A Note on Conceptualism

In this essay, I intend to make the case for a Conceptualist view of names and language.  Conceptualism is a particular kind of Cluster Descriptivism, with some additional features.  In Part I, I will start by introducing some history of the theory of names, in order to set the stage.  I will describe Mill's Referential Theory of Names, and Frege's notion of Sense, and its motivation.  Finally, I will present and refute Kripke's refutation of Descriptivism.  In Part II, I will provide more detail on just what constitutes a concept.  I will provide the justification for the notion, and describe some of the ways that concepts function.  In Part III, I will describe how the Conceptualist notion of words and names can resolve some of the puzzles that have bedevilled various topics in Philosophy.  My Conclusion will provide a brief summary of what I have documented as the roles that concepts play in our dealing with the world around us, and then provide some insight on the  philosophical significance of the Conceptualist vision.

Part I -- On Sense and Reference

Mill -- Referential Theory of Meaning

In his System of Logic (Mill 2002), John Stuart Mill accepts the then traditional doctrine that propositions used to describe the world contain (among other things) subject and predicate terms.  These terms he called names.  Mill claimed that all names denote either individuals or the attributes of individuals.  A general name connotes an attribute and denotes all individuals which have that attribute (subsequently called the extension of the attribute).  Thus, 'red' connotes the attribute redness, and denotes all things that have that attribute.  Some singular names (what Russell later called "ordinary proper names") only denote; they have no connotation in that they have no relation to a particular attribute.  "Geoffrey" is such a name.  But most singular names both denote and connote.  They do so by connoting the attribute(s) that uniquely identify the denotee.  Thus, "the publisher of Pathways to Philosophy" is a singular name.  It denotes the same individual as is denoted by "Geoffrey".  But unlike "Geoffrey" it also connotes the attribute of being the publisher of Pathways to Philosophy, an attribute that uniquely identifies Geoffrey.  To Mill, the meaning of a proposition -- its cognitive "import" -- is determined by the connotation of its parts; the exception being ordinary proper names, where the meaning is determined by the denotation.

For example, the "import" (meaning) of the word "Aristotle" is just Aristotle -- that unique person, and no more.  It does not mean "The writer of Nicomachean Ethics".  Hence, the proposition "Aristotle was mortal" says only that that unique person was mortal.  It does not say that the writer of Nicomachean Ethics was mortal.  That is, Mill allows that Aristotle might not have written Nicomachean Ethics, and that the writer of Nicomachean Ethics might not have been mortal.  More pointedly, for any given proposition about Aristotle, one can use the proper name without believing that proposition to be true of Aristotle.  This will become important during the discussion of Kripke, below.

Mill's account of linguistic meaning faces three serious difficulties.  Firstly, it does not properly handle co-referring proper names.  "Cicero" and "Tully" are ordinary proper names for the same ontological object -- Marcus Tullius Cicero (106 BC -- 43 BC), Roman philosopher, statesman, lawyer, orator, and political theorist(1).  Consider the propositions --

(1)   "Cicero is Cicero."

(2)   "Cicero is Tully."

If ordinary proper names are purely denotative, then on Mill's account, these two propositions have the same cognitive "import".  This does not capture the intuition that (1) is tautological while (2) is interesting and informative for someone who does not know that the two names denote the same individual. 

Secondly is the problem that arises when ordinary proper names are used within propositional attitude reports.  Propositional attitude reports concern the cognitive relations people bear to propositions (Mckay & Nelson 2010).  These relations are described by such verbs as believe, think, want, desire, hope, knows, fear, and so forth.  Consider these two --

(3)   "Ann believes that Cicero was a famous Roman orator."

(4)   "Ann believes that Tully was a famous Roman orator."

If Ann does not know that these two proper names both refer to Marcus Tullius Cicero, then she could very easily believe (3) but not (4) -- (3) could be true, but (4) false (or vice versa, of course).  Co-referring names are not substitutable within propositional attitude reports salva veritate.  With a Millian view of names, where the cognitive import of the name is just the referent, they should be. 

Thirdly is the problem that arises from proper names that do not denote a referent.  Consider the statement --

(5)   "Santa Claus is a jolly old elf."

There is no ontological entity denoted by the name "Santa Claus".  So according to Mill, that name has no cognitive import.  Yet "Santa Claus" is sufficiently meaningful that we can have a lengthy and possibly enjoyable (and obviously meaningful) discussion about the attributes of Santa Claus.  Given these three problems, Mill's notion of "import" clearly does not seem to correspond with the notion of "meaning". 

Frege -- Sense and Reference

In order to resolve these difficulties, Gottlob Frege in his 1892 paper "Über Sinn und Bedeutung" (1892/1980) proposed that in addition to a reference (what Mill called the denotation), a proper name possesses what Frege called a "sense" (Sinn in German) -- some aspect of the way its reference is thought of that can differ between two co-referring names.  The difference between Cicero and Tully, for example, is a "difference in the mode of presentation of that which is designated".  The sense of an expression is "that wherein the mode of presentation is contained".  According to Frege, sense determines reference.  Any two expressions with the same sense will also have the same reference, but not the other way around.  Thus, one can know both the names Cicero and Tully without realizing that they refer to the same object, because they present that object in different ways, that is, they have different senses.

So what is a Fregean "sense"?  Frege leaves the matter somewhat unclear.  At one time, it was common to identify the sense of a name with an identifying description, which would put Frege's view close to the later Russell's descriptive theory of names.  For example, the name "Cicero" might mean "the famous Roman orator" while "Tully" might mean "the famous Roman statesman".  Thus the reference would be whatever fits the description.  However, an analysis of Frege's words casts strong doubt on this position.  Pelletier and Linsky (2005), in their analysis of Frege's theories of descriptions, state:

"In all the theories suggested by Frege's words, he sought to make definite descriptions be terms, that is, be name-like in character. By this we mean that not only are they syntactically singular in nature, like proper names, but also that (as much as possible) they behave semantically like paradigm proper names in that they designate some item of reality, i.e., some object in the domain of discourse."

And indeed, Frege himself claims that definite descriptions are proper names, and not the other way around: "The Bezeichnung <indication> of a single object can also consist of several words or other signs. For brevity, let every such Bezeichnung be called a proper name" (1892, p.57).  And again

"It may perhaps be granted that every grammatically well-formed expression figuring as a proper name always has a Sinn. But this is not to say that to the Sinn there also corresponds a Bedeutung. The words 'the celestial body most distant from the Earth' have a Sinn, but it is very doubtful they also have a Bedeutung." (1892, p.58)

Descriptions, therefore, have senses of their own.  So we would be left with either descriptions that serve as their own sense or an endless chain or circle of descriptions.  What is generally accepted, however, is that Frege certainly did not mean that the sense of a name is merely a collection of ideas a particular user of a name happens to associate with it (Zalta 2013). 

Because they figure into the meanings of terms in a public language and can be communicated, senses must be objective.  It must be possible for the two of us to share the sense of a name.  Hence sense cannot be internal to the using mind.  Frege argues, in "The Thought" (1956), that senses can't be mental items:

"If every thought requires an owner and belongs to the contents of his consciousness, then the thought has this owner alone; and there is no science common to many on which many could work, but perhaps I have my science, a totality of thoughts whose owner I am, and another person has his. Each of us is concerned with the contents of his own consciousness. No contradiction between the two sciences would then be possible, and it would really be idle to dispute about truth; as idle, indeed almost as ludicrous, as for two people to dispute whether a hundred-mark note were genuine, where each meant the one he had in his pocket and understood the word 'genuine' in his own particular sense." (Frege 1956. Pg 301)

To Frege, then, senses cannot be mental entities.  They are abstract objects of some sort, inhabiting a "third realm" (Chalmers 2002).  Whatever they are, Frege thinks, senses must be available to more than one thinker.

Russell -- Descriptive Theory

Bertrand Russell disagreed with Frege on the relationship between names (Fregean singular terms) and descriptions.  Frege maintained that descriptions are names.  Russell reverses this relationship and argues that names are descriptions.  Russell's theory of descriptions was initially put forth in his 1905 essay On Denoting (Russell 1905).  His theory is focused on the logical form of expressions involving denoting phrases.  He separates them into two groups.  Definite descriptions purport to denote one definite object, for example "the King of France".  Indefinite descriptions purport to denote ambiguously, for example "a resident of Oz".  One of the problems motivating Russell's analysis is that, as we have seen, certain descriptions are meaningful but do not truly refer to anything -- if, for example, there is no King of France, or Land of Oz.  Russell's approach was to translate the simple surface grammar into a complex structure using quantificational logic syntax.  So, for example, we get --

(6)   "the King of France" becomes "∃x(F(x) & ∀y(F(y) → x=y))"

(7)   "a resident of Oz" becomes "∃x(Z(x))"

On the Fregean analysis, existence and uniqueness are understood as presuppositions of such descriptions, rather than part of the content asserted by them.  The sentence "The present King of France is bald", for example, isn't used to claim that there exists a unique present King of France.  Instead, that is part of the presupposition of the sentence, and what it says is that this presupposed individual is bald.  If the presupposition fails, the description fails to refer, and the sentence as a whole fails to express a proposition.  The Fregean analysis thus accepts truth value gaps and failures of the Law of Excluded Middle.  Both the sentence "The present King of France is bald" and its negation fail to refer (because the presupposition of an existing present King of France fails), and thus both fail to express a proposition, and both have no truth value.

