Download - Frege´s distenction between sense and reference

8/19/2019 Frege´s distenction between sense and reference.

1/17

Frege’s Distinction Between Sense and Reference

Gideon Makin*University of Birmingham, England.

Abstract

The article presents Frege’s distinction between Sense and Reference. After a short introduction,it explains the puzzle which gave rise to the distinction; Frege’s earlier solution, and his reasonsfor its later repudiation. The distinction, which embodies Frege’s second solution, is then discussedin two phases. The first, which is restricted to proper names, sets out its most basic features. Thesecond discusses ‘empty’ names; indirect speech, and the distinction for predicates and for complete sentences. Finally, two criticisms, by Russell and by Kripke, are briefly set out.

Frege’s distinction between Sense and Reference comes as a corrective to a simpler, morenaı̈ve, conception of a word’s meaning .1 On the naı̈ve view, a word’s meaning consists inits standing for an object; but the reasoning underlying the distinction maintains that evenin what seems to be the simplest type of case, i.e., that of proper names (e.g., ‘John’,‘London’, ‘the capital of France’), assuming such ‘standing for’ (‘referring’ in the new the-ory’s vocabulary) exhausts a name’s meaning has untenable consequences. The remedy isto recognize an additional theoretical notion of a name’s sense: roughly, the way in whichits referent is presented, identified, or picket out.2 ‘Yuri Gagarin’ and ‘The first human inspace’ – both regarded by Frege as proper names – designate one and the same individual;

they have the same reference . But how each picks out that individual, their senses, differ.We are thus led to distinguish within the formerly unitary notion of ‘meaning’, twoingredients: sense and reference. Frege conceived of this dual conception as extending toall types of expressions, including complete sentences (for the sense of a complete declara-tive sentence Frege used the term ‘thought’, maintaining that its truth value , i.e., the true,or the false, was its reference). Russell’s theory of definite descriptions (with regard tocomplex names), and the Millian (after J. S. Mill) ‘direct reference’ view (for simpleproper names), which is close to the naı̈ve view, are the principal theoretical alternativesto this view. To begin with, we shall focus on proper names, which is where Frege’sprincipal case for drawing the distinction lies.

Frege put forth the distinction (in his 1892 essay ‘On Sense and Reference’) as a solu-tion to a particular puzzle; one to which he had proposed a very different solution some

years earlier (in his Concept-Script of 1879). After explaining the puzzle (Section 1); Frege’sfirst solution, and its later repudiation (Section 2); we will discuss some of the principaltheses regarding sense and reference and provide a glimpse of issues they give rise to (Sec-tions 3 and 4). Finally, we will briefly discuss two criticisms of the distinction (Sec-tion 5).

1. The Puzzle

The puzzle arose from Frege’s reflecting upon identity statements where two differentnames serve to assert a strict and literal identity (e.g., ‘2 + 2 = 4’; ‘the author of Waverleyis Scott’).3 On the naı̈ve view, according to which a name’s meaning consists in its

Philosophy Compass 5/2 (2010): 147–163, 10.1111/j.1747-9991.2009.00277.x

ª 2010 The AuthorJournal Compilation ª 2010 Blackwell Publishing Ltd


2/17

standing for a definite object, substituting a name for another standing for the same objectought to leave the sentence’s meaning unchanged. And indeed, in some cases this will beso. But in other cases, and it is only these that give rise to the puzzle, such a substitutionseems to change the meaning.

In Frege’s best-known example ‘Hesperus’ names a heavenly body observed at a cer-tain position in the sky in the morning, and ‘Phosphorus’ a heavenly body observed insome other position in the sky in the evening . Consider first:

(1) Hesperus = Hesperus

This identity is trivial, and establishing its truth requires no special investigation. But nowconsider that, following astronomical investigations, it transpires that Hesperus is Phos-phorus. So,

(2) Hesperus = Phosphorus,

which results from substituting the names of the same object in (1), is true. But unlike(1), (2) expresses a substantial astronomical discovery, namely, that the two are one and thesame heavenly body. (2) is informative while (1) is not.4 But if, following the naı̈ve view,we take a name’s meaning to consist in nothing more than its standing for the namedobject, (2) should have meant exactly the same as (1). We will return for a second, closer,look at the puzzle later. This provisional statement will do for now.

Before turning to solutions to this puzzle, it will be useful to introduce a concept andhighlight an assumption which underlie it – although not because either is particularlycontroversial. What we loosely spoke of above as the meaning of a sentence might becalled its content. A declarative sentence’s content may be characterized as ‘what is said’,

what one strives to preserve in translation. Thus, two people who believe or know thesame thing (but, let us suppose, having no common language cannot be said to relate tothe same sentence ) are said to believe or know the same content.5 ‘Content’ enables us toexpress an assumption underlying the puzzle in a slightly more neutral way. The identityof a sentence’s content is fixed (as a rule; there may be exceptions) by the contributionsof its constituent words. A word’s content may thus be identified with the contributionit makes to the content of sentences in which it occurs. (The mode in which these wordsare combined is of course important too, but we can leave this to one side in the presentcontext.) This thesis is known as compositionality, and in its simplest form, which Fregehappened to subscribe to, the words’ contents are considered to be parts of the sentence

content. As we saw, the naı̈ve view identifies the contribution, or content, of a proper name with its reference.

2. Frege’s First Solution

In the last paragraphs but one we tried to capture the informativeness of (2) with thephrase ‘that the two are one and the same’ (heavenly body), but this was plainly incoher-ent: what could ‘the two’ here mean when, as we are assuming, only one object is inquestion? Two what are one and the same? How can the content of the discovery thatHesperus is Phosphorus be coherently described?

One answer which suggests itself focuses on the situation involving two distinct names.What one knows, i.e., the content of such an informative identity statement, is that the two names designate one and the same object . Such was Frege’s solution to the puzzle in his

148 Frege’s Distinction Between Sense and Reference

ª 2010 The Author Philosophy Compass 5/2 (2010): 147–163, 10.1111/j.1747-9991.2009.00277.xJournal Compilation ª 2010 Blackwell Publishing Ltd


3/17

earlier work Concept-Script (§8). And indeed, knowing this (unlike knowing that Hesperusis Hesperus) does not appear to be trivial.

