PhilPapers Survey: Classical or Non-Classical Logic?

For me one of the most surprising results in the PhilPapers Survey was the result of the logic question. In the target group 51.5% accept or lean towards classical logic, whereas 15.3% accept or lean towards non-classical logic. For all respondents, the distribution was: 44.3% versus 20.1%. I have seen people around the web say that they were surprised that so many accept or lean towards non-classical logic. So, let me explain why I was surprised that the numbers were not higher for non-classical logic.

First, as many commentators on the web have pointed out, philosophy undergraduate students often mistakenly believe that if you adhere to classical logic, you are required to treat corresponding English expressions accordingly, for example, they believe that you are required to treat the indicative conditional as a material conditional. Sometimes their logic teachers are responsible for inducing this belief in them. In any event, this belief often motivates undergraduate students (and some graduate students) to reject classical logic, or at least it has motivated many of my undergraduate students. What were the numbers, then, for undergraduate students? Hugely different from the target group: 37.3% accept or lean towards classical logic, whereas 26.7% accept or lean towards non-classical. But there is still a majority for classical logic.

Second, and more importantly, I would have thought that the target faculty had interpreted the question: "Logic: classical or non-classical?" as meaning "What do you believe is the correct logic for reasoning?". If you have a consistent premise-set, you will do well if you reason according to classical logic. But if you have an inconsistent belief-set, you will do terribly if you reason according to classical logic. Hence, classical logic cannot be the correct logic for reasoning in general. But perhaps the question was predominantly read as meaning: "What do you believe is the correct logic for reasoning, given a consistent premise set?". And, I am sure there are other more sophisticated ways of reading the question that can explain the attraction of classical logic.

Third, it's surprising that the numbers for the "other" category were so high. When I have talked to people in the target faculty about logic, a fair number have been sympathetic to logical pluralism. A common view is that we cannot narrow down the number of correct logics to one. But the question wasn't about whether or not we can narrow down the number of correct logics to one. The question was about whether classical or non-classical logic is correct in some respect, which was not specified. Perhaps if you are a logical pluralist, you will answer "neither". But even those who are logical pluralists could have read the question as "What do you believe is the correct logic for reasoning given some arbitrarily chosen premise set", in which case "non-classical logic" would have been an appropriate answer.

These are some of the reasons I was surprised by the results for the logic question. I want to raise a different, but not unrelated, point. At first I was very surprised that so many philosophers don't have determinate views about core issues. I think this mostly explains my errors in the metasurvey. But, on second thought, this is probably not what is going on. Rather, what is going on is that most questions have readings that will make a fair number of philosophers with determinate views say "other". The issue came up on the message board on PhilPapers discussing the surveys. David Bourget was surprised by the results for mental content. David Chalmers responded that one could hold that internalism about mental content is correct and yet think that some mental content is wide. But I bet some philosophers who hold the same views as Chalmers answered "other" to the mental content question, for this exact reason. I did not do that myself, but I considered doing it. In fact, for all of the questions, this sort of ambiguity may have explained the high numbers for the "other" category. For example, for the logic question, people might have thought that if they picked "classical", they would rule out the possibility that it sometimes might be preferable to reason in accordance with non-classical logic.

One final point: I have not yet mentioned the growing interest in the logical paradoxes as a factor. The logical paradoxes are sometimes used to motivate non-classical logic. However, it is not obvious to me that a significant number of philosophers take the paradoxes to motivate non-classical logic. Whether the paradoxes do do this is a very interesting and difficult question. It cannot be answered without saying what we mean by "correct logic". Perhaps languages come with a consequence relation. If this is so, then the Liar paradox may well be used to motivate the view that the consequence relation in English is non-classical. But there are lots of other options too. A recent attractive view is that the semantics for English, despite being inconsistent, is classically closed (variations on this view are held by, e.g. Kevin Scharp, Doug Patterson, Kirk Ludwig and Matti Eklund). Personally, I am more attracted to non-classical inconsistency views. I do not think non-classical inconsistency views entail dialetheism. I think one can take English to be inconsistent, closed under a paraconsistent consequence relation, and yet hold that all contradictions are logical falsehoods (but not logical truths). In terms of the "other" category on the survey, I suspect that if the growing interest in the paradoxes had any influence on the results at all, then it would have been in terms of placing more people in the "other" category.

