Logic and Philosophy of Logic


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Tarski’s convention T: condition beta. South American Journal of Logic. 1, 3–32.

John Corcoran and Leonardo Weber


HISTORICAL NOTE: This paper is the culmination of a years-long joint effort by the two authors. A preliminary report appeared in 2013: Corcoran-Weber, Bulletin of Symbolic Logic, 19 (2013) 510–11. Their co-operative work was conducted by email dialogue in which each author’s work was developed and corrected by the other. Each section went through several iterations. The final version was the result of dozens of reciprocal exchanges; it is impossible to allocate credit. Each author learned from and taught the other. During this time they consulted several other scholars including the Tarski experts David Hitchcock, James Smith, and Albert Visser.

The senior author expresses his deep gratitude to the junior author. Moreover the senior author acknowledges publicly what he has already said privately, viz. that without the junior author’s help and mastery of ... (read more)

REQUEST: Please send errors, omissions, and suggestions. I am especially interested in citations made in non-English publications.

Some of the entries have already been found to be flawed. For example, Tarski’s expression ‘materially adequate’ was misinterpreted in at least one article and it was misused in another where ‘materially correct’ should have been used. This “session” provides an opportunity to bring more flaws to light.


Acknowledgements: Each of these entries was presented at meetings of The Buffalo Logic Dictionary Project sponsored by The Buffalo Logic Colloquium. The members of the colloquium read drafts before the meetings and were generous with corrections, objections, and suggestions. Usually one 90-minute meeting was devoted to one entry although in some cases, for example, “axiomatic method”, took more than one meeting. Moreover, about half of the entries are rewrites of similarly named entries in the 1995 first edition.

I am trying to start a discussion for teaching INSEPARABILITY OF LOGIC AND ETHICS. A COLLEAGUE WROTE: I'm going to be teaching your "Inseparability of Logic and Ethics" in a couple weeks. I was wondering if you had any tips on doing so or thoughts about points to emphasize. I've always loved the paper and found your pedagogical techniques quite helpful.
MY ADVICE TO MY COLLEAGUE: First, before assigning the paper to be read, ask the students to look up “ethics” and “logic” in a dictionary or other reference work and then to write a paragraph on what the two have to do with each other. Second, after the students were supposed to have read the paper, ask them what they got out of it. Just let them talk and prompt them where necessary. No contentiousness. Third, read the first page aloud to them and see what happens. As you go read chunks aloud and ask questions—just like I did teaching you Tarski’s truth-definition paper. Fourth, go around the clas ... (read more)



Corcoran’s 2009 ARISTOTLE’S DEMONSTRATIVE LOGIC deals decisively with several issues that had previously been handled by vague speculation and dogmatic pontification if at all. One possible example: Corcoran [2009, p. 13] proves conclusively that the imperfect syllogisms Baroco and Bocardo—which Aristotle completed indirectly [by reductio-ad-impossible]—cannot be completed directly. More generally, Corcoran shows that no valid premise-conclusion argument, regardless of the number of premises,  having an existential negative [“particular negative” or “O-proposition”] as a premise can be completed using a direct deduction—assuming of course that no premises are redundant and that the conclusion is not among the premises. To be clear this means that for no such argument is it possible to deduce the conclusion from the premises without using reductio.

This result, called the EXISTENTIAL-NEGATIVE EXCLUSION [ENE], was circulated informally by Corcoran much earlier but it seem ... (read more)


JOHN CORCORAN AND HASSAN MASOUD, Three-logical-theories redux.

  The 1969 paper, “Three logical theories” [1], considers three logical systems all based on the same interpreted language and having the same semantics.

  The first, a logistic system LS, codifies tautologies (logical truths)—using tautological axioms and tautology-preserving rules that are not required to be consequence-preserving.

  The second, a consequence system CS, codifies valid premise-conclusion arguments—using tautological axioms and consequence-preserving rules that are not required to be cogency-preserving [2]. A rule is cogency-preserving if in every application the conclusion is known to follow from its premises if the premises are all known to follow from their premises.

  The third, a deductive system DS, codifies deductions, or cogent argumentations [2]—using cogency-preserving rules. The derivations in a DS represent deduction: the process by which conclusions are deduced from premises, i. e. the way knowl ... (read more)


JOHN CORCORAN, Two-method errors.

  Where there are two or more methods for the same thing, sometimes errors occur if two are mixed. Two-method errors, TMEs, occur in technical contexts but they occur more frequently in non-technical writing. Examples of both are cited.

