Tag: philosophy

What Could Be the Most Basic Logic?

Bas van Fraassen1 Comment

It was only in the 19th century that alternatives to Euclidean geometry appeared.  What was to be respected as the most basic geometry for the physical sciences: Euclidean, non-Euclidean with constant curvature, projective?  Frege, Poincare, Russell, and Whitehead were, to various degrees, on the conservative side on this question.>[1]  

In the 20th, alternatives to classical logic appeared, even as it was being created in its present form.  First Intuitionistic logic, then quantum logic, and then relevant and paraconsistent logics, each with a special claim be more basic, more general in its applicability, than classical logic.

Conservative voices were certainly heard.  John Burgess told his seminars “Heretics in logic should be hissed away!”.  David Lewis described relevant and paraconsistent logic as logic for equivocators.  The other side was not quiet.  Just as Hans Reichenbach gave a story of coherent experience in a non-Euclidean space, so Graham Priest wrote a story of characters remaining seemingly coherent throughout a self-contradictory experience.

Unlike in the case of Euclidean geometry, the alternatives offered for propositional logic have all been weaker than classical logic.  So how weak can we go?  What is weaker, but still sufficiently strong, to qualify as “the” logic, logic simpliciter? 

I am very attracted to the idea that a certain subclassical logic (FDE) has a better claim than classical logic to be “the” logic, the most basic logic.  It is well studied, and would be quite easy to teach as a first logic class. Beall (2018) provides relevant arguments here – the arguments are substantial, and deserve discussion.  But I propose to reflect on what the question involves, how it is to be understood, from my own point of view, to say why I find FDE attractive, and what open questions I still have.

1.      A case for FDE

The question what is the most basic logic sounds factual, but I cannot see how it could be.  However, a normative claim of the form

Logic L is the weakest logic to be respected in the formulation of empirical or abstract theories

seems to make good sense.  We had the historical precedent of Hilary Putnam’s claiming this for quantum logic.  I will come back to that claim below, but I see good reasons to say that FDE is a much better candidate.

2.      Starting a case for FDE

FDE has no theorems.  FDE is just the FDE consequence relation, the relation originally called tautological entailment, and FDE recognizes no tautologies.  Let us call a logic truly simple if it has no theorems.

To be clear: I take L to be a logic only if it is a closure operator on the set of sentences of a particular syntax.  The members of L(X) are the consequences of X in L, or the L-consequences of X; they are also called the sentences that X entails in L.  A sentence A is a theorem  of L iff A is a member of L(X) for all X.  The reason why FDE has no theorems is that it meets the variable-sharing requirement: that is to say, B is an L-consequence of A only there is an atomic sentence that is a component of both B and A.

So the initial case for FDE can be this: it is truly simple, as it must be, because

logic does not bring us truths, it is the neutral arbiter for reasoning and argumentation, and supplies no answers of its own. 

To assess this case we need a clear notion of what counts as a logic (beyond its being a closure operator), and what counts as supplying answers.  If I answered someone’s question with “Maybe so and maybe not”, she might well say that I have not told her anything.  But is that literally true?  A. N. Prior once made a little joke, “What’s all the fuss about Excluded Middle?  Either it is true or it is not!”.  We would have laughed less if there had been no Intuitionistic logic.

3.      Allowance for pluralism

My colleague Mark Johnston like to say that the big lesson of 20th century philosophy was that nothing reduces to anything else.  In philosophy of science pluralism, the denial that for every scientific theory there is a reduction to physics, has been having a good deal of play.

As I mentioned, FDE’s notable feature is the variable-sharing condition for entailment.  If A and B have no atomic sentences in common, then A does not entail B in FDE.  So to formulate two theories that are logically entirely independent, choose two disjoint subsets of the atomic sentences of the language.  Within FDE, theories which are formulated in the resulting disjoint sublanguages will lack any connection whatsoever.    

4.      Could FDE be a little too weak?

The most conservative extension, it seems to me, would be to add the falsum, ⊥.  It’s a common impression that adding this as a logical sign, with the stipulation that all sentences are consequences of ⊥, is cost-less.  

But if we added it to FDE semantics with the stipulation that ⊥ is false and never true, on all interpretations, then we get a tautology after all: ~⊥.  The corresponding logic, call it FDE+, then has ~ ⊥ as a theorem.   So FDE+ is not truly simple, it fails the above criterion for being “the” logic.  Despite that common impression, it is stronger than FDE, although the addition looks at once minimal and important.  Is FDE missing out on too much?

How should we think of FDE+?  

Option one is to say that ⊥, a propositional constant, is a substantive statement, that adding it is like adding “Snow is white”, so its addition is simply the creation of a theory of FDE.

Option two is to say that FDE+ is a mixed logic, not a pure logic.  The criterion I would propose for this option is this:

A logic L defined on a syntax X is pure if and only if every syntactic category except that of the syncategoremata (the logical and punctuation signs) is subject to the rule of substitution.

So for example, in FDE the only relevant category is the sentences, and if any premises X entails A, in FDE, then any systematic substitution of sentences for atomic sentences in X entails the corresponding substitution in A.  

But in FDE+ substitution for atomic sentence ⊥ does not preserve entailment in general.  Hence FDE is a pure logic, and FDE+ is not.

The two options are not exclusive.  By the usual definition, a theory of logic L is a set of sentences closed under entailment in L.  So the set of theorems of FDE+ is a theory of FDE.  However, it is a theory of a very special sort, not like the sort of theory that takes the third atomic sentence (which happens to be “Snow is white”) as its axiom.  

