Sep 29, 2010
Sep 27, 2010
On ridicule (again)
| 01 A: We have eight ounces left. That should last us for a couple of days a least 02 B: Heh yeah, I guess so. 03 A: Twenty-four days I would estimate. 04 B: Eight ounces?! 05 A: Sure. We smoke a lid in two or three days. ((Intervening discussion deleted)) 16 B: That’s like- that’s like drinking eight or nine kegs every week. 17 C: Or smoking two packs of cigarettes every day. 18 D: EHHH-heh-heh-heh-heh 19 B: Yeah(.) Only I don’t smoke two packs of cigarettes every- 20 C: Three? Four? 21 B: No. Not nearly that many. |
Note, however, that some things are never to be ridiculed.Sep 25, 2010
Most nerds die deflowered?
I wonder if the idea underlying the concept of “lexical gap” is indeed a feasible one. This definitely touches upon a subject we approached here in some occasions, namely reference, but also upon how linguistic intuition works. I use now the word ‘linguistic intuition’ in a broad, Chomskyan sense of “the competence of you, Mr. Native Language User, to assign features to linguistic expressions”. This competence could be applied to purely syntactical attributes such as ‘grammaticality’, to take Chomsky’s example, but can also refer to less technical issues such as “meaningful”, “appropriate”, “funny” etc. A linguistic theory, according to this view, is ‘feasible’ if it is non-contradictory and it meets the speaker’s intuition when assigning these features.
Let us assume now that there-should-be-a-word-for-it-ness is such a feature and thus has a corresponding competence of assigning it. It is this – or partly the use of this – intuition that makes Hank ask “What’s the word for when there should be a word for something but there isn’t?” However, as with grammaticality or appropriateness, the prior question is “Is there such feature as X?”. One has to assume that there is such feature as ‘grammaticality’ (= the syntactically correct vs.. the syntactically incorrect) in order for a linguistic theory to be able to asses linguistic expressions (= to say ‘this is grammatically correct’, ‘this is incorrect’ etc.). Note that the feature should not necessarily be a binary one. In the case of appropriateness, an expression could be more or less appropriate in a certain context.
Then Hank’s steps are pretty intuitive. ‘What’s the word for non-virgin?’ ‘What’s the Romanian word for shallow?’ etc. If there-should-be-a-word-for-it-ness is assumed as such, then it feels perfectly normal to have a symbol for a referent which we know it’s there. If we discover a new plant, wouldn’t we christen it? If we discover a new plant that suddenly becomes very very common around the world, wouldn’t we have even more reasons to christen it? I believe the answer to both these questions is Yes, but that this does not do justice to generalizing there-should-be-a-word-for-it-ness into a linguistic feature. I’m not very certain where the line should be drawn, but I think that there certainly is such a line.
For instance, why shouldn’t we have an adjective for “looking-like-a-tree”? Why shouldn’t we have a verb for “waking-up-very-late-and-producing-a-very-noisy-yawn”? These do not seem just as usual (more the less necessary), do they? So how do we allocate the feature there-should-be-a-word-for-it ? It is a truism that the relation between the symbols and the referent is purely arbitrary. In other words, it just happens that we call a chair ‘a chair’ and there’s nothing a priori about it, i.e., there’s nothing logically inconsistent with using the symbol ‘zum Ghhc4’ for the object which we perceive as having the qualities of what-we-now-know-as-a-chair. But does this mean that we can go around ascribing words to the world? I feel that the answer is No simply because I feel that there is no need for a verb ‘feel-that-the-answer-is-No’-ing, just as we are perfectly comfortable with using noun-phrases (e.g. definite descriptions such as ‘the man with a black jacket’) instead of simple nouns.
“Discard-poisonous-smells-while-protecting-your-rhinal-passages”-ing?
Sep 21, 2010
Trash talk, dirty talk, back talk
Speaking of pragmatics and what pragmaticians occupy their time with, I find it weirdly funny when they politely describe not-that-usual linguistic behavior. We humans are filthy things, and do things that are even filthier; but the theorist must be formal, elegant, and… well, “theoretical”. Here’s (Levinson, 1992, pp. 71-72) speaking about how constraints apply to speakers, and how rituals function as a Wittgensteinian ‘language game’. Illustration: yo momma jokes.
A simple example is provided by Labov’s (1972b) description of the activity of “sounding” among the Black community of New York. Essentially, this consists in the competitive exchange of ritual insults governed by structural constraints of two types. The first is that “sounds” or turns at ritually insulting should be constructed in a specific fashion, which Labov (1972b: 153) represents as follows:
T(B) is so X that P
where T is the target of the sound, normally a relative (typically the mother) of B, the adresee, X is a pejorative attribute like fat, poor, dirty, etc., and P is some proposition that must, when applied to T, be false (otherwise the ritual insult will become a genuine insult). The second type of structural constraint governs appropriate sequencing: if A sounds on B, B should reply with a sound based on A’s sound but which “tops” (i.e. is considered more ingenuous), and, if possible, A should then try to top that or alternatively try another kind of sound. After each stage the audience makes a vocal assessment of the sound:
A: your mother so old she got spider webs under her arms
C: awwwww!
B: your mother so old she fart dust
C: Ho lawd!
Well…
Sep 20, 2010
Sep 19, 2010
The pragma-dialectical approach to unexpressed premises
Continuing the subject from the last post, we will take a look at Chapter 6 from (Eemeren & Grootendorst’s, 1992) entitled “Unexpressed premises in argumentative discourse.” (pp. 60-72)
In the process of reconstructing unexpressed premises, the two authors distinguish at first between the logical and the pragmatic level. They note however that the two intertwine: “the logical analysis is instrumental for the pragmatic analysis” and the decision to logically reconstruct in the first place is based on pragmatic considerations. Although a criterion of validity is used, the two authors do not want this to be regarded as a commitment to a deductivist point of view. The two basic deductive system they opt for (propositional and first-order predicate logic) are only chosen for the sake of simplicity. This could of course be a way of implying that using different logical systems in what they call the “logical level” is possible, though no reason is offered as to why this may be thus.
The way in which pragma-dialecticians pick out unexpressed premises from other implicit elements is similar to the “gap-filler criterion” proposed by Govier. The logical validity criterion states that “analyzed as conveying an indirect speech act, the missing premise can be added to the argument so that the invalidity is corrected”. On what basis does one begin to make such reconstructions? Here, Eemeren & Grootendorst offer a more precise justification. First, the responsibility condition for the complex speech act of argumentation states that the speaker is committed to seeing the argumentation as an acceptable defense of his standpoint. (According to the pragma-dialectical approach, arguing for something is a way of committing yourself to the acceptability of the standpoint and, a fortiori, of the argumentation, see speech-act conditions for argumentation here). Second, the listener (and, of course, the analyst), to the extent that argumentation is advanced sincerely, “will be inclined to apply the same criteria of acceptability as himself [the speaker]. These criteria will include criterion of logical validity” (p. 62). If the argument is not already fully explicit, i.e. if the literal interpretation produces an invalid argument, and if the two conditions are met, the listener can supply the unexpressed premises. In simple cases this could be of the form: “Angie is a real woman, therefore Angie is nosy”, with the missing premise “All real women are nosy”. Since the unexpressed premise is a “special sort of indirect speech act”, reconstructing it has something from Searle’s treatment of indirect speech acts (check that here).
