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LINGUISTIX&LOGIK, Tony Marmo's blog
Tuesday, 20 July 2004


I am very happy to announce that my dear friend and colleague Martin Honcoop's work, Dynamic Excursions on Weak Islands, has been re-edited and published via the Semantics Archive. Martin, a proud disciple of both Groenendijk and Szabolcsi, was a very competent linguist, a true expert in many things and I had the privilege to meet him during his short life time and call him a friend. He together with Marcel den Dikken, Eddy Ruys and Rene Mulder made up an outstanding group of young formalists unmatched by their country-fellows (either of their age or younger). Martin was exceptionally patient when had to explain what formal linguistics is about to fanatic and intolerant empiricists. After Mulder had moved to the publishing business and Marcel gone to the States, it is not exaggerate to say that when Martin died, one quarter of the future of formal Linguistics in the Netherlands perished too. We all miss him a lot and I congratulate the blessed soul who put his paper in the Semantics Archive.

Posted by Tony Marmo at 17:31 BST
Updated: Monday, 9 August 2004 08:08 BST
Monday, 19 July 2004

Boolean networks with variable number of inputs (K)

Metod Skarja, Barbara Remic, and Igor Jerman

We studied a random Boolean network model with a variable number of inputs K per element. An interesting feature of this model, compared to the well-known fixed- Knetworks, is its higher orderliness. It seems that the distribution of connectivity alone contributes to a certain amount of order. In the present research, we tried to disentangle some of the reasons for this unexpected order. We also studied the influence of different numbers of source elements (elements with no inputs) on the network's dynamics. An analysis carried out on the networks with an average value of K= 2 revealed a correlation between the number of source elements and the dynamic diversity of the network. As a diversity measure we used the number of attractors, their lengths and similarity. As a quantitative measure of the attractors' similarity, we developed two methods, one taking into account the size and the overlapping of the frozen areas, and the other in which active elements are also taken into account. As the number of source elements increases, the dynamic diversity of the networks does likewise: the number of attractors increases exponentially, while their similarity diminishes linearly. The length of attractors remains approximately the same, which indicates that the orderliness of the networks remains the same. We also determined the level of order that originates from the canalizing properties of Boolean functions and the propagation of this influence through the network. This source of order can account only for one-half of the frozen elements; the other half presumably freezes due to the complex dynamics of the network. Our work also demonstrates that different ways of assigning and redirecting connections between elements may influence the results significantly. Studying such systems can also help with modeling and understanding a complex organization and self-ordering in biological systems, especially the genetic ones.

Keywords: Boolean networks , biological systems, connectivity distribution, variable K,
sources of order, canalization, frozen elements, no input elements (source elements), attractor similarity, effective distribution, genetic networks , high orderliness.


Posted by Tony Marmo at 17:57 BST
Updated: Monday, 9 August 2004 08:09 BST
Friday, 16 July 2004

We have often heard the same complaint when an influential linguist, such as Chomsky or Kayne, releases a new paper: Oh no! He changed everything again!

A lot of non-theoretic linguists, who are inquisitors sank in the darkness of 19th century empiricist dogmas, are very reactionary in this sense: they hate changes in the theoretic framework, they do not want any of them and deem it absurd to change things all the time. But, if the concepts of some form of thought never change then it is not real science.

Now, newspapers around the world give us the good example of what solid science really means:

Hawking finds hole in his theory

Source: Associated Press, The Globe and Mail

After almost 30 years of arguing a black hole swallows up everything that falls into it, astrophysicist Stephen Hawking did a scientific back-flip Thursday.

The world famous author of a Brief History of Time said he and other scientists had it wrong -- the galactic traps may in fact allow information to escape.

The findings, which Dr. Hawking is due to present at the 17th International Conference on General Relativity and Gravitation in Dublin on July 21, could help solve the "black hole information paradox," which is a crucial puzzle of modern physics.

Current theory holds that Hawking radiation contains no information about the matter inside a black hole and once the black hole has evaporated, all the information within it is lost.

However this conflicts with a central tenet of quantum physics, which says such information can never be completely wiped out.

Congratulations Professor Hawking! You are a truly wise man!

Read more:

Het Volk
Los Andes
The Australian
Corriere della Sera
La Cr?nica de Hoy
The Houston Chronicle
The Guardian
The Globe and Mail
The Independent
El Mundo
No Olhar
El Periodico de Catalunya
RP Online
The Telegraph
Ziua Magazin

Posted by Tony Marmo at 10:32 BST
Updated: Monday, 9 August 2004 08:10 BST

Roumyana Pancheva has a paper on the present perfect tense puzzle, a linguistic phenomenon:

Another Perfect Puzzle

The interaction of the perfect with temporal adverbials is the domain of
the well-known present perfect puzzle (Klein 1992) - the fact that certain
adverbials are prohibited with the present perfect in English (though not
some other languages) while acceptable with non-present perfects. As is
generally agreed, the prohibition is against past specific adverbials (cf.
Heny 1982, Klein 1992, Giorgi and Pianesi 1998, a.o.).
This paper adds yet another puzzle to the area of perfect-adverbial
interactions. It establishes a new generalization regarding the modification
of perfects by both past and non-past specific temporal adverbials. The
puzzling facts are illustrated in (1).

(1) a. ?? We saw John last night. He had arrived yesterday...
b. We saw John this morning. He had arrived yesterday...
c. We saw John last night. He had arrived the same day...

Adverbials like yesterday are allowed in past perfects, and they may specify
the time of the event, as in (1b).However, their presence is restricted,
depending on what the reference time in the past perfect is. The reference
time is the interval which tenses relate to the speech time, and which the
event time is situated relative to. In the case of the past perfects in (1), the
reference time is a past interval anaphoric to the reference time of the
preceding past sentences: last night in (1a) vs. this morning in (1b). The
choice of a reference time contained in the interval denoted by the adverbial
modifying the perfect results in degraded acceptability, as in (1a).
When the reference time in the past perfect is not contained in the denotation
of the adverbial modifying the perfect, the result is an acceptable sentence, as
in (1b).

