Doubting my take

My last post here was started a long time ago, and as I recently completed it I began to have doubts about my own characterisation of Carnap’s “core programme” (as I have been calling it).

Was Carnap really advocating formal science?

My doubt on this score was re-enforced by my earlier realisation that in key passages of Bertrand Russell, he was not advocating that others do what he had done in Principia Mathematica, he was advocating what he intended to do thenceforth having learnt from that experience, viz.: use "the method of logical construction", without directly using formal notations or proofs.

If we look at what Carnap actually said, retrospectively in his intellectual autobiography, there is no explicit programme of formalisation, he talks of:

the application of the new logical instrument for the purposes of analyzing scientific concepts and of clarifying philosophical problems

There is no suggestion here of any transformation to science, nor even a commitment to the use of formal notations by philosophers.  Was my interpretation of Carnap's programme mere wishful thinking?

There is no doubt that Carnap was an advocate of the use of formal notations.  Quite early in his development he tells us, having been introduced to modern logic by attending Frege's lectures on the Begriffsscrift, that he began to feel he did not really understand something until he had formalised it. A sequence of his most important works directly address problems which might be considered pre-requisite for extensive deployment of formal systems, beginning with his Abriss der Logistik (1929), a logic textbook to spread the word, through the classic Logical Syntax of Language (1934), advocating pluralistic precision through syntax, to Meaning and Necessity (1947), addressing formal semantics and modal logics.  To what extent, if any, he expected scientists to take them up, rather than perhaps deriving benefit from conceptual analysis undertaken by philosophers, is unclear.

Why does this matter?

It is of particular interest to me because of my own special interest in a broadly scoped application of formal logic and its automation, and my identification of a triumvirate of philosophers whose aspirations were broadly in the same direction, and in whose footsteps I conceived of myself as following.  Those three philosophers were:

1. Aristotle - for his Organon and the conception of demonstrative science it enunciates.
2. Leibniz - for his idea of a Universal Characteristic and Calculus Ratiocinator, providing a mechanical decision procedure for formalised science.
3. Carnap - for his devotion to the application of formal logic to science.

They are placed in the triumvirate for the ideas which they conceived and promoted.  None of the three were at all successful in realising their aims.  Aristotle's best approach to formalised logic, the syllogistic, fell well short of the deductive needs of mathematics and science, but sufficed to give Leibniz the illusion that scientific truth might be decidable.  Leibniz's ideas were prescient, but his ideas on how they could be accomplished (or even what could be accomplished) were fundamentally flawed.  In many ways the promise of Carnap's Logical Positivism proved illusory, and was to be refined by him into a softer Logical Empiricism, moderated particularly in its approach to the meaning and confirmation of synthetic propositions.  Many important parts of his ideas about the application of logic to science remained intact, including fundamental features such as the clean distinction between analytic and synthetic propositions, his linguistic pluralism and ontological conventionalism, and his positive attitude toward and work on semantics for formal notations.

It is Carnap's position in my trilogy of predecessors which might have been threatened by doubts about his commitment to formal science, but he remains for me, despite any such doubts, the man who sought to rework Russell's achievement (with Whitehead) in Principia Mathematica and deliver similar results across the whole of empirical science, and for that he stays well in place.

Beyond that incompletely realised vision, Carnap is significant for me as the philosopher who has seemed the closest predecessor to my own philosophical views.   In consideration of that connection, as a part of articulating my own  forward strategy, I will be considering how the changes which have taken place since Carnap was alive might have affected his vision and program.

If he were starting now, what would have been the vision, and how might he have sought to realise it?

Carnap's core programme

In his intellectual autobiography Carnap places front and centre, as his philosophical mission, a programme for the formalisation of philosophy and science (broadly taken) inspired primarily by Frege's concept notation and Russell's conception of "scientific method in philosophy".