  We can say “Abe knows whether Ben draws” in two other ways: ‘Abe knows whether or not Ben draws’ or ‘Abe knows whether Ben draws or not’. But a TME occurs in ‘Abe knows whether or not Ben draws or not’.

  We can say “Abe knows how Ben looks” using ‘Abe knows what Ben looks like’. But a TME occurs in ‘Abe knows what Ben looks’ and also in ‘Abe knows how Ben looks like’. Again, we can deny that Abe knows Ben by prefixing ‘It isn’t   that’ or by interpolating ‘doesn’t’. But a TME occurs in trying to deny that Abe knows Ben by using ‘It isn’t that Abe doesn’t know Ben’.

  There are two standard ways of defining truth for first-order languages: using finite sequences or infinite sequences. Quine’s discussion in the 1970 first ... (read more)


► JOHN CORCORAN AND WILLIAM FRANK, Cosmic Justice Hypotheses.

  This applied-logic lecture builds on [1] arguing that character traits fostered by logic serve clarity and understanding in ethics, confirming hopeful views of Alfred Tarski [2, Preface, and personal communication].

  Hypotheses in one strict usage are propositions not known to be true and not known to be false or—more loosely—propositions so considered for discussion purposes [1, p. 38].

   Logic studies hypotheses by determining their implications (propositions they imply) and their implicants (propositions that imply them). Logic also studies hypotheses by seeing how variations affect implications and implicants. People versed in logical methods are more inclined to enjoy working with hypotheses and less inclined to dismiss them or to accept them without sufficient evidence.

  Cosmic Justice Hypotheses (CJHs), such as “in the fullness of time every act will be rewarded or punished in exact proportion to its goodness or badness ... (read more)

Are there contemporary philosophers who argue that logic is concrete and particular? (More precisely I think the view would have to be that logics are concrete particulars.)

I'm toying with the idea of advancing that thesis, and I'm sure I'm not the first or only person to think this. But I don't know much about the field and in particular don't know what the relevant names would be.
Any help here would be appreciated.

Latest replies: Permanent link: http://philpapers.org/post/8519 Reply

Hi Jack,

Nice paper!. However, if I may, I wasn't convinced by your response to objection five. The objection, I take it, is that the intuitions you are marshaling about incoherence derive from a non-moral standpoint, that is, they are intuitions that arise when one is doing metaethics and not when one is actually moralizing.  And it seems undeniable that Moore paradoxical sentences are straightforwardly bizarre when uttered by persons in the context of actual moralizing (just imagine actually having the relevant conversation). At the outset of your paper, you correctly note that expressivism is a theory about actual moralizing, so it seems like this is one objection to which you should be very sensitive.  You respond:

This is not really a rejection of C3, but a rejection of C1, since it admits that it is not always the case that affective or conative attitudes are expressed by moral assertions. If non-cognitive mental states are only sometimes expressed by moral assertions, then the clai ... (read more)

Latest replies: Permanent link: http://philpapers.org/post/7909 Reply

Reification is considered a fallacy but why is so little written on this topic? Specifically,
I am interested in the reification of terms such as Being, Nothingness (in Sartre's work) and especially in Heidegger's Being and Time. I agree with the critics who argue that these terms, and much of these books are exemplary examples of reification. Can one then argue that existentialism and some phenomenology are extensively fallacious? Defenders of  Heidegger, Sartre, Marcel and others would say that analytic reason is inapplicable to their philosophies, but I think this is nonsense.
Latest replies: Permanent link: http://philpapers.org/post/7859 Reply

Your article is very interesting.

In the same spirit I propose a more modal formalism to speak about "true announcements" and "learning" : http://philpapers.org/rec/MARFPS

This representation allow to make the difference between a world before and after the learning act. Then it becomes easier to deal with expression about knowledge and learning.


Your work is technically very interesting neverthless I have some remarks.

1/ I don't always understand the claim that the Fitch Paradox threatens Anti-Realist philosophy.
If everybody accepts the Knowability Principle restricted to basic propositions,
it sounds more like a victory than a defeat for the knowability advocates.
It seems that what is threatened is more the capacity of modal logic to represent the knowability.

2/ In your intuitionistic frame, as you say in proposition 5.8, it is impossible to have 'A' and 'not K A' in the same world.
So the Fitch Paradox is avoided but the result is a very poor epistemic logic where you cannot express that some truths are unknown.

3/ more technically in the figure below the proposition 5.7
I don't understand what happens in the world y.
You have      y Rk y ;    y Rk z ;    y: p   z: not p
but you have not    'y: not K p' .
Does it stand that 'y: not not K p' ?
It is very counterintuitive.