Read it

Posted by Tony Marmo at 07:24 BST
Updated: Monday, 9 August 2004 08:11 BST
Thursday, 15 July 2004

Brian Leiter has a very important and interesting post on expertise and knowledge, which is both a defence of scientists against ignorance and a starting point to discuss what kind of attitude is really 'arrogance' and whetherit is or is not something natural of academic life. Although I do not agree with one line of his text, where he says that 'science is not a democracy', his paper in its entirety seems correct and highly relevant to other issues of this blog:

Arrogance and Knowledge

by Brian Leiter, July the 13th, 2004

Andrea Lafferty, executive director of the Traditional Values Coalition, a conservative religious organization, delivers what could be the signature line for our backwards times in America:

There's an arrogance in the scientific community that they know better than the average American.[Source the NYT]

In fact, of course, scientists do know quite a bit better than the average American about the matters for which their scientific expertise equips them. Those with knowledge, surprisingly, know more than those who are ignorant. Is that arrogance?

As Chris Mooney remarked , science is not a democracy,
[sic] and in a democratic culture, that inevitably becomes a cause of resentment, as Ms. Lafferty's comment attests. This resentment of competence was first made vivid to me when I appeared on CNN more than a year ago to discuss the textbook selection process in Texas. When I dismissed the argument that the textbook selection process should be democratic (which it isn't, though it pretends to be) on the grounds that competent educators should vet textbooks, not political and religious groups, the CNN host, Anderson Cooper, cut me rather short: that reply clearly made him uncomfortable, and he changed the topic to how the selection process wasn't really democratic anyway.

Resentment of competence was also a motif suggested by my exchange with Professor Eastman --one of the ignorant law professors shilling for teaching creationist lies to schoolchildren--who used that favorite rhetorical device of the anti-Darwin crowd by referring to its tyrannical orthodoxy. Unfortunately, as I noted on that occasion, views that are correct ought to be orthodox, and they ought to exercise the tyranny appropriate to truth, namely, a tyranny over falsehood and dishonesty.

But when truth and knowledge clash with deep-seated prejudices--especially those reinforced from the pulpit and in the public culture--resentment towards the arrogance of those with knowledge and competence grows.

Unfortunately, I don't see much room for compromise in this domain. Knowledge and competence can not become meek and abashed merely to avoid offending the vanity of the undereducated, the parochial, and the unworldly. The Enlightenment dream was to extend the blessings of reason and knowledge as widely as possible. In the United States, that Enlightenment project has been stymied: at the highest echelons of the culture, the material and institutional support for the pursuit of knowledge and competence is unparalleled, yet the fruits of these labors are often either regarded with suspicion and resentment in the public culture at large--or simply go unrecognized and unnoted altogether.

Could there be a greater failure of the Enlightenment project than that a huge majority of U.S. citizens actually believe there is an intellectual competition between Darwin's theory of evolution by natural selection and intelligent design creationism? Or that the President of the country publically affirms their skepticism, without being held up for ridicule in the media and the public culture?

These are, for various reasons, scary times in [the United States of] America, but the increasingly brazen haughtiness of the purveyors of ignorance and lies--who cloak their backwardness in the judgmental rhetorc of "arrogance" and a none-too-subtle appeal to the "ordinary" person's sense of democratic equality--may be the most worrisome development of all. That the empire of ignorance spreads its domain portends calamities from which it could take centuries to heal.

Permanent link

Posted by Tony Marmo at 00:35 BST
Updated: Thursday, 15 July 2004 01:00 BST
Sunday, 11 July 2004

Purver and Ginzburg shed some light on the Semantics of Noun Phrases, from the perspective of the HPSG school, which I both respect and dissent from:

Clarifying Noun Phrase Semantics

Matthew Purver and Jonathan Ginzburg

Reprise questions are a common dialogue device allowing a conversational participant to request clarification of the meaning intended by a speaker when uttering a word or phrase. As such they can act as semantic probes, providing us with information about what meaning can be associated with word and phrase types and thus helping to sharpen the principle of compositionality. This paper discusses the evidence provided by reprise questions concerning the meaning of nouns, noun phrases and determiners. Our central claim is that reprise questions strongly suggest that quantified noun phrases denote (situation-dependent) individuals-or sets of individuals-rather than sets of sets, or properties of properties. We outline a resulting analysis within the HPSG framework, and discuss its extension to such phenomena as quantifier scope, anaphora and monotone decreasing quantifiers.

Download link

Posted by Tony Marmo at 07:19 BST
Updated: Monday, 9 August 2004 08:12 BST
Saturday, 10 July 2004


Yoad Winter on Choice Functions

Winter's page has many papers, and his concerns include computational linguistics. It is worthy to check it. One of his recent works, Choice Functions and the Semantics of Indefinites, is a sort of advanced introduction to the issue.

Methinks that choice functions can be used for almost any thing in semantics. Hamblin approaches, according to what the more experienced folks told me, began with questions. Thenceforth, Kratzer and many others have applied them to the semantics of scope. But, for me, the obvious application of Hamblin approach would firstly be binding/linking theory. It seems that there have already been some attempts to do so. (Anyone correct me if I'm wrong, please).

To my dismay, however, people still insist in separating binding from control. I love syntax though, I dislike a syntactic configuration solution for binding and control. A choice function solution is more agreeable to my intuitions.


One friend from This is not the name of the blog has a crucial question:


by Chris Tillman

I'm probably overlooking something obvious, but I was wondering if someone could help me out with this.

Uses of 'without' sometimes help express conjunctions with a negated conjunct, as in 'Al is going to the store without Mary going'. This should be symbolized as A & ~ M. Sometimes it is used to express a conditional, as in 'Without going to the store, John will have nothing to eat for dinner.' Here is the sentence that is troubling me:

(S) Bill drinks without Harry drinking.

Should (S) be read as a conjunction, a conditional or neither? And if neither, then what?