Open question: how could we spell out this difference between these two sorts of theories?  

5.      Might FDE be too strong?

FDE is weak compared to classical logic, but not very weak.  What about challenges to FDE as too strong?  

It seems to me that any response to such a challenge would have be to argue that a notion of consequence weaker than FDE would be at best a closure operator of logical interest.  But the distinction cannot be empty or a matter of fiat.

Distributivity

The first challenge to classical logic that is also a challenge to FDE came from Birkhoff and von Neumann, and was to distributivity.  They introduced quantum logic, and at one point Hilary Putnam championed that as candidate for “the” logic.  Putnam’s arguments did not fare well.[2]  

But there are simpler examples that mimic quantum logic in the relevant respect.

Logic of approximate value-attributions  

Let the propositions (which sentences can take as semantic content) be the couples [m, E], with E  an interval of real numbers – to be read as “the quantity in question (m) has a value in E”.

The empty set 𝜙 is counted as an interval.  The operations on these propositions are defined:

[m, E]  ∧ [m, F] = [m, E ∩ F]

[m, E]  v [m, F]  =  [m, E Θ F], 

where E Θ F the least interval that contains E ∪ F

Then if E, F, G are the disjoint intervals  (0.3, 0.7), [0, 0.3], and [0.7, 1],  

[m, E]  ∧ ([m, F] v [m, G]) = [m, E] ∧ ([ m, [0,1]]  = [m, E]

([m, E]  ∧ ([m, F]) v ([m, E]  ∧ ([m, G]) = [m, 𝜙]

which violates distributivity.

This looks like a good challenge to distributivity if the little language I described is a good part of our natural language, and if it can be said to have a logic of its own.

The open question:  

if we can isolate any identifiable fragment of natural language  and show that taken in and by itself, it has a logical structure that violates a certain principle, must “the” logic, the basic logic, then lack that principle?

Closure and conflict

We get a different, more radical, challenge from deontic logic.  In certain deontic logics there is allowance for conflicting obligations.  Suppose an agent is obliged to do X and also obliged to refrain from doing X, for reasons that cannot be reconciled.  By what logical principles do these obligations imply further obligations?  At first blush, if doing X requires doing something else, then he is obliged to do that as well, and similarly for what ~X requires.  But he cannot be obliged to both do and refrain from doing X: ought implies can.

Accordingly, Ali Farjami introduced the Up operator.  It is defined parasitic on classical logic: a set X is closed under Up exactly if X contains the classical logical consequences of each of its members.  For such an agent, caught up in moral conflict, the set of obligations he has is Up-closed, but not classical-logic closed.

If we took Up to be a logic, then it would be a logic in which premises A, B do not entail (A & B). Thus FDE has a principle which is violated in this context.

To head off this challenge one reposte might be that in deontic logic this sort of logical closure applies within the scope of a prefix.  The analogy to draw on may be with prefixes like “In Greek mythology …”, “In Heinlein’s All You Zombies …”.  

Another reposte can be that FDE offers its own response to the person in irresolvable moral conflict.  He could accept that the set of statements A such that he is obliged to see to it that A, is an FDE theory, not a classical theory.  Then he could say: “I am obliged to see to it that A, and also that ~A, and also that (A & ~A).  But that does not mean that anything goes, I have landed in a moral conflict, but not in a moral black hole.”

Deontic logic and motivation from ethical dilemmas only provide the origin for the challenge, and may be disputed.  Those aside, we still have a challenge to meet.

We have here another departure from both classical logic and FDE in and identifiable fragment of natural language.  So we have to consider the challenge abstractly as well.  And it can be applied directly to FDE.

Up is a closure operator on sets of sentences, just as is any logic.  Indeed, if C is any closure operator on sets of sentences then the operator

Cu:   Cu(X) = ∪{C({A}): A in X}

is also a closure operator thereon.  (See Appendix.)

So we can also ask about FDEu.  Is it a better candidate to be “the” logic?  

FDEu is weaker than FDE, and it is both pure and truly simple.  But it sounds outrageous, that logic should lack the rule of conjunction introduction!

6.      Coda

We could give up and just say: for any language game that could be played there is a logic – that is all.

But a normative claim of form

Logic L is the weakest logic to be respected in the formulation of empirical or abstract theories

refers to things of real life importance.  We are not talking about just any language game.  

Last open question:  if we focus on the general concept of empirical and abstract theories, can we find constraints on how strong that weakest logic has to be?

FDE is both pure and truly simple. Among the well-worked out, well studied, and widely applicable logics that we already have, it is the only one that is both pure and truly simple.  That is the best case I can make for it so far.

7.      APPENDIX

An operator C on a set X is a closure operator iff it maps subsets of X to subsets of X such that:

  1. X ⊆ C(X)
  2. CC(X) = C(X)
  3. If X ⊆ Y then C(X) ⊆ C(Y)

Definition.  Cu(X) = ∪{C({A}): A in X}.  

Proof that Cu is a closure operator:

  •  X ⊆ Cu(X).  For if A is in X, then A is in C({A}), hence in Cu(X).
  •  CuCu (X) = Cu(X).  Right to left follows from the preceding.  Suppose A is in CuCu (X).  Then there is a member B of Cu(X) such that A is in C({B}), and a member  E of X such that B is in C({E}). Therefore A is in CC({E}).  But CC({E}) = C({E}), so A is in  Cu(X).  
  • If X ⊆ Y then Cu(X) ⊆ Cu(Y).  For suppose X ⊆ Y. Then {C({A}): A in X} ⊆ {C({A}): A in Y}, so Cu(X) ⊆  Cu(Y).