But a few years later (in ‘On Sense and Reference’) Frege came to recognize that thissolution was fatally flawed. The problem is not that it is not true as far as it goes, butrather that its account of the content known in such cases cannot be right. Precisely, whyFrege found this answer objectionable deserves careful attention not merely from an anti-quarian’s interest, but because it is a valuable guide to the solution he ultimately arrivedat. Because the first solution suffers from a number of rather glaring faults it is easy to getdistracted, as many commentators have, and focus on those which seem to the writer themost damaging. But since our current interest in the first solution is as a guide to thesense ⁄ reference distinction, we focus on the only fault which Frege found need to discuss

– even if he might have justifiably picked others.What dawned upon Frege only years after proposing this solution was that since any-

thing we please can serve as the name of any given object (e.g., that the word ‘Paris’names the particular city it does is, at least in principle, purely a matter of convention),giving this naming relation a constitutive role in what is known, i.e., the content, renders

the putative item of knowledge one which depends upon arbitrary convention. But whenwe know that Hesperus is Phosphorus, or that 2 + 2 = 4, what we know, the content, isentirely objective ; and it does not depend in any way upon convention, linguistic or other (to think otherwise is to confuse what is known, the content of our knowledge, with themeans of expressing it). Many commentators take Frege’s point against his former solu-tion to be that it mistakes one item of knowledge for another (i.e., an astronomical onefor a linguistic one); but close examination of his wording in ‘On Sense and Reference’suggests that the problem for him was not the conflation of items of knowledge. It was,rather, that he thought the proposed content could not count as an item of knowledge atall – a label which he reserves for what is objective. We will see later that there is more

to Frege’s first solution than has been related here, but this gives the gist both of the firstsolution and of his grounds for repudiating it.

3. The New Solution – The Basics

The most salient feature of the new solution Frege put in its place is the distinctionbetween two ingredients in the notion of meaning: Sense and Reference. The refer-ence of a name is, by and large, the notion familiar from the naı̈ve view; but thenotion of sense is an innovation (or, rather, as we shall see shortly, almost so). Distin-guishing two ingredients in a name’s meaning – it is names generally, not only in iden-

tity statements, that are at stake – makes it possible to maintain that two names sharethe one, but not the other; and thus that the content of an identity sentence involvingsuch a pair can be both true (on account of the identity of reference) and informative(on account of the diversity of senses). The move from (1) to (2) above keeps the ref-erence constant, but changes the sense. The possibility of distinct names having thesame sense is not ruled out, it is only maintained that this is not the case when a trueidentity is informative. What is ruled out, although, is the possibility of names havingthe same sense but different references. Having distinct senses is necessary, not suffi-cient, for names to have distinct references. But what then is a sense? After some com-ments introducing this notion at the intuitive level, our answer will come in two

installments. The first focuses on its two most essential features: its determining the ref-erent; and its objectivity. Once these are in place, the following section will expandour view beyond the most basic cases.

Frege’s Distinction Between Sense and Reference 149



4/17

3.1 SENSE DETERMINES REFERENCE

Since Frege grouped complex and simple names together, what a particular name’ssense might be is easy enough to tell when the name is a complex expression (as with‘the first human in space’). But Frege maintained that simple names, too, have a sense.His examples invite one to think of the sense as a particular mode in which the name’s

referent is presented; and this is most naturally cashed out by some definite description(a phrase of the form ‘the so and so’ in the singular) which only the referent fits. For example, for a name like ‘Aristotle’ this might be ‘the teacher of Alexander the Greatand pupil of Plato’ or ‘The teacher of Alexander who was born in Stagira’. Thedescription must contain sufficient information to determine a unique referent, i.e., dis-tinguish it from anything else whatsoever. But which, then, of the myriad of senseswhich determine Aristotle, is the sense of ‘Aristotle’? Frege acknowledges the answer may vary from speakers to speaker. The sense I associate with the name, the informa-tion that would enable me , if challenged, to single him out, may well differ from thatavailable to you. The sense one associates with a name thus reflects one’s knowledge,

experience, and conceptual resources. Such diversity is tolerable, and does not hinder communication, so long as the reference (what we speak about) is the same, but in aformal language of a demonstrative science it is unacceptable: each name must alwaysexpress the same sense. A name’s sense may be thought of as the content of a descriptivephrase in a manner analogous to that in which we spoke earlier of the content of acomplete declarative sentence.

Frege’s novelty was to conceive of a name’s meaning as involving two, rather than asingle, entity, but it would be a mistake to picture this to oneself in a diagram where twoarrows point from the name, one to the sense, the other to the reference. The correctimage would rather be of one arrow pointing from the name to its sense, and another

from that sense to the referent . The name’s relation to its referent breaks down into its rela-tion to the sense, and that sense’s relation to the referent. The notion of sense may thusalso be regarded as Frege’s answer to ‘what does the relation between a name and its ref-erent consist in?’ About the first of these two relations – Frege speaks of a name expressing its sense and referring to its referent – he has precious little to say; but the sense’s relationto the referent is a vital part of the theory, and it is commonly captured by the dictum‘sense determines reference’.

Having characterized sense as a mode of presentation of the referent, the dictum mayseem rather obvious. And yet, there are possible misunderstandings we need to guardagainst. ‘The president of the U.S.’, it might be thought, determines different individuals

at different times. But saying this is to confuse the phrase , a linguistic entity, and a sense,which is not. Once a sense has been selected, the identity of the referent is thereby fixed.There is no room for maneuver. It is of the very essence of each sense to determine theparticular referent it does, and its determining any other is an outright impossibility. Thus‘the president of the U.S.’ must be regarded as an incomplete expressions of a sense – inthis instance, the completion would specify a time – and not the expression of a definitesense which requires supplementation to determine a referent. The sense, which is anabstract entity, determines the reference (as we shall see shortly, if any) by and of itself.Many expositions append ‘sense determines reference’ with ‘given the facts’, as if whichreferent a given sense determines depended on some additional factor. But as common-

sense and natural as this addition might seem, there is no evidence for the need for it inFrege’s writings and, as we shall see when we expand our view to include complete sen-tences, rather conclusive evidence to the contrary.




5/17

As with sentence-contents (about which more below), the chief role of sense, as canbe seen from reflecting on the puzzle, is as an epistemic object. What one’s mind directlyengages with when thinking of an object, or understanding a sentence about it. We relateto a sense by grasping it, which is what understanding the attached name consists in. Butbeing grasped leaves no trace on the sense itself, which is an abstract and immutableentity. Since sense determines reference, by grasping a sense one enters into a relationwith the referent as well; and this is the closest, epistemically, one can get to the referent.There is no more direct epistemic route leading from one’s words (or thoughts) to it.

