Grice on "Logical Construction"

--- One item in Grice Archive on "The Logical Construction of Personal Identity". Why this emphasis on this Cambridge expression?

In what follows I will comment on Bernard Linsky's excellent entry, on 'logical construction' for the encyclopaedia of one of Grice's favourite universities: Stanford ("the fact that it's close to home helps").

Linksy writes at:

http://plato.stanford.edu/entries/logical-construction/

"Russell referrs to several different definitions and philosophical analyses as providing a 'logical construction' of certain entities and expressions."

"The examples Russell cites are:"

i. Frege's and Russell's definition of "number" as "a class of equinumerous classes".

ii. Grice's favourite: the theory of definite descriptions.

iii. The construction of matter -- or nu, physicalism (n for noumenon) from sense data, or phu, phenomenalism"

"and several others", Linksy notes.

"Generally, an expression for such an entities is callee an "incomplete symbols" and the entity itself, apres Bentham a "logical fiction" (Bentham on LEGAL fiction).

"The notion of 'logical construction', then, originates with Russell's
logicist programme of reducing mathematics to logic, was widely used by Russell, and led to the later Logical Positivist notion of construction and ultimately the widespread use of set theoretic models in philosophy."

Linksy goes on:

"Russell's most specific formulation of logical construction as a method in Philosophy comes from his essay "Logical Atomism"".

Linsky quotes directly from Russell:

One very important heuristic

maxim which Dr. Alfred North Whitehead and I found,

by experience, to be applicable in

mathematical logic, and have since applied to

various other fields, is a form of Occam's Razor.

--- cfr. Grice, Modified Occam's Razor.


"When some set of supposed entities has
neat logical properties, it turns out,
in a great many instances, that the supposed entities
can be replaced by purely logical structures
composed of entities which have not
such neat properties."

Russell goes on:

"In that case, in interpreting a
body of propositions hitherto
believed to be about the supposed entities,
we can substitute the logical
structures without altering any of
the detail of the body of propositions in
question. This is an economy, because an
entity with neat logical properties is always
inferred, and if the propositions in which such an entity occurs
can be interpreted without making this inference,
the ground for the inference fails, and our body of propositions is secured against the need of a doubtful step."

"The principle may be stated in the following form:

Whenever possible, substitute
constructions out of known entities
for inferences to unknown entities

(Russell, The philosophy of logical atomism. 1924:160)

Linksy comments:

"Russell is speaking of logical constructions
in this memorable passage from his "Philosophy of Logical Atomism"
lectures."

The method of `postulating' what

we want has many advantages; they are the same as the advantages of theft over honest toil.

Let us leave them to others and proceed with our honest toil.

(1918:71)


Linsky adds:

"The notion of logical construction appears frequently with the idea that what is defined is a "logical fiction", and an "incomplete symbol". The latter term derives from the use of contextual definitions, providing an analysis of each sentence in which a defined symbol may occur without, however, giving an explicit definition, an equation or universal statement giving necessary and sufficient conditions for the application of the term in isolation. The terms "fiction" and "incomplete symbol" apply with differing aptness to various constructions."

GRICE AND BOOLOS ON PLURALITY.

"Russell's first use of construction, and the model for later constructions, is the Frege/Russell definition of 'number' as classes."

"This follows the kind of definitions used in the arithmetization of analysis of the preceding century, in particular, Dedekind's earlier construction of real numbers as bounded classes in the rational numbers. Russell's logicist program could not rest content with postulates for the fundamental objects of mathematics such as the Peano Axioms for the natural numbers. Instead numbers were to be defined as classes of equinumerous classes."

"Russell also refers to this method as "abstraction", now known as the abstraction of an equivalence class. The definition of equinumerosity, or of the existence of a one to one mapping between two classes, also called "similarity", is solely in terms of logical notions of quantifiers and identity. With the numbers defined, for example, two as the class of all two membered sets, or pairs, the properties of numbers could be derived by logical means alone."

ILLUSTRATION 2. Cfr. Grice, "Definite descriptions in Russell and in the vernacular", cited by Bealer, in "Quality and concept".

Linsky:

"The most influential of Russell's constructions was the theory of descriptions from his paper "On Denoting" in 1905. Russell's theory provides an analysis of sentences of the form

`The alpha is beta'

where

`The alpha'

-- Grice's example in WoW:vi, "Jones's dog".

"is called a definite decription. The analysis
proposes that

`The alpha is beta' is equivalent to

`There is one and only one alpha and it is beta'.

With this analysis, the logical properties of descriptions can now be deduced using just the logic of quantifiers and identity."

"Among the theorems in *14 of Principia Mathematica are those showing what follows."

"First, if there is just one alpha then

`The alpha is alpha' is 1, and if there is not, then

`The alpha is beta'

is always 0 and, crucially for the logical manipulation of descriptions."

"Second, if

the alpha = the beta,

and the alpha is gamma,

then the beta is gamma."

"I.e. proper (uniquely referring) descriptions behave like singular terms."

"Some of these results are contentious," Linsky notes. But who does he quote? Grice's 'tutee' at St. John's.