8.      REFERENCES

Beall, Jc. (2018) “The Simple Argument for Subclassical Logic”. Philosophical Issues.

Cook, Roy T.  (2018) “Logic, Counterexamples, and Translation”.  Pp. 17- 43 in Geoffrey Hellman and Roy T. Cook (Eds.) (2018) Hilary Putnam on Logic and Mathematics.  Springer.

Hellman, Geoffrey (1980). “Quantum logic and meaning”. Proceedings of the Philosophy of Science Association 2: 493–511.

Putnam, Hilary (1968) “Is Logic Empirical” Pp. 216-241 in Cohen, R. and Wartofsky, M. (Eds.). (1968). Boston studies in the philosophy of science (Vol. 5). Dordrecht.   Reprinted as “The logic of quantum mechanics”. Pp. 174–197 in Putnam, H. (1975). Mathematics, matter, and method: Philosophical papers (Vol. I). Cambridge.

Russell, Bertrand (1897) An Essay on the Foundations of Geometry. Cambridge.

NOTES

[1] For example, Russell concluded that the choice between Euclidean and non-Euclidean geometries is empirical, but spaces that lack constant curvature “we found logically unsound and impossible to know, and therefore to be condemned a priori (Russell 1897: 118).

[2] See Hellman (1980) and Cook (2018) especially for critical examination of Putnam’s argument.

The curious roles atomic sentences can play (1)

Bas van FraassenLeave a comment

[A reflection on papers by Hiz and Thomason, listed at the end.  Throughout I will use my own symbols for connectives, to keep the text uniform.]

Atomic sentences, we say, are not a special species.  They could be anything; they are just the ones we leave unanalyzed.  What we study is the structures built from them, such as truth-fuctional compounds.

But that innocuous looking “They could be anything” opens up some leeway.  It allows that the atomic sentences could have values or express propositions that the complex sentences cannot.  I will discuss two examples of how this leeway can be exploited for proofs of incompleteness.

The story I want to tell starts with a small error by Paul Halmos in 1956.

Halmos and Hiz

 In his 1956 paper Paul Halmos wanted to display the classical propositional calculus with just & and ~ as primitive connectives.  (Looks familiar, what could be the problem?)  As guide he took the presentation in Hilbert and Ackermann, with v and ~ as primitives. For brevity and ease of reading they had introduced “x ⊃ y” as abbreviation for “~x v y”.

  1. (x v x) ⊃ x
  2. x ⊃ (x v y)
  3. (x v y) ⊃ (y v x)
  4. (x v y) ⊃ (z v x . ⊃ . z v y )

Knowing how truth functions work, Halmos (1956: 368) treated “x v y”  as abbreviation of “~(~x & ~y)” and “x ⊃ y” as abbreviation of “~(x & ~y), to read Hilbert and Ackermann’s axioms. That means that his formulation, with ~ and & primitive, was this:

  1. ~[~(~x & ~y) & ~x]
  2. ~[x & ~~(~x & ~y)]
  3. ~[~(~x & ~y) & ~~(~y & ~x)]
  4. ~[~(~x & ~y) & ~[~[~(~z & ~x) & ~~(~z & ~y)]]]

But, unlike what it translates (Hilbert and Ackermann’s), this set  of axioms is not complete!

Henryk Hiz (1958) showed why not.  (He mentioned that Halmos had raised the possibility himself in a conversation, and Rosser had done so as well, in a letter to Halmos.)

Let’s look for a difference in the roles of atomic sentences and of complex sentences in Halmos’ axiom set.  What springs to the eye in Axiom b. is that there is an occurence of x that is preceded by ~, and one that is not so preceded but ‘stands by itself’.  So we can make trouble by allowing an atomic sentence x to take values that a negated sentence ~x cannot have.  

That is what Hiz does, with this three-valued truth-table where an atomic sentence x could have value 1, 2, or 3, but ~x can only have values 1 or 3. 

(He writes A and N for my  & and ~.) 

So if x has value 2 then ~(~x & x) has value ~ (~2 & 2) = ~(1 & 2) = ~1 = 3, which is not designated.  So there is a classical tautology, the traditional Non-Contradiction Principle, that does not receive a designated value.  

In this three-valued logic neither conjunction nor negation behaves classically, but all of Halmos’ axioms have the designated value 1.  So his formulation of classical sentential logic is sound but not complete.

Thomason

Thomason’s (2018) argument and technique, which I discussed in a previous post, were very close to Hiz’, but applied to modal logic.

In modal logic the basic K axiom can be formulated in at least these three ways:

  1. □(x ⊃ y) ⊃ (□x ⊃ □y)
  2. ◊(x v y) ≡  (◊x v ◊y)
  3. ~◊~(x ⊃ y) ⊃ (~◊~x ⊃ ~◊~y)

The third is a translation of the first with “□” translated as “~◊~”.  In the previous post (“Is Possiblity-Necessity Duality Just a Definition”, 07/17/2025) I explained Thomason’s model in which that third formulation of K is satisfied, but the Duality principle is shown to be independent.  Here I will show that satisfaction of Axiom (iii) is compatible with a violation of Axiom (ii). 

Thomason presented a model with 8 values for the propositions.  I’ll use here the smaller 5-valued model which I described in the post. My presentation here, in a slightly adapted form, is sufficient for our purpose.  