See it

Posted by Tony Marmo at 14:34 BST
Updated: Monday, 9 August 2004 08:13 BST
Friday, 9 July 2004

On contradictions

By Walter Carnielli
(Source: The Paraconsistency Webgroup)
Dear Friends,

Please see below some comments on Dick's views expressed in
"On contradictions".
I would like to encourage you all to participate in the
Paraconsistency discussion list of the WCP'2000, by subscribing
or just sending copies of our discussions to the list:


I agree with (what I think was) the conclusion of Fred's talk that we don't have any good arguments for the law of non-contradiction. It's too basic--either we accept it or we don't. Any argument for it we've seen or can imagine uses that law either explicitly or implicitly.

OK, but is not the situation the same for many other laws too? For basic laws concerning natural numbers? After all, when you start enumerating any kind of arguments about numbers, you are already using numbers. Or the grammarians using established grammar to explain grammatical rules.

However, I now think that we do accept some contradictions as true in our daily lives.


Posted by Tony Marmo at 14:05 BST
Updated: Monday, 9 August 2004 08:14 BST



16th European Summer School in
Logic, Language and Information

Universite Henri Poincare
Nancy, France
9-20 August, 2004

Semantic approaches to binding theory

Binding Theory, which is concerned with sentence-internal constraints on anaphora, was originally (Chomsky 1983) conceived in syntactic terms as conditions on the distribution of indices:
Condition A
Anaphors are locally bound
*Johni thinks that himselfi is clever.
Condition B
Pronominals are locally free
*Hei likes himi.
Condition C
R-expressions are free
*Hei thinks that Johni is clever.

But other researchers have attempted to derive these constraints from lexical semantics or the interpretative procedure rather than the syntax. Some (e.g. Reinhart 1983, Heim 1993, Fox 2000, Buring 2002) add a semantic component to a syntactic core, but others are more radically semantic (e.g. works by Jacoboson, Keenan, and more recently Barker & Shan and Butler, among others). The workshop will provide a forum to compare and assess these diverse proposals as well as to present the results of recent linguistic work to non-linguists.

Note: ESSLLI is the annual summer school of FoLLI, the European Association for Logic, Language and Information.

Posted by Tony Marmo at 06:25 BST
Updated: Monday, 9 August 2004 08:16 BST
Tuesday, 6 July 2004


Jackendoff talk: semantics must be generative

by Nick

On Friday (4th) I heard Ray Jackendoff give the keynote lecture at a conference organised by the UCL Centre for Human Communication which my department (UCL Phonetics and Linguistics) is part of (in some way I don't understand).

What he said may not be news to anyone else, but I hadn't heard it, not having read any of his recent stuff, except the bits about music.

Broadly, he thinks that mainstream - ie Chomskyan - linguistics is on the wrong track by supposing that syntax is the only generative component needed in the grammar, so that phonology and semantics need only interpret the output from syntax.


Posted by Tony Marmo at 02:26 BST
Updated: Monday, 9 August 2004 08:17 BST
Wednesday, 30 June 2004

Topic: Cognition & Epistemology

Can Justification Just Fall Short of Knowledge?

By Matt Weiner

From the Certain Doubts blog

We all know that justified true belief can fail to be knowledge when funny stuff happens (or at least most of us think this). What I want to ask is whether a JTB can fail to be knowledge for a more mundane reason-because the belief is justified, but it isn't justified enough to count as knowledge.

Another way, perhaps, to put this is to question a line from section 6 of Ralph's paper "The Aim of Belief" : "[T]here is no way for a rational thinker to pursue the truth except in a way that, if it succeeds, will result in knowledge." Is this so?

Here's a case I'd like to survey you on. Charlie Brown, a baseball general manager, is trying to decide who to pick in the amateur draft. He looks at the prospects and comes to believe, based on his high school performance, that Joe Shlabotnik will be a good major league player someday. Indeed, Joe does turn out to be a good major leaguer. So Charlie had a true belief; it also seems as though it may have been justified, because it was based on performance. Yet I would think that it falls short of knowledge, because predicting someone's eventual major league performance on the basis of his high school performance is too uncertain.

(Apologies to non-baseball fans; the argument probably transfers to any sport, though baseball performance is notoriously difficult to predict.)

Indeed, I'd argue that Charlie is much better off knowing that his pursuit of the truth about Joe's future performance will not result in knowledge. I'm convinced by Tim Williamson's argument that one of the advantages of knowledge over JTB is that it is less likely to be abandoned in the face of counterevidence. Yet Charlie should be ready to abandon his belief in Joe's future in the face of counterevidence. Given the chancy nature of baseball prospects, a general manager has to be prepared to abandon someone who looked promising but who isn't panning out, or he may damage his team by keeping on an underperforming player. Players who you know to be good will be kept in the lineup after a poor start (I remember Barry Bonds batting under .200 one May when he was in Pittsburgh and going on to win the MVP-er, sorry again to non-baseball fans); players who you think to be good won't.

Does this case convince you? Do you think Charlie is only justified in believing that Joe will probably be good? Do you think it casts any sort of light on the kind of justification that's necessary for knowledge?


Posted by Tony Marmo at 17:25 BST
Updated: Monday, 9 August 2004 08:19 BST
Saturday, 26 June 2004
I have found this interesting article at the Musings from the Lehigh Valley log:

Knowledge and Stability

by Joe Shieber
June 08, 2004

Marc Moffett has been considering some interesting questions concerning knowledge and stable belief and justification at Close Range. In response to some probing questions, he submitted a follow-up post, including the following example:

The other day I was going out of town and was supposed to call some friends when I got into the airport. My wife wrote their number down and I glanced over it. As I was leaving, she reminded me to take the number. I said, 'I know it' and proceeded to recite it from memory. Knowing that the number was still fresh in my mind her response was, 'Do you really know it?'

Marc suggests that the example shows that knowledge sometimes requires not simply reliably-produced true belief (let's grant that the short-term memorial faculty allowing Marc to rattle off the number correctly is reliable), but stable belief, or stably justified belief. Marc claims that we have an intuitive grasp of stability and instability to which he can appeal in making this suggestion. However, and without meaning to be difficult, I still don't know what stability is; nevertheless, let's leave this problem aside.