SEP Entry

A new (summer 2009) edition of our Stanford Encyclopedia entry on the knowability paradox is now online.

Inconsistency Theories of Semantic Paradox

Here is a short review I just wrote of "Inconsistency Theories of Semantic Paradox".

SEP Entry

A new version of our Stanford Encyclopedia entry on the knowability paradox is now online.

Knowability Book

Joe's knowability book is becoming more real.

Call for Papers: Key Terms in Logic

CALL FOR PAPERS:

KEY TERMS IN LOGIC - Continuum
edited by Federica Russo and Jon Williamson

The book will provide short introductions (between 50 and 1000 words) to key
terms, authors and texts in logic and reasoning.

For the list of key terms, authors and texts click here.

Selected pieces will also be published in The Reasoner.

If you would like to contribute, please contact: TheReasoner@kent.ac.uk.

Relevant Consequence

Since my talk here at ANU last Thursday I have been thinking a lot about how to define 'relevant consequence'. There are various reasons why one might want a notion of relevant consequence (in addition to the standand notion of necessary consequence). For example, various attitudes are closed under some consequence relation. But they are not closed under necessary consequence. For example, 'I believe that snow is white' does not entail 'I believe that Goldbach's conjecture is true'. There is a lot of literature on how to define 'relevance'. One notion which I believe is due to (or at least inspired by) Graham Priest goes like this. q is a relevant consequence p iff q is a consequence of p, and q does not introduce any new non-logical constants (of course, it may be that new non-logical constants are introduced in the derivation of q from p, e.g. if existential elimination is applied). I like this way of defining 'relevant consequence'. But it is too strict for my purposes. I want 'I own a car' to be a relevant consequence of 'I own a Porsche', but 'car' is a new non-logical constant. So, I was thinking the following might do as a definition of 'relevant consequence'. q is a relevant consequence of p iff q is a consequence of p, and if q introduces a new non-logical constant P2, then P2 is a minimal predicate, and for some minimal predicate P1 in P, necessarily, all P1 are P2. Given this notion, 'I own a car' is a relevant consequence of 'I own a Porsche', because it is true that necessarily, all Porsches are cars. I can't think of any obvious counterexamples to this way of defining 'relevant consequence', though I am sure there are some.

PHIBOOK - The Yearbook for Philosophical Logic

The web-site for PHIBOOK is now up and running.

PHIBOOK is an annual volume devoted to philosophical logic and its relation to philosophy and science with particular emphasis on multi- agent and modal systems, active agency and social software. The yearbook is intended to inform the community of current and future directions of research and activity in philosophical logic, major events, books and important papers of the past year but also leaves extensive room for discussion in terms of columns, opinion pieces, and critical reports.

Editors:
Alexandru Baltag (Oxford)
Johan van Benthem (Amsterdam / Stanford)
Branden Fitelson (Berkeley)
Vincent F. Hendricks (Roskilde)
Hannes Leitgeb (Bristol)
Fenrong Liu (Beijing / Amsterdam)
Eric Pacuit (Stanford)
Bryan Renne (CUNY)
John Symons (El Paso)

PHIBOOK/2007 will be available in May 2008

SUBMISSIONS/DEADLINES

PHIBOOK invites authors to submit extensive survey (expositional) papers (30-50 pages) on philosophical logic (including inductive logic, modal, alethic logic, temporal logic, epistemic logic, deontic logic, conditional logic ... with special focus on multi-modal logics and active agency) and its relations to notably epistemology, methodology, philosophy of science, philosophy of language, philosophy of mind, and its applications and philosophical significance in computer science, information theory, cognitive science, mathematics, linguistics, economics and game theory ...