This structure (matrix)is made up of the familiar 2-atom Boolean lattice B = {T, 1, ~1, ⊥} with the addition of an ‘alien’ element k.  The meet and join on B are operators ∧ and  +. The operator ~ is the usual complement on on B.  The only designated element is T.

To extend the operators to the alient element, we set ~k = ~1.  So x can take any of the five values but ~x can only have a value in B.

What about the joins and meets of elements when one of them is alien?  They are all in B too, with these definitions:

Define.  x* = ~~x, called the Twin of x.  (Clearly x = x* except that k* = 1.) 

Define.  For any elements x and y:   x & y = x* ∧ y*, and x v y = x* + y*.

Finally the possibity operator is defined by: ◊x = T iff x = 1 or T;  ◊x =  ⊥ otherwise.  

Instances of Axiom (iii.) always get the desigated value (by inspection; note that every non-modal sentential part starts with ~). 

But in Axiom (ii) we see the leeway, due to the fact that x can be any element.  The negation, join, or meet of anything with anything can only take values in B.  So Axiom (ii) does not always get a designated value, for if we set x = y = k, we get the result:

◊(k v k) = ◊(k* + k*) = ◊1 = T

(◊k v ◊k) =  ⊥* +  ⊥* =  ⊥

In Thomason’s article this technique is used to show that with formulation (iii) of K, the duality ¬◊¬x = □x is independent, and needs to be added as an axiom rather than a definition.  

Axiom (ii.), with the attendant rules changed mutatis mutandis, and the Duality introduced as a definition, is a complete formulation of system K (cf. Chellas 1980: 117, 122).  A formulation that has Axiom(iii) instead of Axiom (ii) is not.  

Hiz’ warning was well taken.

References

Chellas, Brian F. (1980) Modal Logic: An Introduction. Cambridge.

Hiz, Henryk  (1958) “A Warning about Translating Axioms”. Am. Math. Monthly 65: 613-614.

Thomason, Richmond H. (2018) “Independence of the Dual Axiom in Modal K with Primitive  ◊”.  Notre Dame Journal of Formal Logic 59: 381-385.

Feyerabend and Sellars on Language and Experience

Bas van FraassenLeave a comment
  • 1.         Feyerabend on experience and its reports      1
  • 2.         Severing meaning from use    2
  • 3.         Interpretation  2
  • 4.         Theory-laden-ness of natural language          4
  • 5.         What could interpretation be then?    5
  • 6.         The contemporaneous debates about meaning           5
  • 7.         Wilfrid Sellars on meaning    6
  • 8.         Application to Feyerabend’s account 8
  • 9.         CODA: What is my language?           9

When someone in that crowded theatre shouted “Phlogiston escaping!” we knew that it was false, but of course we ran out at once.

This is a good example to illustrate Paul Feyerabend’s pragmatic theory of observation, as I will explain below.  Feyerabend did leave some questions unanswered.  Thinking about those questions led me to something that I had found perplexing, in Wilfrid Sellars’ correspondence with Roderick Chisholm about intentionality.  

1.         Feyerabend on experience and its reports

When Paul Feyerabend presented his “Attempt at a realistic interpretation of experience” to the Aristotelian Society in February 1958, much of the new scientific realism was already in place.[1] While Feyerabend presents his ideas in an explicit, detailed critique of positivist views of science and experience, we can (and his peers then could) proceed at once to his positive contribution.

This begins with a presentation of the pragmatic theory of observation, which is in the first place about what counts as an observation language.[2]  There are four pragmatic conditions for observation reporting, that we can summarize (using Feyerabend’s own terms) as:

Definition. L is an observation language for a community C of observers, set S of situations, and set A of sentences of L exactly if there is a function F (‘association’) which maps S into the powerset of A, such that given a situation s in S, the members of C are able to come to a quick unanimous decision about whether to accept to reject the sentences in the set F(s), and their acceptance of any of these sentences in F(s) is a reliable indicator of their being in situation s.[3]   

These conditions include nothing at all about the meaning of those sentences.  The role of observation report is entirely separated from any reference to meaning or reference.  

2.        Severing meaning from use

Suppose that in community C the utterance of p is a reliable indicator of the presence of fire to the utterer.  The syntax of p is irrelevant:  p can be learned to have this use by conditioning.  It could be “boojum!” or “fire!” or “phlogiston escaping!” or “rapid oxidation!”.  

“Observability is a pragmatic concept” (Feyerabend 1958:146).  That is, it is a concept that belongs to the analysis of the conditions and contexts of the use of language.  The distinction is Charles Morris’: in semantics we abstract from use, to concentrate on the word-world relation, while in pragmatics the relation studied is three-fold: word, world, user.  

In observation reportage, humans function as measuring instruments.  Perhaps in your car, a red light goes on if and only if the engine is overheating.  There is no logical connection between the color of the light and the temperature of the engine.  But if the light goes on and I ask you “what does that mean?” or “what does that signify?” you will answer “that the engine is overheating”. 

When this little dialogue is transposed, from measurement output to observation reportage, it becomes an example of what Feyerabend calls interpretation.

3.        Interpretation

For L to be not just an observation language but a fully-fledged observation language, Feyerabend submits, it must have an interpretation which determines what its sentences “are supposed to assert” (Feyerabend 1958: 145-46).  

