one and the same context, one can accept [A] and deny [B].

[F4] The morning star = The evening star

The first two steps in reasoning are quite straightforward. From [F1] and [F3] it follows:

[F5] [A] and [B] express different propositions.

and from [F2] and [F4] we obtain:

[F6] [A] and [B] have the same denotation.

Now for the slightly problematic step (supposedly from [F5] and [F6]):

[F7] The proposition expressed by [A] is not the denotation of [A] and the proposition expressed by [B] is not the denotation of [B]

To see why [F7] doesn't follow from [F5] and [F6], let's represent these more formally. "D(p)" stands for "the denotation of "p" " and "S(p)" stands for "the proposition expressed by (the sense of) "p" ".

[F5'] S(A) ≠S(B)
[F6'] D(A)=D(B)
[F7'] D(A)≠S(A) & D(B)≠S(B)

Now consider two models, in which:

[model 1] D(A)=S(A) & D(B)≠S(B)
[model 2] D(B)=S(B) & D(A)≠S(A)

In each of those models [F5'] and [F6'] are true, and yet [F7'] false (it's helps to draw a diagram here). Of course, there are at least two worries. One is that each of the models is not too uniform: the denotation of one of the sentences is identical with its sense, whereas the denotation of the other isn't identical with its sense. Another worry is that there are no clear reasons why any of these situations is to be preferred over the other. Hence, it seems sensible to use an extra assumption which captures the idea that the answer to the question whether denotations of sentences are their senses should have a general answer, that is, that either all sentences denote their senses, or no sentence does:
[F+] D(A)=S(A) ⇔D(B)=S(B)

In fact, [F7'] follows from [F5'], [F6'] and [F+]. For suppose that [F5'], [F6'] and [F+] are true and yet [F7'] is false:

[F7-] ~[D(A)≠S(A) & D(B)≠S(B)]

DeMorgan applied to [F7-] gives us:

[F7-a] D(A)=S(A) v D(B)=S(B)

Now, let's do a proof by cases. Suppose:

[A1] D(A)=S(A)

With [F+] this entails:

[A2] D(B)=S(B)

But transitivity of identity applied to [A1], [F6'] and [A2] gives us:

[A3] S(A)=S(B)

which contradicts [F5'].

An argument for the other case is analogous. Suppose:

[B1] D(B)=S(B)

An application of [F+] yields:

[B2] D(A)=S(A)

Transitivity of identity applied to [B1], [F6'] and [B2] gives us:

[B3] S(A)=S(B)

which contradicts [F5'].

If you find this formulation useful, feel free to use it in class (it would be nice if you let me know if you do, though).

Monday, March 29, 2010

A historical remark on the nominal description theory

I haven't been posting in a while, being swamped with teaching duties and so on. Right now, I'm looking at M. Morris's An Introduction to the Philosophy of Language, which in those respects that currently interest me contains, I think, more material than, say, Miller's or Lycan's textbooks (having said that, these books on the other hand have other virtues). On pp 86ff Morris is talking about what he calls a simple nominal description theory, according to which a name n connotes the description `the object called n' (or something to that effect). This, of course, seems to violate Kripke's non-circularity restriction; yet, it has been interestingly developed by K. Bach (Thought and Reference). Anyway, my point is rather short and historical - although this view hasn't been associated with anyone in the Frege-Russell period, this sort of approach has been around for a while, and I'm quite positive that at least Lesniewski hold that view. Here's a relevant bit from L's 1911 paper, in my translation:

J.S. Mill says that not all names have connotations. Among those which have no connotations are, according to Mill, proper names such as, e.g., Paul, Caesar on the one hand, and some of the names of attributes on the other. If this were really so, one could foresee certain difficulties in regarding as analytic those positive existential propositions whose subjects are just such names without connotation. Yet even the names which I have mentioned and which according to Mill have no connotation, in my opinion, have connotation; proper names connote the property of possessing a name which sounds like the given proper name, whereas the names of attributes regarded by Mill as lacking connotation, connote either the property of possessing such names, or the property of complete identity with entities which bear such names. Thus, e.g., the name ‘Paul’ connotes the property of having the name ‘Paul’, the name ‘redness’ connotes the property of having the name ‘redness’. Instead of ‘Paul’ we can then say ‘a being which has the name ‘Paul”, instead of ‘redness’ — a being which is completely identical with beings that bear the name ‘redness’. . . I shall touch here upon Husserl’s thesis that one proper name, e.g., Socrates’, can name various objects only because it is ambiguous, just as names such as ‘redness’; I do not think this is the case — these names would be equivocal only if, while denoting various objects, they also connoted different properties. In fact the word ‘Socrates’, while denoting different objects, connotes always one property, that is the property of bearing the name ‘Socrates’.