Whereas Frege had the strongest influence on me in the fields of logic and semantics, in my philosophical thinking in general I learned most from Bertrand Russell. In the winter of 1921 I read his book, Our Knowledge of the External World, as a Field For Scientific Method in Philosophy. Some passages made an especially vivid impression on me because they formulated clearly and explicitly a view of the aim and method of philosophy which I had implicitly held for some time. In the Preface he speaks about "the logical-analytic method of philosophy" and refers to Frege's work as the first complete example of this method. And on the very last pages of the book he gives a summarizing characterization of this philosophical method in the following words:

The study of logic becomes the central study in philosophy: it gives the method of research in philosophy, just as mathematics gives the method in physics. 

All this supposed knowledge in the traditional systems must be swept away, and a new beginning must be made. 

To the large and still growing body of men engaged in the pursuit of science,  ...  the new method, successful already in such time-honored problems as number, infinity, continuity, space and time, should make an appeal which the older methods have wholly failed to make. The one and only condition, I believe, which is necessary in order to secure for philosophy in the near future an achievement surpassing all that has hitherto been accomplished by philosophers, is the creation of a school of men with scientific training and philosophical interests, unhampered by the traditions of the past, and not misled by the literary methods of those who copy the ancients in all except their merits.

I felt as if this appeal had been directed to me personally. To work in this spirit would be my task from now on! And indeed henceforth the application of the new logical instrument for the purposes of analyzing scientific concepts and of clarifying philosophical problems has been the essential aim of my philosophical activity.from his "Intellectual autobiography" in The Philosophy of Rudolf Carnap, p13.

What I want to draw attention to is the stark difference between this scarcely ever mentioned central aim of Carnap's philosophy, "the application of the new logical instrument for the purposes of analyzing scientific concepts and of clarifying philosophical problems has been the essential aim of my philosophical activity", and the aspects of his philosophy more frequently discussed.  Those two most prominent parts of Carnap's philosophy were his early work on the structure of appearances, and his attempt to identify the meaning to empirical propositions with their verification conditions, the "verification principle".

Not only have these two aspects been given undue prominence, but also their significance has been grossly distorted.  By many Carnap is thought of to this day as a phenomenalist, whose empiricism was so rooted in the verification principle that the whole edifice was discredited by critique of the verification principle.   W.V. Quine did not share in any mass delusion about the significance of these aspects of Carnap's philosophy.  He incisively zeroed in on a fundamental principle which really was central, the analytic/synthetic distinction.  His attack on this principle, in essence a radical scepticism about semantics, was enough to turn his contemporaries against Carnap and thrust himself forward into global pre-eminence.

In my next I will look closer at Carnap's core programme.

To mock a mockingbird: Smullyaniana

Speranza

There was a recent post to the "Carnap Corner" on "Deep Learning Eternal Truth" by R. B. Jones (the founder of Carnap Corner, as it happens).

I thought I would drop a line (or two, as the implicature goes) about Smullyan.

That would be Raymond Merrill Smullyan, a very prolific philosopher whose interests seem to correspond, shall we say, with Carnap's and indeed, Jones's.

Jones makes in his post on "Deep Learning" a passing reference to the catastrophe (not a word Jones uses) brought by Goedel. And Smullyan then has a whole book on Goedelian paradoxes that should amuse Jones.

Smullyan's career is eclectic. He holds a MA, and a PhD from Princeton -- His dissertation being on "Theory of Formal Systems".

He is best known to Griceians for a passing reference in Grice's "Vacuous Names" and for Smullyan's "First Order Logic".

When Grice gave his second William James lecture on logic and conversation, he starts by referring to what he calls, yes, a 'commonplace' in philosophical logic. The commonplace that there is, or appears to be (Grice is so guarded it hurts), between:

not
and
or
if
all
some (if not all)
the

and their formal counterparts: ~, /\, \/, ), (Ax), (Ex), (ix).

And the commonplace is repeated by Smullyan.

Of course, Grice will go on to argue -- not so much in THAT lecture but the two following ones, especially Lecture V, concerning if/) -- that this commonplace RESTS ON A BIG MISTAKE!

The mistake is due to the inability -- by Smullyan and others, onto which we can add Carnap and Quine -- especially the Quine of "Methods of Logic", that P. F. Strawson refers to in his introduction to "Philosophical Logic" (Oxford readings in philosophy) -- to perceive an implicature.