What I want to do here is suggest an alternate diagnosis for Marc's example. To do so, let me first present one of my own:

The other day I was sitting in a restaurant with my wife, planning our summer vacation while perusing the menu. My wife wanted to go to Germany to visit her family, while I wanted to spend most of the trip visiting Denmark and Norway. Finally, I acquiesced to her wishes just as the waitress was coming to take our order. Right before the waitress interrupted our discussion, I told my wife, 'Okay, we'll go to Germany this summer.' Then the waitress took our orders -- first my wife's, then mine. I ordered the duck breast and broccoli rabe. After the waitress left, my wife simply said, 'Are you sure?' Wishing to tease her, I answered, 'Yes, I'm in the mood for some duck.' She smiled and then repeated, 'Are you really sure?' At which point I reassured her that I'm happy to go to Germany.

This (fictional!) conversation seems to me perfectly possible. The question, 'Are you really sure?' doesn't indicate that my wife thought me unsure about the duck and broccoli rabe; rather, it indicates that I should return to the question at issue -- that of our summer vacation plans.

Similarly, in the case that Marc presents, his wife's question, 'Do you really know it?' doesn't deny that he now knows the number; rather, it indicates that his rattling off the number is an attempt to change the subject. The real question at issue is whether his knowledge involves the sort of reliable process that would underwrite his knowing the number once he reaches his destination. So Marc is correct when he notes that his wife's question was perfectly proper; she needn't have asked, 'Will you know it when you arrive?' However, he is incorrect, I would offer, in suggesting that the interpretation of his wife's question involves the introduction of the notion -- as yet unexplained -- of stability. Rather, in asking the question his wife was asking, 'Do you have the sort of knowledge (i.e., knowledge produced by a faculty reliable over the course of your trip) at issue in our discussion thus far?'


The case you offer is quite complex (more complex, I think, than the original). As I see it, there are two ways of construing it neither of which threaten my position.

On the first way of construing it, your assertion that you are sure that you want to order the duck is to be understood literally (though playfully). In this case, my initial reaction is that the follow-up question of whether or not you are really sure is not appropriate. So I guess I don't believe that "really" has the revert-to-conversational-thread use that you suggest.

Why then does your example read reasonably well? Because on the second reading, your assertion that your are sure that you want the duck is used to conversationally implicate that you are happy with the Germany decision and that you have already moved on. In this case, the use of "really" is apt and functions as I suggested in the original example (Are you sure or merely feigning?)

Posted by: marc | June 9, 2004 07:36 AM

What I say in the previous comment doesn't do justice to your case. Even if you grant me the discourse function of "really", the general point is just that my wife is asking whether or not I have the right sort of knowledge.

The picture then is that knowledge simpliciter defines a genus of knowledge relations which are further individuated by the type of faculty which produces/sustains the associated belief. So in the case, though it is true that I have knowledge-1 (i.e., the sort of knowledge produced and sustained by perception-cum-short term memory), what is required is that I have knowledge-2 (i.e., the sort of knowledge produced and sustained by perception-cum-medium term memory). So my wife asking whether I really know-2 the number or if I am just faking it (by relying on my knowledge-1).

Now, unless there is a principled way of restricting the determination relations, the cost of this view is a very great deal of ambiguity in the word "knows". I'm not sure why the resulting view is preferable. I suspect, however, that what is bugging you is the contextualist component (since the stability view is consistent with reliablism). The idea is that, on the stability view, whether or not I know that the number is such-and-such depends on the context. On your alternative, however, there is an upward necessitation from knowing-n to knowing simpliciter. As a result, you will get to say (context independently) that I know-simpliciter the number.

Is that the crux of the disagreement?

Posted by: marc | June 10, 2004 02:45 PM

Your second post precisely captures the crux of our disagreement, Marc. Thanks for revisiting the question, and for taking the time to spell out the disagreement so clearly. On a related note, thanks for posting your paper on these issues at your website. As soon as I've had a chance to go through it carefully (in the next week or so), I'm sure I'll be posting some further thoughts on the very interesting issues you address there.

Posted by: j.s. | June 11, 2004 11:34 AM

Posted by Tony Marmo at 01:41 BST
Friday, 25 June 2004

The debate on Understanding and Knowledge goes on.

Post your comments if you will.

Posted by Tony Marmo at 17:24 BST

Not Every Truth Can Be Known:

at least, not all at once

According to the knowability thesis, every truth is knowable. Fitch's paradox refutes the knowability thesis by showing that if we are not omniscient, then not only are some truths not known, but there are some truths that are not knowable. In this paper, I propose a weakening of the knowability thesis (which I call the "conjunctive knowability thesis") to the effect that for every truth pthere is a collection of truths such that
(i) each of them is knowable and
(ii) their conjunction is equivalent to p.

I show that the conjunctive knowability thesis avoids triviality arguments against it, and that it fares very differently depending on one other issue connecting knowledge and possibility. If some things are knowable but false, then the conjunctive knowability thesis is trivially true. On the other hand, if knowability entails truth, the conjunctive knowability thesis is coherent, but only if the logic of possibility is quite weak.

Greg Restall


I am glad to be among the first persons to see it online. Now, let me make some comments about the manner the paradox is presented at the online encyclopedia:

Fitch's (1963) paradox challenges `common sense', as any paradox does. Still, there are ways to begin explicating or describing a paradox adequately. Surely, it is better to depart from ideas that everyone may intuitively agree to.

Everyone's intuition is that what is knowable is not necessarily known. In the same manner, not everything that is visible has been seen.

The way Fitch's paradox is presented in Stanford Encyclopedia is misleading for larger audiences. It says that the principle of knowability claims all truths are knowable ( (KP) p ? ?Kp). Then it concludes: "If one accepts the knowability principle, she must deny that there are unknown truths. (...) In sum, if all truths are knowable, then all truths are known. `

Well, if I accept (1) bellow:

(1) a. All Humans are mortal.
b. Greg Restall is human.
c. Thus, Greg Restall is mortal.

Should I deny that there are humans who are not dead? Should I conclude that Greg Restall is dead just because he is mortal? Should (1a) and (c) be understood as (2) and (3)?

(2) All humans are dead.
(3) Greg Restall is dead.

What may happen does not necessarily happens. One must make a difference between what is ` x`-able and what is already ` x`-ed.