3.2 THE OBJECTIVITY OF SENSE

The chief misunderstanding Frege was concerned to eradicate was thinking of a sensealong the lines of an idea. He never tired of insisting that this is not what he had in mind,and exploited every opportunity to stress the difference between senses and ideas. Themost crucial difference he points out is that ideas are numerically distinct for differentpersons. The idea I attach to ‘Aristotle’ may or may not resemble (perhaps even perfectly

so) the idea you attach to the same word, but it cannot possibly be strictly and literallythe same idea, since the one is in my mind (or some would say, head) and the other in

yours. We cannot perceive or ‘have’ each other’s ideas – there can be no question of lit-erally sharing them. By contrast, we may well grasp one and the same sense, which isobjective and not in anyone’s mind. Just how vital the objectivity of sense was for Fregebecomes even clearer by reflecting on this notion’s ancestry in his thinking – whichbrings us to taking another, closer, look at his first solution to the puzzle.

When sketching that solution (in Section 2), we followed Frege’s own retrospectiveaccount of it in ‘On Sense and Reference’. But Concept-Script §8 contains a rather importantaddition, which the retrospective account omits to mention. If, as explained earlier, the con-

tent of an identity statement is that the two names refer to the same object , then it would seem tofollow that all cases where different names flank the identity sign ought to be equally informa-tive. But Frege was well aware that this is not the case, e.g., most clearly when a name is intro-duced as an abbreviation of another expression. How then are we to distinguish between thecases? Having stated the solution explained earlier, Frege illustrates how to each of the twonames of a single point in a geometrical construction there corresponds a different ‘way of determining’ it. It is when the different names ‘go along’ with distinct ways of determining,that the identity is informative (thus implying that when the associated ‘ways of determining’do not differ, there is no informativeness to account for). It is the possibility of such differencesthat justifies the need for a symbol for identity of content in the concept-script language.

The Concept-Script notion of ‘way of determining’ is clearly a precursor of the later notion of sense for proper names. When considering §8 as a whole, it appears that thisnotion, rather than the ‘special’ content it assigns to names, carries the burden of explain-ing why (some) identities are informative. And yet, Frege does not count the ‘ways of determining’ as part of a name’s content . Instead, he speaks of it as merely ‘going along’with the name – a rather loose and vague phrase.

The question thus naturally arises: if Frege recognized, in Concept-Script, a notionwhich is effectively the same as the later notion of sense for proper names, and used it toexplain the informativeness of identity statements, why were a dozen more years requiredbefore he gave it its due status by admitting it into a name’s content? What feature of

any substance (as opposed to the label) had changed about this notion between Concept-Script and ‘On Sense and Reference’? What might have prevented him from admitting itinto the content in Concept-Script ?




6/17

Since in ‘On Sense and Reference’, Frege ignored this whole strand of his former solution,no direct answer is to be found in his writings. And yet, one difference between the Concept-Script ’s notion of ‘way of determining’ and the later notion of sense suggests itself, at least tothe present writer, as the key to the most plausible explanation. In ‘On Sense and Reference’,Frege came to recognize ‘ways of determining’ (or rather ‘modes of presentation’) as objective.6

It thus seems plausible to suppose that in Concept-Script, reluctance to commit himself on their objectivity, and thus to include them in the contents of names, forced Frege to make names – difference between which are unquestionably objective – their own content. His later recog-nition that this position was untenable, led him to recognize ‘ways of determining’ as objec-tive, i.e., as embodied in mind- and language-independent entities (which, as ‘On Sense andReference’ makes plain, renders his earlier appeal to names superfluous).7

4. The Distinction – The Broader Picture

Our discussion so far was confined to the simplest kind of case, i.e., proper names withfamiliar, concrete, objects as referents. This helped simplify the task of laying down the

distinction’s foundations, but to gain a full picture we must expand our gaze on three dif-ferent fronts which open before us by raising the following three questions: First, can asense (or sense-expressing name) fail to determine a referent? Second, having character-ized the referent as what using a name results in speaking about, is it possible to speakabout a sense? Third, does the distinction apply to expressions other than proper names?Frege’s short answers would have been ‘Yes’ to all three. Let us take up each in turn.

4.1 EMPTY NAMES

When one regards ‘the so and so’ phrases, as Frege did, as proper names, it is easy to

think of names which seem intelligible but have no reference – at least not in anystraightforward sense. Frege himself gave the examples ‘the celestial body most distantfrom the earth’ and ‘the least rapidly converging series’, and admitted that some simplenames too, e.g., of fictional characters like ‘Odysseus’, lack reference. For a monolithicconception of meaning, like the naı̈ve theory’s, such names present a stark dilemma: onemust either find some special ontological status for their putative referents (Meinong isknown for having taken such a course), or deny outright their very intelligibility, dismiss-ing them as empty sounds (earlier Frege seems to have taken that course8). But a dualconception of meaning opens the way, which Frege indeed took, to account for theintelligibility by admitting such a name has a sense, while denying that it has reference. A

language containing such names is in a sense defective, and Frege makes it clear that in alanguage designed for scientific use no such names are to be allowed. And yet, one canhardly deny that he admitted the possibility of such ‘empty’ names.9 An important effectsuch names have on sentence containing them will surface later when we come to thesenses of complete sentences; but another, more immediate one, seems to be this: since if there is no referent there can hardly be a way in which the referent is presented, a ‘modeof presentation of a referent’ cannot be regarded as defining the notion of sense in general

– there are senses to which this characterization does not apply.

4.2 SENSE AND INDIRECT SPEECH

The second of our three questions stems from the characterization of a name’s referent,as opposed to its sense, as what its use effects speech about . Does this leave room for




7/17


8/17

in the scope of propositional attitudes to preserve truth-value. To see why this is so, weneed to take a second and closer look at the puzzle.

First, it is worth noting – something Frege realized only after Concept-Script – that it isnot essential that the puzzle deal with an identity statement.11 The fundamental problemis the same with a pair like:

(5) Hesperus is bright

and

(6) Phosphorus is bright,

neither of which is known a priori . The naı̈ve theory is at loss to explain how, as seemsto be the case, a subject may believe or know the one but not the other if, as it main-tains, the two have the exact same content. But what does noting that a subject knows(5) but not (6) amount to? It is, I suggest, to contrast in effect another pair of contents,

namely (e.g.):

(7) Tom knows that Hesperus is bright

and

(8) Tom knows that Phosphorus is bright.