Or you can just use the injecting kit
But at this point the analysis is incomplete because there are many other candidates that would render “Angie is a real woman, therefore Angie is nosy” valid. The pragmatic criterion, and with this one moves toward the pragmatic level, is that the reconstructed version of the argument must conform “to all the rules of communication” (63). To make things clear, the two authors introduce the difference between what they call the logical minimum and the pragmatic optimum. The former – which is the “if CON, then C” from Govier’s text – is superfluous. All it does is state explicitly what both the speaker and the listener assume: that the conclusion follows from the premises. The latter is “the premise that makes the argument valid and also prevents a violation of … any rule of communication” (p. 64). At this point, the two authors arrive at a principle with some degree of generality. They say: “Predominantly, this is a matter of generalizing the logical minimum, making it as informative as possible without ascribing unwarranted commitments to the speaker and formulating it in a colloquial way that it fits in with the rest of the argumentative discourse” (idem). In our case, such a pragmatic optimum would be “Real women are nosy”.[1] To assert the argument and to deny this would amount to a pragmatic inconsistency.
When different, equally validating premises are available, the context should be taken into account. In fact, it is almost impossible to assess the adequacy of the missing premise if little is known about the context. The procedure is, then: (1) determine argument and conclusion, (2) det. relevant contextual information, (3) det. logical minimum, (4) det. most informative, (5) det. least commitment attributing. In the last part of the chapter, the two authors scrutinize briefly the reasoning patterns one can use to begin reconstructing the logical minimum. In general, this is based on simple syllogistic or propositional logic.
Let’s take their example (pp. 67-68).
Context
Father, mother and daughter are finishing supper. The daughter is looking rather depressed.
Mother: “There’s no sense in waiting for Mr. Right to come along, dear: I never did”
Analysis
Standpoint: It makes no sense for you to wait for Mr. Right
Argumentation: I never waited for Mr. Right
Logical minimum: If I never waited for Mr. Right, then it makes no sense for you to do it
Pragmatic optimum(1): As far as your love life is concerned, you should always behave like me
Pragmatic optimum(2): You should always behave like me
Pragmatic optimum(3): I always do what makes sense
Pragmatic optimum(4): One should always do what makes sense.
Choice
(2) Mother may consider herself an expert only in love affairs
(3) Mother may know that she herself makes mistakes
(4) Mother may find that other people than her daughter are free to do foolish things
Given the restricted contextual information (1) is more informative than the logical minimum and is less attributing than (2)-(4).
[1] This is a surprising choice from the authors’ part. So at one end we have the logical minimum. At the other we have the outdone, over the top, over-attributing generalization. In the middle, we have the pragmatic optimum. Now, of all the statements that can possibly fit this role, the one chosen is, I think, the most semantically ambiguous. I think the only difference between “All real women are nosy” and “Real women are nosy” is that the latter is more ambiguous. Could it be that this is what is meant by “fit in with the rest of the argumentative discourse”?
Sep 18, 2010
Govier on ‘missing premises’
This is a summary of (Govier, 1987). The article, something of a classic along with others written on the same theme by Walton, Tindale, Ennis and Hitchcock, deals more with what not to do when considering missing/unexpressed premises. It is stressed right from the beginning that, despite the title, there is no one problem of missing premises. Moreover, there seems to be a distinction between deciding what arguments have missing premise(s) and what premises are missing.
The deductivist tradition, which holds “all good argument” as deductively valid, resolves the problem of missing premises by stipulating that “an argument must be supplemented with additional premises until it becomes deductively valid” (82). After this operation, i.e. after it’s fully reconstructed, the argument can render itself to critical scrutiny: truth of the premises makes the argument good, falsity – bad or poor. According to Govier, the first “curious” consequence is that logic can only be used for reconstruction. The second one is that not only the associated conditional (the “If CON, then C”, which is a pure reiteration of what is expressed[1]) can be easily used, but any other statement which entails it. Third, there is virtually no way of dealing with non-deductive arguments such as argument from analogy, for which a deductive reconstruction is inappropriate.
Another option is supplying a generalized version of the “If CON, then C”[2]. But in this case, we might be “committing the unhappy author to sweeping premises” (86). They could be critically useful (for the appraisal of the argument) but they are interpretively questionable. The third option, going for a text-based version of the needed premises, can lead to an indefinite multiplication of statements which become pedantic but not very useful. As Govier puts it, they can give rise to a “critical and pedagogical monster”.
The usual argument you have in the middle of the desert.
With a horse. Who looks like Anton Chigurgh.
And who’s pointing a hoof at you.
The first important distinction – in order to arrive at both a useful and an accurate reconstruction – is to separate the concept of “missing premise” from that of “assumption”. The main reason goes like this: since acts of communication are not possible without taking for granted an array of assumptions, every argument will turn out to be an enthymeme. But there are other reasons: if we start supplying assumptions, where do we stop? It is clear, then, that some reduction must be made. Following Robert Ennis, Govier underlines that “only one unstated assumption is the missing premise” and that is the one which functions as a “gap filler”; in other words, which, by virtue of its form and content, fills the inferential gap from argument to conclusion.
But now which one is it? Govier argues that a universal answer cannot be given to this question because every reconstruction pre-supposes a theory of argument. The analyst finds an argument “gappy” only in the light of some known, well-formed and legitimate scheme or generalized form. What’s more, different theoretical views will ‘find’ different missing premises according to their purpose. This leads to an interesting conclusion and that is “In the absence of universally applicable notion of complete argument, it appears that the missing premise is a product of the reflective mind. Like Humean causes, it is thrust upon the external text by the active intellect – of the critic.” (Govier, 1982). Nevertheless, some general principles exist: a charitable reconstruction, for example, will mean filling out the best possible argument for that conclusion. Charity must be balanced by interpretive accuracy: “select those that cohere with the beliefs, intentions and commitments of the arguer”. These principles may weigh differently for different purposes, but it’s for the better that they are always observed and that the critic is aware of his position.
[1] “If CON, then C” stands for “If conjunction of the premises, then conclusion.” For instance, the associated conditional of the argument “You are a cheap bastard because you have cheap jeans” is “If you have cheap jeans, then you are a cheap bastard” (which makes the argument deductively valid). It is said to be purely reiterative because it does nothing more than reformulate what is already expressed in a Toulminian warrant form. For instance, the associated
[2] In our case, “All cheap-jeans-wearers are bastards”.
Sep 16, 2010
Forget Batman. Introducing mathematical logic!
[I never thought I’d say this on this blog, but this post contains NO SPOILERS]
Title: Logicomix
Authors: Apostolos Doxiadis & Christos H. Papadimitriou
Publisher: Bloomsbury
Year: 2009
What a yummy reading! If you generally like cookies, and you can imagine them being in a jar, in a big transparent jar, which you own (and are able to open), then for you I will equate Logicomix with a big big jar of natty cookies.
