tag:blogger.com,1999:blog-4987609114415205593.post4083046102069369580..comments2024-03-28T13:40:26.497+00:00Comments on M-Phi: Van Benthem on system imprisonmentJeffrey Ketlandhttp://www.blogger.com/profile/01753975411670884721noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-4987609114415205593.post-73751481252050876452011-09-07T13:42:01.941+01:002011-09-07T13:42:01.941+01:00Hi Jeff, I'm running around a bit in the next ...Hi Jeff, I'm running around a bit in the next couple of days, but I'll send you the paper and the chapter soon.<br />It will be a shame if you are not in Munich next week! But it's for a good cause, one I'm very sympathetic to :)Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-4200552565489091532011-09-06T20:56:12.904+01:002011-09-06T20:56:12.904+01:00I'm in Edinburgh! Not sure if I can make the M...I'm in Edinburgh! Not sure if I can make the MCMP thing in Munich for various reasons. (One being that I want to spend more time with my family before the teaching begins.)<br /><br />Yes, I'd really like to read the chapter (and the earlier paper, but I'm not on academia ...).Jeffrey Ketlandhttps://www.blogger.com/profile/01753975411670884721noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-50839621421236968462011-09-06T20:23:47.164+01:002011-09-06T20:23:47.164+01:00Jeff, quick answer (I should really be turning off...Jeff, quick answer (I should really be turning off the computer now!): formal systems are models of whatever their target phenomena are, in each case, very much like in physics. As you may recall, in my talk in Munich last June I said that syllogistic, for example, is a model (for a restricted language) of the truth-preservation definition of validity at the beginning of the Prior Analytics. When I was doing formalizations of medieval logical theories, the target phenomenon was the theory in question, understood as a conceptual structure, *not* its expression in actual text. Of course, I could only apprehend this conceptual structure through the text, but once this was done, I could throw the ladder away and go straight from concepts to formalism.<br />I've been writing on all this just this week; if you are interested, I can send you the chapter as soon as it is more or less ready for consumption, and perhaps we can discuss it next week when I'm in Munich -- you WILL be there, I suppose! :)Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-40752866321878375652011-09-06T20:16:14.456+01:002011-09-06T20:16:14.456+01:00Hi Catarina,
But then the question becomes: what ...Hi Catarina, <br />But then the question becomes: what is a "formal system" a model of? My attitude is based on my background in physics. We have a physical system P. We define a simplified and approximate mathematical model M. There are transfer principles between M and P.<br /><br />Here is the sort of physics problem I used to do as a physics undergrad in classical mechanics. <br />A small ball slides down from the top of a hemispheric dome. It leaves contact with the dome at a certain point. I can define a mathematical model of this and compute the angle. I can also do an experiment, which confirms the prediction. Since the model is idealized, I can de-idealize in various ways.<br /><br />I just googled and this problem is solved here:<br /><br />http://minerva.union.edu/labrakes/Work_and_Energy_Problems_Solutions.pdf<br /><br />But I can't quite see what the object of the modelling is on your approach. <br /><br />(I agree with bits, and disagree with bits, of what Johan says here. I'd comment that Russell says in HWP somewhere that Theses on Feuerbach contained the earliest version of the pragmatist theory of truth.)<br /><br />Cheers, <br /><br />JeffJeffrey Ketlandhttps://www.blogger.com/profile/01753975411670884721noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-32769977107264582712011-09-06T19:42:00.941+01:002011-09-06T19:42:00.941+01:00@Roy and @Jeff,