(We might just as well have used ‘believes’, ‘says’, etc.). The puzzle concerns not Tom’sconsistency, but the naı̈ve theorist’s: How can the one be true and the other false, if

substituting co-referring names (in this context) leaves the content unchanged? Surely, thesame content cannot be both true and false. This is the essence of the puzzle, and it isconcerned with indirect speech. If the distinction is not a means to account for indirectspeech, it will not resolve the puzzle either.

Spelling this out for Frege’s examples in ‘On Sense and Reference’ requiresan additional step. We are told that ‘a = a’ is trivial, uninformative, and known a pri-ori , while ‘a = b’ is a surprise, informative, and a substantial discovery. But what arethese contrasts getting at? Why can we not just respond to these contrasts with ‘Sowhat?’

Noting that ‘a = b’ is a surprise or a discovery is, again, to implicitly contrast the two

broader contents ‘S knows that a = a’ and ‘S knows that a = b’. Since a discovery issomething one had not known formerly, it implies that at some earlier point in time(i.e., before the discovery was made), it was not known, and since ‘a = a’ can be assumedto have been known even then, the two broader contents must have then had contrastingtruth-values. As the only difference between the two is the result of substituting co-refer-ring names, the reference cannot be, at least not exclusively, what determines the embed-ded content’s identity (what is known) and thus, by parity, not a name’s solecontribution to content generally.

The puzzle’s direct moral is a negative one: it tells us what a name’s content is not,not what it is. However, indirectly it strongly suggests that whatever the alternative con-

tent might be, it should (unless we wish to drop the reference completely, which wouldbe absurd) determine the referent, which implies, in turn, that relating (directly) to it, isrelating (indirectly) to the referent as well.




9/17

4.3 THE DISTINCTION FOR EXPRESSIONS OTHER THAN PROPER NAMES

4.3.1 The Sense and Reference of Complete SentencesComing now to the last of the three questions listed earlier. Frege held that (properlyfunctioning) linguistic expressions of all kinds have both sense and reference. Now thatthe distinction has been laid down for proper names, it remains to see how it applies to

the other two categories of expressions Frege recognized, namely function-names, a cate-gory comprising of all concept- and relation-words (adjectives, verbs, adverbs, preposi-tions, and logical constants); and complete sentences. Applying the distinction tosentences is by far the more interesting case, and we will begin with it.

In ‘On Sense and Reference’, Frege’s case for taking a sentence’s truth-value (its beingtrue, or false, as the case may be) as its referent is as follows. Having establishes the distinc-tion for proper names in the narrow sense – the qualification is called for because ulti-mately, he regards complete declarative sentences as proper names too – he raises thequestion whether the distinction might apply to complete sentences as well. He reasonsthat if sentences have both sense and reference, what we have called the sentence’s content

– which from this point on he labels a ‘Thought’ (henceforth invariably capitalized toindicate the Fregean sense) – cannot be the reference. The reasoning tacitly appeals to aversion of a principle encountered earlier, namely compositionality, confined to the refer-ences of expressions. Substituting co-referring parts for each other, should not affect thereference of the whole.12 Since substituting names which have the same reference canchange the Thought expressed (this, as we now know, happens when they have differentsenses), the Thought cannot be the sentence’s referent. If either, it must be its sense.

Next, Frege poses the following question: Assuming that complete declarativesentences have senses, do they (in general) have references too? Might they fail to have areference? He replies that they have no reference when a constituent name has no refer-

ence. If one assumes the name ‘Odysseus’ has no reference, then one does not inquireafter the truth of sentences in which it occurs. This suggests that the parts having a refer-ence, and the whole being either true or false, go hand in hand. When the first is miss-ing, we have no interest in proceeding beyond the Thought (which, we now assume, isthe sense) to the reference. Sentences in fiction contain ‘empty’ names, and thus lack atruth-value. We seek a sentence’s truth-value only if we assume that its constituent nameshave references.

This leads to taking a sentence’s truth-value to be its reference. Frege maintained thattruth and falsity are not, as one is inclines to think, predicates of sentences – citing that pre-fixing ‘it is true that…’ to a sentence does not alter the content expressed – but rather objects

sentences refer to. Thus, while proper names in the narrow sense have all kinds of objectsas referents, with complete declarative sentences there are only two objects they can possi-bly refer to: the true or the false. He reasons that because sentences (like proper names inthe narrow sense) are complete or ‘saturated’ expressions (as opposed to predicates, whichare unsaturated), they are proper names, not predicates; and their referents are thereforeobjects. (Ultimately, denying they are properties is all Frege’s classifying them as objectsamounts to, there is no implication that you can pick them up in your hand, or see themthrough a telescope. He considers them to be logical objects, as numbers are too.)

This argumentation leaves much to be desired. Frege seems to have established, atmost, that if sentences have both sense and reference, then the Thought or content, and

the truth-value are, respectively, the most plausible candidates for these roles among thenotions we are already familiar with. (Note that, unlike the distinction for proper names,for sentences the theory introduces no new element which was not familiar beforehand.)




10/17

Fortunately, one can find in Frege’s writings yet another route leading to the admissionof truth-values as the referents of sentence. In ‘Function and Concept’, a paper Fregedelivered shortly before ‘On Sense and Reference’ was published, the chief topic is notsense and reference. Nonetheless, the distinction gets its first mention in that earlier paper, and although it does not discuss the distinction for proper names, it does containan argument for regarding truth-values as referents of complete sentences. This argumentflows from Frege’s conceiving concepts as a special case of functions.

We are all familiar with functional expressions such as ‘2 + x’. We say, e.g., that thefunction’s value for the argument 3 (i.e., the result of plugging 3 in the variable’s place) is5, and that it is 4 for the argument 2; and since 2 + 3 = 5, the expressions ‘2 + 3’ and‘5’ have the exact same referent. But functions, as Frege used the term, are not confinedto mathematics, and ‘the mother of x’ is a function in precisely the same sense (e.g., for the argument Isaac it has the value Sarah; for the argument Ishmael the value Hagar ).

Frege extended the notion of a function to include concepts. While functions of thefamiliar kind, like those above, have ordinary objects, or numbers, as their values; whenan argument expression is plugged into a concept expression, such as ‘x is wise’, the

resultant expression is a complete declarative sentence. Regarding it as a function givesrise to the question: What might its value be? What does the completed expression standfor? Surely there is something about the resultant expression which is sensitive to whichargument we plug in - just as the values of the functions considered above were sensitiveto which individual name we plugged into the argument place. Frege observes thatamong the arguments a concept like ‘x is wise’ can take, for some the result will be atrue sentence, for others a false one. It is significant, too, to note what the resultingtruth-value is not sensitive to: as long as the arguments inserted have the same reference ,the truth-value of the resulting sentence will remain unchanged (mere changes of sense,are irrelevant). He thus proposed taking the truth-values as the values of concepts

(regarded as a special case of functions). Just as ‘2 + 3’ stands for the number 5, so does‘Socrates is wise’ stand for, or refer to, the true. This route depends on taking the name’sbearer as its referent, but not on recognizing name senses.