The cover rightly announces “An Epic Search for Truth”, but “∀[geek(x)→buy-book(x)]” could just as well have been the subtitle. Also, the book’s sleeve says “This innovative graphic novel is based on the early life of the brilliant philosopher Bertrand Russell” but having read it, one can properly change this unfaithfully sober introductory note into: “Look. Remember logic and maths and philosophy and all the famous swoon-manufacturers? I can prove that… well, I cannot prove that, but I can go some way towards showing you that, dispensed with tutti i dettagli tecnici, the story of these subjects is brillarious. Somewhat offtopic, not the author account for his choice for this particular mathematician among other possible ones: “he was the only one of these characters who was not a mega-nerd”. Fair enough!
It all starts with Bertie as a little boy, raised by a stroppy, militant Catholic grandmother whom everyone called „Lady John”. It was at this early stage, gravelled by Lady John’s portentous imperatives („You shall be well-groomed at all times”, „You shall never go barefoot”, „No Xbox”, „No YouTube”...), that pint-sized Bertie acquired his longing for solid foundations. What was behind and beneath rules? What can be so certain as to give rise to such unyielding laws? Very soon – lucky for us – he was about to find out that religion and morals weren’t bags in which to search for ideals such as certitude or infallibility. But science was!
And what is physical science if not applied mathematics? His first tutor – rigorous, though religiously-lax – introduced Bertie “to a very old gentleman”: Euclid. Now this gentleman was all about necessity... demonstration... all day long, QED this, QED that... Nevertheless, following this trail deeper and deeper Bertie discovered the uncanny, undisputed axioms. As the carroty tutor put it: “Even old Euclid has to take something for granted...” Let us pause and read the actual excerpt from Russell’s autobiographical essays:
Geometry in those days was still ‘Euclid’. My brother began at the beginning with the definitions. These I accepted readily enough. But he came next to the axioms. ‘These’, he said, ‘can’t be proved, but they have to be assumed before the rest can be proved.’ At these words my hopes crumbled. I had thought it would be wonderful to find something that one could prove, and then it turned out that this could only be done by means of assumptions of which there was no proof. I looked at my brother with a sort of indignation and said: ‘But why should I admit these things if they can’t be proved?’ (Russell, 2009, p. 29)
One Boolean-driven adolescence later, Bertrand Russell goes to Jena to meet the minute ill-tempered Frege and his Begriffsschrift, and this is how it all starts. Because, as we know, Frege’s lifework, Die Grundlagen der Arithmetik (The Foundations of Arithmetic), omitted one foundation-demolishing point: (what we now know as) Russell’s Paradox, the discovery of which went something like this:
Thus the odyssey begins. Whitehead, Cantor, Moore, Hilbert, international congresses, Peano, war, prison, Wittgenstein, pacifism, love, universal quantifiers... It should be fairly obvious at this point that the villain is not Dr. Doom, Green Goblin or Magneto, but ContraDiction. Mmwhahahhaaaa!
| | (Previous-Guy voice:) At the dawn of a century, when the incontrovertibleness of axiomatic set-theory was de-energized by an anonymous Brit, everything was rumbling… The starting points of mathematical knowledge, the bare essentials of logical processes, the Gotham City of Proof – if I may – must be saved from the wicked wide-reaching limbs of Contradiction. Beware! Or, put differently, ¬∀(x)φ(x), where ‘x’ is rock-hard arithmetical certainty. |
No wonder whatever that madness is the other major motif of the book. “In this particular branch of mathematics - mathematical logic - there was a very, very high incidence of serious mental illness. That was something we found particularly interesting”, said the author. In all this, Kurt Gödel appears at the end as a deus-ex machina. Will they succeed?
Sep 15, 2010
The critical discussion is a British thing
I bet pragma-dialecticians would be proud of how well their ideal model applies here. Be patient until 7:11!
Sep 14, 2010
Speech Act Theory 101. What is a speech act?
I’ve been asked a lot of times…
Actually, I’ve only been asked once, but I’ve been thinking about it. What is the best thing to start with? All of a sudden, you wake up one morning and say to yourself: “Man, how I wish I’d start reading something related to argumentation theory!” So you’ll be something like:
Is he left-clicking a mouse there?
This is highly improbable, but it’s for pedagogic purposes: what do you do? Aristotle? Whatley? Perelman? Toulmin? Hamblin? I think the best, most solid place to start with is Speech Acts theory. Searle’s “What is a speech act” (Searle, 1965) in particular.
(this is a summary I once did for one of my classes, so it’s a bit stiff)
This article appeared precisely ten years after J. L. Austin’s famous William James lectures (1955, published for the first time in 1962 as How to Do Things With Words). This betokens not only Austin’s major influence on Searle’s thesis (which would appear as Speech Acts: An Essay in the Philosophy of Language in 1969) but also Searle’s interest to advance and improve what Austin had started. The main objective in “What is a speech act?” is to shed some light on the theoretical account which could lead to such betterments. To perform a speech act is to “engage in a rule-governed form of behavior” (40). In order to understand the implications of this definition, Searle seeks to explain three closely-related concepts, which constitute the focal point of the theory of speech acts: rule(s), proposition and meaning.
There are two kinds of rules which are relevant for the study of language: regulative and constitutive. The ones in the first category “regulate antecedently existing forms of behavior” (41) and could be likened to rules of etiquette. They usually take have the imperative form “Do/Don’t do X”, e.g. “Do not talk with your mouth full”. Constitutive rules, on the other hand, create the very form of behavior they regulate. These latter ones could be compared to rules of games. As Searle notes, they are “almost tautological in character” and can sometimes appear as an “analytic truth” (41) because they take the form of partial definitions: “a checkmate is made if the king is attacked in such way that no move will leave it unattacked.” Constitutive rules should be understood not as do’s and don’ts, but as “X counts as Y”. Illocutionary acts (i.e. speech acts) are performed in accordance with sets of constitutive rules. Searle comes back to illustrate this at the end of the article.
The proposition (or propositional content) of a speech act is the act of referring and predicating. Thus, when I utter “Is my sister here?” and “My sister is here”, I use the same propositional content (i.e. I refer to my sister and predicate the act of being here) to perform different speech acts: a question and a statement. One must distinguish then between propositional content and illocutionary force. In some case, the illocutionary force is made explicit by “function-indicating devices” (43), e.g. “I promise that I will be there”.
As regards meaning, Searle takes as a starting point Grice definition: to say that a speaker S meant something by x is to say that ‘S intended the utterance x to produce some effect in an audience by means of the recognition of this intention’. The term “effect” there is ambiguous since, in uttering something, one can produce an illocutionary (intention-recognizing) as well as a perlocutionary (convention-recognizing) effect.
In the final section, Searle exemplifies the necessary and sufficient conditions for the performance of speech acts by describing the speech act of promising. In regard of what they regulate, Searle dubs these propositional content conditions, preparatory conditions, sincerity condition and essential condition. He then includes these insights into the new definition of ‘meaning’.