I prefer the way you start presenting the paradox in your paper. The text at the Online Encyclopedia causes the wrong idea from the start, although it re-presents the paradox in the proper manner further on.

Tony Marmo at April 24, 2004 06:07 PM

Bravo! I love this paper. I'll still be thinking about it for a long time I'm sure, but initially, two comments. (i) In the middle block of paragraph 23 there are some p's which should beq's. Were you not taught as a lad to mind your p's and q's? Sorry, couldn't resist 8-) (ii) There's something weird about formalising `P is knowable' as \Diamond KP where \Diamond is an ordinary alethic modal operator. It's knowable that there is milk in the fridge (M)---go and look. It's not knowable that the colour of this banana is killer yellow---look at it and die. I would have thought it is not knowable that there is no milk in the fridge---because there is milk in the fridge! But \Diamond KM is true---there's an (alethically) accessible world in which you drink all the milk, and in which you (then) know there is no milk in the fridge. So to my ears, if P is not true, then not only is P not known, but P cannot be known, i.e. P is not knowable. In fact "You cannot know P unless P is true" is just the truth condition on knowledge (not "You do not know P unless P is true"). So if \Diamond KP is to mean that P is knowable, then the following must be true (at every world in every model): \Diamond KP --> P. This will then make (3) on p.7 not a truism, but a falsism! (For (\exists q)(\Diamond Kq\wedge \Diamond K\neg q) to be true, q\wedge\neg q (i.e. "q and not q" for the tex-illiterate) would have to be true.) But then your version of the knowability thesis does not follow from a truism (at least not this one, because it is a falsism) and so is not (yet shown to be) almost trivially true.

Nick Smith
at April 24, 2004 09:57 PM

In Mathematics one works with constants, variables and incognitae, not only propositions. In Formal Semantics we know that we cannot account for linguistic phenomena without the notions of `contant' and `variable'. A Semantics without variables could yield many paradoxes and/or miss important data respecting human languages.

Now, I ask both of you this: hasn't the notion of incognita a place within Logic? You have [[x]] but you do not know the denotation of [[x]]. You can only know it after, let us say, you solve an equation or inequation, or a problem. I guess that, for instance, the correct Semantics of questions like:

(1) Who gave Cinderella a poisoned apple?

would imply that x in (2) is better understood as an incognita:

(2) Who is x, such as x gave Cinderella a poisoned apple?

In Cinderella's traditional story the answer is [[x]]=none, for none gave her a poisoned apple. You find the denotation of the incognita in the same manner as you find the solution of an equation.

Now, my question to both of you:

What if one tried to see the knowability paradox as an argument in favour of the notion of incognita within a Logic system?

Tony Marmo at April 25, 2004 05:57 PM

A question: Can "Every truth is conjunctively knowable" be read as form of logical pluralism? That is, if there is "conjunctively knowable" might there also be "foo knowable"?

If there is more than one way of knowing, then we might enquire whether Fitch meant K as all ways of knowing, or just one way. Does the paradox remain if K meant all ways?

RdR at April 30, 2004 06:30 AM

I am not a Logician though, I think I can answer your question:

If there is more than one sort of mental process that you call `to know', then you actually have more than one predicate.

Suppose you have two ways of `knowing', represented by K and G. Then if there is a proposition p and we do not know it, you can write:


To write that we know we do not know p, it could be:


In such case, I guess it is more difficult to build a similar paradox, but one could try it. I hope the others correct me if I said anything wrong.

Tony Marmo at April 30, 2004 07:53 AM

Yes, if we allow multiple ways of knowing, we might know in one way that we (don't) know in another way [your G(notK(p))].

But my question was (twofold) whether Fitch distinguished such multiple ways of knowing (which in Greg's paper would mean multiple ways of deriving logical consequences), and whether the paradox would hold if Fitch's interpretation of knowing was "for all ways of knowing".

That is, should we read the knowability thesis as (p)(K) (p -> <>Kp) ? And can we derive from that the paradox (p)(K) (<>K(p & -Kp)), given that that derivation also uses a particular K.

RdR at April 30, 2004 09:58 AM

As far as I understand Fitch's paradox, it assumes that there is only one kind of `known' predicate (K).

But one has to take Philosophy into account and, yeah, to know that something exists may be considered one way of knowing. To know what such thing is, to be able to define or describe it is another way or part of knowing it.

As I said before, the issue about assuming that there is p such that we do not know p is that actually we know or assume that it exists, but we cannot say what is its denotation or describe it, etc.

In many sciences it is often the case that in order to explain certain facts one has to relate them to some unknown or yet to be discovered entity, whose existence is already accepted by scientists, but which seem to lack a denotatum or cannot be defined or characterised.

Tony Marmo at April 30, 2004 11:01 AM

I think multiple ways of knowing might be a way around the paradox. Kp & K-Gp is not necessarily a paradox. For example, let's say K is "knowing theoretically" and G is "knowing empirically". I may theoretically know p and theoretically know that I don't empirically know p.

However, are multiple ways of knowing necessary?

Let's say that there is only one way of knowing. According to <>K( p & -Kp) such knowing is allowed to be higher order. But then other paradoxes seem possible. If numerals are names of sentences and K operates on sentences or names of sentences and 1 is the name of (K-1), then 1 seems paradoxical.

So, maybe we don't allow K to be higher-order. But that would imply that the first K in <>K( p & -Kp) is different (in extension at least) than the second K. So, multiple ways of knowing seem necessary.

RdR at April 30, 2004 02:43 PM

By the way, in Romance Languages we have two verbs for the English `to know':

[1] Portuguese `saber', French `savoir'


[2] Pt `conhecer', Fr `connaitre'.

The first has to do with the word `wisdom' in English and also with the kind of knowledge that enables someone to do something, i.e., the idea of `know-how'.

The second has to with the idea of `knowledge' in English and also refers to a kind of experience that is part of a collective, ie, to get a share of a common knowledge or to share knowledge.

Some people feel that the first implies `deeper knowing'. On the other hand, you may use the second to express the idea that you met someone or found something.