When all the relevant evidence is considered, there is a case to be made for regardingthe distinction for complete sentences as preceding the distinction for proper names inthe proper logical, as opposed to expository, order of things. Truth, for Frege, is the mostimportant logical notion, and it is its role in determining a sentence’s truth that confersthe status of referent on a name’ bearer, rather than this identification being one’s startingpoint.13 Before moving on to the distinction for predicates, two remarks need to bemade. One regarding the application of ‘sense determines reference’ to Thoughts and

truth-values; the other on Thoughts’ objectivity.Since complete sentences are ultimately, on Frege’s view, a species of proper names,

‘sense determines reference’ requires no additional invocation. The Thought (expressedby a declarative sentence) determines the (sentence’s) truth-value just as a name’s sensedetermines its referent. When discussing proper names (in the narrow sense), we said thata sense determines the referent it does by and of itself. No additional conditions arerequired; and when there seem to be, this is only because the sense in question has notbeen expressed fully. In the case of complete sentences, this has consequence which maystrike one as a rather surprising. The Thought expressed by a sentence, its sense, deter-mines it reference, i.e., its truth-value, regardless of anything else. It is natural to suppose

that a Thought’s truth or falsity depend not only on the Thought itself, but also on ‘thefacts’; but nothing Frege says warrants such supplementation. On the contrary, in a dis-cussion of the notion of truth (in the posthumously published ‘Logic’ of 1897) he insists




11/17

that a Thought is true or otherwise not, as one might think, relative to this or that beingthe case - a conception of truth known as ‘correspondence’ - but is so in itself. Hecompletely rejects the correspondence conception of truth for Thoughts, and it is onlyThoughts, on Frege’s view, which are true or false in the primary sense – whatever else issaid to be true or false (e.g., a sentence) derives this title from the associated Thoughtbeing so.

One reason why the truth of a Thought is not to be conceived as relative to ‘the facts’is there being (so far as it can be judged from his writings) no such category in Frege’sontology. At one point he remarks that facts are nothing other than true Thoughts,14 butthis does not provide anything a Thought might fit or fail to fit. Another feature of theontology of sense and reference which is easily overlooked is that what was said earlier about the objectivity of senses of proper names, applies to Thoughts too; and it applies tofalse Thoughts just as it does to true ones. False Thoughts are just as objective as are trueones. The difference lies in their respective referents, not in the objectivity or reality of the Thought, or of its referent.

In arguing for taking truth-values as the referents of complete sentences (and mathe-

matical equations) Frege appeals to a fundamental principle we mentioned earlier, namelycompositionality. The principle asserts that the reference of the complete sentence isdetermined by the references of its parts – leaving aside how those parts are combined15

– and similarly, the sense of the complete sentence, a Thought, is determined by thesenses of its parts. It is a complex made up exclusively of senses. A sentence containing aname which has no reference – a possibility mentioned earlier – will itself have no refer-ence, i.e., be neither true nor false. In such cases although there is a Thought, there is notruth-value. A sentence’s relation to the Thought it expresses and, in turn, to the truth-value is not, on Frege’s view, merely analogous with a proper name’s relation to its senseand reference. The two are instances of the very same relation.

The most relevant theoretical alternative to a Fregean Thought is Russell’s notion of aproposition. The two share the roles of being what is involved in inference, primarybearer of truth and falsity, the object of belief and knowledge, and the meaning of sen-tences. But unlike Frege, Russell admitted both objects (which for Frege can only be ref-erents) and sense-like entities (‘denoting concepts’ in his terminology) which determinereferents, as constituents of propositions (the latter were dropped with the advent of theTheory of Descriptions).

4.3.2 The Sense and Reference of PredicatesFinally, we come to predicates, that is, concept- and functions-words (for brevity I will

use ‘concepts’ for both). Frege maintained that they too, have both sense and reference,but with hardly any discussion or argument as we have seen with regard to proper namesand complete sentences. Explaining the distinction’s application to their case is compli-cated by two facts. First, before Frege and the distinction ever enter the scene, the tradi-tional conception of concepts already distinguishes between the concept itself (alsoreferred to as an ‘intension’), and the things (if any) the concept applies to, namely, theconcept’s extension; and concepts are taken to be related many-one to their extensions.(To borrow a famous illustration, ‘creatures with a heart’ and ‘creatures with kidneys’express distinct concepts, or different intensions, but have the same extension.) On thisview, too, concepts, like senses, are invariably abstract, and determine their extension in

just the way a sense is said to determine its reference16

So in the case of concept-words,we seem to recognize something at least very similar to the sense ⁄ reference distinctioneven before that distinction is made. The other complicating fact is that once Frege




12/17

adopts the distinction he shifts to a non-standard use of the term ‘concept’. This may or may not be justified in the light of his views on other aspects of this subject – somethingwe will not go into here – but it can easily breed confusion. On Frege’s modified use of the term ‘concept’ (to avoid confusion I will mark it ‘conceptF’) ‘creatures with a heart’and ‘creatures with kidneys’ express one and the same conceptF (not two, as on the morecommon terminology). ConceptsF and their extensions

17 are related one–one, not (as innormal use, and Frege’s earlier writings), many–one. It is conceptsF that Frege regards asthe references of concept-words. This fits in with what he takes to be the references of other expressions since, as he notes (and in conformity with the principle already appealed toabove), so long as we substitute a concept-word with another with the same extension, thesentence’s truth-value will not change. What then is a concept-word’s sense?

Not surprisingly, Frege’s maintains that conceptsF, too, have modes of presentation.The earlier example of ‘creatures with a heart’ and ‘creatures with kidneys’ might serveto illustrate this. Both express one and the same conceptF, but each presents it in a differ-ent way. We thus end up with a distinction between sense and reference for concept-words as well. But it seems questionable whether this distinction, unlike those for proper

names and complete sentences, adds anything theoretically substantial to the pre-Fregeanconception, or whether it is a mere re-labeling of elements of a familiar distinction in anattempt to produce a neat uniformity with the distinction for names and sentences.