It's not that 'and' and '/\' differ, but if we say:

i. Sally, in our alley, got pregnant and married.
ii. Sally, in our alley, married and got pregnant.

Logically, they are equivalent. If the 'implicatures' differ, that's because there are, to use Carnap's label, some 'pragmatic' or 'general features of discourse' (as Grice puts it in "Prolegomena", Lecture I), at play, so that if you are narrating events, you proceed orderly.

This was noted by Urmson before Grice, and indeed by the Greeks before the English! Urmson's example (in "Philosophical Analysis between the two war worlds") is amusing:

iii. Smith got into bed and took off his trousers.
iv. Smith took off his trousers and got into bed.

When Grice delievered his lecture on "Presupposition and Conversational Implicature" (in the original transcript) he used that example, but the segment was edited out when he included that lecture in his WoW (Way of Words).

There are other fascinating facets about Smullyan. He was, like Grice, fascinated with Dodgson, Goedel, Boole, Cantor, and all the interesting names that should fascinate a Carnapian.

Smullyan had a taste for paradoxes, but he never lost his faith that first-order logic was the solution to it all, almost!

Grice and Carnap on the value of formalism

Speranza's post connecting Dick and (of course) Grice to Carnap contains a quote from Grice which is reminiscent of something which Carnap says in his "Intellectual Autobiography".

Grice said, apparently, :

"If you cannot put it in symbols it's not worth saying it."

Rather uncompromising!

Long before him Carnap (a more radical enthusiast for symbolic logic) more modestly (when writing about how he felt early in his PhD research) wrote:

"When I considered a concept or proposition occurring in a philosophical or scientific discussion, I thought that I understood it clearly only if I felt that I could express it, if I wanted to, in symbolic  language."

That was published 1963, but talks about his views just after the first world war.

Marcus Dick makes it to "Dear Carnap, Dear Van" -- and Grice

Speranza

The 'and Grice' is what I call the ObG: i.e. any post should have some Griceian implicature to it!

There was a post in the Grice Club some time ago, which was basically a quotation from P. M. S. Hacker's essay on Witters (or Wittgenstein, if you must).

I love Hacker because, with G. P. Baker, they succeeded Grice (when he left for Berkeley) as tutorial fellows in philosophy at St. John's.

Anyway,

Hacker has this thing, like I do, matter of fact, for alphabetical ordering.

And he manages to try to list the members of what J. L. Austin called his 'kindergarten' -- i.e. the members of that play group that he led and that met on Saturday mornings. The list starts -- I shall use set-theoretical formulation to please Jones:

PG = {Dick, Grice, ...}

-- the members of the class needed to fill some requisites: they had to be younger than Austin himself, and full-time Oxonian 'dons' -- no students allowed, or professors, for that matter!

In any case, note that Dick is the first in the list, followed by Grice.

I found that charming.

I don't think Hacker is trying anything too deep, or historiographical, since, for one, give me five minutes or so, and I shall find members for the play group starting with A, B, and C -- so Dick would NOT be the first!

In any case, why does this relate to Carnap's Corner?

Well, in "Dear Carnap, Dear Van: The Quine-Carnap Correspondence and Related Work," edited by Richard Creath, we read:

"Among it various communications from Marcus Dick, trying to get in touch with us."

So, yes, Dick made it to the Carnap annals, too!

The interesting thing is that those 'various communications' could never be reciprocated because Marcus Dick left no 'future address', if you can believe that!

Ah, well.

Quinton knew Dick from his All Souls days, and he used to say (as a reciprocation for Dick saying, "No much competition here, Richard" -- addressing Richard Wollheim) that he had never met a professional philosopher at Oxford who, like Dick, had never published 'a single word'.

Quinton is of course being hyperbolic. Why?

Well, Quine, in his autobiography, refers to Dick as being an outstanding Commonwealth Fellow at Harvard, and having produced some 'outstanding work' in that area (under Quine, of course).

So, I would think that if Dick never published a single word, he must have published (on Quine's blackboard) a symbol, or two!

The connection between Dick and Grice is more tenous, or shall I say, implicatural, in nature!