Tony Marmo at April 30, 2004 03:38 PM


Some French examples to illustrate the case:

(1) Je sais qu'il y a des choses inconnues. I know that there are unknown things.

(2) Je sais qu'il y a des choses que je ne connais pas. I know there are things I do not know. (The first verb is `savoir', the second is `connaitre').

Tony Marmo at April 30, 2004 04:08 PM

I'm loving the comments! What fun to have such interested and interesting readers.

A few responses. Clearly Nick is right, there's a reading of knowable according to which what is knowable is true. I'm tempted to say that this reading is a confused scope issue, resulting from the following reasoning: necessarily, what is known is true, therefore, if you can know something, it is true. But that doesn't follow at all. It's just follows that if you can know something it can be true.

Anyway, I'll add a section to the paper indicating what one can say about conjunctive knowability in the case where we say that only truths are knowable.

As to incognita , I'm not sure about what to think about this. I s'pose I'm not sure what is the best way to talk about objects of intentional attitudes in the case of complete ignorance.

Different kinds of knowledge? I think that Fitch's paradox is restatable if we talk about being known-in-any-which-way. Let's say that something is known-in-any-which-way, if it's known in way-1 or way-2 or way-3, etc. Or so suspect anyway.

Greg Restall at April 30, 2004 04:49 PM

I left a message to Kai von Fintel and friends in his weblog, sort of inviting them all to come and speak their minds. I hope he read all of this and may say something.

In one of Kai von Fintel's courses in Intentional Semantics, he explains that `to know' in English has to with a reflexive world accessibility relation:

(0) wRw

It is the only `opaque' verb that has this character in English. Thus, this should explain a sentence like (1) is odd, but (2) is ok:

(1) #Bob knows that John Howard is the Prime Minister of France.

(2) Bob assumes that John Howard is the Prime Minister of France.

You cannot fix (1) as (1'), although (2') is an option:

(1') #*Bob WRONGLY knows that JH is the PM of France.

(2') Bob WRONGLY assumes that JH is the PM of France.

But, I wished Kai von Fintel could give us more details of such analysis in the way he uses it.

Tony Marmo at April 30, 2004 05:10 PM

About knowing and linguistics: I think Germanic languages make similar distinctions. In Dutch there is "weten" and "kennen". I can say, "Ik ken Jan" (I know John) and "Ik weet logica" (I know logic), but not "Ik weet Jan". Similarly, "Ik ken logica" would sound provincial. To me "kennen" is more like "knowing by acquaintance" and "weten" is more like "knowing by learning" (some skill or fact).

About knowing-anywhich-way: Don't we still run into reflexive paradoxes? It would mean the second K in <>K(p & -Kp) would include the same knowing as the first K. That is, reflexive knowing about the sentence that asserts the knowledge. So, paradoxes like "I know I don't know this sentence" would be possible.

RdR at May 2, 2004 11:35 AM

Richard, on knowing-any-which-way, I think I misunderstood the original motivation for the distinction. I'm happy with having knowledge tout court as a disjunction of knowing1, knowing2, knowing3, etc., because I think that the knowability paradox isn't a real problem. I reckon that we non-omniscient knowers should just bite the bullet and say that some truths are not knowable in any way at all.

If you want to distinguish between different kinds of knowing as a way of saving yourself from Fitch's paradox, then you'll need to resist that conclusion, of course.

Greg Restall at May 3, 2004 04:14 PM

Oh, and some news for everyone. I've managed to get a bit further with the paper on the basis of Nick's comment that on some views of knowability, to be knowable is to be true. (So <>K pentails p.)

It turns out that if to be knowable is to be true, then (modulo some sane choices about how propositional quantification works) conjunctive knowability is inconsistent with the S4 axiom for possibility: that <><> pentails <> p. That came out of the blue for me: I didn't see that coming at all , so thanks, Nick, for pointing me in the direction of thinking about this.

If we're happy for possibility to be weak (below S4) and knowledge to be weak (also below S4), then it turns out that there are models in which at every point every proposition is conjunctively knowable, and at every point not all truths are known, so we don't have a collapse into omniscience.

I'll write this up in gory detail soon.

Greg Restall at May 3, 2004 04:23 PM

Thanks Greg, that's agreeable: I would refute Fitch's paradox on the grounds that K can't be reflexively higher-order (on pain of a version of the liar's paradox). However, each kind of knowing might be known by a different kind of knowing (higher level), which allows us to talk about knowability but escapes Fitch's paradox.

RdR at May 3, 2004 05:04 PM

The paper's been updated. The current file is version 0.85, and it contains the gory detail I mentioned above. Check paragraphs 3.11 and 5.1 to 5.8 for the really new bits.

The proof of the failure of transitivity is not as nice as I'd like it to be, but it will do for now. If I can come up with anything nicer, I'll update it again.

It needs some nice pictures, too. But that will come later. I need some sleep.

Greg Restall at May 4, 2004 12:40 AM

Yeah, version 8.5 has more pages and is clearer.

Do you intend to compare your approach with Beall (2000)?

Tony Marmo at May 4, 2004 04:07 AM

Tony: I don't intend to compare my approach with JC's (2000) account, except for my throwaway lines in paragraph 1.4. Do you think I should do more than that?

My reasons for not are that I'm presupposing that the reasoning to Fitch's conclusion is valid, I'm then reflecting on what that should tell us about knowability. It has struck me that in the case of p& ~K p, the verificationist should say that both pand ~K pare knowable, and that might be enough to be getting on with, even if the conjunction isn't knowable. The paper is an exploration of what one can do with that move.

Therefore, the kinds of moves that try to contract the propositional logic of the situation -- to make it possible that ( p& ~K p) is known -- don't appeal to me.

Of course, JC is an extremely bright guy, and one with whom I enjoy collaborating . This isn't to say that we agree on everything.

Greg Restall at May 5, 2004 10:10 AM

Well, to be honest with you, in Linguistics people always ask you to write an overview of what the others have done before you advance your own thoughts. I think it is a choire to do it in every paper. I am not doing it anymore, because journals always impose page limits.

I just asked it because I began to search Beall's paper thru the internet.