After reading Searle’s “What is a speech act?”, you’ll be able to see how this guy – while reasonably funny – is confusing ‘speech act’ and ‘indirect speech act’ (and, in some cases, ‘speech act’ and ‘perlocution’).
PS:
Don’t be misled by the title. It won’t go 102, 103, etc. You can, however, search “speech acts” on this blog, or go directly to some of the related posts: J.L. Austin’s How to do things with words, J. Searle’s Speech Acts, “Indirect speech acts”, “A Taxonomy of illocutionary acts”.
Sep 10, 2010
Reference. Part IV – Saul Kripke
This fourth (and last) part of the series on reference deals with the subject of proper names. I know it sounds tedious, it certainly did to me at first, but I assure you it can become an absorbing subject once you pose the right questions. In fact, experiencing the rumpus around proper names, David Kaplan famously remarked that “if it weren’t for the problem of how to get the kids to come in for dinner, I’d be inclined to just junk them” (quoted in Abbott, 2010, p. 100). This account will stop at, and insist upon, Saul Kripke’s Naming and Necessity. When Kripke delivered his lectures at Princeton University (1970), which later became what we now know as Naming and Necessity, philosophers like Mill, Frege, Russell, Wittgenstein II, Searle and Strawson were the leading figures which had undertook to incommode their brains with the problem(s) of proper names. It’s awfully-succinct-synopsis-time!
Mill included proper names in a special “denotation-without-connotation” category. According to this view, although proper names denote an individual (person, dog, city), it is not part of their meaning (as it is the case with definite descriptions) that they convey any attributes of that individual. As Abbott condensed it, “you have the name and you have the [thing] itself, and that’s all there is.” (2010, p. 15). This didn’t really fit Frege’s sense-reference dichotomy (1982). If the name and the object “is all there is”, how come different names standing for the same object seem to amount to different propositions (or thoughts)? The whole Morning Star/Evening Star/Venus issue was then resolved by Frege quite effortlessly, as an extraneous point in a footnote[1].
For Russell, Frege’s elucidation fit perfectly into his Theory of Descriptions. We would then be able to answer why one can speak of Aristotle, the denotation of which one has never met: it is because they are in fact employing definite descriptions. Searle and Strawson were to continue this “descriptivist” (i.e. names as definite descriptions) standpoint in what was to be called “cluster view”. Proper names, according to cluster descriptivism, express not one but a bunch of descriptions, from which we can typically select those that are necessary or sufficient.
Aristotle, Shmaristotle… same guy!
Kripke begins by pushing descriptivism to its inevitable limits: if the actual sense of a name is a definite description, then, strictly speaking, they are not names but descriptions (“abbreviated descriptions”). In order to ‘make sense’, a name must have at least one description that can replace it, so we can say it is “short for at least one property”. This leads descriptivists to the idea (endorsed by Russell, in some respects) that the only ‘pure’ proper names in natural language are demonstratives (‘this’, ‘that’), used ostensively to point at the referent (1980, p. 27).
Although very much in line with certain epistemologies, the descriptivist perspective is in fact quite unintuitive. If “Aristotle” is to mean “the greatest man who studied with Plato” (or any other description from a cluster), then saying “Aristotle was the greatest man who studied with Plato” seems an a priori truth. Moreover, this conception of proper names would make counterfactual thinking rather queer if not illogical:
But then, when we say counterfactually 'suppose Aristotle had never gone into philosophy at all', we need not mean 'suppose a man who studied with Plato, and taught Alexander the Great, and wrote this and that, and so on, had never gone into philosophy at all', which might seem like a contradiction. We need only mean, 'suppose that that man had never gone into philosophy at all' (p. 57)
What would allow one to surpass these counter-intuitive flaws of any descriptivist account, is to view proper names as rigid designators. What this means is that, contrary to the way a description ‘behaves’ in other possible worlds, a rigid designator cannot vary its reference. It is possible to conceive of such rigidity because (and here is the beauty of late analytic philosophy): “Aristotle might not have been Aristotle” strikes us as false. We can imagine that Aristotle could not have been named ‘Aristotle’, but once we have fixed the reference, once – if you like Carnapian terminology – the intension picks the same individual out of each possible world, there is no such possible world where that individual is not (what we refer to as) Aristotle.
To make this slightly more clear, we can say that, as regards the name “Aristotle”, we can do two major things: “define it” (in terms of contingent properties) or “use it to fix a reference” (in terms of necessary properties in all possible worlds”). We can define “Aristotle” (arbitrarily) as “the man who wrote Nicomachean Ethics”, or we could fix the reference of “Aristotle” as a set of criteria of identity across possible worlds. This does not mean that this set of criteria (Aristotlehood) is easily identifiable. If we do this, as regards the first, we can imagine “the man who wrote Nicomachean Ethics” being someone else than Aristotle. We can also imagine someone saying “Aristotle” and not referring to the individual Aristotle – a student misreading his notes, thinking that Aristotle wrote The Republic, and thus referring to Plato. But we cannot imagine Aristotle being someone else that he was. The fact that he at least existed, seems a necessary truth.
In fact, this is also extendable to certain common names. Take for example “gold” or “tiger”. If tomorrow, Kripke argues, scientist will discover that what we see as (more or less) yellow when we look at gold is an optical illusion, and that the color is in fact blue, the newspaper would not say “There is no gold”, but “Gold is in fact blue”. We use ‘gold’, in this case, as a rigid designator – to pick out a certain kind of object. The way the reference is fixed is not a synonym for the term. According to this view, “terms for natural kinds are much closer to proper names than is ordinarily supposed”.
Kripke (p. 90ff) further argues that the ‘connection’ between a name and its referent is extralinguistic. That is, it is a sort of original “baptism” (which could be imaginary or real). So names, in this sense, stem from this act of baptism though the actual property we use to perform the baptism is contingent. Moreover, it could be untrue. But once it is established, it designates the individual rigidly and for all speakers from a community using the name, “Name” can be used as a rigid designator.
Let me wrap really quick it up by saying what we did not do here, since I think it’s quite obvious what we in fact did:
(1) We have in no way covered thoroughly neither the subject of reference nor the theoretical views of definite descriptions or proper names. This was only a nontechnical glimpse of it. There are many areas of reference which haven’t been covered here (some not even mentioned). If, by ‘reference’, we understand noun-phrases, i.e. each phrase the use of which can refer, than we have skipped a lot.
(2) We haven’t always presented the whole story. One has to remember that, after momentous articles such as Frege’s “On Sense and Reference” or books such as Kripke’s Naming and Necessity, a dreary heap of books, articles and mini-articles are always readily written. A complete view is almost impossible. No view is, I assumed, worse. So I planned on landing somewhere in between.