Else I wrote a dissertation on these points.
I have published a - maybe insufi ... (read more)

I have a question...

A classical, Tarskian system standardly contains homophonic definitions as the base clauses, e.g.,

'G' denotes Gs.

This is understood to be a sentence of the metalanguage (ML) which defines a predicate of the object language (OL). And when ML contains OL, the standard assumption is that the expression 'G' used on the right-hand side is identical to the expression mentioned on the left...so that numerically one expression, 'G', is an expression of both ML and of OL.

However, if homophonic definitions are admissible, then (given the compositionality of negation) the following sentence also seems admissible into the system as a definition:

'G' denotes x iff x is ~G.

But such an interpretation suffices for paradox in OL. For instance,  'Socrates is G' will be true in OL iff it is not true in OL (contra PNC). So apparently the second definition is not admissible in a classical system. But (again by the compositionality of negation) that means the former cannot b ... (read more)
Latest replies:
  • Panu Raatikainen, 2012-05-14 : Yes, it can... The essential point is that languages in the Tarskian setting must be interpreted languages. Hence, if yo... (read more)
  • T. Parent, 2012-05-15 : Thanks very much Panu! I will read your paper in the next few days. I will post again if furBest, Ted
  • T. Parent, 2012-06-10 : Dear Panu (and anyone else who may be reading), I enjoyed your paper very much. Your most helpful thought was the one yo... (read more)
Permanent link: http://philpapers.org/post/6843 Reply


Please could someone help me with the above question.

For example, is there a difference between the propositions:

Edinburgh is the capital of Scotland.


The proposition 'Edinburgh is the capital of Scotland' is true.

Given that the second proposition is a proposition about the first proposition, it seems to me that they can't be the same proposition.

Latest replies: Permanent link: http://philpapers.org/post/6699 Reply

Here's an argument that you can't suppose the Liar, where the Liar is, basically, "this very sentence is false."

If you can't suppose the liar, then one common way of setting forth the argument leading to paradox won't work--since it requires you to suppose the liar.

(It's more common, probably, for it to require you to suppose the liar is true. Whether the below argument successfully extends to that supposition isn't something I've thought through yet.)

What do you think of the argument?

I worry about line 4. What do we know (or what do different people think they know) about how to individuate thoughts?

Should I be worrying about any of the other three premises?

Thanks for any comments. It's outside my field (as you can probably tell!) and doesn't really engage directly, as far as I can see, with any of the technical material people usually (need to) discuss when dealing with the liar paradox--which is probably a bad thing I'm afraid.

1.   A =­def  A is false. (definition)<?xml:namespace prefi ... (read more)

Latest replies: Permanent link: http://philpapers.org/post/6649 Reply

notation : I use ! for 'not'

Perhaps you can avoid paradox but you have to admit this very strange proposition :
K !K x ->  !P K x
If you know that you ignore (x) it's impossible that you know (x)

I don't see how it could be compatible with the knowability principle :
x ->  P K x
else you can't have
(x) and (K !K x)

(excuse me if this message is out of place, I ignore the policy of tis forum,
excuse also my probable mistakes in english)
Latest replies: Permanent link: http://philpapers.org/post/6605 Reply


coming from a bioinformatics background (aiming to represent the argumentative structure of research publications) I seek advice to clarify the concepts "argument" and "conditional".

Can these concepts, along with premise/antecedent and conclusion/consequent, interchangeably be used or are there actual differences in definition, meaning and/or use of these terms?

I'd be grateful for any advice on this and direction to relevant sources.

Latest replies: Permanent link: http://philpapers.org/post/5595 Reply

This is awesome. Tractatus power!

I'm currently a postgraduate studying philosophy of mind. I have studied logic, but only at undergraduate level, and it was over 30 years ago. So I apologise for the probable naivety of this question.
I'm going to take the liberty of quoting from Melvin Bragg's email newsletter about a radio programme on logic hosted by him, broadcast yesterday on the UK station BBC Radio 4. In a post-programme discussion between the participants,

A C Grayling, usually more slicingly exact than a Gillette razor, defended vagueness in the following terms: if he rushed into a bedroom at two o’clock in the morning and shouted “Fire!” this could open a wide range of possibilities for any logical person.  Was he talking about a candle being lit downstairs?  Was he talking about something that had happened in another place?  But we mere mortals would be vague enough to understand that the house was ablaze and rush out.  Something to be said for vagueness then. (Melvyn Bragg's In Ou ... (read more)
Latest replies: Permanent link: http://philpapers.org/post/4883 Reply

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