But we know that in his later phase of his philosophical development, Grice grew more formalistic and logicist. Indeed, the obituary for P. F. Strawson has a gem: Grice once told Strawson,

"If you cannot put it in symbols it's not worth saying it."

-- whatever that meant! Strawson was impressed, and retorted!

But I would think that Carnap, Grice, and why not, Dick, enjoyed the profuse use of 'symbols', or logical notation to make their ideas clear -- or not! (I have a friend who always reprimands me for putting things in 'logical formal' notation -- "Life is not algebra!" he would shout!)

Hintikka, Carnap, and Grice

Speranza

Jaakko Hintikka was born in Vantaa, Helsinki, Finland.

Hintikka studied mathematics with Rolf Nevanlinna and philosophy with 
Georg Henrik von Wright at the University of Helsinki where defended his 
doctoral dissertation on distributive normal forms.

So we see the cross-reference mathematics -- as per mathematics logic, that
today, for example, is taught at Oxford not within the Sub-Faculty of
Philosophy  but across the street, so that people enrolled in disciplines other
than  Philosophy can attend. The chair is called "Mathematical logic" -- and
philosophy.

Grice loved Wright and he borrowed from him (but never returned) the word 
'alethic'. That Hintikka was inspired by these two people (and these two
fields:  mathematical logic and philosophy -- moral theory --) to write his
essay on  'distributive normal forms' is interesting.

Geary commented: "A distributive normal form is not as normal as it 
seems," and adds with sarcasm: "especially if you catch it  undistributed!".

After his Ph.D. studies Hintikka worked as junior fellow at Harvard  and
became (independently of Stig Kanger) the founder of possible world 
semantics. 

The keyterm is Leibniz, as in Leibniz's world: the best of all possible 
worlds. Woody Allen (who wrote "Irrational man") and Barrett (who wrote 
"Irrational man") have something to say about this, because Leibniz is concerned 
with the "best" (morally best) of all possible worlds and Lucas (the
character  in Allen's film fallaciously thinks he has discovered it!). Hintikka's
treatment  is more abstract: he uses subindexes w1 w2 w3 wn to represent
each world.  Thus

"All man is rational"

is true in all possible worlds if for any world n, man is rational.

Hintikka published his groundbreaking work "Knowledge and Belief" on 
epistemic logic -- the semantics of which is 'possible-worlds'. He uses now two 
dyadic operators:

B(A, p)

and

K(A, p)

to represent that A believes and knows that p respectively. He liked to 
play with 'paradoxes' like

K(A, p) --> KK(A, p)

i.e. if you know that God exists, you know that you know that God  exists.

Hintikka was appointed professor of Practical Philosophy at Helsinki -- 
which was a good thing since, having been born there, he never got lost! In 
fact, he moved not far from the house where he had been born. And a nice
house  it was, too!

Hintikka later became professor of philosophy at Stanford -- which is  a
bit away from Helsinki, if just more or less at the same distance from the 
beach (different beaches, admittedly).

Stanford, with Hintikka, Patrick Suppes and Dagfinn Föllesdal, and the 
programme initiated by Grice "Hands across the Bay" from across the Bay in 
UC/Berkeley -- became one of the leading centres of philosophy of science and 
philosophical logic, if not conceptual analysis: Urmson and S. N. Hampshire 
also taught there.

Hintikka’s new interests included inductive logic and semantic information.
He would say, "What's the good of a philosopher if you don't have a new 
interest?"

He shared his time between Stanford and Helsinki for a while.

Later Hintikka started his work with D. Reidel’s Publishing Company (later 
Kluwer Academic Publishers) in Holland as the editor-in-chief of the
journal  "Synthese" and the book series "The Synthese Library" -- which Geary
calls  "hardly synthetic".

This activity made Hintikka the most influential editor of philosophical 
works. In fact, he was co-editor of a festschrift, as it were, for Quine, who
had written "Words and Objections". This came out in Reidel as Words and 
ObjectIONS -- what's the good of a philosophical theory if you are not going
to  criticise it, as Joaquin Phoenix says in "Irrational man"? -- and they
invited  H. P. Grice to contribute. Grice took his time -- which delayed the
publication  of the thing -- and Hintikka was strict with deadlines -- but
eventually the  thing came out with Grice's "Vacuous Names" in it, and a
short reply by Quine  crediting Grice's brilliancy.