As mentioned above, in making an observation, an organism is acting as a measuring instrument:

“What the observational situation determines (causally) is the acceptance or the rejection of a sentence, i.e. a physical event. In so far as this causal chain involves our own organism we are on a par with physical instruments. But we also interpret the indications of these instruments … and this interpretation is an additional act.” (Feyerabend 1958: 146)

How is that done?  Suppose again that that in community C the utterance of p is a reliable indicator of the presence of situation s to the utterer.  When you, who may or may not be a member of C, interpret that utterance of p, you will describe situation s in your own language, and in accordance with your assumptions, presuppositions, theories, and linguistic practices of the community to which you belong.

Accordingly, examples of interpretation must take the following sort of form:

[1] Observers in community C reliably reliably agree to “Phlogiston is escaping” in the presence of fire and reject it in the absence of fire.

[2] Observers in community C reliably agree to “There is fire” in the presence of phlogiston escaping and reject it in the absence of phlogiston escaping.

[3] Observers in community C reliably agree to “Phlogiston is escaping” in the presence of rapid oxidation, and reject it in the absence of rapid oxidation.

Could any of this be said by a member of community C?  

Yes, in the case of [1] or [2], and definitely not in the case of [3].  So in each case we have to take into account who could offer such an interpretation, and what language that person would be speaking.

I think this important, and to be emphasized:  to understand [1]-[3] properly we must in each case imagine ourselves inside the community – possibly, but not generally community C – where we make the statement, or are addressed by someone making that statement.  For in each case the imagined speaker takes for granted or presupposes that the addressees understand the words used to describe the relevant situation.  More: the speaker takes for granted that the addressees would describe those situations in the same way.   

Speakers in a given community report on their experience, by means of words which may apply either correctly or incorrectly (or not be descriptive at all) to what they are actually experiencing.  This is very far from the idea that the semantic content of the observation report describes anything like an immediately, unmediated content of the ‘given’.

Standing outside a certain community we say that they reported reliably on an experience, which they most certainly had, by asserting that there was a phlogiston escape.  They took it to be that.  In that case, how can we think of observation reports as providing the data to which our theories are accountable?

In philosophy of language elsewhere the corresponding question was: how could there be successful reference by means of a false description?  The response was a turn from semantics to pragmatics. On Russell’s theory of descriptions, the phrase “the so-and-so” denotes entity x if and only if x is so-and-so and nothing else is so-and-so.  Keith Donnellan (1966) argued that we may keep the term “denote” for this, but then must recognize another use for which he offered the term “refer”.  That is, someone may use “the so-and-so” to denote what that phrase denotes (whenever it denotes anything), but will be  using it to refer to something which it does not denote, when the conditions are felicitous for that use. 

Plausible ordinary examples abound. For example, there is in the room exactly one man who appears to be drinking a martini, and in discussing him we refer to him as “the man with the martini”.  Our communication about him may be entirely successful, all (or most of) we say about him may be true, although in fact what is in his glass is just water.  David Lewis offered an especially nice example:  “Help me, Stephanie, the cat is fighting with the other cat again!”  In this example the phrase “the cat” does not actually denote anything, but Lewis used it successfully to refer to a specific cat –  a cat he falsely described as being the only cat there! – nevertheless.

In Donnellan’s terminology, denotation is a (semantic) relation between words and things while reference is a (pragmatic) relation between users and use, words, and things.

We can make a similar distinction about truth and a related notion of correctness under the circumstances:  

an observer may be making a correct observation report of fire by asserting “there is phlogiston escaping”, although that statement is literally false.

4.        Theory-laden-ness of natural language

How we interpret the output of a measuring device depends on the theories we currently accept. Galileo designed an instrument to measure the force of the vacuum; today we interprets its results as measuring atmospheric pressure.  Feyerabend insists that the same goes for our observation reports, and codifies this as:

“thesis I: the interpretation of an observation-language is determined by the theories which we use to explain what we observe, and it changes as soon as those theories change.” (Feyerabend 1958: 163, his italics)[4]

When it comes to such an observation report as “Fire!”, that was once interpreted, in a certain community, as reporting a rapid phlogiston escape.  Members of that community could equally well shout “Phlogiston escaping!”, and if they did, everyone, in theoretical agreement or not, would be well advised to prevent themselves from getting burned.

If thesis I. is correct then the way we understand observation reports will change as our theories change.  Is that consequence of the thesis in accord with our history?  

Observational language in use may appear not to change as theories change, because the syntax does not change.  From this we should not infer that meaning is invariant.[5]  One example Feyerabend offers is the changing interpretation of color-reports (Feyerabend 1958: 160-162).  Once the Doppler effect for light is discovered, the report “x is red” is interpreted as a relational statement, with the relative velocity of observer and observed entered as the additional parameter.  On the “human” level, the actual practice of color-reporting does not change, for there the velocities are too small for the effect to be noticed.  But the interpretation does: the scientifically literate will interpret color observation reports by describing the situation in question with reference to that relative velocity.

The realist account of experience which Feyerabend submits is therefore along the following lines:

The interpreter, speaking his own current natural language and from within his own cluster of accepted scientific theories, has no difficulty referring to the relevant situations, generally by means of descriptions that he takes to be correct, and classifying the putative observation statement as a report about that situation if the above pragmatic conditions are satisfied. 

It seems to me that we should understand Feyerabend’s lecture with reference to the background in which he developed these ideas.  Salient in this respect is the, by then already accepted, new scientific realism in the Minnesota Center for the Philosophy of Science, which Feyerabend had joined in 1957.

Wilfrid Sellars, Thomas Kuhn, Paul Feyerabend, and Norwood Russell Hanson all insisted on the theory-laden-ness of our language in use.  There was a great difference between their approach to the language of science and the way logical positivists had thought about language.  The new realists’ lack of interest in the logical syntax of language is understandable.  For scientific theories are presented in our current natural language, though augmented with mathematics.  The language of science is not, in itself, an uninterpreted calculus that needs to have meaning bestowed on it!  