For Strawson, Linsky notes, "noted that

`The present king of france is bald' should be truth valueless since there is no present king of France, rather than "plainly false", as Russell's theory predicts."

-- or stipulates. But Grice was so offended by Strawson's manoevure -- "Especially coming from my pupil", that he never forgave him.

Linksy goes on:

"The theory of descriptions introduces Russell's notion of incomplete symbol. Definite descriptions `The F' do not show up in the formal analysis of sentences in which they occur, thus `The F is H' becomes."

(x) [(y)(ALPHAy y=x) & BETAx]

"of which no subformula, or continuous segment, can be identified as the analysis of
`The F'.

"Much as talk about "the average family" as in "The average family has 2.2 children" becomes "The number of children in families divided by the number of families = 2.2", there is no portion of that analysis that corresponds with "the average family"."

"Instead we have a formula for eliminating such expressions from contexts in which they occur, hence the notion of "incomplete symbol" and the related "contextual definition"."

LOGICAL FORM

"It is standard to see in this the origins of the distinction between between surface grammatical form and logical form, and thus the origin of linguistic analysis as a method in philosophy which operates by seeing past superficial linguistic form to underlying philosophical analysis."

"NO MEINONGIAN JUNGLE" (Grice, "Vacuous Names")

"The theory of descriptions has been criticized by some linguists who see descriptions and other noun phrases as full fledged constituents of sentences, and who see the sharp distinction between grammatical and logical form as a mistake.
The theory of descriptions is often described as a model for avoiding ontological commitment to objects such as Meinongian subsistent entities, and so logical constructions in general are often seen as being chiefly aimed at ontological goals. In fact, that goal is at most peripheral to most constructions. Rather the goal is to allow the proof of propositions that would otherwise have to be assumed as axioms or hypotheses. Nor need the ontological goal be always elimination of problematic entities. Other constructions should be seen more as reductions of one class of entity to another, or replacements of one notion by a more precise, mathematical, substitute."

-----

Third illustration:

"Russell's "No-Class" theory of classes from *20 of Principia Mathematica provides a contextual definition like the theory of descriptions. One of Russell's early diagnoses of the paradoxes was that they showed that classes could not be objects. Indeed he seems to have come across his paradox of the class of all classes that are not members of themselves by applying Cantor's argument to show that there are more classes of objects than objects. Hence, he concluded, classes could not be objects. Inspired by the theory of descriptions, Russell proposed that to say something G of the class of Fs , G{x: Fx}, is to say that there is some property H coextensive with (true of the same things as) F such that H is G. Extensionality of sets is thus derivable, rather than postulated. If F and H are coextensive then anything true of {x: Fx} will be true of {x: Hx}. Features of sets then follow from the features of the logic of properties, the "ramified theory of types". Because classes would seem to be individuals of some sort, but on analysis are found not to be, Russell speaks of them as "logical fictions", an expression which echoes Jeremy Bentham's notion of a "legal fiction". Because statements attributing a property to particular classes are analyzed by existential sentences saying that there is some propositional function having that property, this construction should not be seen as avoiding ontological commitment entirely, but rather of reducing classes to propositional functions. The properties of classes are really properties of propositional functions and for every class said to have a property there really is some propositional function having that property."

-- Other examples.

Linsky goes on:


"For other constructions such as propositions a contextual definition is not provided. In any case, constructions do not appear as the referents of logically proper names, and so by that account are not part of the fundamental "furniture" of the world."

J. WISDOM.

"Early critical discussions of constructions, such as Wisdom's, stressed the contrast between logically proper names, which do refer, and constructions, which were thus seen as ontologically innocent."

Linsky adds the case that appealed to both Carnap and Grice: phenomenalism.


"Beginning with The Problems of Philosophy in 1912, Russell turned repeatedly to the problem of matter. Part of the problem is to find a refution of Berkeleyan idealism, of showing how the existence and real nature of matter can be proved. In Problems Russell argues that matter is a well supported hypothesis that explains our experiences. Matter is known only indirectly, "by description", as the cause, whatever it may be, of our sense data, which we know "by acquaintance". This is the notion of hypothesis which Russell contrasts with construction in the passage above. Russell saw an analogy between the case of simply hypothesizing the existence of numbers with certain properties, those described by axioms, and hypothesizing the existence of matter. While we distinguish the certain knowledge we may have of mathematical entities from the contingent knowledge of material objects, Russell says that there are certain "neat" features of matter which are just too tidy to have turned out by accident. Examples include the most general spatiotemporal properties of objects, that no two can occupy the same place at the same time, and so on. Material objects are now to be seen as collections of sense data. Influenced by William James, Russell defended a "neutral monism" by which matter and minds were both to be constructed from sense data, but in different ways. Intuitively, the sense data occuring as they do "in" a mind, are material to construct that mind, the sense data derived from an object from different points of view to constructthat object. Russell saw some support for this in the theory of relativity, and the fundumental importance of frames of reference in the new physics.""