As I think I mentioned many times...@Roy and @Jeff,<br /><br />As I think I mentioned many times, I believe that the view that formal languages are models of so-called natural languages is misguided. I of course like the bit of them being *models*, but I reject the claim that natural languages is what they are models *of*. Just yesterday I wrote the section of my book where I criticize this position (referring to Roy and Stewart indeed!). But rather than giving you my arguments against it, let me quote Johan again (again, from the paper whose source shall remain unnamed for now). I agree with most of the points he makes in this passage:<br /><br />"The idea that logical languages may, or may not, be good ‘models’ for a given natural language is still in line with the idea that some fixed reality is given, which logical systems are then supposed to model. In that sense, the very term ‘semantics’ is conservative, because the given natural language becomes the yardstick for judging the quality of the logical system. But a logical system is not just a model for natural language, or some reasoning practice. It is also a tool for independent conceptual analysis of some cognitive activity, which can bring to light important features that are not encoded in natural language as we have it. In that sense, logical systems can also be much more radical in their thrust, helping us, as Marx advocated, to move away from interpreting the world to changing it. I find nothing repugnant to the idea that we might want to change natural language because of logical considerations. In fact, I often worry about the adjective “natural”, which often hides a sort of unthinking admiration for what is supposed to be pristine ‘nature’. In reality, ‘natural language’ is about as natural as a Dutch polder or a Chinese lake: constantly tinkered with by humans. What also helps in seeing this broader conceptual horizon is the fact that a language is first and foremost a practice, not the algebra with operators that Montague saw as its core."Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-30916700609510021502011-09-06T19:25:03.447+01:002011-09-06T19:25:03.447+01:00@Sam, The paper has been uploaded and the link can...@Sam, The paper has been uploaded and the link can be found in the text above.Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-33396765546374470032011-09-06T17:30:30.984+01:002011-09-06T17:30:30.984+01:00Hi Catarina,
Thanks. If you do get time to upload...Hi Catarina,<br /><br />Thanks. If you do get time to upload it, that would be great.<br /><br />Best,<br />SamSam Robertshttps://www.blogger.com/profile/07195370003468343442noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-42627670174231763692011-09-06T17:21:41.727+01:002011-09-06T17:21:41.727+01:00@Sam
The idea is that if you have a term logic wi...@Sam<br /><br />The idea is that if you have a term logic without variables, the whole thing becomes a matter of scope (whether the modal operator ranges over the whole sentence or only over a part of it, namely the predicate), so it's not about the modality being attributed to a sentence or to a thing. As I said, I have a paper on this but somehow I can't find it on the internet anymore (it used to be there). If I have the time I'ii upload it to my academia page later today.Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-70902627251235051982011-09-06T14:27:46.582+01:002011-09-06T14:27:46.582+01:00Roy, saying formalization is modelling is fine wit...Roy, saying formalization is modelling is fine with me. In teaching, I usually say: formalization is a translation mapping (into a formalized language) that approximately models the logical consequence relation between the propositions expressed in natural language.<br /><br />But as you say, the thing is:<br /><br />"but is replaced with the quite difficult task of delineating exactly what aspects of the model we can, and cannot, treat as genuinely representative of the phenomenon in question"<br /><br />Indeed. If M is the "model" (what is a model?) and T is the "target phenomenon" (what exactly is that?), then what is their relation and how are properties of T inferred from those of M? Even distinguishing between the "model" and the "phenomenon" is not easy here.<br /><br />Suppose I formalize:<br /><br />(i) Anyone who draws a circle draws an ellipse<br /><br />as,<br /><br />(ii) $\forall x(\exists y(Cy \wedge Dxy) \rightarrow \exists y(Ey \wedge Dxy))$<br /><br />I think the question is: what is being modelled? What has to be preserved under this translation? <br />Maybe this is the logical form of (i); or maybe how (i) fits into an overall pattern of natural language implications; or maybe how it fits into a pattern of inferences; possibly other candidates.<br /><br />And there is an intermediate between the natural language sentence and the formalized string, that Quine calls "regimentation", and we usually call translating into "loglish". For example,<br /><br />(iii) For any person $x$, if $x$ draws a circle, then $x$ draws an ellipse.