The Russellian approach is designed to avoid this logical consequence.  Russell saw a solution from which it was possible to express a proposition with definitive truth conditions, adhering to the Law of the Excluded Middle, but without the unsavory metaphysical commitment to nonexistent objects or concepts, or to abstract objects of some sort, inhabiting a "third realm".  Russell's solution to the three challenges that afflict the Millian direct-reference theory, was to stop treating descriptions as if they functioned as proper names, and instead treat them as if they were subject-predicate phrases -- as existentially quantified general phrases.  Since their first development, both Russell's Theory of Descriptions and his Theory of (ordinary proper) Names have been hugely influential and well-received within the philosophy of language(2).  

As a result of a distinction that Russell drew between what he called "knowledge by acquaintance" and "knowledge by description" (Russell 1910, Fumerton 2009), he separated the class of names into "logically proper names" and "ordinary proper names".  Logically proper names are words such as "this" or "that" which refer to perceptions of which an agent is immediately aware -- they provide the agent with knowledge by acquaintance.  All other names are "ordinary" proper names, which provide an agent with knowledge only by description.  Russell's claim is that everyday names are not really genuine Millian names -- having direct referents.  Only logically proper names are genuine Millian names.  Ordinary proper names might look like Millian names, but they are not Millian names at the level of logical form.  Russell argued that instead, they are equivalent to definite descriptions.  Indeed he says they "abbreviate" or "disguise" descriptions.  Just as definite descriptions are singular terms only in the form of surface grammar, the same is true of ordinary proper names themselves. 

Both Frege and Russell are called "Descriptivists" because each, for different reasons, argued that ordinary proper names should be understood in terms of the definite description that picks out (if it does) the unique referent in the world.  For Frege, the sense of an ordinary proper name is something like (but as we have seen above, not actually) a definite description.  For Russell "the thought in the mind of a person using a proper name correctly can generally only be expressed explicitly if we replace the proper name by a description"(Russell 1917, Pg 114).  And that description is to be interpreted in terms of existentially quantified logic to avoid any existential presuppositions.  Russell does, however, make allowances for the fact that the requisite description

"will vary for different people, or for the same person at different times (the description in our minds will probably be some more or less vague mass of historical knowledge far more, in most cases, than is required to identify him), … but so long as the object to which the name applies remains constant, the particular description involved usually makes no difference to the truth or falsehood of the proposition in which the name appears."(1917, Pg 114)

Russell does agree with Frege (and with Mill for that matter), that words are ordinarily used to talk about things, not ideas. "If words are used in the ordinary way, what one intends to speak of is their reference"(Frege 1892, Pg 58).  "[A]ll words have meaning, in the simple sense that they are symbols that stand for something other than themselves."(Russell 1903. Pg 47).  For Russell, however, what distinguishes both definite descriptions and ordinary proper names from genuine "logically" proper names (like the individual constants of logic), is not that they do have (Fregean) senses but that they do not have references.  They do have denotations, but these are not their semantic values (Bach 2004).

There is an obvious problem with the original Fregean or Russellian versions of descriptivism -- what is now called "Simple Descriptivism".  The choice of "The writer of Nicomachean Ethics" as the description synonymous with "Aristotle" seems arbitrary.  There are other equally unique and just as informative alternative descriptions.  Why not "the Stagiran pupil of Plato born in 384 BC"?  Counter-factual scenarios also pose problems for a single description, or even a fixed conjunction of descriptions.  Suppose it was Aristotle's son who wrote Nicomachean Ethics.  Would he be the referent of "Aristotle"?  Or suppose that the Stagiran pupil of Plato was actually born in 386.  Would that person still  be "Aristotle"?

Cluster Descriptivism

The main improvement to Descriptivism that has been suggested to resolve these difficulties is "Cluster Descriptivism".  An outline of this theory was famously put forward by John Searle (1958) and Peter Strawson (1959; 180 ff.).  The theory maintains that a name corresponds to a cluster of definite descriptions.  No less a personage than Wittgenstein was an early advocate of a cluster descriptivism theory of names:

"By 'Moses' I mean the man who did what the Bible records of Moses, or at any rate, much of it. But how much? Have I decided how much of it must turn out to be false in order that I should give up my statement? So is my use of the name 'Moses' fixed and determined for all possible cases? Is it not the case that I have, so to speak, a whole series of props in readiness, and am ready to lean on one if another should be taken from under me and vice versa?" (Wittgenstein 1953, P 79)

In a 1958 article (Searle 1958), John Searle introduced his "Cluster Theory" of proper names as an extension of Frege's notion of the sense of a name.  In that article, he asks what the linguistic function is of proper names, and what difference there is between a proper name and other singular referring descriptions.  Both purport to refer to particular objects.  His answer is that proper names, unlike definite descriptions, refer "without presupposing any stage settings or any special contextual conditions surrounding the utterance of the expression".  Proper names do not normally specify or imply any particular characteristics of the objects to which they refer.  Instead, a proper name presupposes that the object being referred to has some set of characteristics, without specifying which ones.

"Now what I am arguing is that the descriptive force of 'This is Aristotle' is to assert that a sufficient but so far unspecified number of [a set of uniquely referring descriptive] statements are true of this object.  Therefore, referring uses of 'Aristotle' presuppose the existence of an object of whom a sufficient but so far unspecified number of these statements are true." (Searle 1958, Pg 171)

It is the function of proper names, Searle argues, to allow us to avoid using a description to refer to an object.  He also points out that proper names are not logically equivalent to a set of descriptions, for that would render proper names superfluous. 

"But the uniqueness and immense pragmatic convenience of proper names in our language lies precisely in the fact that they enable us to refer publicly to objects without being forced to raise issues and come to agreement on what descriptive characteristics constitute the identity of the object.  . . .  Thus the looseness of the criteria for proper names is a necessary condition for isolating the referring function from the describing function of language." (Searle 1958, Pg 172)

Searle argues, therefore, that a proper name is a label for a set of uniquely referring descriptions, but not a synonym for that set.  He does not explicitly state, but only implies, that this cluster of descriptions need not be a publicly agreed set.  In the last paragraph of his article, he implies that different people might have different clusters.  Of course, all that really matters for the two of us to successfully refer to the same object with the same proper name, is that our respective clusters of descriptions uniquely pick out the same referent in the world -- no matter how different our respective clusters might happen to be.  This is a point emphasised by Strawson:

"in order for an identifying reference to a particular to be made, there must be some true empirical proposition known, in some not too exacting sense of this word, to the speaker, to the effect that there is just one particular which answers to a certain description. Mutatis mutandis, a similar condition must be satisfied for a hearer, in order for it to be the case that there is some particular which the hearer takes the speaker to be referring to." (Strawson 1959, Pg 183)

Strawson explores the conditions of correctly describing Aristotle in the cluster of descriptions that is the meaning of the name "Aristotle" as it is used by two people.  Suppose that the two of us each list all of the properties we believe uniquely pick out Aristotle as the referent of the name.  It is not likely that our two lists coincide exactly.  But, according to Strawson, "it would not be too much to say that it requires that there should exist one and only one person of whom some reasonable proportion of these propositions is true" (Strawson 1959, Pg 191).  If it should turn out that there is more than one person of whom a reasonable proportion of those propositions is true, it is indeterminate which person we are referring to by the name.  Strawson echoes Searle in maintaining that it is the looseness of the set-membership conditions that is the main attraction of using proper names:

"we might speak of a presupposition-set of propositions. The propositions making up the composite description of Socrates would form such a set. Neither the limits of such a set, nor the question of what constitutes a reasonable, or sufficient, proportion of its members will in general be precisely fixed for any putatively term-introducing proper name. This is not a deficiency in the notion of a presupposition-set; it is part of the efficiency of proper names." (Strawson 1959, Pg 192)

Kripke -- Refutation Refuted

The most influential critic of the Descriptivist theory of (ordinary proper) names, has been Saul Kripke.  In his January 1970 lectures at Princeton University (collected and published as Naming and Necessity (Kripke 1980)), Kripke presented what has become widely recognized as the definitive refutation of the Descriptivist theory of names.  Less widely recognized have been the many demonstrations that Kripke's "refutation" is itself fatally flawed in many ways.  (See, for example, Searle 1969, Dummett 1973, Searle 1983, Katz 1990, Green 1998, Sosa 2001, Nelson 2002, Stanley 2002, Baumann 2010)

Kripke begins his argument by first setting up a pair of "theses" that together define a cluster theory version of descriptivism that will be the target of his critique.  The description associated by a speaker with a name N is "the individual who possesses most of the properties F, such that the speaker believes 'N is F'".  Next he sets up a pair of theses establishing Descriptivism (as defined) as a theory of reference.  The name N refers to whatever individual object (if any) is denoted by the description associated with N by its speaker.  Then he adds the two theses that will form the basis for his argument that Descriptivism fails.  The speaker knows a priori that N refers to whatever its associated description singles out (if there is such a thing), and it is necessary that N refers to something singled out by its associated description (again, if there is such a thing).  Finally, he adds a non-circularity condition that will prevent "being the referent of N" being part of the description.  Descriptivism is supposed to be an account of reference, an answer to the question "In virtue of what does a particular word or phrase refer to a particular thing?"  So Descriptivism is supposed to explain what it is in virtue of which something is the referent of "Aristotle".  That individual's being the referent of "Aristotle" cannot, on pain of circularity, explain its being the referent of "Aristotle".  Here are the six theses quoted from Naming and Necessity, Lecture II (Kripke 1980, Pg 71).