The distinction for concept-words completes the picture and enables the invocation of two parallel principles of compositionality: A sentence’s reference, its truth-value, isdetermined by the references of its constituents parts. A sentence’s sense, the Thought, isdetermined by the senses of its constituent parts.

5. Two Criticisms of the Distinction

5.1 RUSSELL’S CRITICISM IN ‘ON DENOTING’

In Section 4.2, we mentioned that in reported speech our words refer to what is ordinar-ily their sense. The reference of the whole subordinate clause (what follows ‘that…’) isthe Thought that clause (ordinarily) expresses, not its truth-value, and the referents of indi-vidual names within that clause refer to (what are ordinarily) their senses, not their refer-ents. Since no expression refers unless it has a sense, such names must also express somesense.

Let us consider a particular instance mentioned earlier. Imagine yourself hearing Tomsay, in normal circumstances ‘Aristotle was a philosopher’ and that you understand

perfectly what he said. You then report this event by saying:

(9) Tom said that Aristotle was a philosopher.

You have no reason to doubt that you fully understand what you are saying. There isnothing particularly tricky involved in saying (9). (We are not concerned here with itstruth, but only with what understanding it entails.) Now let us examine (9) from thestandpoint of Frege’s theory. The reference of ‘Aristotle’ here is its ordinary sense. Ignor-ing the difficulty arising from the fact that you may not know (or indeed, need to know)which sense Tom associated with his utterance of ‘Aristotle’ (which may, as noted earlier,

differ from the one you normally do); we can still ask, since your use of ‘Aristotle’ mustexpress some sense, which sense, according to Frege’s theory, is it? We know this sense’sreference is the sense of Tom’s expression, and let us suppose that you somehow know




13/17

this to be ‘the Teacher of Alexander born in Stagira’ which is thus your utterance’s refer-ence. But it is the sense you expressed we are now asking about. Imagine yourself saying(9), and simply ask yourself ‘Which sense was I associating with my utterance of ‘Aristotle’?’

You might think it is

(10) The sense of the teacher of Alexander who was born in Stagira,

but this will not do. As a moment’s reflection will reveal, since the teacher of Alexander the Great born in Stagira is Aristotle, and since Aristotle was a human being, not a lin-guistic expression, he does not have a sense. Modifying the example so that the embed-ded phrase’s referent will be of a kind that does have a sense (e.g., the sense of the firstline of Gray’s Elegy) will still not give us the sense we are after. (10) gives us the sense of the reference of those words, not those words’ own sense.

Alternatively, we might try:

(11) The sense of ‘Alexander’s Teacher who was born in Stagira’.

Unlike (10), here the embedded phrase is mentioned, not used. It refers to the enclosedwords, not their meaning. But (11) involves a mistake which at root is the same as theone recognition of which, as we saw earlier, led Frege to abandon his former theory.The mistake, namely, of appealing to a relation which is merely conventional, to individ-uate something which is supposed to be objective. The relation between sense and refer-ence (including where the referent is itself a sense) is an intrinsic, logical one. Specifyinga sense by appeal to a sound pattern, makes our specification relative to, and thus depen-dent upon, a particular arbitrary convention (the same is not true, e.g., of (10), althoughany specification will, of course, use language).

Moreover, even if we ignore this problem, (11)’s appearing to specify a definite senseis illusory. The sense we are trying to capture is one whose reference is the sense of thementioned phrase. But like any referent there are infinitely many senses which determineit; which of those does (11) specify? There is no route leading back from the reference tothe sense; so we cannot tell, from having identified the reference, what sense is involved.

The appeal of the distinction, when it was initially made for names as we ordinarilyuse them, was crucially dependent on our experience, as speakers. The thesis that nameshave senses is appealing partly because we can usually think of a specific sense (or several)which might be a plausible candidate for the one we express or grasp in a particular instance. This linked the theoretical notion – which would otherwise remain merely pro-

grammatic – with our experience as speakers. But this link disappears into thin air whenwe follow the theory to the next step. We are still supposed to grasp a specific sense, butwe are at loss to say which one it is. And if for all we know, it could be any one of aninfinite set of theoretically possible candidates, what plausibility is there to our maintain-ing that we grasp it?

The difficulty is not over the being of a sense of the kind we are after – any sense hasinfinitely many senses determining it, and there is no problem in admitting second- or higher-level senses. It is, rather, that despite supposing, with Frege, that we had expressedand therefore grasped a particular sense, we have no idea which sense it is. Russell is not arguing that the distinction is inconsistent or leads to contradiction but, more simply, that

the consequence just revealed shows that it had not been properly thought through. Theburden of proof lies, Russell seems to have thought, squarely with the theory’s propo-nent: he must explain which sense has been expressed. The critic, on the other hand, is




14/17

not even trying to establish that no such an explanation is possible. It is damaging enoughthat no explanation is forthcoming; and such appears to have remained the case ever sinceRussell struck upon the problem in 1905. This difficulty persuaded Russell that Frege’sdistinction, as well as his own, similar, view (which he endorsed up until he struck uponthe Theory of Descriptions) were untenable, saying it involved ‘certain rather curious dif-ficulties, which seem in themselves to prove that the theory which leads to such difficul-ties must be wrong’ (1956, 48).

The above gives the gist of Russell’s criticism of the distinction in ‘On Denoting’,although the specific context in which Russell raised it was an attempt to devise a (logi-cally conspicuous) symbol for talking about a sense (or as he calls them ‘meanings’ or ‘denoting complexes’), and his discovering that no coherent interpretation of such a sym-bol effected speech about the desired sense.18 Despite being by far the oldest criticism of the distinction, and appearing in what is arguably the most influential paper ever writtenin the analytic tradition of philosophy, this criticism has had virtually no influence. Thesimple reason for this is that it had not been understood and this, in turn, may beexplained, at least partly, by the obscurity of the passage in which Russell articulated it,

and by the fact that the relevant (posthumous Russellian) manuscripts which assist one inconquering that obscurity were only published in 1994.19

5.2 KRIPKE’S CRITICISM AND THE ‘DIRECT REFERENCE’ VIEW

From the mid-1960s and early 1970s on, a number of writers, most prominently SaulKripke in ‘Naming and Necessity’, advanced the merits of a view akin to what we earlier called ‘the naı̈ve view’, i.e., that a name’s meaning, or contribution to the meaning of sen-tences in which it occurs, is exhausted by its picking out a referent, without the mediationof anything conceptual. The case is largely an attack on the view that names have senses.