And so, when Feyerabend says that to be full-fledged language the observation language needs to have an interpretation, it can be taken for granted that this interpretation can be given in natural language, and be based on the currently accepted scientific theories which were formulated in our natural language in use.

But there is still an important difference between our four protagonists.  Wilfrid Sellars, unlike the other three, was intent on engaging with a wide-ranging diversity of traditional issues in philosophy.  His rejection of the earlier realism of Roy Wood Sellars’ generation, as well as of Carnap’s logical positivism, came along with systematically developed responses to those issues.  What an interpretation is, what meaning is, taken as a general question, Sellars could not leave  unaddressed. 

5.        What could interpretation be then?

What is clear enough, and in 1957 had already been clear for some time, is that there is no simple relation between observation terms and theoretical terms.  Not even for the speaker who formulates the interpretation.  The idea of an operational definition of such terms as “oxidation” does not get anywhere.  What about the converse?  Do the sorts of interpretation exhibited above as [1]-[3] offer anything like a definition of the terms used for observation reports?

If someone in our community says “Fire is rapid oxidation”, could we parse that as “Our observation term “fire” means rapid oxidation”?  

That is plausible at first blush.  To make it plausible to us today may not be easy, used as we are to the sparsity of semantic accounts that take only truth and reference into account.  We could certainly say that any actual proper reporting use of “fire” will refer to an instance of rapid oxidation.  But actual reference is not enough to determine meaning.  

Nevertheless it would seem that to interpret “Fire!” in Feyerabend’s sense, is to say that it means that there is rapid oxidation.  For that is just a parallel to the example of the driver who, seeing a red light in his car, says “this means that the engine is overheating”.  

But what is meant by “means” in that sort of assertion?  

Feyerabend criticizes two accounts of the meaning of observation terms, ones he attributes to positivist philosophers of science, but does not give one of his own.[6]  

6.        The contemporaneous debates about meaning

Willard Van Orman Quine had thrown a wrench into this topic of meaning, with his “Two dogmas of empiricism” (1951) and its trenchant, though rather behavioristic, critique of meaning, analyticity, and synonymy.  

In response, Rudolf Carnap pointed insistently to the distinction between pragmatics and semantics, in his “Meaning and Synonymy in Natural Languages” (Carnap 1955).  Denotation, extension, and truth, studied in abstraction from use, are the subject of semantics, and Quine is right to find a solid basis for philosophical analysis there.  But meaning, intension, and intensional relations like synonymy are the subject of study in pragmatics, which brings in patterns in usage.  Carnap insists that these patterns, based in dispositions to use words in certain ways, fix considerably more than extension.  As an example he suggests that different linguists might translate “Pferd”, as used by a German speaker, Karl, as “horse” or instead as “horse or unicorn”.  While the extensions of those English phrases are the same, that there is a difference can be put to the test by asking for Karl’s response to pictures and stories.  

While I (and I think Sellars) would speak of linguistic commitments rather than linguistic dispositions, I take Carnap’s to be an adequate response to Quine’s main arguments (and have nothing good to say about the others).  Nevertheless, Carnap’s response does not throw much light on the basic concepts of pragmatics, and does not go far toward providing pragmatics with a sound theoretical basis.[7]  In the Minnesota Circle, where Feyerabend resided at the time, there was a much farther reaching attempt to do so, in progress, at the hands of Wilfrid Sellars.

7.         Wilfrid Sellars on meaning

Sellars’ correspondence with Roderick Chisholm about intentionality had been published just then, as an Appendix to the Minnesota Studies in Philosophy of Science (Sellars and Chisholm 1957 ).  There an enigmatic, and perhaps somewhat unfortunate, assertion by Sellars introduces what I see as the central theme in Sellars’ analysis.

Meaning, interpretation, translation

Chisholm held that we have thoughts, and the meaning our statements have is the thoughts they express.  As Sellars understands this, it implies that such a sentence as 

[a] “Hund” (in German) means dog

has the form 

“Hund” expresses t, and t is about dogs.

which states that there are certain relations between three things.  Each of these relations is a  word-thing relation.  So this way of understanding meaning statements remains solidly within semantics rather than pragmatics.[8]

The dialogue between these two eminently subtle thinkers is eminently subtle, but I think that the crucial clue to Sellars’ view arrives in this passage in Sellars’ letter of August 31, 1956:

“Thus, while I agree with you that the rubric

” .. . ” means – – –

is not constructible in Rylean terms ( ‘Behaviorese,’ I have called it), I also insist

that it is not to be analysed in terms of

“. . .” expresses t, and t is about – – -.

My solution is that “‘ .. .’ means – – -” is the core of a unique mode of discourse which is as distinct from the description and explanation of empirical fact, as is the language of prescription and justification.”  (Sellars and Chisholm 1957 : 527)

Chisholm is puzzled. Prescriptions, he writes, are neither true nor false.  But isn’t such a semantic statement as [a] “’Hund’ (in German) means dog” true?  

Sellars agrees that it is true.  That admission introduces a negative analogy to prescriptions.  But Sellars insists there is more to [a] than that it is true, so some positive analogy remains.