(1)     To every name or designating expression 'X', there corresponds a cluster of properties, namely the family of those properties φ such that A believes 'φX'.

(2)     One of the properties, or some conjointly, are believed by A to pick out some individual uniquely.

(3)     If most, or a weighted most, of the φ's are satisfied by one unique object Y, then Y is the referent of 'X'.

(4)     If the vote yields no unique object, 'X' does not refer.

(5)     The statement, "If X exists, then X has most of the φ's" is known a priori by the speaker.

(6)     The statement, "If X exists, then X has most of the φ's" expresses a necessary truth (in the idiolect of the speaker).

(C)  For any successful theory, the account must not be circular. The properties which are used in the vote must not themselves involve the notion of reference in such a way that it is ultimately impossible to eliminate.

Using these six theses as his foil, Kripke provides three separate arguments that Descriptivism (as he has defined it) fails.  He offers a modal argument, an epistemic argument and a semantic argument.

          

The Modal Argument

"It just is not, in any intuitive sense of necessity, a necessary truth that Aristotle had the properties commonly attributed to him.  . . .  It would seem that it's a contingent fact that Aristotle ever did any of the things commonly attributed to him today" (Pg 74-75)

Suppose, Kripke argues, that associated with the name "Aristotle" is a long list of particular properties that we (jointly or individually) associate with the person of Aristotle.  He then argues that it is possible that in some other possible world (i.e. counterfactually), the person of Aristotle might have existed but have none of these properties.  It is possible, he suggests, that all of the properties we associate with Aristotle in another possible world belong to another individual, or to no one at all.  Yet we still refer to the person of Aristotle with the name "Aristotle".  Hence Descriptivism must be false.

Kripke would argue that there is an individual in each possible world (where he exists) that is Aristotle, by stipulation, whether we can properly identify him or not.  Kripke thinks that ordinary proper names are "rigid designators" -- a rigid designator picks out the same object in each possible world in which it exists.  Kripke defines a possible world as simply a set of counterfactual conditions build on our world conceptually (in our imagination); it does not really exist (or subsist) as a real thing. Possible worlds are stipulated, not discovered, according to Kripke. 

"It is because we can refer (rigidly) to [Aristotle], and stipulate that we are speaking of what might have happened to him (under certain circumstances), that 'transworld identifications' are unproblematic in such cases." (Pg 49)

We do not set up a set of identifying conditions for Aristotle and look for anyone who satisfies those conditions in other possible worlds, we stipulate that Aristotle exists in those relevant possible worlds.

But Kripke here using a Millian direct-reference notion of the name.  He is stipulating, in other words, that there could be a person of Aristotle that has none of the properties by which we would identify that person as Aristotle.  And this the Descriptivist would deny.  According to the Descriptivist the very notion of "a person of Aristotle" involves a notion of how we pick that person out of the world.  One cannot use the name "Aristotle" without involving some identifying properties. 

Suppose we had a "Magic-Scope" that would let us view any particular time, place, and possible world at will.  We use the Magic-Scope in this actual world (in ancient Greece, say) to pick out a particular person and say "Hey, that person over there is Aristotle" -- defining the person of Aristotle by ostension.  How do we do choose which member of a crowd we should point to as the person of Aristotle?  It has to be a non-random choice, based on some set of properties that we think identify the person of Aristotle.  Let's pick out two people standing side by side, and label them P1 and P2.  It is P1 that we think has all of the identifying properties of Aristotle, and so we choose to point to P1 and call him "Aristotle".  Let's further suppose that P2 has all of the identifying properties of Alexander (Aristotle's pupil), so we choose to call him "Alexander".  But now, let's move the Magic-Scope from this possible world to another.  We know, because "Aristotle" is a rigid designator, that P1 is the person of Aristotle.  But let's also suppose that some of the identifying properties that in this actual world belong to the person we chose to call "Aristotle" now belong to P2 instead of P1.  As we go from one possible world to the next, more of those properties switch from P1 to P2.  Pretty soon, we will reach a possible world where P1 is "Aristotle" by Kripke's stipulation, but P2 has all of the identifying properties that P1 has in this actual world.  Which of P1 and P2 should be identified as "Aristotle"?  In fact, which of the pair is P1?  And how are we to decide that point if not by some identifying properties?  

"for although the man (Nixon) might not have been the President, it is not the case that he might not have been Nixon" (Pg 49)

Kripke, it would seem, would maintain that it is P1 that is Aristotle -- because that is what was stipulated in conceiving the possible world, and the name directly references the object.  Descriptivists would argue that it would be P2 that is Aristotle, because that object has all of the properties we use to identify Aristotle.  A Descriptivist would argue that rigid designation has its limits.  And Kripke is attempting to refute Descriptivism by using a Millian notion of a name, something that Descriptivism has already denied.

The Epistemic Argument

Every sentence of the following form is both knowable a priori, and true:

a)        If the F exists, then the F is the F.

Now suppose that N is some name whose meaning, according to the description theory of names, is given by the description "the F".  Then the principle of substituting synonyms salva veritate leads to the claim that the following sentence form is also both knowable a priori and true:

b)       If the F exists, then N is the F.

But Kripke argues that for many name-description pairs which might be employed in a descriptivist theory, this will not hold.  Compare these two:

c)        If the greatest philosopher of antiquity exists, then the greatest philosopher of antiquity is the greatest philosopher of antiquity.

d)       If the greatest philosopher of antiquity exists, then Aristotle is the greatest philosopher of antiquity.

Statement (c) is (from (a)) both knowable a priori and true.  Whereas (d) is not necessarily true, and is knowable only a posteriori.  It is therefore not the case that N is synonymous with "the F".  Hence the description theory of names is false.

If simple descriptivism is considered, where "the F" is a simple fixed concatenation of property predicates identifying the referent-in-the-world, then Kripke's claim that (d) is not necessarily true, and is knowable only a posteriori is simply false.  It is the definition of simple descriptivism that N and "the F" are synonymous.  If the only description providing the referent identification for the name "Aristotle" is "the greatest philosopher of antiquity", the statement (d) is, contra Kripke, both knowable a priori and true.

On the other hand, if cluster descriptivism is considered, where "the F" consists of a cluster of property predicates of which most, or a weighted most are satisfied by the identified referent-in-the-world, then statement (d) is malformed.  Given cluster descriptivism, it would not reflect the statement form given in in (b).  Statement (d) would have to be rephrased as

d')   If {an object with the most, or a weighted most, of the property predicates in the cluster labelled "Aristotle"} exists, then Aristotle is {an object with the most, or a weighted most, of the property predicates in the cluster labelled "Aristotle"}.

And with this re-phrasing, it is now just as obvious as with (c) that statement (d') is both knowable a priori and true.

The Semantic Argument

Kripke makes this argument using the (fictional) scenario of Godel and Schmidt.  Suppose the only thing you know about Godel is that he was the man who proved an important mathematical theorem, called the incompleteness of arithmetic.  Now suppose that Godel was not really the author of this theorem.  A man called "Schmidt" actually did the work in question.  His friend Godel somehow got hold of the manuscript and claimed credit for the work, which was thereafter attributed to Godel.  Thus he has become known as the man who proved the incompleteness of arithmetic.  For most people who have heard the name 'Godel', the claim that Godel discovered the incompleteness theorem is the only thing they have ever heard about Godel. When they use the name 'Godel,' are they talking about:
            (A) the person who really discovered the incompleteness of arithmetic?
            or
            (B) the person who got hold of the manuscript and claimed credit for the work?

The issue that Kripke is raising here is the question of whether, when something goes wrong as a result of a believer's false beliefs, we should say that they have a "true belief about A (Schmidt)" or a "false belief about B (Godel)".  Kripke uses a Millian conception of names to assume that by using the name "Godel" I refer to the person of Godel, and when I believe that he is the one who discovered the incompleteness of arithmetic, I have a false belief about Godel.

A simple descriptivist would use the name "Godel" to refer to the person who really discovered the incompleteness of arithmetic -- the person that Kripke calls "Schmidt".  In other words, a simple descriptivist might find herself using the "wrong" name for the referent-in-the-world.  Although, to a simple descriptivist, it would not be a "wrong" name.  A simple descriptivist would be prompted to ask "Wrong according to what standard?"  If I use the name "Godel" to refer to the person who actually proved the theorem, I may be using the wrong name according to someone who has more information about Godel and Schmidt (like Kripke).  But then I would be wrong only according to their standard.  According to Descriptivism, there is no fact of the matter beyond what each of us identifies by description.  So my "wrong" use of the name Godel is wrong only relative to some other person's identification of Godel by some other description than the one I am using.

If cluster descriptivism is considered, on the other hand, then the cluster of descriptions must take into account the property of being called "Godel" by other people in the linguistic community.  And in that case, because there would be (given the scenario) a linguistic convention to call the person who got hold of the manuscript and claimed credit for the work "Godel", if I believed that "Godel" is the name of the person who proved the theorem, I would have a false belief about Godel.  Note that the addition to the description cluster of the property of being referred to by other people as "Godel" does not contravene Kripke's condition (C).  How you use the name is a datum I need to consider if I want to be successful in talking about the same thing you are talking about.  This is not a circular definition of reference.