The criticism first sets up what it calls ‘the descriptive theory of names’ in a versionwhich, although certainly not Frege’s, makes it fair to count him as subscribing to its fun-damental thesis, namely, that a name’s meaning is given by (the content of) some definitedescription which the speaker associates with it, and which determines its referent.Although Frege never explicitly commits himself to this thesis, the illustrations he pro-vides strongly suggest such an understanding and, more importantly, no viable alternativeunderstanding, which has any bearing on our experience as speakers, is on offer. (A mereprogrammatic notion, whereby something which determines the referent is associated withnames we use, does not get us anywhere.)

The criticism spells out a number of consequences which would follow if the

descriptive theory of names were true, and argues that they are plainly false. (I sim-plify them to avoid issues which are not relevant to the criticism of Frege.) Since, aswe already know, different speakers may associate different senses with the samename, the discussion is relativized to a speaker S, who associates description D withthe proper name ‘N’ (which is thus meaningful in S’s idiolect). The descriptive theoryis committed to the following:

(I) S believes that exactly one thing satisfies D.(II) If S’s belief is true, then ‘N’ refers to that thing, otherwise ‘N’ does not refer.(III) If N exists, it is necessarily true that it satisfies D.

This is a somewhat simplified and truncated version, but it will do to give the gist of thecriticism. Kripke tests these theses on names of famous persons, taking D to be what a




15/17

normal speaker, who uses and understands the name, might come up with if asked ‘Whois N?’ (the nature of the criticism drives us to consider cases where the speaker knowsleast about the name-bearer while still succeeding to refer. Of course he may well knowa lot more).

Let us take as an example the name ‘Gödel’, and ‘the person who proved the incom-pleteness of arithmetic’ as the sense S associates with it (let us further assume, S knowsnothing more about him). The criticism then argues that:

Contrary to (I), S’s use of ‘Gödel’ may still refer to Gödel even if S does not believethat the description is satisfied by exactly one thing.

Contrary to (II), S’s use of ‘Gödel’ would not fail to refer even if it turned out thatthe alleged proof was somehow faulty (and thus that no one satisfies D). Nor is it the casethat if, unknown to S, the proof was actually the work of someone else, say, a littleknown figure called ‘Schmidt’, this would make Schmidt the referent of S’s use of ‘Gödel’.

Contrary to (III), ‘Gödel proved the incompleteness of arithmetic’ is not a necessarytruth. It is at least plausible to say that Gödel might not have proved the incompleteness

of arithmetic (e.g., had he died as an infant); and certainly does not have to mean thesame as ‘the person who proved the incompleteness of arithmetic might not have provedthe incompleteness of arithmetic’.

The descriptive view’s commitment to the theses under attack flows from its regard-ing the description (that the speaker associates with a name as its sense) as giving the name’s meaning , serving (for that speaker) like a definition. But underlying the specificpoints above is also a broader and more fundamental issue. Frege’s notion of sense isintended as an answer to what, Kripke maintains, are two distinct questions. One is‘What is a name’s contribution to the meaning of sentences in which it occurs?’; theother ‘What makes it the case that this (i.e., our reply to the first question) is the

name’s meaning?’. Once the two questions are separated, and thus the possibility of giv-ing quite a different answer to each, is recognized, the direct reference view no longer appears untenable. To illustrate: Kripke’s answer to the first question is: the name’s ref-erent, and nothing more. In reply to the second, he puts forward what he describes asa mere ‘picture’. A causal-historical chain links the referent’s ‘baptism’, when it was firstgiven the name (however, far in the past this may have been), to the speaker. Each linkof this chain involves the passing of the name (the sound) and its association with itsreferent from one speaker to another. In this way, one’s use of a name can refer to theobject at the root of the chain even though he may not have sufficient descriptiveinformation to single it out.

But it is fair to ask how does the direct reference view handle the puzzle which gaverise to the distinction in the first place? Kripke does not offer an answer to this, but other advocates of the view do. A pair of sentences differing only in ‘Hesperus’ having beenreplaced by ‘Phosphorus’ express the same proposition, have the exact same content, not(as Frege would have it) two different ones. To account for the possibility of a subjectbelieving the one but not the other, Nathan Salmon20 proposes that (again, contrary toFrege’s view) a subject may misidentify a proposition he grasps. In special circumstances, asubject may grasp a proposition and believe it, encounter it again in a different contextand, failing to recognize it is the same proposition, not believe it. This happens if on eachoccasion the subject takes the name’s referent (which, on this view, is literally a constitu-

ent of the proposition) in a different way. Belief, accordingly, is not a two-place relationbetween subject and proposition, but rather a three-place relation involving also the wayin which the proposition is taken by the subject. The way in which the proposition is




16/17

taken by the believer – any of Frege’s illustrations of names with different senses deter-mining the same referent would fit the phenomenon described by Salmon – is directlyinherited from the way in which the referent is taken by him (the other constituent areirrelevant to this third element of the belief relation). So, after all the twists and turns, itseems that we have ended up with something surprisingly similar to Frege’s notion of sense for proper names, alas, without it being part of the content of the sentence express-ing that belief, and yet, it is part of that belief.

Short Biography

Gideon Makin obtained his DPhil from Oxford in 1995. Since then, he has held postsand taught at the Universities of Oxford, Stirling, and Birmingham. His book The Meta-

physicians of Meaning – Russell and Frege on Sense and Denotation appeared in 2000 inRoutledge’s ‘International Studies in Philosophy’ Series. He is currently an honoraryResearch Fellow at the University of Birmingham, England.

Notes

* Email: [email protected].

1 The original German ‘Sinn’ and ‘Bedeutung’ have also been translated ‘Sense’ and ‘Meaning’ and, less frequently,‘Meaning’ and ‘Denotation’. Since Frege was consciously introducing these as novel technical terms, appeals tocommon usage in either language are immaterial.2 Strictly speaking, one should distinguish the referent , the object spoken about, and reference , the word’s property of singling out that object. However, it is fairly common to use the latter for both, without this breeding any confu-sion.3 The broader context was Frege’s exploring the prospect of proving a thesis in the philosophy of mathematicsknown as logicism. On this view, all mathematical truths, and all the fundamental concepts mathematics requires,