[1] Frege wrote: “In the case of an actual proper name such as 'Aristotle' opinions as to the sense may differ. It might, for instance, be taken to be the following: the pupil of Plato and teacher of Alexander the Great. Anybody who does this will attach another sense to the sentence 'Aristotle was born in Stagira'”
Proper names
Oh, this is such, such an accurate introduction to our next subject. Someone said that, due to the excessive amount of humour, people tend to overlook just how wise Ricky Gervais can sometimes be. That someone could have easily refered to this moment
PS: As the observant reader of this blog will have already noticed, prolonging the topic of “reference” will lead us farther and farther from the field of argumentation. I do not regard this as a defect. I do however intend to eventually remedy it by swerving towards my (our?) main interests.
Sep 8, 2010
Reference. Part III – P. F. Strawson
Let’s review what has been said so far on the subject of reference. Detailed accounts of what I will sketch in the next two paragraphs can be found in Part I and Part II.
Gottlob Frege was the first[1] to try to pinpoint the ancient-old correspondence theory of meaning. Inelegantly put, the “how come words stand for things” issue? Does it apply to all words? And what is the nature of the connection between the two worlds: the linguistic and the factual? As we have seen, the first problem he encountered regarded the nature of identity statements. If the reference of a statement is its truth value, what changes, if not the reference, when we substitute co-referential expressions? In other words if “Bill is chunky” or “Your brother is chunky” or “That guy over there is chunky” have the same truth value (assuming that “Bill”, “Your brother” and “That guy” refer to the same object), what changes? There’s definitely something changing because you could know “Bill” is “his brother” and not know that he’s “that guy over there” (or know that “he’s that guy over there” but not know that he is “Bill” or “his brother”). Frege’s answer to this, as we have seen, was the introduction of sense. “This “sense” of a word or phrase is what distinguishes otherwise coreferential expressions. Ringo Starr and the Beatles’ most famous drummer may have identical referents, but are distinguished by their senses.” (Carlson, 2004, p. 79).
Some years later, Bertrand Russell showed that, although Frege was right in making some of the claims, his distinction could not give an accurate account for the phenomenon of “empty names” (and was, all things considered, an unfruitful theory). Russell’s famous article (“On denoting”) was in fact concerned with disproving another explanation of how come empty names “work”, i.e. how come “The present king of France is bald” is not meaningless, despite its lack of reference. Philosophers like Alexis Meinong (and even Frege) ended up formulating some very dubious ontological positions. Amongst them was that the statement “The present king of France”, assuming that there’s no referent for this in the real world, must have a reference in some other world or subsist in some form as an object.
P. F. Strawson (1919-2006) was an English philosopher representing the earlier generation of the new, shiny and promising analytic philosophy, and whom monochrome exposure seems to have turned into a badass of supreme style.
This is pure British pimpin.
Apparently, chuck-norrisness wasn’t only a feature of his looks. In 1950[2] he wrote a paper called “On referring”, in which he announced: “I think it is true to say that Russell's Theory of Descriptions […] embodies some fundamental mistakes” and “I think that Russell is unquestionably wrong”. To speak like this about a 45 year-old undisputed theory… Anyhow, his paper is valuable not only for the unfavorable judgments it presents, but also for the manner in which it disentangles Russell’s theory. As we will see in later posts, Strawson’s view is not state-of-the-art in semantics (nor in pragmatics, for that matter), but it draws some very basic distinctions which are now widely acknowledged.
Strawson begins by extracting (p. 320) two principles upon which Russell (implicitly) based his theory:
(1) Only logical proper names can occur as (genuine) subjects of sentences.
(2) A logical proper name is meaningless if there isn’t one single object it designates.
What the first principle tells us is that grammatical subjects (‘X’ from the sentence ‘X is such-and-such’) must designate uniquely in order to actually be logical subjects. So if “The king of France is bald” – which, by the way, Strawson changes to “The king of France is wise”, not sure why –, if that proposition is not meaningless, and it isn’t, then either:
(a) “There is a king of France” is a logically proper name (cannot be the case)
(b) The form of the sentence (‘X is such and such’) is misleading. And it should be analyzed as a certain type of existential statement, where the definite description (‘X’) disappears.
From this point on, we know the story.
Roughly put, Strawson’s pretension is that, although Russell was not in error when rewriting definite descriptions in that way, he wasn’t doing what he was purporting to do. According to Strawson, the three sentences[3] which make up Russell’s analysis:
do describe circumstances which are at least necessary conditions of anyone making a true assertion by uttering the sentence S [i.e. “The king of France is wise”]. But, as I hope to show, to say this is not at all the same thing as to say that Russell has given a correct account of the use of the sentence. 324
What Strawson hoped to show is that “referring” is not wholly a semantic phenomenon, but also (and, in fact, mainly) a pragmatic phenomenon. To refer (or ‘mention’, Strawson seems to use them interchangeably) is to do something. And sentences do not do things. This is so straightforward that it scarcely needs any clarification. Furthermore, he illustrates it even simpler: Had someone uttered “The king of France is blad” in the 14th Century, it would have been a true proposition. That is, it would have been a true use of the sentence ‘The king of France is bald’.
This is just an example of a broader issue one needs to clarify. A sentence (one and the same sentence) can be used in different contexts or occasions and thus produce different truth-values. Truth-values are functions of the use of a sentence. Sentences are neither true nor false. So, although syntactically correct, the sentence ‘The king of France is bald’, just like, say, ‘This chair is brown’ has no truth-value. To ask about the truth-value of a sentence is to ask of its uses. An analogous treatment can of course be applied to expressions (i.e. ‘The king of France’ in “The king of France is bald”). To say that the expression refers to (or mentions) something “would be a derivative way of speaking, like describing a knife as cutting well” (Abbott, p. 2). Another distinction, though not directly relevant for now, can be made between “use” and “utterance”. “[I]t will make sufficiently clear what I mean by an utterance of a sentence if I say that the two men who simultaneously uttered the sentence in the reign of Louis XIV made two different utterances of the same sentence, though they made the same use of the sentence.” (p. 329)
With this in mind, turning back to our worn-out example, speaking of the truth-value of the use of the sentence “The king of France is wise” in a context where France is not a monarchy is absurd.
Now suppose someone were in fact to say to you with a perfectly serious air : " The king of France is wise ". Would you say, "That's untrue" ? I think it's quite certain that you wouldn't. But suppose he went on to ask you whether you thought that what he had just said mas true, or was false; whether you agreed or disagreed with what he had just said. I think you would be inclined, with some hesitation, to say that you didn't do either; that the question of whether his statement was true or false simply didn't arise, because there was no such person as the king of France.
The reason why the question “simply didn’t arise” is that he is not saying neither of Russell’s necessary conditions, though he is implying them. This sense of “implication” was the father of the later presupposition. The speaker seriously uttering (today) “The king of France is wise”, would be confronted with his or her presupposition failure. We wouldn’t say “that’s false”, but (and if we were Strawson) something really-really British like “I'm afraid you must be under a misapprehension”. Note, nevertheless, that the sentence still has a significance and that is because “to talk about the meaning of an expression or sentence is not to talk about its use on a particular occasion, but about the rules, habits, conventions governing its correct use, on all occasions, to refer or to assert.”