In the case of Godel and Schmidt, whether a belief about who discovered the incompleteness of arithmetic is a false belief about Godel or a true belief about Schmidt depends on what other identifying descriptions have weight in the cluster of descriptions labelled "Godel".  To a cluster descriptivist, there is no fact of the matter beyond what is picked out by the weighted most of the cluster of descriptions involved.  A public discussion of what is or is not true of Godel is possible because within each of our clusters that are labelled "Godel" will be descriptions (beliefs) that are not true of the referent-in-the-world picked out by the weighted most of those descriptions.  As well, there will be some descriptions that reflect the speaker's intention to actually refer to what others in the linguistic community are referring to.  How much weight the speaker assigns to these latter descriptions will depend on the speaker's beliefs about how right or wrong the linguistic community might be.  We may, as a result of our different clusters of descriptions and the different weight we place on those descriptions, find ourselves disagreeing about which object we are referring to when we use a particular name.  If I have a copy of the police report on Godel's murder of Schmidt, I will not place much weight on the community's convention in using "Godel."  So you might think of "Godel" as the person who discovered the theorem, whereas I know better.

The Causal-Historical Theory of Reference

The alternative to Descriptivism that Kripke offers is the Causal-Historical theory of reference.

"Someone ... is born; his parents call him by a certain name. They talk about him to their friends. Other people meet him. Through various sorts of talk the name is spread from link to link as if by a chain. ... A certain passage of communication leading ultimately to the man [Feynman] himself does reach the speaker. [The speaker] is then referring to Feynman even though he can't identify him uniquely."(Pg 91)

Kripke identifies two kinds of name use.  Original use involves baptism or dubbing, and is explained by ostension or description.  It is the first appearance of the name, and it has the meaning and referent that the original user chooses.  For derived use, the referent of the name is the thing referred to by the original user of the name, as transmitted down a chain of communication.  To Kripke, it does not matter what you think.  All that matters is the objective fact of a chain of communication.

"On our view, it is not how the speaker thinks he got the reference, but the actual chain of communication, which is relevant." (Pg 91)

A chain of use-transmission is reference-preserving if and only if derived uses of the name refer to the same thing as the original use.  If the receiver chooses not to use the name to refer to the same thing as the original user, or when the receiver mistakes the thing that the name was originally used for, the use-transmission chain can be misinforming.  The standard example is "Madagascar" which is supposed to have changed from referring to a coastal region of Africa to the island which is now its customary referent.  Kripke uses the example of "Santa Claus" which he suggests may have originally been used to refer to "a certain historical saint", but now does not.

Interestingly, the cluster theory of names is perfectly consistent with Kripke's causal-historical theory.  Kripke speaks in terms of causes when talking about the use-transmission chain.  The cluster theory talks about the same use-transmission chain in terms of the intention of the speaker to use the name to refer to the same referent as is customary in her linguistic community.  Talking in terms of causes is talking at the level of physical interactions.  Talking at the level of intentions and beliefs is talking about the same phenomena in mental terms.  Both forms of talking are mutually consistent. 

For all of the reasons provided here, Kripke's "refutation" of the Descriptivist theory of names simply does not work.  The Cluster Theory can defeat all of Kripke's arguments, and is fully consistent with his suggested alternative.

Part II -- Concepts

I now want to introduce the notion of a "concept".  According to the online Compact Oxford Dictionary(3), "concept" is "an abstract idea" or (philosophically) "an idea or mental image which corresponds to some distinct entity or class of entities, or to its essential features, or determines the application of a term (especially a predicate), and thus plays a part in the use of reason or language".

There is a fundamental ambiguity in the common usage of the word "concept".  On the one hand, a concept is frequently treated as if it is something out there in the world: "the Newtonian concept of mass".  It is spoken of as though it exists independently of anyone who actually knows or grasps it.  Likewise, "grasping a concept" suggests a parallel with grasping a physical object, although somehow doing it with one's mind instead of one's hand.  On the other hand, a concept is regarded as an entity within one's head, a private entity, a product of the imagination that can be conveyed to others only imperfectly by means of language, gesture, drawing, or some other means of communication.  Ray Jackendoff (1989), following Chomsky's (1986) differentiation between E-Language and I-Language, calls these two different senses of "concept" as "E-concept" (an external artifact, having independent objective existence) and "I-concept" (a body of internally encoded information).  For this essay, I intend all occurrences of "concept" to mean "I-concept". 

Within the realm of cognitive science, the functionality of pattern recognition is scientifically accepted.  It plays an important role in our explanation of the functioning of biological neural systems (brains), and is central to research into Artificial Neural Networks -- a key area of artificial intelligence research.  Several models guiding recent AI research, including artificial neural networks and massively parallel processing (as well as some traditional AI approaches) incorporate work on pattern recognition processing (Wolfram 2002).  Scientific experiments with both humans and animals show that pattern recognition is a very established capability of the mind (Margolis 1987). There is no serious doubt that the brain has the ability to recognize patterns, react to patterns, remember patterns, repeat patterns, associate patterns, etc.  The notion of a pattern recognized is a "concept".

Concepts, therefore, are constituents of thoughts.  They are crucial to such psychological processes as categorization, inference, memory, learning, and decision making.  This notion is unabashedly mental in nature.  As such, the concept as a recognized pattern is a private psychological entity, taking as its starting point the representational theory of mind.  The representational theory of mind is usually understood as taking beliefs and other propositional attitudes to be relations between an agent and a mental representation -- a concept.  (See, for example, Fodor 1987.)  It does not damage this notion of a concept to view it as a particular kind of mental existent with a characteristic type of functional role.  This mental-representation-as-functional-role view of concepts is the orthodox position of the cognitive sciences (see Pinker 1994).  As such, it enjoys widespread acceptance in the philosophy of mind, particularly among those philosophers who consider themselves aligned with research in the cognitive sciences (see, for example, Harman 1987, Millikan 2000, Fodor 2003, Margolis & Laurence 2007).

The notion of concepts as mental entities of representation has a long history.  It can be traced as far back as Aristotle.  Locke called them "ideas".  But the modern version of this notion of a concept has its roots in Pragmatism.

"All knowledge is in terms of concepts. If these concepts correspond to something that is to be found in reality they are real and man's knowledge has a foundation in fact; if they do not correspond to anything in reality they are not real and man's knowledge is of mere figments of his own imagination."
               
Moore 1961. American Pragmatism: Peirce, James, & Dewey, p27.

My own image of a concept is that of a "cognitive pigeon hole" that stores all the data constituting a pattern recognized in the input stream.  A concept is a collection of information that we consider to be similar in some very specific respects. 

All the immediate products of our senses are interpreted in the brain as "percepts" (and I mean to be quite neutral on the debate over the nature of these percepts).  We each and always are bombarded with a continuous stream of percepts -- sensory inputs that an act of focused attention can differentiate into lines, shapes, colours, texture, smells, tastes, movements, sounds, and so forth.  The first stage (and I am using that term loosely) in the transition between percepts and concepts is the pre-conscious integration of these percepts into "things" (using scare-quotes to indicate that I mean to be very neutral as to just what sort of stuff "things" are, and to allow all possibilities free reign).  Percepts are integrated into "things" as we begin to recognize that certain reports from our senses "go together", based on some rules/guidelines we have learned (or otherwise acquired) on how to recognize what stuff "goes together".  Alternatively, or quite probably in parallel, some percepts are integrated into "things" very early in the pre-conscious processing of sensory inputs, and we learn to differentiate features rather than assemble features.  On either account, "things" are drawn to our conscious attention, differentiated from other "things" and the background noise, and are as yet unlabeled and unclassified.  

A concept is a mental integration of two or more of these "things" which are isolated according to a set of characteristics (properties) across which they are recognized as similar -- the basis of pattern recognition.  The elements involved may be any aspect of reality -- "things": entities, attributes, actions, qualities, relationships, events, phenomena, etc.; they may be perceptual concretes ("percepts") or other, earlier formed concepts.  The act of isolation involved is a process of abstraction: i.e. a selective mental focus that takes out or separates a certain aspect of reality from all others.  The uniting involved is an integration, i.e. a blending of the units into a single, new mental entity which is used thereafter as a single unit of thought.  The three key processes involved in concept formation are the three that are essential to consciousness -- taking apart and putting together; differentiation, abstraction, and integration.  Differentiation is the process of grasping differences, of distinguishing one or more "things" from the others and the background noise, of recognizing one sort of pattern instead of another.  Abstraction is the process of extracting common qualities from specific examples, of leaving out of consideration one or more properties of a complex set of "things" so as to attend to other associations or attributes; of considering something independently of particular properties.  Integration is the process of uniting elements into an inseparable whole. 

I should point out at this juncture, that whether (or how much of) these rules/principles of integration, differentiation, abstraction, and pattern recognition are learned consciously or unconsciously, or are "learned" genetically and are pre-wired in our brain circuitry, is a matter of some debate.  It is also a matter of some debate whether the discrimination of a "thing" (a single entity or a pattern across multiple entities) from its background is a consequence of our focus of attention, or a consequence of something innate to the way the brain processes nerve impulses from the sensory organs.  Fortunately, these detailed debates need not be of concern for this essay. It is sufficient for the current discussion that we do discriminate a "thing" from its background.