can ultimately be derived from, and defined in terms of, a small number of truths and concepts of general logic.Having found natural language to be inadequate for this task, Frege set out to devise an artificial logical language, a‘concept-script’, in which such a proof was to be carried out. When he came to introduce the symbol for identityin that language, he noticed that the very need for such a symbol called for special justification.4 Frege speaks of such pairs as differing in ‘cognitive value’.5 Frege’s principal characterization of what is essentially the same notion is somewhat different. In Concept-Script §3, he says that two sentences have the same conceptual content if everything that logically follows from the one(together with other sentences), also follows from the other (together with those same sentences). Frege’s notion of conceptual content is designed, first and foremost, to capture all and only what is relevant to logical inference.6 That Frege held sense to be objective is, of course, beyond doubt; but while in Concept-Script he neither assertsnor denies the objectivity of ‘ways of determining’, his avoiding a commitment to their objectivity seems likely,first, in view of his highly selective attitude, as evidenced in §3, to admit anything into conceptual content; and sec-ond, because one of the two ‘ways of determining’ used to illustrate this notion in Concept-Script §8 (directly inexperience) seems both not to be objective, and is (unlike the other way in the same illustration) of a kind which isnever found in Frege’s numerous illustrations of the notion of sense (nor does he ever regard any sense as beingmore direct than another). When considering this proposal one needs to bear in mind, first, that the question of theobjectivity of a mode of determining is distinct from that of the objectivity of what is determined ; and second, that if ‘modes of determining’ are to be objective, then all must be; it will not do if only some are.7 For alternative views and a spirited exchange on Frege’s positions in, Concept-Script §8 and the transition to ‘OnSense and Reference’ see May; Thau and Caplan; Heck; Bar-Elli.8 See ‘Dialogue with Pünjer’ 60 [99] and ‘Seventeen Key Sentences on Logic’ 174 (proposition 10) for simplenames; and a footnote in §74 of The Foundations of Arithmetic for complex names.9 For diverse views on this, see Evans 22–32; Dummett (1981) 45–46, and Makin 112–116.10 See, e.g., Dummett (1973) 109.11 Thus ‘On Sense and Reference’ addresses a more general form of the puzzle than Concept-Script did, and accord-

ingly drops the limitation to identity statements, which are merely a special case.12 This principle, it might be thought, is rather ad hoc ; but reflecting upon the substitution, in complex names, of co-referential constituent names (e.g., the occurrence of ‘Tom’ in ‘Tom’s father’), shows this is not so.




17/17

13 See Sluga 157–161.14 See ‘Thought’ 342. This view is closely linked with Frege’s view of truth as absolute, ultimate and irreducible, for which see ‘Thought’ 326–327; also, (more extensively) ‘Logic’ of 1897 in Posthumous Writings 128–133.15 We can do this because we confine ourselves to the effects of substituting a single expression, or word, in a sen-tence while leaving the remainder, and thus the effect of the combination, unchanged.16 It may argued that this is in fact the true home of the ‘determines’ relation in our discussion. Concepts (both inFrege’s pre-Sense ⁄ Reference terminology, and in the new sense this term acquired with the distinction) are

regarded as objective, and depend on neither mind nor language.17 To be precise, Frege replaces the notion of an extension with that of a value-range, but this does not affect thepoint at stake.18 For an extensive discussion of Russell’s argument see Makin 22–44 and 208–222. In a recently published paper Kripke (2008, especially 190–191) articulates what strikes the present writer as essentially the same problem, eventhough Kripke does not relate it to Russell’s criticism.19 Primarily ‘On Fundamentals’ §§35–39.20 Chapter 8.

Works Cited

Bar-Elli, G. ‘Identity in Frege’s Begriffsschrift : Where Both Thau-Caplan and Heck are Wrong.’ Canadian Journal of

Philosophy 36 (2006): 355–370Dummett, M. Frege: Philosophy of Language . London: Duckworth, 1973. ——. The Interpretation of Frege’s Philosophy. London: Duckworth, 1981.Evans, G. The Varieties of Reference . Oxford: Clarendon Press, 1982.Frege, G. ‘Conceptual Notation’ (1879). Conceptual Notation and Related Articles. Ed. T. Bynum. Oxford: Clarendon

Press, 1972. 101–203. (§8 also in (Ed.) Beaney. 64–65). ——. ‘Seventeen Key Sentences on Logic.’ Posthumous Writings. Eds. H. Hermes, F. Kambartel, F. Kaulbach.

Oxford: Blackwell, 1979. 174–175. ——. ‘Dialogue With Pünjer on Existence’ (Before 1884). Posthumous Writings. Eds. H. Hermes, F. Kambartel, F.

Kaulbach. Oxford: Blackwell, 1979. 53–67. ——. ‘Logic’ (1897). Posthumous Writings. Eds. H. Hermes, F. Kambartel, F. Kaulbach. Oxford: Blackwell, 1979.

126–151. ——. The Foundations of Arithmetic (1884). Oxford: Blackwell, 1986.

——. ‘Function and Concept’ (1891). The Frege Reader . Ed. M. Beaney. Oxford: Blackwell, 1997. 130–148. ——. ‘On Sense and Reference’ (1892). The Frege Reader . Ed. M. Beaney. Oxford: Blackwell, 1997. 151–171. ——. ‘Thought’ (1918). The Frege Reader . Ed. M. Beaney. Oxford: Blackwell, 1997. 325–345.Heck, R. ‘Frege on Identity and Identity Statements: A Reply to Thau and Caplan.’ Canadian Journal of Philosophy

33 (2003): 83–102.Kripke, S. Naming and Necessity (1970). Oxford: Blackwell, 1980.

——. ‘Frege’s Theory of Sense and Reference: Some Exegetical Notes.’ Theoria 74 (2008): 181–218.Makin, G. The Metaphysicians of Meaning . London and New York: Routledge, 2000.May, R. ‘Frege on Identity Statements.’ Semantic Interfaces: Reference, Anaphora and Aspect . Eds. C. Cecchetto, G.

Chierchia, M.T. Guasti. Stanford: CSLI Publications, 2001. 1–50.Russell, B. ‘On Denoting’ (1905). Logic and Knowledge . Ed. R.C. Marsh. London: Allen & Unwin, 1956. 41–56.

——. ‘On Fundamentals’ (1905). The Collected Papers of Bertrand Russell, vol. 4 Foundations of Logic 1903-05 . Ed. A.Urquhart. London and New York: Routledge and Kegan Paul, 1994. 360–413

Salmon, N. Frege’s Puzzle . Cambridge, MA: MIT Press, 1986.Sluga, H. Gottlob Frege . London, Boston and Henley: Routledge & Kegan Paul, 1980.Thau, M. and Caplan, B. ‘What’s Puzzling Gottlob Frege?’ Canadian Journal of Philosophy 31 (2001): 159–200.



Download - Frege´s distenction between sense and reference

Top Related