To teach someone a bit of German by saying “’Hund’ (in German) means dog” requires that this person is, like the teacher, a user of the English word “dog”.  Sellars writes that in such a case, 

“there is an important sense in which this statement does not describe the role of “Hund” in the German language, though it implies such a description.  (Remote parallel : When I express the intention of doing A, I am not predicting that I will do A, yet there is a sense in which the expression of the intention implies the corresponding prediction.)” ” (Sellars and Chisholm 1957 : 532)[9]

There is indeed an important distinction between the expression of an intention, and the statement that one has that intention.  Imagine asking someone “Will you marry me?” and receiving as answer the statement “I do in fact have the intention to marry you, and such intentions are typically followed by marriage”.  Imagine, in contrast, that the answer had been the expression of intention in the words “Yes, I will marry you”. The latter is surely what the suitor hoped, not the former.  Expressing the intention is different from stating that she has that intention.  Nevertheless, if she expressed the intention to do so, the suitor would have warrant to infer the statement that she does in fact have that intention.

We may still, like Chisholm, be at a loss as to how this clarifies the discourse about meaning.  Sellars then goes on to explain his point in a different way, by recourse to Church’s translation test.  I think we can see that employed here as follows, in an attempt to teach someone a bit of German.  Suppose that 

[A] “Hund” is a word for dogs

were just a statement of fact.  Then its German translation would also be a statement of fact, with the same information content.  That translation is

[B] „Hund“ ist ein Wort für Hunde. 

But, although that is certainly true, [B] does not have the same status as [A].  Indeed, the student might already know enough German to realize that sentences of form [B] are always true, even while not knowing the reference of “Hund”.  For [B] has the status for a German speaker which 

            [C] “Dog” is a word for dogs

has for a speaker of English, while [A] does not have that status. [10]

Relation to Feyerabend’s realistic interpretation

It may seem that I have gone astray, into something not related to Feyerabend’s provocative Thesis I.  But not so.  

In his answer to Chisholm, Sellars refers unavoidably to distinct communities with different languages.  The informative [A] must be presumed to be addressed to someone sufficiently far in the English speaking community to understand “means dog in German” or “is a word for dogs”.  The speaker of [A] takes that for granted, presupposes that, and we are here at the crucial point also made above about assertions [1]-[3].  

It is a crucial point for meaning or interpretation in general.  In his lectures collected as The Metaphysics of Epistemology, Sellars clarifies this with the distinction between 

            [D] “und” (in German) means and

and 

[E] “und” (in German) means the same as “va” in Sanskrit”.   (Cf. Sellars 1989: 240)[11]  

The important difference between [D] and [E] lies in their presuppositions, when taken as items in a dialogue or communication.  The assertion of [D] presupposes understanding of the English “and”, it is addressed to someone taken to have in his own vocabulary all that follows the word “means” .  In contrast, [E] does not presuppose understanding of any Sanskrit.  The assertion of [E] conveys factual information only, a relation between elements of two languages outside the addressee’s community.  

If we tried to deal with these examples of ‘meaning’ discourse solely within semantics – that is, with attention only to the relation words bear to the world, independent or abstracted from contexts of use — we would be at a loss.  Ignoring what is presupposed when a speaker addresses someone with [D], we would have to construe [D] as

            [F]  “und” (in German) means the same as “and” in English.

But [F], although it is an English sentence and must be assumed to be addressed to an English speaker, does not presuppose that the addressee has “and” in their vocabulary.  If that is implausible (for how can someone have a significant amount of English, and not have “and”?), an example in which the target words has some unusual synonyms will serve:

            [F*] “Hund” (in German) means the same as “canine” in English.

That information would not suffice for addressees who knew English but did not have the word “canine” in their vocabulary.

Within pragmatics, then, [D] does not have the status of a simple assertion of the form “a is related R-ly to b”.  Instead [D] is part of an intra-communal discourse, meaningful in certain contexts and meaningless in others.

8.        Application to Feyerabend’s account

Let us go back now to Feyerabend’s realist interpretation of experience and its reportage, as I codified it in

[1] Observers in community C reliably agree to “Phlogiston is escaping” in the presence of fire and reject it in the absence of fire.

[2] Observers in community C reliably agree to “There is fire” in the presence of phlogiston escaping and reject it in the absence of phlogiston escaping.

[3] Observers in community C reliably agree to “Phlogiston is escaping” in the presence of rapid oxidation, and reject it in the absence of rapid oxidation.

Imagine ourselves in a distinct community C*, where we speak an English that is by now so thoroughly, relevantly theory-laden, that we would be entirely at a loss if we heard any apparent difference in usage between “fire” and “rapid oxidation” .

To begin, we would have no qualms about rejecting [2] altogether, while parsing [1] as

            [1*] “phlogiston is escaping” (in C language) means that fire is present.

This would be on a par, for us, with

            [1**] That the red light is on means that the engine is overheating,

though we would definitely reject as false:

            [1***] “The red light is on” means the same as “the engine is overheating”.           

We would also say that 

            [4] “fire is present” is a phrase for episodes of rapid oxidation,

and, if pressed, we would have to agree to the rather awkwardly worded

            [3*] “phlogiston is escaping” (in C language) means there is rapid oxidation occurring.

Note well that [4] is in our community a pragmatic tautology, and that [1*] and [3*] make sense only as intra-communal discourse by us, as accurate statements about another community’s observation language.

At the same time we would surely reject:

[3**] “phlogiston is escaping” (in C language) means the same as “there is rapid oxidation occurring” in our language.

For the meaning of “phlogiston is escaping” can only be explained in terms of phlogiston theory, which we do not accept, and which we take to be false.   It is [3*], and not the falsehood [3**] that motivates us to leave the theatre if someone shouts “Phlogiston escaping!”, even while we judge the shouter to be shouting a falsehood.