The next stage in the transition between percepts and concepts is the application of some classifying characteristics -- matching the properties observed of the "thing" with our existing cognitive pigeon holes (already recognized patterns).  Each of those pigeon holes contains a collection of previously encountered "things" that are recognized as similar -- constitute a pattern -- across some collection of properties.  The newly encountered "thing" is then matched to those collections of pattern defining similarity characteristics to slot the "thing" into the appropriate pigeon hole -- to recognize that it fits within an already discriminated pattern.  It may, of course, "fit" into more than one pigeon hole.  And it may, equally of course, not fit neatly into any existing pigeon hole.  It is only when we discriminate some percepts from others, and collect sets of percepts together with others, that we begin to operate at the level of concepts.  When a particular "thing" is integrated as a representative member of a larger class of similar entities, it is called an "existent" of the generalized "concept" that is the class of which it is a member.  Each "thing" discriminated from the background is collected together under the umbrella of a particular concept, based on a meaningful set of "essential characteristics" -- those across which we recognize that the members of the collection are similar.  

Concepts are thus mental entities which, at the base or "concrete" level, represent a collection of individual perceptions.  However, at succeeding levels of abstraction or integration, concepts can represent a collection of other concepts, relationships between percepts or concepts, activities of percepts or concepts, and all of the other attributes that we associate with things observed about Reality.  In this way, a particular concept can be built upon other concepts into a hierarchical structure.  Each higher concept can consist of any suitable collection of prior concepts and previous percepts. 

New concepts are formed, new patterns are recognized, by collecting a set of existents ("things" and/or other concepts) with all of their multitude of particular attributes, and then dispensing from further consideration all but a few key "essential characteristics".  Any one particular existent may thus be subsumed under the umbrella of numerous concepts.  And there is no constraint on how many hierarchies a particular lower level concept might join.  So the whole is a multi-connected network.  The hierarchical network of concepts grows constantly in all directions. The formation of higher or wider concepts in the hierarchy occurs as we develop a wider breadth of knowledge and generalize or abstract to a broader classification of "essential characteristics".  The formation of deeper or narrower concepts occurs as we develop a more intensive knowledge of some area and gain new insight into which characteristics become "essential" to our understanding of reality.  Concepts are not formed randomly.  They are formed in the context of the individual's perceptions of Reality.  The differences and similarities that are observed are those that are relevant to the individual's need to understand and manipulate his environment. The context is the entire content of the mind involved, present and past percepts and concepts included.

"We begin with objects that look dissimilar. We compare, find patterns, analogies with what we already know. We distance ourselves and create abstractions, laws, systems, using transformations, mappings, and metaphors. This is how mathematics grows increasingly abstract and powerful; it is how music obtains much of its power, with grand structures growing out of small details. This form of comprehension underlies much of Western thought. We pursue knowledge that is universal in its perspective but its powers are grounded in the particular. We use principles that are shared but reveal details that are distinct." (Rothstein 1995).

Although he is here talking specifically about music and mathematics, I take Rothstein's description to be valid for all concept formation.

In order to take advantage of the cognitive economy achieved by collecting all of the incredible volume of percepts together into a relatively small number of cognitive pigeon holes, we need some way to reference the individual collections.  Here is where words come into play.  To each cognitive pigeon hole, we attach one or more words or phrases.  The concept associated with a language tag is how we understand the meaning or cognitive significance of that tag.  The word-to-concept association is not necessarily one-to-one.  Sometimes this is a consequence of rules of English grammar that control the formation of parts of speech from basic elements -- such as "quick" and "quickly" or the (in)famous irregular verb conjugation of "determined" (as in "I am determined", "You are stubborn", and "He is pig-headed").  But it is also a consequence of a cognitive recognition of relative synonymy -- such as (say) "fast" and "quick" or "Cicero" and "Tully".  If you can distinguish the "things" that form the associated concept from all other "things" in your knowledge, you have fully understood the meaning of the concept and the word(s) associated with it.  It is difficult to discuss this process, and provide examples, since the process is almost an entirely unconscious (or "pre-conscious") one.  The very act of discussion pre-supposes the concepts that are the end result of the process.  

For convenience of contemplation and discussion, I choose to divide the universe of mental pigeon-holes into two kinds.  But I do not wish to suggest that there is any fundamental difference in these two sets.  All concepts are a collection of a broad range of instances (experiences and/or other concepts) gathered together on the basis of some recognized pattern, in order to treat them together as a single cognitive unit.

Collection Concepts - are denoted by language words that are not "ordinary proper names".  They include such ideas as "chair", "run", "red", "fast", etc.  They are formed based on the cognitive recognition of similarities across multiple entities.  Through a process of abstraction, similar differentiated entities are collected together as existents under the umbrella of a single idea. A Collection-Concept allows the cognitive processes to deal efficiently with a set of similar entities as a single identified pattern, rather than as an open-ended collection of unique entities.  The defining ("essential") properties of any Collection-Concept are the characteristics across which the subsumed entities are recognized as similar.  The entities that are differentiated and abstracted together can be actions (verbs), properties or universals (adjectives, adverbs), entities or particulars, relationships between entities or concepts, and so forth. 

Description Concepts - are denoted by language words that are "ordinary proper names".  They are formed based on the cognitive recognition that multiple pieces of information about Reality are similar in that they are information about a single ontological entity.  A Description-Concept allows the cognitive processes to deal efficiently with a broad range of information about some particular entity as a single identified pattern, rather than as an open-ended collection of unique pieces of information.  Description Concepts are not limited to "formal labels" since it is also possible to use multi-word descriptive labels to designate the concept one has of some entity.  One might have a description-concept labelled "the nice old guy who is the crossing guard up at 5th and Vine". 

There is no material difference between the two kinds of concepts, it is merely the way I have chosen to divide up the field.  Complex relational concepts like "the locus of points half-way between you and me", might be dumped into either category with no damage to the theory.

Part III -- Concepts in Action: Resolving the Puzzles

The connection between this discussion of concepts and the previous discussion of the Cluster Descriptiveism theory of names should be fairly obvious by this point.  Concepts just are the clusters of descriptions that the Cluster Theory holds explains how ordinary proper names refer to their referent-in-the-world.  Equivalently, the cluster of descriptions that form the basis of an ordinary proper name just is the concept that has been tagged by that name.  Although a concept is a pattern recognized in the input stream of our consciousness, in order to describe the contents of that concept to someone else, a cluster of descriptive statements is all that we have.  Accepting concepts as the basis of the Cluster Theory allows the theory to be generalized from ordinary proper names to all names of all things: particulars, universals, entities, attributes, actions, qualities, relationships, events, phenomena, etc.

Grue

Because a concept is essentially a pattern that we have already recognized within the input stream, not something we might recognize if the input stream were different, the Conceptualist approach to names explains why "grue" is classified as a perverse predicate.  We can intentionally create a new concept (like "grue") based on descriptions, but we readily recognize that such a specially constructed concept is different from normal.  That is why we classify such concepts as belonging to the pattern "perverse".

Nelson Goodman first presented his "new riddle of induction" in a 1946 paper (Goodman 1946) and then elaborated on his idea in 1955 in his Fact, Fiction and Forecast (Goodman 1955).  Goodman presents his riddle in the context of Hempel's theory of confirmation (Hemple 1965) and Hempel's discussion of how we can tell which hypotheses are confirmed by any given evidence.  Goodman's riddle thus involves the question of how we can justify our choices of the patterns onto which we project into the future.  How, in Goodman's words, do we distinguish between law-like, confirmable, projectible predicates from non-law-like, un-confirmable, non-projectible predicates?

From the collection of particular observations that all emeralds so far observed have been green, Goodman proposes that two incompatible hypotheses (patterns) can be supported:

(a)     All emeralds are green, and

(b)    All emeralds are grue.

The predicate "grue" Goodman defines as applying "to all things examined before t just in case they are green, but to other things just in case they are blue."(Goodman 1979, Pg 74)  Note that contrary to many interpretations (see, for example Barker & Atchinsein 1960, Swinburne 1968, Hesse 1969, Blackburn 1969, Kripke 1982), "grue" does not entail that things already observed will change colour after time t, and need not be understood as a colour predicate.  Goodman's "new riddle of induction" is the problem of explaining in a principled way just why it is that "grue" but not "green" is readily recognized as perverse.

All grue-like predicates contain within them a reference to some boundary -- either temporal (as in grue), spatial, or relational -- across which is proposed some kind of change in the observed pattern, a change for which we have no empirical support.  And it is the existence of that anticipated, but inexplicable, change that makes the predicate perverse.  The fact that all the emeralds we have so far examined have been green, offers no support whatever to the hypothesis that after some time t, the next emerald we examine will be blue.  This difficulty exists for all grue-like predicates.

This difficulty persists, even though Goodman argues that the boundary in the case of "grue" is not a necessary feature of the predicate.  He argues that "green" and "blue" can be defined in terms of "grue" and "bleen" -- and within those definitions, it is "green" and "blue" that would contain the temporal boundary, while "grue" and "bleen" would be the unbounded predicates.  Goodman suggests that by defining "green" and "blue" in terms of "grue" and "bleen" we would be making "green" and "blue" the perverse predicates, to the salvation of "grue" and "bleen". 

But by doing so, Goodman seems to gloss over the significance of what it would mean to recognize a pattern in our experiences, and how that would translate into the meaning of an unbounded predicate.  You can't meaningfully recognize a suggested pattern in our mass of experiential data if that suggested pattern would require more data than is in hand at the moment.  Hence, any proper analysis of induction must necessarily take place within an "all things considered" environment.  To recognize a globally meaningful pattern in our empirical evidence, we would need access to the global mass of evidence.  And that, of course, we do not have. 