Before ending P. F. Strawson’s moment of awesomeness, let us note that these ideas were not new. Ferdinand de Saussure had made a similar distinction between the language (as linguistic system) and the language (as use of that linguistic system). In French, this distinction has correspondingly different nouns. We speak of langage [lɑ̃gaʒ] as a system of signs, and of parole [paʀɔl] as the use of that system. Those who come here often know that we have seen this meta-theoretical principle put into practice here. I have never seen this correlation being made anywhere. Plausible or not, Strawson does not mention anyone (not even Frege’s sense, where it would have been appropriate) because of his badassitude.
[1] It should be noted, however, that some pre-modern accounts had existed. J. S. Mill is often seen as the first philosopher interested in the problem of meaning. For instance, it is to him that we owe the distinction between “denotation” and “connotation”. Maybe we will touch upon Mill’s contributions when we will review Kripke’s Naming and Necessity (1972). More specifically, the second chapter of Mill’s A System of Logic, entitled “On names”.
[2] That is no less than 45 years after Russell’s “On denoting”. It is a token of Russell’s weird longevity that he actually got to respond to the criticism presented by Strawson. And no earlier than 7 years later!
[3] (1) ∃x[rule(x, France), (2) ∀y[rule(y, France) → y=x, and (3) wise(x)
Sep 6, 2010
Reference. Part II – Russell’s solution
This post might come across as moot for several reasons. Those who know what happened after (and with) Russell’s theory of descriptions, the small coup d'état in semantics some 40 years ago involving names such as P.F. Strawson, Saul Kripke, Hilary Putnam, David Kaplan, and Keith Donnellan, might take a dim view of it. What’s more, someone genuinely interested in the matter can find a satisfactory overview of the theory on the web (here or, even better, here). However, I will try to focus on the context of its appearance, on the one hand, and its outcome, on the other, more than on the technicalities the theory involves.
Two things should be noted here. First the puzzle to which Russell sought to give an answer and second, but not less important, Russell’s attacking angle. Let’s look at the puzzle. The age-old conception of discourse as “symbols that represent objects” had been questioned and in fact partly refuted by Frege’s article. If “Superman” and “Clark Kent” designate the same individual – we say the terms are “coreferential” – then (1a) “Superman is Clark Kent” or (1b) “Clark Kent is the man who saved Louis Lane” should be something of a tautology or an a priori statement in virtue of the meaning of its constituents. However not only that (1) is different from (2) “Superman is Superman” or “Clark Kent is Clark Kent”, but one could know truths about one without being aware of the other. If we state (3) and (4):
(3) Louis Lane knew Superman could fly
(4) Louis Lane knew Clark Kent could fly,
the first seems true while the other does not. Frege’s way out of this was postulating the difference in “mode of determination”, which later became the term sense. Replacing “Superman” and “Clark Kent” changes the meaning of a sentence since the terms have different senses. But Russell didn’t accept this.
Ghastly intermezzo.
If this is not the scariest picture you’ve seen today,
I don’t know what you are occupying your time with.
What, what happened to poor Bertie’s forehead?
Marching on.
In a famously obscure passage from “On Denoting”, sometimes known as ‘the Grey’s Elegy passage’ (Russell, 1905, p. 486), Russell rejects Frege’s set of terms (“reference-sense”), as either indistinguishable in analysis or unnecessarily restrictive[1]. Russell’s solution to the puzzle was to treat definite descriptions as quantifications. By “definite descriptions” we mean those of the form ‘the so-and-so’ – ‘the man who saved Louis Lane’, ‘the middle of a segment’, ‘the object on the table’. By “quantifications” we mean logical operators such as ‘every’, ‘none’, ‘some’ etc. Why does treating ‘the’ as a quantifier make a difference? Because by not treating the expression as a referring expression, and treating it as a quantifier, you can actually reduce it to a relation between two properties. Remember what Russell said last time about properties (i.e. predicates), that they are known by acquaintance, (i.e. in “All swans are white”, we conceive of the concept of whiteness)? Well then, accordingly, if we manage to turn “The so-and-so is such-and-such” into an open sentence – a sentence with variables – of the form “All/Any/Every such-and-such is such-and-such”, we reduce descriptions to knowledge by acquaintance. All that one needs is to be acquainted with the properties and with the relevant syntax.
Before I illustrate, let us note that this is not just a different notation; it is – so to speak – a different translation. What Russell is basically saying is this: In the case of expressions such as the so-and-so, natural language is deceiving. And that is because these expressions do not have a meaning on their own, they do not refer to anything, but instead – and if we translate properly – they express a relation, or several, between two variables. The conclusion Russell needed, and to which he finally arrived, was: “Thus in every proposition that we can apprehend (i.e. not only in those whose truth or falsehood we can judge of, but in all that we can think about), all the constituents are really entities with which we have immediate acquaintance.” (1905, p. 492).
The logical answer along with the notation are in fact remarkably simple. In predicate logic (at least as it was developed at that time – mostly by Frege), properties apply to the variable noted between brackets. So,
(1) No swan is black
(2) ~Ǝ[swan(x) & black(x)]
(3) There is no such thing (~Ǝ) as an entity (x) which is both (&) a swan and black.
To take another (somewhat different example):
(1) Everyone was there
(2) ∀x[person(x) → is-there(x)]
(3) Whatever (x) may be, if he was a person, he was there.
How does this apply to ‘the such-and-such’ expressions? Let us embrace the overexploited example “The King of France is bald”, since we will use it again with our second puzzle – that of empty names. According to Russell, when we say “The King of France is bald”, we actually say the conjunction of:
(1) There is a king of France.
(2) There is not more than one king of France.
(3) There is nothing which is king of France and is not wise.
∃x[rule(x, France) & ∀y[rule(y, France) → y=x] & bald(x)]
In predicate logic form, as Russell writes, what has been achieved was “a reduction of all propositions in which denoting phrases occur to forms in which no such phrases occur.” (1905, p. 482). Thus, the denoting phrase, if properly analyzed, it disappears.
But this in fact actually leads to a solution for the other major problem. Remember Russell’s funny remark about “Hegelians loving a synthesis”? I will cite the passage again, for it reveals the problem of the so-called empty names “The Golden Mountain”, “The King of France”.
By the law of excluded middle, either “A is B” or “A is not B” must be true. Hence either "the present King of France is bald” or “the present King of France is not bald” must be true. Yet if we enumerated the things that are bald, and then the things that are not bald, we should not find the present King of France in either list. Hegelians, who love a synthesis, will probably conclude that he wears a wig.” (Russell, 1905, p. 485)
So what, in view of the newly proposed translation, could Russell’s response be? Well, since expressions such as ‘the so-and-so’, on closer scrutiny, turn out to be quantifiers, the puzzle itself is not a puzzle at all. If we properly analyze what is meant by “A” or “B” when they are empty names or definite descriptions, the description disappears. Now, of course, this answer (The puzzle is not a puzzle at all) needs further refinement. For that, we need to introduce another term, “scope” (and, in fact, more importantly, “scope ambiguity”). Will dwell on this in part 3 of this post, which seems to stretch alarmingly...