For more information click here.

Impossible Objects

In this eery short story from 1997 written by Graham Priest the main character finds a mysterious box in Richard Sylvan's home. The story reminded me of the importance of being intellectually unassuming. Even if classical logic is true, it is far from clear that we know that it is. As a minimum, Priest's line should bring about some doubt and maybe some intellectual modesty.

A New Solution to the Knowability Paradox

MOVING TO FRONT FROM SEP. 7

Joe Salerno has an interesting post on the knowability paradox over at Knowability. The knowability paradox is this (this is Jon Kvanvig's take on it). Suppose, for reductio, that all truths are knowable but that not all truths are known. Then there is a truth p, such that p & p is unknown. This truth is knowable. So, assuming that 'know' distributes over conjunction, it is possible that (p is known and it is known that p is unknown). So by the factivity of 'know', it is possible that (p is known and p is unknown). Contradiction. So, it is a theorem that if all truths are knowable, then all truths are known (assuming classical logic). But we also know that if all truths are known, then all truths are knowable. So, it is a theorem of classical (epistemic) logic that all truths are knowable iff all truths are known. QED.

The equivalence is prima facie puzzling. But, Joe argues, Nicholas Rescher's Epistemic Logic (2005) gives us a simple reason to believe that it is a logical truth that there are more truths than knowables. We can think only a countable number of propositions but there are uncountably many truths. So, there is nothing puzzling about the equivalence. Both sides are logical falsehoods.

Fitch, Church and Nagel Papers (Salerno)

Berit has publicly shamed me as one of her all too quiet guest bloggers. So I'm cross posting this from Knowability.

Below is a chronological catalog of archival documentation pertaining to the early history of Fitch's knowability paradox. The items were identified for the first time by myself or those aiding my research. I discuss their content in "Knowability Noir: 1945-1963", which will appear in New Essays on the Knowability Paradox.

The documents can be found in one of three archives:

(FFP) Frederic B. Fitch Papers: Manuscripts and Archives. Yale University Library.

(ACP) Alonzo Church Papers: Department of Rare Books and Special Collections. Princeton University Library.

(ENP) Ernest Nagel Papers: Rare Book and Manuscript Library. Columbia University.

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* Church, Alonzo. "First Anonymous Referee Report on Fitch's 'A Definition of Value'". January or February 1945. Hand written by Alonzo Church to Ernest Nagel, coeditor of JSL. Contains the first proof of the modal epistemic result, today known as the knowability paradox. (ENP: Box 1)

An edition of this and the second referee report (listed below) is being prepared by Julien Murzi and myself for publication in New Essays on the Knowability Paradox.

* Nagel, E. "Letter to Church: March 6, 1945". Explains that Fitch has returned the manuscript and offered replies to the first report. (ACP: Box 20)

* "Second Anonymous Referee Report on Fitch's 'A Definition of Value'". Late March or early April 1945. Includes a more formal characterization of the knowability result in Lewis and Langford's proof theory. Includes replies to Fitch's discussion of the first report. (ENP: Box 1)

* Nagel, E. "Letter to Church: April 13, 1945". Announces that Fitch has withdrawn his paper owing to a defect in his definition of value. (ACP: Box **)

* Fitch, F. "A Logical Analysis of Some Value Concepts". Fitch's December 23, 1961 Presidential Address to the Association for Symbolic Logic. (FFP: Box 33)

* Fitch, F. "A Logical Analysis of Some Value Concepts". Penultimate draft. (FFP: Box 33)

* Postcard to Fitch: January 18, 1963. Regarding remaining typographical edits to be made prior to the printing of "A Logical Analysis of Some Value Concepts" in JSL. (FFP: Box 33)