But the obvious perverseness of Goodman's Grue, does nothing to resolve the deeper point that Goodman was attempting to demonstrate.  The only support we have for the predicates that we do project into the future, are the patterns that we do recognize in the evidence we do have on hand.  And the only basis for preferring one pattern hypothesis versus another pattern hypothesis within the same body of evidence, is that one pattern covers a greater body of the empirical evidence without lapping over the limits of the data.  If, as Goodman supposes in the case of "grue" versus "green", there is no discernable difference in the suitability of two identified yet incompatible patterns, given the currently available evidence, then there simply is no basis in the empirical evidence on which to prefer one pattern hypothesis over another.  Choosing between them must be based on other criteria.  But induction never takes place in isolation.  It is always a process of "all things considered" pattern recognition.  Goodman's "grue", although fully compatible with the evidence in hand, overlaps the data.  It thus posits a pattern that we cannot recognize in the input stream.  It can only exist as an arbitrary construction, and as such belongs with other such arbitrary constructions within the pattern labelled "perverse".

This distinction between "perverse" and "normal" concepts explains why we are not free to associate whatever descriptions we like with a name.  The purpose of classifying descriptions and perceptual evidence into concepts is to take advantage of the cognitive economy of uniting all of this data into a single thing to think about.  We do not form concepts unless there is a cognitive advantage for doing so.  Even the perverse concept of "grue" is formed only to allow economies in a discussion of Goodman's philosophical arguments.  For normal concepts, we seek those patterns that most readily provide good answers on how reality is going to respond to us.  With limited evidence, "Earth, Air, Fire and Water" once seemed to be a good set of concepts.  With more evidence, we now have 100 or so concepts for the basic elements of nature.  Perverse predicates have limited usefulness, and are therefore rejected in favour of more useful predicates.

In one sense, I am quite free to associate whatever descriptions I like with a name (or rather, more correctly, to associate a name with any bundle of descriptions).  In another sense, I am constrained both by the desire that the concepts I employ have some cognitive economy for me, and my desire that the names I use mean something to you when I use them. 

Two-Stage Connection to Reality

The three Millian challenges were (1) co-referring names; (2) names in propositional attitude reports; and (3) empty names.  All three can be easily resolved if we adopt the Conceptualist view that the connection between a name and the referent-in-the-world is actually a two-stage connection, rather than the one-stage connection assumed by Mill.  If we consider the denotation of a name to be the concept (cluster of descriptions) rather than the referent-in-the-world, the puzzles disappear.  "Cicero" denotes one concept.  "Tully" denotes another concept.  So it is to be expected that

(2)   "Cicero is Tully."

is interesting and informative for someone who does not know that the two concepts happen, in this actual world, to pick out the same referent-in-the-world.  And there is no longer any problem with propositional attitude reports.

(3)   "Ann believes that Cicero was a famous Roman orator."

(4)   "Ann believes that Tully was a famous Roman orator."

When translated into the language of concepts, and the two stage connection to reality, these become

(3')  "Ann believes that the concept labelled 'Cicero' includes the description that he was a famous Roman orator."

(4')  "Ann believes that the concept labelled 'Tully' includes the description that he was a famous Roman orator."

Since the tow names no longer have the same referents, it is no longer a puzzle that one might be true while the other might be false.  And of course, (5) "Santa Claus is a jolly old elf." becomes (5') "The concept labelled 'Santa Claus' contains the description that he is a jolly old elf".  The translation provided here is only necessary, of course, to highlight what is happening.  If Conceptualism is correct, all uses of names (of anything) denote the concept, and not the referent-in-the-world.  Getting to the referent-in-the-world is a second step of finding out (identifying by description) just what entity in the world matches the descriptions (if there is any).

Concepts are thus very like Fregean Senses.  The big difference, however, is that Frege understood Senses to be non-subjective entities that could be shared between people.  Concepts, however, are purely subjective.  The concern that forced Frege to conclude that Senses were non-subjective was the puzzle of how two people could talk about the same thing if the Sinn was not available to both.  What would make any two people's Sense of "Aristotle" coincide sufficiently that communication could be successful?  Frege thought the only answer was that both people would have to have access to the same Sense.  But modern Philosophy of Language has pretty much recognized that the words we use in language are a more or less (how much is debated) a matter of convention. (See, for example, Lewis 1969, Schiffer 1972, Bennett 1976, Loar 1976, Blackburn 1984, Davis 2003, Rescorla 2011.)  So it is the process of learning the conventions involved in using the name "Aristotle" that ensures that our two Senses become sufficiently aligned that communication can be successful. 

And as shown in the discussion of Kripke's "Refutation" of Descriptivism, A Conceptualist (cum Cluster Descriptivist) will argue that Kripke's 5th and 6th theses are indeed a priori and necessary respectively.  In order for some referent-in-the-world to be an X is for it to have "most of the φ's".  That is what constitutes "being an X".  There is no other way to "get" to an X other than by identifying it as having "most of the φ's".  If we disagree on what referent-in-the-world is X, there is no fact of the matter to resolve our disagreement (other than by updating at least one of our concepts with additional "φ's").

         

         

Kripke's Puzzle About Belief

In his "A Puzzle About Belief", Saul Kripke (Kripke 1976) presents his famous puzzle as part of a defense of a Millian conception of names.  He starts off by claiming that the standard criticism of Millianism, based on the fact that co-referring names are not interchangeable in belief ascriptions (propositional attitude reports) salva veritate, is based on a logical fallacy.  He claims that the criticism is based on the principle of substitution, and that it is improper to convict Millianism on the basis of a problem with the principle of substitution.  He argues that the same reductio ad absurdum conclusion can be reached without using the principle of substitution.  He demonstrates that the problem of apparently conflicting beliefs can be arrived at using the principles of disquotation and translation, or just the principle of disquotation.  He suggests that the problem of apparently conflicting beliefs must be due to these principles that are employed in the arugments, and not necessarily to the nature of Millianism.  And then he suggests that because it is not obvious why these various "intuitively obvious" principles should lead to the contradictory beliefs, it represents a real puzzle that must be solved.

However, as pointed out by a number of authors, most notably David Sosa, Kripke's reasoning is still based on a thoroughly Millian conception of names.  As Sosa lays out in his "The Import of the Puzzle About Belief"(Sosa 1996), Kripke's arguments depend on the Millian concept that a given name has only one semantic contribution.  Kripke relies on the premise that if an argument finds itself using two instances of some name, then the semantic import of both instances must be the same.  This is most easily seen in Kripke's Paderewski Puzzle.  Here is how Sosa analyzes Kripke's argument:-

(1)   Peter is rational.

Assumption.

(2) Peter, on reflection, assents to "Paderewski has musical talent".

Assumption.

(3) Peter, on reflection, assents to "Paderewski does not have musical talent".

Assumption.

(4) Peter believes that Paderewski has musical talent.

From 2 & Disquotation.

(5) Peter believes that Paderewski does not have musical talent.

From 3 & Disquotation.

(6) Peter believes that Paderewski has musical talent and Peter believes that Paderewski does not have musical talent.

From 4, 5 & Conjunction.

(7) If Peter believes that Paderewski has musical talent and Peter believes that Paderewski does not have musical talent, then Peter has contradictory beliefs.

Definition.

(8) Peter has contradictory beliefs.

From 6, 7 & Modus Ponens.

(9) If Peter has contradictory beliefs, then Peter is not rational.

Definition.

(10) Peter is not rational.

From 8, 9 & Modus Ponens.

 

Kripke, of course, claims that because this reductio ad absurdum conclusion is not reached by using the principle of substitution, as used in the traditional criticism of Millianism that I mentioned above, it cannot be used to criticize the Millain theory of names.  At most, he claims, it can be used to criticize the principle of disquotation that he uses here, because it is the only logical principle used that is not universally accepted as part of standard logic.

However, it is fairly obvious that step (6) is only acceptable if the word "Paderewski" has a common semantic role in both (4) and (5).  And this, argues Sosa, is the Millian conception of names.  Intuitively, it is not an acceptable step if Peter does not know that the two people he calls "Padewerski" are one and the same person. 

That Kripke has in mind a Millian theory of names is clear from two separate lines of evidence.  The first is his quick dismissal of the "Frege-Russellian tradition" of a descriptive theory of names.  Significantly, he assumes that a descriptive theory of names would necessarily involve a "defining description" of the name -- what is now called Simple Descriptivism.  And he argues that because this particular concept of a descriptive theory of names does not work in the case of Feynman (a name Kripke suggests has a defining description of "a physicist") and Gell-Mann (a name Kripke suggests also has a defining description of "a physicist"), no sort of descriptive theory of names will work.  Kripke also quickly dismisses the cluster theory of names, probably because he thinks he has provided a definitive refutation of that theory (see Kripke -- Refutation Refuted above).

The second clear evidence that Kripke is thinking in terms of a Millian theory of names throughout his article, is his asking "Does Pierre, or does he not, believe that London is pretty?"  He is thinking that by using the name "London" he can be referring to a unique referent-in-the-world.  But if a Millian theory of names is the not proper way to understand names, this question is illegitimate.

Sosa goes on to analyze all of the examples that Kripke presents, and shows that the same common Millian step is used to generate the "puzzle" that Kripke finds in the results.  So, contra Kripke's conclusions, his argument strengthens rather than weakens the reductio ad absurdum conclusion that the Millian conception of names is untenable.