[1] Elegant restatements of that passage could be found in John Searle’s “Russell’s objections to Frege’s theory of sense and reference” (1958), and thorough explanations in Makin (2000, p. 203ff).
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Sep 4, 2010
Russell’s ‘acquaintance’ and ‘description’
Since the second part of the post on reference will concern Bertrand Russell’s theory of descriptions, and since this theory was devised to back up a long tradition of British empiricism that culminated in Russell’s thought, an intermission seems appropriate. For that, we shall occupy our attention with a certain section from The Problems of Philosophy, reprinted as “Knowledge by Acquaintance and Knowledge by Description” in (Russell, 1961, pp. 217-224).
The simple question Russell seems to answer is this: How can we know the things we don’t feel/see/hear/touch? How do I know that World War II began in 1939? How do I know that the girl in the other room is my sister? How do we know that tomorrow is Sunday?
First, the distinction. Russell writes:
We shall say that we have acquaintance with anything of which we are directly aware. (217)
We can say that what Russell refers to here is a sort of direct knowledge of sense-data (color, shape etc.). One shouldn’t, at this point, throw caution in the wind and say that we are acquainted with objects, for – at least in Russell’s terminology – there’s a big metaphysical gap between the object itself and the sense-data we receive of that object. The sum of the latter could be called the object’s appearance, and it is known by acquaintance. Although “there is no state of mind in which we are directly aware of the table [i.e. the physical object itself]” (218), we can always know it by description. Russell writes:
We shall say that an object is 'known by description' when we know that it is 'the so-and-so’ (222)
In other words, the only way we can really ‘touch’ the object itself, is by knowing true statements about it. Generically, a true statement about an object the physical world will be of the form “[description] is [description]”[1]. Descriptions can be ambiguous (or indefinite) as when we say ‘a man’, ‘a cat’, ‘a winner’, but can also be more or less definite ‘the man who you met last week’, ‘the cat that landed in the pool’, ‘the winner of Miss America’. We will see that, not without controversy, Russell includes proper names in the category of definite descriptions[2].
What does this have to do with empiricism? To answer this, we must look at some special forms of acquaintance, in the above-given sense. Russell notes that, if our capacity of knowledge by acquaintance would have only been exercised as to sense-data, our existence would be limited to things we perceive. However, to quote an example given in the early pages of The Problems of Philosophy, if we cover the table with a tablecloth and thus cease to perceive, we know the table is still there.
This happens because we are capable of being acquainted with other things such as past events (through memory) or ourselves (through introspection). As regards introspection, to follow Russell’s example, we could easily notice that we sometimes are not only aware of some existing thing, e.g. the sun, but also of ‘my-seing-the-sun’. This, along with knowledge of sense-data and past events is called “knowledge of particulars”. But we are also capable of knowing what Russell calls ‘universals’. Universals are “general ideas” such as wetness, tidiness, brotherhood (220). Every time we predicate something of some other thing, e.g. ‘The snow is white’, we are acquainted with a concept, in this case – whiteness. This use of knowledge, which Russell calles conceiving, is one of the main ways back to the empiricist postulates.
The fundamental principle in the analysis of propositions containing descriptions is this: Every proposition which toe can understand must be composed wholly of constituents with which we are acquainted. (223, italics in original)
What is particular in the proposition is subject of ‘acquaintance of particulars’, what is general – subject of ‘acquaintance of universals’. I can understand ‘John is tall’, and know its truth-values, because I can perceive the sense-datum of John’s body, and because I can conceive the concept of tallness. I can even understand expressions such as “a guy without money”, but it would not form a proposition since it would be composed only of descriptions.
Definite descriptions (‘the so-and-so’), as we will see, are the highly problematic to corroborate with this epistemology. It is why Russell devised the TOD, and it is why he wrote in 1919, while in prison,
… in this chapter we shall consider the word the in the singular, and in the next chapter we shall consider the word the in the plural. It may be thought excessive to devote two chapters to one word, but to the philosophical mathematician it is a word of very great importances: like Browning's grammarian with the enclitic δε, I would give the doctrine of this word if I were “dead from the waist down” and not merely in prison.
To which, Standford Enciclopedia of Philosophy notes: „Strong stuff!”.
[1] This is, roughly, the P(x) in any first-order logic.
[2] Or, more precise, a cluster of definite descriptions. He writes: “When we, who did not know Bismarck, make a judgment about him, 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”. Many philosophers actually subscribed to this idea, John Searle strangely being one of them: “the descriptive force of ‘This is Aristotle’ is to assert that a sufficient but so far unspecified number of these statements are true of this object.” (Searle, 1958, p. 171). The main problem with this is that such ‘identifying expressions’ seem neither necessary nor sufficient in order for the proper name to be used (and have a referent). See (Abbott, 2010, pp. 102ff) for the whole controversy.
Sep 2, 2010
Reference. Part I – Gottlob Frege
Let me settle the scope of this post as low and demure as I can, so that the reader will value simplicity (and simplification) over completeness. What I wanted to do some days ago – after reading and reviewing this – is discuss in more detail the concept of ‘reference’ as a pragmatic phenomenon. However, as soon as I started rambling through notes, I realized that this cannot be done without appealing to earlier conceptions of ‘reference’, namely, those which endeavor to explicate it, and its problems, semantically. Whether I have a right to draw this thick line between semantics and pragmatics in describing the history of the notion of ‘reference’ is plainly debatable, and it would make little sense to try to advocate for it here. It is nonetheless fairly common to group the two articles I’m about to discuss, and all those which followed them uncritically, into what might be called the ‘semantic parentage’ of reference analysis (see e.g. Kripke, 1977; Carlson, 2004, Abbott, 2010).
The two articles in question, Gottlob Frege’s “On Sense and Reference” (Frege, 1892) and Bertrand Russell’s “On Denoting” (Russell, 1905) are arguably the most referred-to, far-reaching and influential papers of the analytic tradition of philosophy. The momentous apparition of “On Denoting” and its influence in subsequent literature of philosophy is very hard to overstate. It was Russell’s famous ‘wig-joke’[1] that, enthusiastically (albeit unaware of the deep waters ahead) literally put an end to the idealist mode of philosophizing.
However, the two articles are notoriously difficult, and at times obscure, especially for someone not distinctly interested in the unfathomable give-and-takes of philosophy of language (e.g. myself). That is why the purpose of this post, and I hope I’ll be able to pack it together into only one post, is to offer a simplifying exegesis rather than a full review. I’ll start with Frege and then turn to Russell, though it is not unusual for the two authors to be treated in reverse order (e.g. Makin, 2000).
Frege’s sad story
When “Über Sinn und Bedeutung” was published in 1892, Gottlob Frege (1848-1925) had already written two of his major works: Begriffsschrift (1879) and The Foundations of Arithmetic (1884). These works were generally interested in a sort of “purification” of formal language, the removal of all that is subjective, e.g., presupposition, so that nothing intuitive can sneak in unnoticed. Hence Begriffsschrift is often left untranslated, and it would mean “concept-language” or “concepts-put-into-formulas/notations”. It is precisely this sort of endeavour that characterized logicism in early twentieth century – i.e. the reduction of mathematics (or arithmentic, to be more precise) to logical relations.