Linksy notes:

"These prominent examples are not the only use of the notion of construction in Russell's thought. In Principia Mathematica the multiple relation theory of propositions is introduced by saying that propositions are "incomplete symbols". Russell's multiple relation theory, that he held from 1910 to 1919 or so, argued that the constitituents of propositions, say"

i. Desdemona loves Cassio.

which is 1, are unified in a way that does not make it the case that they constitute a fact by themselves. Those constituents occur only in the context of beliefs, say,

ii. Othello judges that Desdemona loves Cassio.

The real fact consists of a relation of Belief holding between the constituents Othello, Desdemona and Cassio, thus

B(o, d , L, c).

"Because one might also have believed propositions of other structures, such as

B (o, F, a)

-- there need to be many such relations B, thus the "multiple" relation theory. Like the construction of numbers, this construction abstracts out what a number of occurrences of a belief have in common, a believer and various objects in a certain order. The analysis also makes the proposition an incomplete symbol because there is no constituent in the analysis of `x believes that p' that corresponds to `p'."

Linsky adds:

"Russell also suggests that propositional functions are logical constructions when he says that they are "nothing", but "nonetheless important for that". (1918, p. 96) Propositional functions are abstracted from their values, propositions. The propositional function

x is human.

is abstracted from its values

Socrates is human.
Plato is human.

"etc. Viewing propositional functions as constructions from propositions which are in turn constructions by the multiple relation theory helps to make sense of the theory of types of propositional functions in Principia Mathematica."

"The notion of "incomplete symbol" does not make as much sense as "construction" when applied to propositional functions and propositions. This usage requires a broadening of the notion."

From Russell to Grice and beyond.

Linsky:

"The notion of logical construction had a great impact on the future course of analytic philosophy. One line of influence was via the notion of a contextual definition, or paraphrase, intended to minimize ontological commitment and to be a model of philosophical analysis. The distinction between the surface appearance of definite descriptions, as singular terms, and the fully analyzed sentences from which they seem to disappear was seen as a model for making problematic notions disappear upon analysis. The theory of descriptions has been viewed as a paradigm of philosophical analysis."

PHENOMENALISM in Carnap and Grice.

Linsky:

"A more technical strand in analytic philosophy was influenced by the construction of matter. Rudolf Carnap was attempted to carry out the construction of matter from sense data, and later Nelson Goodman continued the project. More generally, however, the use of set theoretic constructions became widespread among philosophers, and continues in the construction of set theoretic models, both in the sense of logic where they model formal theories, and as objects of interest in their own right.""

Grice objects to different senses of 'prior' here:

conceptual priority: sense datum conceptually prior to 'material object'.
epistemic priority:sense datum epistemically prior to 'material object'.
---- In "Reply to Richards"

---

Linsky quotes from: Carnap, R. , The Logical Structure of the World & Pseudo Problems in Philosophy, trans. R.George, Berkeley: University of California Press, 1967. Goodman, N., The Structure of Appearance, Cambridge Mass: Harvard University Press, 1951. Russell, B., 1905, "On Denoting", in Robert Marsh, Logic and Knowledge: Essays 1901-1950 , London: George Allen and Unwin, 1956, 39-56. 1918, "The Philosophy of Logical Atomism" in The Philosophy of Logical Atomism , D.F.Pears, ed. Lasalle: Open Court, 1985, 35-155. 1924, "Logical Atomism", in The Philosophy of Logical Atomism , D.F.Pears, ed., Lasalle: Open Court, 1985, 157-181.
Russell, B., 1912, The Problems of Philosophy , Oxford: Oxford University Press, reprinted 1967. Whitehead, A.N., and Russell,B.: 1925, Principia Mathematica Vol.I., second ed., Cambridge: Cambridge University Press, 1925.
Wisdom, J., 1931, "Logical Constructions (I.).", Mind , XL , April, 188-216.
Related Entries suggested by Stanford: Russell, Bertrand | Russell's Paradox | definite descriptions | Carnap, Rudolf

---- Our gist here:

'personal identity'.

Grice is discussing Broad's classfications of personal identity approaches. The 'logical construction' is just one of them.

As Grice notes, "Preliminary Valediction", 'philosophical analysis' -- "these two words were in every progressive lip in people living between the two great wars."

--

But 'logical construction' was NOT necessarily understood as "linguistic entity". So one has to be careful there.

Grice quotes from Gallie, who had made a similar comment.

Grice's paper, "Persona Identity", quoting from Broad and Gallie, appeared in Mind 1941. The topic always fascinated Grice. He quotes from Locke and goes on to immerse into the true Scots tradition on this: Hume, and the common-sense school of Scottish philosophy.

Later, with impetus from J. C. Haugeland, Grice will focus on "Hume's vagaries with personal identity."

Being Grice's first published effort, it is fascinating to see how well it was received by Oxford authors such as Quinton and Parfitt.

In Stanford, J. R. Perry gave it a good go, when he included it in his influential collection, and with an exegetical introduction, in "Personal Identity": one of the few items published by the now defunct, "University of California Press, at Berkeley" (Those were the days).