The solution to Kripke's "puzzle" is therefore quite obvious.  It is to adopt a non-Millian theory of names that gives a name some version of Fregean "sense", in addition to its role of denoting a referent.  If the "sense" of the name Padewerski in (4) and (5) above is different, then the conjunction operation in (6) would be invalid, and the "puzzling" conclusion impossible to reach. 

Intentionality and Putnam's Twin Earth

The term "intentionality" refers to the phenomenon that mental states/attitudes/concepts are about, are directed on, or represent other things (Jacob 2010).  "Intentionality" is this rather vaguely understood notion of "aboutness".  There is something that I affirm, deny, interpret, understand, believe, hope, wish, like, love, hate, (and according to some, perceive or sense), and so forth.  The modern use of the term was initiated by Brentano towards the end of the 19th Century(4).  He claimed that every mental state has intentionality and is directed towards an "intentional object".  Intentionality is the "aboutness" of propositional attitudes.  The intentional object is what the propositional attitude is "about".

So-called "Frege cases" are examples of multiple words/names/expressions all referring to one referent-in-the-world.  The example I used above was the case of "Cicero" and "Tully".  These two names refer to the same object.  Frege noted that when used within intentional idioms (propositional attitude reports), co-referring names are not substitutable salva veritate.  If Ann believes that Cicero is a Roman orator, that does not entail that she believes that Tully is a Roman orator.  Ann may not know they co-refer.  "Frege cases" are used to argue that the meaning of a word/name/expression is not simply the referent-in-the-word.  As we saw above, Frege argued that a name must have more than just the referent as its meaning.  He proposed that names also have "senses".  To Frege, as I pointed out above, senses were not subjective entities, but rather objective entities in the public domain.  They must be external to the minds that use them.  But if they are external, goes the "meaning externalist" orthodoxy, then the nature of intentionality cannot be explained just by the physical properties of the brain.

"Twin Earth cases" reverse the many-to-one relationship of Frege cases -- one word/name/expression having multiple referents-in-the-world.  The initial "Twin-Earth case" was proposed by Hillary Putnam in his paper Meaning and Reference (Putnam 1973), and further explored in his The Meaning of 'Meaning' (Putnam 1975).  Putnam's example is the case of Oscar on the Earth, and Toscar on Twin-Earth both using the word "water" to talk/think about the clear, odourless liquid that comes out of taps, falls as rain, fills lakes and streams, and slakes thirst.  Putnam argued that since Oscar and Toscar are ex hypothesi physically identical, there is nothing physical in their brains to distinguish the fact that when Oscar thinks about "water" he is thinking about "H2O", and when Toscar thinks about "water" he is thinking about "XYZ".  Putnam famously concludes that "meaning ain't just in the head".  Again if the intentional (proposition attitude) relation is defined by something external, then the nature of intentionality cannot be explained just by the physical properties of the brain.

The "externalist" about intentionality employs both kinds of cases to show that intentionality (the "aboutness" of mental states and propositional attitudes) derives not just from stuff within the brain (so-called "narrow content" in the words of Fodor (1987), Millikan (2004) and Dennett (1987)), but requires stuff in the world as well (so-called "broad content" in the words of Putnam (1975), Horgan & Tienson (2002), Dretske (1996), and Burge(1986)).  When Ann affirms that Cicero is a Roman orator, what her affirmation is about involves something outside of Ann -- the Fregean objective sense of "Cicero".  When Toscar wants some "water", what his want is about involves something outside of Toscar -- the fact that to Toscar, what he calls "water" is not made of H2O, but actually made of XYZ.  The externalist understands these cases through the premise that the intentional (propositional attitude) relationship involved between a name/word/expression and the referent-in-the-world is single-stage. 

But the Conceptualist interpretation of these cases is that the relationship involved is two-stage.  The referent of a name like "Cicero" or of a word like "water" is actually a mental existent (a concept, a cluster of descriptions, a recognized pattern).  What picks out the referent-in-the-world of any word is a whole collection of descriptions and other contextually relevant information, internal to the mind using that information.  This is not something that grants an objective sense of meaning to the name, as argued by Frege, Kripke, and other meaning-externalists.  What ensures that we both pick out the same referent-in-the-world (if and when we do) is the conventional nature of language acquisition.

In Oscar's mind the word "water" refers to a subjective collection of information that in this actual world just happens to pick out H2O.  In Toscar's mind, the word "water" refers to exactly the same subjective collection of information (ex hypothesi), but in his world it just happens to pick out XYZ.

Accepting the intentional (propositional attitude) relation as existing not between a mental state and a referent-in-the-world, but between a mental state and a mental "concept," also solves a couple of classic "paradoxes of intentionality".  The first is that the intentional object need not exist.  If Billy believes that Santa Claus is coming, then "Santa Claus" is a real mental object (a concept) that just happens to have no referent-in-the-world.  The second is that a mental state can bear an intentional relation to something general, without their being any particular referent-in-the-world that the state bears that relationship to.  If Ann wants a cat, but has no particular cat in mind, then Ann's mental state of wanting bears an intentional relationship to her concept of a cat without having to pick out a particular cat. 

What Frege cases demonstrate is that Fregean "senses" are not objective as Frege claimed.  Cicero and Tully do not involve the same intentional object, even though when those descriptions are projected on the world they happen to pick out the same referent-in-the-world.  What Twin-Earth cases demonstrate is that in different scenarios (different possible worlds), the (ex hypothesi) identical collection of information can pick out different referents-in-the-world.  Contra Putnam, "meaning is entirely in the head."  Intentionality is a two-stage relation to the world, not a one-stage relation to the world.

Particulars and Universals

"Particulars" is a metaphysical/ontological category for entities that have attributes.  (I mean attributes other than "existence" -- if "existence" is indeed an attribute.)  An attribute is a quality, character, characteristic, or property that is or can be attributed to a thing.  It is part of the definition of a "particular" that particulars have some sort of relationship with attributes, or characteristics.  Exactly how that relationship is described depends on the metaphysical theory one adopts.  (See, for example, Quine 1948, Loux 2002, Bacon 2011, Cohen 2012)  For the moment, however, I am going to use the terminology that particulars "have" attributes.  But by this I mean to be neutral as to just what the relationship is between the particular and the attributes associated with it.

The three most widely discussed theories of particulars are the substratum theory, the substance theory, and the bundle theory (Loux 1978, Loux 2002, Robinson 2013).  The substratum theory maintains that what a particular actually is, is something that underlies the attributes it "has" -- something to which the attributes are "attached" in some fashion.  This means that we could conceptually remove all of the attributes of a particular to be left with nothing but a "bare" particular.  Of course, there would be nothing left by which we could perceive the particular.  Hence, on this theory, a "bare" particular is something that is unperceivable, indescribable, and unknowable.  Most philosophers regard it as a disadvantage if an ontology requires us to grant existence to something that is unperceivable, indescribable, and unknowable

The substance theory dates from Aristotle.  It proposes that a particular has some attributes essentially, while all others it has contingently.  We could not remove an essential attribute of a particular without changing the kind of thing it is.  But any of its contingent attributes we could remove without changing the kind of thing it is.  For example, Aristotle is essentially a man.  We could not remove the attribute of being a man from Aristotle without changing it/him into something that is not a man.  But Aristotle also had a beard.  We could remove the beard without changing Aristotle into something that is not a man.  Unfortunately, it is not at all clear what distinguishes essential from contingent attributes for any given particular.  For example, suppose we are considering Aristotle as an example of a "bearded man".  If we then remove his beard, he is no longer a bearded man.  So by removing an attribute, we have changed Aristotle into something else.  It is not obvious that this sort of change is significantly different from the previous one.

The bundle theory of particulars proposes that a particular is nothing other than a collection of attributes.  If we were to remove all of the attributes of a particular, there would be nothing left.  The bundle theory of particulars is maintained by those metaphysicians who argue that particulars are not a fundamental category of existents.  They are derivative, and based on the existence of attributes (or more precisely, universals).  The problem that bundle theorists have inadequately addressed, is the nature of the relationship between the attributes that are bundled together as a specific particular -- what it is that keeps the bundle together as a unit; and why this specific bundle of attributes rather than another.

What all these theories accept as given is that particulars exist independently of how we think about them, and that it is the function of metaphysics/ontology to describe how they exist.  But one of the difficulties with this approach, is the problem of boundaries.  How is it that we draw the boundaries we do around the particulars we identify.  Ontologists have come up with all sorts of explanations, the most famous of which is the theory of natural kinds (Mellor 1977, Kripke 1980 Lecture III, Bird 2012).  This theory maintains that there are "natural kinds" of particulars out there for us to discover, and it is up to us to discover what natural kinds actually exist in the world.  And it is up to the ontologists to provide descriptions of what it is that makes one natural kind different from another. 

The Conceptualist theory, however, posits that what marks the boundaries of a particular is our current cognitive purpose.  Contrary to the standard approach, particulars do not exist independently of how we think of them.  If one is a metaphysical realist (as a Conceptualist has to be), then one can accept that the world as a whole exists independently of how we think of it.  But the boundaries of any given particular are drawn to suit our cognitive purposes.  They are not given by the world for us to discover.  The boundaries of a particular can change as our cognitive purpose changes.  The conceptualist approach thus renders the differences between the substratum theory, substance theory, and bundle theory of particulars into questions of different cognitive purposes. 