<br /><br />Presumably, (iii) is be thought of as synonymous with (i)? (expressing the same proposition).Jeffrey Ketlandhttps://www.blogger.com/profile/01753975411670884721noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-9271673249688135332011-09-06T10:00:59.337+01:002011-09-06T10:00:59.337+01:00Stu Shapiro and I have been pushing a view about t...Stu Shapiro and I have been pushing a view about the role of formalization in logic (mostly in papers, or his book, on vagueness) which takes seriously the idea that formal systems are merely models, and as such the results we prove about these formal systems don't automatically transfer to the natural languages we were originally interested in. Of course, in our work, we emphasize that they can transfer, but only with additional philosophical work. One example of this sort of thing is the objection to degree-theoretic semantics (or any precise mathematical model) for vagueness. Philosophers have objected to the use of such formal systems when attempting to understand vagueness on the grounds that they impose a kind of precision that is the very anti-thesis of the phenomenon - vagueness - that we are trying to understand. If we keep in mind that we are only building models, then the objection disappears (but is replaced with the quite difficult task of delineating exactly what aspects of the model we can, and cannot, treat as genuinely representative of the phenomenon in question).RoyTCookhttps://www.blogger.com/profile/05233569728242084863noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-32553247757514353972011-09-05T23:44:14.038+01:002011-09-05T23:44:14.038+01:00Hi Catarina,
Could you say a bit more about what ...Hi Catarina,<br /><br />Could you say a bit more about what problems involving de re modal sentences is sidestepped by moving to a different formal system, and how?<br /><br />Thanks in advance!<br /><br />SamSam Robertshttp://birkbeck.academia.edu/SamRobertsnoreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-81673745671079072152011-09-05T22:52:28.932+01:002011-09-05T22:52:28.932+01:00Thanks, Catarina - I'd say, on my view (I shou...Thanks, Catarina - I'd say, on my view (I shouldn't speak for others, but I think this is what Johan is saying about arithmetic too), mathematicians prove propositions, not sentences, which are merely linguistic vehicles. One can take the sentences, focus on them, formalize them and the official inference rules, identify some basic axioms $\Delta$, etc., and then show various results, e.g., that if formula $\forall x \phi$ can be proved in $\Delta$, then $\phi(x/t)$ can be proved in $\Delta$, etc. But that's mathematical logic, not mathematics more generally. And, furthermore, these meta-claims of mathematical logic are themselves propositions (i.e., simply about formulas, etc., rather than about numbers, functions, fields, metric spaces, etc.).<br /><br />On the opposite view, the <i>mathematician</i> is operating on strings <i>within a system</i>, and that seems to me a very formalist view.<br /><br />To put a similar point, slightly differently, but related to your talk a few months ago at MCMP and your "External Target Phenomenon" post here, suppose $L_1$ is an interpreted natural language (or even a controlled fragment), and $L_2$ is an interpreted formalized language. It seems to me that there are various structure-preserving mappings between $L_1$ and $L_2$ (e.g., translation mappings). This is what, approximately, we mean by adequate formalization.Jeffrey Ketlandhttps://www.blogger.com/profile/01753975411670884721noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-2402017916801579952011-09-05T21:42:13.651+01:002011-09-05T21:42:13.651+01:00The easy answer is 'sentence' of course, b...The easy answer is 'sentence' of course, but perhaps one could have a story on why, even though you operate with strings within a system, in the end what you prove is a content (relative to a given interpretation for the theory -- yet another parameter!).<br /><br />But yes, it's good stuff, and while I think that a certain degree of system imprisonment cannot be avoided (it's the trade-off for some nice things like meta-theory), system-generated problems should really be closely monitored and avoided at all costs.Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-84462186092184225182011-09-05T16:16:13.839+01:002011-09-05T16:16:13.839+01:00Catarina, great - that raises some very good quest...Catarina, great - that raises some very good questions. <br /><br />"Ultimately, what we prove is always relative to a given formal system."<br /><br />On this view, is the thing we prove a proposition or a sentence?Jeffrey Ketlandhttps://www.blogger.com/profile/01753975411670884721noreply@blogger.com