Tony Marmo at May 5, 2004 09:08 PM


As I like to work with models/situations. I think that the following has a good solution to the paradox:

Edgington, (1985) "The Paradox of Knowability" Mind 94, 557-568.

Tony Marmo at May 6, 2004 06:16 PM

By the way, a new paper by John MacFarlane on knowledge attributions might be of interest.

I haven't read it yet. I've found it thru Kai von Fintel's blog.

Tony Marmo at May 12, 2004 09:16 PM

Yes, I've downloaded Macfarlane's paper. I have skimmed through the earlier draft, and I very much like the line (on the assessment relativity of knowledge ascriptions). I'm not sure whether admitting this would change the picture markedly, or keep it pretty much the same. I should have a think about this, but I'm inclined to say that a real consideration of that is for another time and place.

Greg Restall at May 12, 2004 09:44 PM

This sentence by Gere, who also won the Foot in Mouth award by the Plain English Campaign in 2002, is of much greater philosophical interest:

`I know who I am. No one else knows who I am. If I was a giraffe and somebody said I was a snake, I'd think "No, actually I am a giraffe."'

In his post Can Derrida be ever wrong? (september 29 2003), Mark Lieberman makes the claim that Derrida's sentences are nonsensical.

He talks about a game someone played with people who took Derrida seriously. The game consisted of picking one of the long sentences of any document by Derrida and substuting antonyms for its words in order to produce variants of that sentence. Later the original sentence and its variants were presented to people who were supposed to know Derrida's works and the question was: `which sentence is the original?' He claims that Derrida's admirers were unable to establish which one was the original sentence. According to Lieberman, this suggests that Derrida's rethoric is `a sophisticated form of White Noise'.

I confess that Derrida often makes no sense to me either, regardless of whether I read him in English or French. Maybe a Plain French Campaign is in order and French Intelectuals like him should try to express themselves in plain French. But I think the nonsensical aspects of their discourse are not mere instances of odd usage of natural languages. Would Derrida make sense if he wrote his thoughts in simple and direct French????

Tony Marmo at May 16, 2004 02:36 AM


Assume that the answer is no: even if Derrida wrote in plain French his sentences would still mean nothing.

Now we have the following situation: Derrida's admirers think they know that Derrida's sentences mean something. After the game they get to know they do not know what Derrida's sentences mean. But they still assume that Derrida's sentences mean something, whereby they claim they know the sentences mean something but they do not know what their meaning is.

This is a kind of situation where claim that

(1) they know they do not know p.

But (1) is false and yet the falsity of (1) does not entail they know p.

Moreover, if on one hand (1) is false, in natural languages (2) is not the negation of (1):

(2) They do not know they do not know p.

So we go to stage after the aforesaid game was played and Derrida presents his sentences in plain French and everyone finds out that his sentences mean nothing. Now they know that (1) is false. How would one express this `change of knowledge' in a natural language? Would it be (3)?

(3) Now they know that they do not know that they do not know p.

I do not think so. I think that at the stage former admirers of Derrida get at the same conclusion as Lieberman, i.e., they come know that Derrida's sentences mean nothing, the report that would accurately depict this fact is (4):

(4) They know that not p.

Or, if one wants to be more accurate, we have three stages:

(0) They assume they know p When Derrida's sentences seem to make sense.

(1') They assume they know they do not know p. When, after the game, they find out they do not understand Derrida's sentences.

(4') They assume they know that not p. When they find out that in plain French Derrida's sentences mean nothing.

[1] Of course, here I adopt a three values system, where if one does not understand a sentence judges it undecidable and not false.

[2] In all of the aforesaid cases we have to consider that there are two propositional attitudes: `to know' and `to assume'.


The second possible answer is yeas:

yeas, if Derrida re-writes his sentences in plain French they make sense.

Now we get these stages:

(0") They assume that they know p.

When they intially think they understand Derrida's sentences.

(1") They assume they know that they do not know p.

After the game has shown them they cannot understand Derrida's sentences.

(4"a) They assume they know that p.

When finally Derrida re-writes his sentences in plain French and show what they mean. But, assuming the KK thesis, (4"b) is the other possibility:

(4"b) They assume they know that they know p.

Tony Marmo at May 16, 2004 11:52 AM

OK, version 0.95 is uploaded now. This one has pictures . (And a nice new argument, too.)

Greg Restall at May 20, 2004 01:30 AM

Dear Greg,

I have too extra questions for you.

First, I am intrigued by the fact that nobody, who insists in defining opacity as failure to apply Leibniz' substitution of identicals, has tried to relate it to Fitch's paradox. I ask if you could tell me why.

Second, is it accurate that Leibniz' Substitutivity of Identicals principle is from his work `Discourse on Metaphysics'? I could not find it there.

Tony Marmo at May 28, 2004 07:28 PM

On Tony's two questions:

I am intrigued by the fact that nobody, who insists in defining opacity as failure to apply Leibniz' substitution of identicals, has tried to relate it to Fitch's paradox. I ask if you could tell me why.

I'm not really sure why, but here's a conjecture. Most people who are interested in formal treatments of Fitch's paradox do so thinking that the formalism of modal logic is the right way to think of the inferential properties of claims to knowledge. And here, even though we have opacity, we do have substitutivity of logical equivalents in this kind of epistemic contexts. I think that this is an idealisation, but an OK idealisation here. (In the paper I talk about reading Kp as pis a consequence of what is known, and this satisfies the substitutivity of logical equivalents.)

Second, is it accurate that Leibniz' Substitutivity of Identicals principle is from his work `Discourse on Metaphysics'? I could not find it there.

I have no idea! Does anyone around here know?

Greg Restall at May 29, 2004 10:46 PM

Thank you, Greg.

I was thinking of sentences like:

(1) Jimmy knows that Superman can fly.
(2) Superman is Clark Kent.

(3) (?)Jimmy knows that Clark Kent can fly.

If Fitch's paradox is considered:

(4) The Hulk does not know that Bruce Banner is smart.
(5) Bruce Banner is the Hulk.

(6) (?) Bruce Banner knows that the Hulk does not know he is smart. (7) (??) Bruce Banner knows that he does not know that he is smart.