Of course, one of our most important cognitive purposes is to survive.  So the boundaries we choose, for the particulars we identify, will be those most useful in aiding our survival -- those most informative about how the world is going to react.  From the perspective of a conceptualist, therefore, "particulars" are concepts that collect together the information we have available on parts of the world, around which we choose to draw boundaries, to most economically meet our need to understand and predict how the world is going to react to our efforts.  "Particulars" are not fundamental mind-independent entities that we must discover.  If you wish, the entity known as "the world" is the fundamental mind-independent entity.  But "particulars" are concepts that are derivative and somewhat mind-dependent entities.  They exist because and only when we "create" them by drawing suitable boundaries around parts of the world that interest us.

Now every individual particular "has" attributes.  (Remember, for the moment I am being neutral as to the exact nature of this "has" relationship.)  Some particulars have attributes that we would recognize as similar.  For example two different mats, each being a particular, share the attributes of being mats, being flat, being on the floor, being manufactured by the same manufacturer (according to their respective labels), and being (according to the manufacturer's label, say) green in color.  In metaphysics a "universal" is the term used to refer to what individual particulars have in common when they exhibit some resemblance in their respective attributes.  (See, for example, O'Connor 1952, Crockett 1954, Putnam 1970, Agassi & Sagal 1975, Armstrong 1999, Swoyer & Orilia 2011)

The term "universal" is used, in contrast with the term "particular", because universals can be instantiated or exemplified by many particular things (ie. universally), whereas particulars can be instantiated only once -- each particular is unique.  Universals are employed to explain why it is that we judge many particulars similar with respect to some attribute.  The two mats I referred to have in common that they are "Green" according to their labels.  And we can observe that they are very similar in color, even though one of the mats has been washed several times and is a distinctly more faded green.  Presumably, there will be any number of other particulars in the world that we would also judge as being very similar in color to our two mats.

The challenge is how to account for the general agreement that our two green mats have a certain similarity in their respective color attributes.  Or a certain similarity in any other property we might judge they have in common.  Metaphysicians fall into two main camps on this issue.  Realists maintain that universals have real mind-independent existence.  It is the relationship between the particular and the universal that explains why we perceive the two mats as having similar color.  Nominalists and conceptualists deny that universals have real existence.  They claim that independently existing entities are not necessary to explain the perceived similarity in color (or other properties we judge they share).

According to Conceptualism, the relation of resemblance or similarity is the consequence of a combination of our cognitive purposes and our bio-psychological reaction to the inputs from our senses.  We recognize that our two mats are similar in color because we judge that the inputs to our visual cortex result in similar cortical responses, and our previously created set concepts contain one labelled "Green" within which both those cortical responses fall.  Or in briefer terms, the two mats are both Green because our concept of Green covers both ways our visual cortex responds to the incident light.  The same reasoning applies to all general terms.  So for conceptualists, all that exists are the particulars and the words we use to describe them. 

"Universals," like "particulars," are thus both derivative and somewhat mind-dependent entities.  They are concepts that we create -- clusters of descriptions we have tagged with a word -- patterns we have discerned in the sensory input stream.  They both exist because and only when we create them by drawing suitable boundaries around how we react to the world around us. 

Conclusion

Conceptualism views the denotation, the immediate referent, of a word to be a concept -- a subjective mental existent; a cluster of descriptions; a collection of information recognized as being similar by some standard suitable to our purposes; a pattern detected within our input stream of perceptual data, or of our body of already extant concepts.  This makes a concept similar in some respects to a Fregean Sinn.  However, a concept is a purely private subjective entity, not an objective entity.  Since the concept provides the meaning of the words that label it, contra Putnam (and other meaning-externalists) "Meaning is entirely in the head".

Using a Conceptualist notion of meaning, Kripke's critique of Descriptivism can be shown to be invalid.  His entire argument is based on a Millian single-stage direct-reference theory of the meaning of words.  A Conceptualist two-stage theory of meaning renders each of Kripke's arguments unsound.  And it encompasses, without pause, Kripke's suggested alternative of the causal-history theory of meaning.

The Conceptualist vision that words denote subjective concepts that we create as suits our cognitive purpose, and not "things" in the world, informs a whole host of controversies within various areas of philosophy.  In the Philosophy of Language, I have described here the Conceptualist solutions to the three challenges of Millianism, and Goodman's "New Paradox".  In the Philosophy of Mind, I have provided the Conceptualist solution to Kripke's Puzzle About Belief, and described why the Conceptualist is a "Meaning Internalist".  A Conceptualist has to be a Metaphysical Realist, because we do in fact discern patterns in our input steams, and we couldn't do that unless there is something that generates the patterns -- you can't find patterns in random inputs.  So epistemologically, Conceptualism informs discussions of what constitutes "Truth" and "Knowledge".  If these are concepts that we create based on patterns in our input stream, then they cannot be defined based on external factors, yet they also have to be based on an objective reality that we experience.  We do not "create" reality when we discern patterns in the input stream.

"The problem is not with our access to the facts.  The problem is with the set of categories that we have inherited for describing the facts"
                                                                                    (Searle, 1998, Pg 68)

Conceptualism also informs discussions of possible worlds, possibility, necessity, and counterfactual conditionals.  Conceptualism agrees with Kripke (1980) that possible worlds are mental constructs (concepts) that are stipulated, rather than discovered.  This position disagrees with Lewis (1973, 1986) who maintains that possible worlds are real existents. 

Possible worlds are not inspectable.  They are not causally connected with this, the actual world.  We too easily forget that this means that we cannot really inspect any other possible world than the current world.  So the question of whether some statement is true in some possible world, or in all possible worlds, is not a question of empirical investigation.  Whether the statement is necessarily or possibly true must be determined on the basis of factors that are known to us here in this actual world.  What we wish to claim is true or not in one, some, or all possible worlds is so purely by stipulation.  Whatever the answer, the grounding for our concepts of necessity and possibility has to be right before us in this actual world.

Contra Kripke (1980), the problem of trans-world identity is not resolved.  When trying to decide whether a statement like "Possibly, Aristotle had six fingers" is true or not, we do it conceptually, on the basis of what we stipulate about these possible worlds.  But just what is it that (conceptually) picks out an instance of "Aristotle" in any other possible world than this actual world?  Kripke (1980) suggests we do it by stipulation.  Others (including Kripke) have suggested that trans-world identity is established only by identical origins (Mackie 2008).  Kripkean rigid designation not withstanding, we intuitively withhold "sameness/identity" from something that is so different from the proto-type in this world, that it would be unidentifiable (on the basis of descriptive attributes) in another.  Clearly our judgements of necessity and possibility are prior to, and not dependent on the possible worlds semantics.

Necessity is a matter of linguistic definition, not a matter of how things are.  The statement "necessarily, all bachelors are male" is true because of how we define our terms (how we construct boundaries around our concepts), independently of how the rest of the world may be.  Statements which are necessary, which are true in all possible worlds, are true because that is the way that we have defined the concepts we are using.  The question of whether "Aristotle is necessarily human" is true or not depends on how we have defined (set boundaries around the concepts behind) the words "Aristotle" and "human".  If we conceive of "Aristotle" as a collection of descriptions that includes the proposition that he was a human being, then it is true that "Aristotle was necessarily human".  But if we conceive of "Aristotle" as a cluster of descriptions that includes say "the greatest Greek philosopher", but does not include that he was a human being, then we allow it to be possible that Aristotle was not human (possibly he was very much like a wombat).  Determining whether any statement "necessarily P" is true or not is thus a matter of investigating the meaning of the words employed in P (factors which exists in this world) to see if P is "true by definition".  A proposition "true by definition" is true in virtue of the concepts employed in the proposition, rather than by an inspection of the empirical evidence.  Another word often used for this concept of truth is "analytic". 

This Conceptualist approach to propositions being "true by definition" (or "analytic") also clarifies discussions about the rules of logic and mathematics.  Some philosophers think that we discover the rules that reality obeys.  But a Conceptualist would argue that these rules are created by us to describe the patterns we discern in our input streams.  Since they are created by us, they may be incorrect, or not sufficiently accurate for our purposes.  If mathematical or logical theorizing produces some result, the Conceptualist will argue that we still have to inspect the empirical data to discern whether the expected mathematical or logical description is actually sufficiently accurate.  To a Conceptualist, all of logic and mathematics is "true by definition".

Whether the discussion involves the Free Will versus Determinism debate, the Nature of Causation, what constitutes Identity, the nature of Personal Identity, or even the question of what is moral, Conceptualism teaches the participants to be wary of the fact that words denote mental concepts, and not referents-in-the-world.  So there can be a confusing disconnect between our respective concepts and the world, and between your concepts and mine.

 

 

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Notes and References

(1)  Wikipedia contributors;  "Cicero" in Wikipedia, The Free Encyclopedia. URL=<http://en.wikipedia.org/w/index.php?title=Cicero&oldid=554250409>.

(2)  Wikipedia contributors;  "Theory of descriptions" in Wikipedia, The Free Encyclopedia. URL=<http://en.wikipedia.org/w/index.php?title=Theory_of_descriptions&oldid=543498908>.

(3)  <http://oxforddictionaries.com/definition/english/concept?view=uk>.

(4)  Wikipedia contributors;  "Intentionality" in Wikipedia, The Free Encyclopedia. URL=<http://en.wikipedia.org/w/index.php?title=Intentionality&oldid=547734630>.

 

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