The twofold puzzle to which Frege sought to give an answer (and ended up giving two!) regards the mathematical relation of identity (or equality, to follow Black’s translation) and could be stated thus:
- If identity statements are about their referents, then they are trivial or even analytic. If identity statements are about linguistic expression, there seems to be something missing.
The first sentence could be restated as: since symbols are usually representations of actual objects[2], then what I really express by a relation of the type a=b is a relation of identity between the same objects, so no different than a=a – provided of course that a=b is true. In other words, the statement (1a) “John is the head of the department” is equivalent to (1b) “John is John”, since ‘John’ and ‘the head of the department’ refer to the same object (this is sometimes referred to as the principle of substitutivity). However, we feel that, while the statement “John is John” is trivial (analytic), the statement “John is the head of the department” is not. If we regard identity (a=b) as a property of things, than “a=b” and “a=a” could not differ (and the puzzle is that they are certainly of different ‘cognitive value’, with the latter being analytic and the former not).
If, however, we consider identity statements as being about the expressions themselves (not about the objects they represent) then another problem arises. Well, several problems arise, but the most important of them is this: interpreting “a=b” as “Both ‘the symbol a’ and ‘the symbol b’ stand for the same object X” seems like a linguistic characterization of an arbitrary relation between symbols and object. In Frege’s terms, “It would be mediated by the connexion of each of the two signs with the same designated thing.”, which is a matter of arbitrary convention. Why this “arbitrariness” is undesirable[3] is a matter of debate. What we can certainly affirm, as Abbott puts it, is that “‘The morning star is the evening star’ represents a significant astronomical discovery, not some piddling accomplishment of grammarians or lexicographers.” (2010, p. 16).
Short intermezzo.
Powers: first axiomatization of logic; knowledge of eternal, immaterial entities
Weaknesses: Russell's Paradox, unpopular with publishers
Marching on.
The key to solving these problems can be hinted in some passages from The Foundations of Arithmetic and, in “On Sense and Reference”, where it is fully developed, runs like this:
- In order for “a=b” to be true, ‘a’ and ‘b’ must have the same reference. The difference between ‘a’ and ‘b’ is the sense, that is, they are different “modes of presentation” of the same referent.
This definitely solves the problem of (1a), since “John” and “the head of the department” have different senses – they represent the same human being differently. Frege’s example is actually quite self-explanatory:
A difference can arise only if the difference between the signs corresponds to a difference in the mode of presentation of that which is designated. Let a, b, c be the lines connecting the vertices of a triangle with the midpoints of the opposite sides. The point of intersection of a and b is then the same as the point of intersection of b and c. So we have different designations for the same point, and these names ('point of intersection of a and b', 'point of intersection of b and c') likewise indicate the mode of presentation; and hence the statement contains actual knowledge.
But now, if we take the distinction between sense and reference and apply it to sentences, as opposed to (‘mere’) descriptions, some further issues arise. One of the basic principles of syntax, the principle of compositionality, tells us that the meaning of an expression is a function of the meaning of its parts (plus syntactical structure). For example, the meaning of “London’s prime-minister died” is a function of the (meaning of) words “London” and “prime” and “minister” and “die” put together in that exact syntax, not as “prime’s Minister to die london”[4]. Frege supported this principle throughout his Begriffsschrift. Does it apply to the new distinction between sense and reference? This question occupies most part of the rest of the article because the principle of compositionality, once the distinction is introduced, becomes a two-layered principle.
The sense of a sentence is the proposition (or, in Frege’s terms, the thought) it expresses. Let us notice that “Venus is the morning star” is different from “Venus is the evening star”, and support it by saying that, in principle, one could think of the first as true and the second as false, or vice versa. Than we can say that the thought expressed in the two is different, which means that the thought cannot be the reference. It is therefore the sense – this being the only one capable of change. Therefore, the sense of a sentence is the thought/proposition it expresses.
But what about the reference? What is the reference of a sentence? Or, in other words, if the sense changes, what remains constant even when parts of the sentence are replaced? If we replace ‘morning star’ with ‘evening star’ (which would be called coreferential expressions since they refer to the same thing) then, as we have seen, the sense, i.e. the proposition being expressed, changes. But what stays the same? The answer is remarkably simple: its truth value. The truth or falsity of a sentence is not affected by substitution.
But now a final problem arises. What if one part of the sentence has (or appears to have) no reference? What is the reference/truth value of the sentence “The Golden Mountain is 1500m high” – assuming there’s no such thing as a mountain of gold? Or to borrow the overexploited example, what is the truth value of the sentence “The king of France is bald”? Frege’s answer, preserving the principle, is that these propositions will not have a truth value, since one of their constituents is an empty noun-phrase (i.e. a phrase without reference). And here comes the sad part.
Frege was wrong. Because, if non-referential expressions form sentences that lack truth-values, what about the sentence “The king of France does not exist”? This sentence not only has a truth-value, but is evidently true. It was Russell who not only noticed this, but formulated a solution to Frege’s dead end. Sadly, the solution was to give up the distinction between sense and reference altogether.
I didn’t manage to cram it all into one post, so I’ll end with this.
to be continued…
[1] The paragraph is, incidentally, one in which the problem of ‘empty NPs’ is most explicitly put. I will quote it in full: “By the law of excluded middle, either “A is B” or “A is not B” must be true. Hence either "the present King of France is bald” or “the present King of France is not bald” must be true. Yet if we enumerated the things that are bald, and then the things that are not bald, we should not find the present King of France in either list. Hegelians, who love a synthesis, will probably conclude that he wears a wig.” (Russell, 1905, p. 485
[2] Using the term ‘object’ is actually a loose way of stating things, since there are many things we can speak of without them being describable as ‘objects’. This, however, does not alter the meaning of the puzzle. Frege used the term ‘content’ (as in ‘content of thought’, be it abstract or concrete) and in modern semantics we usually speak of ‘referent’ or ‘denotation’. It is also loose in the sense that the symbol is not only a representation of an object but could easily become a referent itself – for example when using quotation marks as in: “Socrates” has eight letters.
[3] The original passage runs as follows:
„What is intended to be said by a = b seems to be that the signs or names 'a' and 'b' designate the same thing, so that those signs themselves would be under discussion; a relation between them would be asserted. But this relation would hold between the names or signs only in so far as they named or designated something. It would be mediated by the connexion of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. In that case the sentence a = b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means.”
Why is the “arbitrary connection” between signs and objects not “proper knowledge” is just one of the possible questions. It should also be noted that Black’s translation is not something scholars agree upon, see (Makin, 2000, pp. 97ff).
[4] This is easily noticeable when expressions become idioms. The principle of compositionality applies to the meaning of “the jacket in one’s closet”, but not to “the skeleton in one’s closet” which has, so to speak, become a single word, i.e. a (shameful) secret. The same expression could be understood both idiomatically and non-idiomatically, e.g. “sleep on something”.