What do you think?

Tony Marmo at May 30, 2004 12:17 AM

Greg and all,

I'm a little slow on commenting, but thought it might be worthwhile even at this late date. I've just completed a ms. on the paradox, following up on my `95 piece on it, and have a further piece, in progress, on my website. It argues that no one can be complacent about Fitch's paradox, simply taking the Fitch's proof as presenting a somewhat surprising result. I need to make some changes to it, but here's one way to put the point. "All truths are knowable" is, if true, necessarily true. "All truths are known" is false, at least when the domain in question is finite minds, but seemingly contingently false. And yet if Fitch's proof is sound, the two claims are logically equivalent. That ought to bother everybody...

jon kvanvig at June 16, 2004 08:03 AM

On Jon Kvanvig's comment:

Yes, that bothers me. I look forward to seeing the ms. to see how the bother dissipates. It should be fun.

Greg Restall at June 17, 2004 01:04 PM

Posted by Tony Marmo at 01:32 BST
Updated: Friday, 25 June 2004 17:48 BST
Wednesday, 23 June 2004

Some Thoughts About the Relationship Between Information and Understanding

Michael O. Luke
Paper to be presented at the American Society for Information Science Conference, San Diego, CA, May 20-22, 1996

That there is a relationship between information and understanding seems intuitively obvious. If we try to express this relationship mathematically, however, it soon becomes clear that the relationship is complex and mysterious. Knowing more about the connection, however, is important, not the least because we need more understanding as our world becomes faster paced and increasingly complex. The influence of increasing the amount of information, increasing the effectiveness of information mining tools and ways of organizing information to aid the cognitive process are briefly discussed.

Introduction: Why the Relationship Matters

Those of you who are expecting to learn something definitive about the relationship between information and understanding, or to find out the results of some project investigating it, will I hope be disappointed with this talk. My subject is indeed the relationship between information and understanding, but this is not something I can tackle in any standard way. I am afraid that you are going to have to do some of the work. What you will see from me is a great deal of ignorance - great dark stretches in the map of understanding the relationship - lit up faintly, here and there with some gleams of insight (I hope you will agree that there are some gleams).

So then what is the relationship between information and understanding? And why even pose such a question? Is there really any value in considering the relationship in any detail? What am I doing even putting the two terms on the table and drawing an arrow from one to the other with a question mark after it? After all, I know only a little about information and understand not much about understanding. What can possibly justify my temerity in raising such an issue at this conference and taking up a half hour of your time dealing with it?

In my own defense, let me suggest that this is one of the most important questions that an organization like ours, contemplating at this conference, as we are, the digital future, possibly can deal with. We practice information science and call ourselves information scientists. As scientists we seek to understand - the thirst to comprehend, to know how things work is, after all, the passion that drives science, for it certainly can only be the thirst to know and not money or fame! We seek to know and we have been puzzling at it for a long time. In this century in particular we seem to have made enormous progress in understanding as our stockpiles of information have grown at a dizzying rate. As information scientists we are interested in information. How does it work?

Surely, then the question of the relationship between these two things, information and understanding, should be no stranger to us, no alien skulking unobtrusively in our midst, but a constant companion. So maybe I am the only person in this room who doesn't understand the relationship fully. I guess if so that would eminently explain why I am up here squirming. I'll tell you a little story before I embark upon the major theme. When I came actually to write this paper, having been e-mailed that the deadline was March 1, it was -40 degrees Celcius at the time, and the sun was coming through the window of my office flat, straight across the farm land, the black soil that grows the world's best durum wheat invisible beneath a heavy mantle of glaring, gleaming white. It was a cryogenic Manitoba winter morning, bright and brittle, and we consoled ourselves by saying, "but it's a dry cold" and thinking of the mosquitoes, black fly, and deer fly we didn't have right now. So putting together the presentation proposal seemed a good idea at the time!

And in fact I still believe it is. So what is the justification for raising the question in this forum? I think it is that we are not really interested in information just for its own sake, revelling merely in piling it up and moving it around. We recognize information as a means to an end. It is what it can do for us, what it has done for us, what we might do to make it do even more that drives us. And what it can do is to promote understanding and to help us acquire knowledge and give us the basis for action, for decisions, for planning and doing. Information is useful - it helps us understand and when we understand we can do useful things, like invent things, develop better strategies for business success, and we even feel better. I am richer not poorer in the face of the rising sun for understanding something about how it may have formed, for how it creates the heat and light that enable life, for knowing how long the light has been travelling before streaming through my window and I an enriched for knowing its relative insignificance in the overall scheme of things in the universe.

It isn't useful in any economic sense this particular knowledge but it helps clear up some of the mystery around me if not the brooding stuff in the background. Information above all is useful, helping education and commerce, powering art and science, driving technology and innovation before it, commerce and industry. Knowing more about the relationship should help us to exploit it more effectively.

And that's not all! My final argument is right now, at this of all times, when we seem to stand poised at the edge of a node of almost cataclysmic change, with not much help of controlling it, maybe thinking ourselves lucky if we can just survive as the storm of change breaks around us, we shall need understanding if we are to have any hope at all of avoiding the perils and steering as best we can for safer ground. Understanding then is a prescription above all for managing, if that's the word, or perhaps more realistically coping with the future, the next millennium and beyond.

I should say that some people have higher aspirations and little patience with lowly old understanding. They have loftier things in mind as the titles of their books attest: "The Wisdom of Teams", "Working Wisdom" and the "The Wisdom of Science", the latter considerably older than the others and not a bad book. Well, I have no quarrel with wisdom? If occasionaly one can stumble across it, recognize it for what it is, and use it, so much the better! I just think that realistically there is more pay dirt in the more prosaic relationship we will explore in this session.

Considering an Equation

Now one of the things that scientists do when contemplating relationships is to seek a law, typically a mathematical expression that links the phenomena in some way, a notational short hand for the force hiding in the action. E=mc2 and that sort of thing. Rarely has something so potent been expressed so economically.


Posted by Tony Marmo at 20:02 BST
Updated: Wednesday, 23 June 2004 20:10 BST

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