Hintikka was appointed to a Research Professorship in the Academy of 
Finland which allowed him to establish a research group of Finnish scholars 
working mainly in logic, philosophy of science, philosophy of language, and 
history of philosophy.

The Academy of Finland owes its name to the Academy of Athens founded by 
Plato. Most countries have Academies: Greece first, then Rome, then Italy,
then  France. Then Finland. Even Britain has its academy and Grice was
appointed FBA  in 1966 but he delayed the deliverance of his philosophical lecture
for the  British Academy to 1971, when he came up with "Intention and
Uncertanity": a  parody on Hart and Hampshire's 'slightly ridiculous' claims in
their joint essay  for "Mind" on intention and certainty.

As a teacher and supervisor, Hintikka was highly influential though the 
richness of his new ideas and research initiatives.

Many of the former students of Hintikka have been appointed to chairs in 
philosophy. To wit: Risto Hilpinen, Raimo Tuomela, Juhani Pietarinen, Ilkka 
Niiniluoto, Simo Knuuttila, Veikko Rantala, Juha Manninen, Lauri Carlson,
Esa  Saarinen, Matti Sintonen, Gabriel Sandu.

Lauri Carlson wrote a Synthese Library essay on "Dialogue games" -- the 
ideas will be later developed by Hintikka himself in his contribution to P. G.
R. I. C. E., the Grice festschrift edited by Grandy and Warner.

Hintikka divorced his first wife Soili.

Hintikka married Merrill Bristow Provence -- Mrs. Hintikka willl later 
co-edit with Vermazen a festschrift for Davidson and they invited H. P. Grice
to  contribute. He did with a brilliant essay on 'akrasia'.

Hintikka and Provence were appointed at Tallahassee, Florida.

Hintikka married Ghita Holmström.

Hintikka became philosophy professor at Boston -- not far from where  he
had been a fellow in the next town -- when he was in Harvard, Massachussets 
-- He would walk from Boston to Cambridge, and back, as he seemed to prefer
the  bookshops in Cambridge than those in Boston.

During his Boston pewriod, Hintikka resided in a 'cottage' (as 
non-New-Englanders call them) at Marlborough.

Marlborough was not named after the person -- via rigid designation -- but 
after the borough.

Hintikka retired from Boston and moved back to Finland.

Besides his activities in research, teaching, and publication, Hintikka 
served in many important positions in international organizations, among
others  vice president of The Association for Symbolic Logic, vice-president and
later  president of the Division of Logic, Methodology and Philosophy of
Science  of the International Union of History and Philosophy of Science
(DLMPS/IUHPS),  president of the Charles S. Peirce Society -- D. Ritchie was
mentioning this  genial philosopher recently -- and the chairman of the
organizing committee of  the Twentieth World Congress of Philosophy.

As a proof of the appreciation of Hintikka’s work, a volume dedicated to 
him in "The Library of Living Philosophers" was published.

Hintikka’s publications cover an exceptionally wide range of topics.

During his career he published lots of books or monographs, edited lots of 
books, and authored lots of essays in international journals or 
collections.

His main works deal with:

-- mathematical logic (proof theory, infinitary logics,  IF-logic)
-- intensional logic and propositional attitudes
-- philosophy of logic and mathematics
-- philosophy of language (game-theoretical semantics, quantifiers, 
anaphora)
-- philosophy of science (interrogative model of inquiry)
-- epistemology, and
-- history of philosophy (Aristotle, Descartes, Kant, Peirce, Frege, 
Wittgenstein, Grice -- in the P. G. R. I. C. E. festschrift).

A genius.

D. P. Henry, R. Carnap, and H. P. Grice

Speranza

In his "Quæstio Subtilissima", D. P. Henry, of Manchester considers R. Carnap's views on metaphysics as nonsense.

R. B. Jones may find the reference interesting.