9.        CODA: What is my language?

Formal semantics did not develop along the route charted by Wilfrid Sellars.[12]  In the above account of meaning there is a crucial distinction between 

  • speakers’ understanding of a words and statement in their own language, 

and 

  • their understanding of words in a language not their own.  

It is not assumed that the language of another community is unintelligible to us, or incommensurable with our own.  

Quite the contrary: someone whose own language is English may be a teacher, teaching German to a French student, who is still learning English while enrolled in that teacher’s German class. 

Equally, someone in our own community, whose language is current chemistry-theory-laden, may teach a history of science class, and depict how persons in a certain historic community reported the presence of fire, using language that was phlogiston-theory-laden.  

Fine so far, but ….

As I reflect on the above account of meaning and interpretation, it seems to me that a great deal is left to rest on the distinction between what is my language, and what is a language that I understand.  

And that raises a further question, that remains to trouble us: what is my language?

10. References

Carnap, Rudolf (1947) Meaning and Necessity: A Study in Semantics and Modal Logic.  Chicago: University of Chicago Press.

Carnap, Rudolf (1955) “Meaning and synonymy in natural languages”.  Philosophical Studies 6: 33-47.

Keith S. Donnellan (1966) “Reference and definite descriptions”.  The Philosophical Review 75: 281-304).

Feyerabend, Paul  (1958) “Attempt at a realistic interpretation of experience”.  Proceedings of the Aristotelian Society 58: 143-170.

Feyerabend, Paul  (1962) “Explanation, Reduction, and Empiricism”.  PP. 103-106 in H. Feigl and G. Maxwell (ed.), Minnesota Studies in the Philosophy of Science, 3: 28-97.

Feyerabend, Paul (1981)  Realism, Rationalism & Scientific Method.  Philosophcial Papers Volume I. Cambridge: Cambridge University Press. 

Kuhn, Thomas (1962) “The Structure of Scientific Revolutions”.  pages  1-173 in the International Encyclopedia of Unified Science II-2. Chicago: University of Chicago Press. 

Sellars, Wilfrid and Roderick Chisholm (1957) “Intentionality and the Mental: a Correspondence”. Minnesota Studies in the Philosophy of Science 2: 507- 539. 

Sellars, Wilfrid (1989) The Metaphysics of Epistemology. Ed.: Pedro Amaral.  Atascadero: Ridgeview Pub. Co.

11.  Notes

[1] In a footnote Feyerabend acknowledges his debt to discussions at the Minnesota Center for Philosophy of Science, where he was a member in 1957.  (Note:  in the published paper that is footnote 22, in the 1981 book reprint it is 31.)  Thomas Kuhn’s The Structure of Scientific Revolutions would appear in the International Encyclopedia of Unified Science in 1962, with an acknowledgement to Feyerabend in its preface.  The Journal of Philosophy (54: 709-712 notes and news, 1957) reported: “A conference, sponsored by the National Science Foundation, was conducted at the Minnesota Center for Philosophy of Science from August 12 to September 14, 1957. The participants were: H. Gavin Alexander, Eva Cassirer, H. Feigl (Director of the Center), P. Feyerabend, C. G. Hempel, G. Maxwell, H. Mehlberg, E. Nagel, H. Putnam, W. Rozeboom, M. Scriven, and W. Sellars. Daily group discussions and essays, circulated as memoranda, treated, extensively and in detail, the logical and philosophical issues of quantum mechanics in particular and of scientific theories in general.”

[2] The term “pragmatic theory of meaning” does not occur in this lecture, but Feyerabend used it afterward; see e.g. Feyerabend 1981: 51, 125.

[3] The inclusion of “unanimous” is meant to indicate that these reactions by the community are reliable or consistent in certain respects, which Feyerabend indicates but does not clarify very far.

[4] This is offered in opposition to the Stability Thesis, that the meaning of observation terms is the same before and after scientific theory change.

[5] Feyerabend (1962: 30) introduces the term “principle of meaning invariance” for what he disputes, whereas in the 1958 lecture he used “Stability Thesis”.

[6] The two accounts he criticizes are the principle of pragmatic meaning (the interpretation of an observational term is determined by its use) and the principle of phenomenological meaning (the interpretation of an observational term is determined by what is ‘given’ by way of feelings and sensations in the appropriate circumstances).  

[7] Carnap’s main achievement, in the development of what he calls the method of extension and intension (Carnap 1947)  was the development of a formal semantics for modal logic, still in abstraction from context- or use-dependence of modal locutions. 

[8] While Chisholm has a quasi-psychological account, with thoughts as central characters, the form of his view is that of the Platonist construal of language and meaning: the word’s meaning is an entity, to which the word bears a certain relation.  

[9] The remote analogy is not very remote, for Sellars asserts without qualification that “semantical statements about linguistic episodes do not describe, but imply a description, of these episodes” (Sellars and Chisholm 1957: 536).

[10] Sellars makes the point in a slightly different way: someone might be told that “Hund” plays in German the same role as “dog” plays in English, and still not know the reference of “Hund”. namely if he has not learned the referring use of “dog”.

[11] The lectures collected in this book were delivered in 1975, and edited in collaboration with Sellars. 

[12] Much work was done to develop formal pragmatics, adapting models of modal logic by adding parameters for contexts, speakers, and agents.  My hope is that this can be complemented by reference to the early discussions of the language of science in practice.