Fregean Sense

by R.M. Sainsbury, King’s College London.


1. Introduction

The main aim of this paper is to show that a more or less Fregean conception of sense is implicitly involved in the supposition that people are sometimes fully justified in engaging in deductive reasoning or in affirming truths of logic. Sense, as envisaged here, attaches to tokens of expressions, and sameness of sense arises when there is an immediate guarantee of sameness of reference.

In this section I set out three background assumptions. In the following section (¤2) I consider some attacks that have been made upon a Fregean conception of sense by Ruth Millikan. In the last section (¤3) I apply what I hope I will by then have established to argue for my main conclusion.

1.1 Sense is a property of tokens

I shall assume that the sense–reference distinction applies at the level of individual utterances: to expression tokens rather than expression types. One reason for this assumption is that it is obvious that a constant sense cannot by itself determine the reference of expression types whose tokens vary in their reference from occasion to occasion; and the determination of reference by sense is absolutely essential to any view deserving to be called Fregean.

Taking utterances as the fundamental bearers of the semantic properties requires adjusting the account of the link between sense and understanding. The basic notion is that of understanding an utterance, which can be equated with grasping its sense. Understanding an expression type is then a matter of being able to understand arbitrary utterances of it, given the required contextual information.

Taking utterances as basic makes room for the possibility that tokens of intuitively non-synonymous types should have the same sense. If on Monday I utter "It is sunny today" you can on Tuesday report me in the words "He said that it was sunny yesterday". In Fregean spirit, I assume that the relevant part of an accurate report of an utterance has the same sense as the utterance reported. So my token of "It is sunny today" has the same sense as your token of "It was sunny yesterday", even though they are of non-synonymous types.

Moreover, the focus on tokens makes vivid the possibility, indeed actuality, that equiform tokens differ in reference, and so highlights the theoretical need for a way of describing the cases in which equiform tokens are alike in reference, and are properly unthinkingly treated as alike. This fact is crucial for ¤3 below.

1.2 Sense without senses

I make use of the notion of sameness of sense, but not of the notion of senses or thoughts as abstract entities. Although there may be theoretical pressures towards abstraction (for example, senses might have a special role to play in an account of indirect discourse, as in Pietrowski 1997), it seems to me useful to start simply with sameness of sense. This helps curb excessive explanatory and reductive pretensions. For example, it makes no room for the idea that senses are entities which are distinguishable from other kinds of things by the fact that we are specially good at recognizing them, at telling when we have been confronted with two different senses as opposed to the same one twice. It also discourages the idea that a sense is some psychological state which a creature could be in independently of its capacities for language or thought, a state whose nature could contribute to an explanation of why we think or understand as we do. By contrast, I shall refrain from assuming that there is any non-semantic way of specifying the relevant features of sense; perhaps there is no other fundamental and reliable way of referring to the sense of "Aristotle" than as I have just done.

1.3 Sense and explanation

Can one explain how it could be that the ancient astronomers believed that Hesperus is Hesperus without believing that Hesperus is Phosphorus by alluding to the fact that "Hesperus" and "Phosphorus" do not stand in the same-sense relation? I think not. One can, indeed, infer from the (presumed) joint truth of the belief-ascriptions that there is a difference in sense in the English words, but this is a long way from connecting with the cognitive mechanisms of the early astronomers. Presumed data such as the joint truth of these belief-ascribing sentences is marked at the level of theory by ascribing distinctness of sense. But that mark does not provide an explanation of the phenomenon except in so far as it connects this case with associated phenomena: for example, with a priori knowledge, with understanding, with rationality. In general, the explanatory value of sense lies in its putative subsumption of a number of apparently distinct phenomena. But if we take any one phenomenon, for example the one about what the ancients believed, to invoke difference of sense is simply to redescribe the phenomenon in the theorist’s preferred vocabulary. It is not to acquire access to some potentially explanatory but distinct fact.

Similarly, though the main claim of this paper is that fully justified logical reasoning implies instances of the same sense relation, this is not to say that the justification of the reasoning can be explained by the relation. There will be something explanatory about the description of the situation in terms of sameness of sense if, and only if, this relation has work to do in other areas (opacity, understanding, etc.). Establishing that there is a single relation which subsumes the various phenomena, and so justifying the modest explanatory role of sense, is a task well beyond the scope of this paper.


II Millikan’s objections to Fregean sense

2.1 Meaning rationalism

In a series of papers (Millikan 1991, 1993a, 1993c), Millikan has adopted a position strongly opposed to Fregean sense. I find her work highly rewarding, even though my use of it consists not in accepting her criticisms, but rather in seeing how a Fregean can properly respond to them.

Her opening shot is the suggestive idea that sense is like sense data. Rather as, in perception, similarities between veridical and non-veridical cases have led people to postulate a genuinely common element, a sense datum, which is the immediate object of perception, so dissimilarities between thoughts of the same have led people to postulate genuinely distinct elements, senses, which are the immediate objects of thought. This analogy reaches its full development in her characterization of a doctrine she calls "meaning rationalism". Unlike the world of real objects, the world of meanings or senses is open to infallible knowledge by any rational mind.

The charge is laid in more concrete detail in her paper "White queen psychology" (1993c), where she characterizes the version of meaning rationalism most relevant to a Fregean by the following three doctrines:

1. Givenness of identity and difference in mode An intact person has the capacity to discern a priori whether two of her thoughts exemplify the same or different semantic modes of kontent presentation.

2. Givenness of univocity in mode An intact person has the capacity to discern a priori whether or not a semantic mode of kontent presentation for her thought is ambiguous (if ambiguity in thought is possible at all).

3. Givenness of meaningfulness An intact person has the capacity to discern a priori whether she is entertaining a thought or instead a meaningless form having no semantics, a mental impression that exemplifies no semantic mode of kontent presentation at all. (1993c, p. 326)

Here "kontent" means content in the sense of Kaplan (1977), and corresponds approximately to the Fregean notion of Bedeutung; so "semantic mode of kontent presentation" corresponds to Fregean sense. Her use of the word "thoughts" is not Fregean (as she notes) for two reasons: since she does not allow for a realm of sense, and thoughts are not kontents, they can only be vehicles of kontents: expressions, or their mental analogues; and she allows subsentential thoughts, counting among thoughts such things as an idea of Alice. Her use of "intact" rather than "rational" corresponds to a disambiguation she believes is required: she thinks that it would be pointless so to define "rational" that the truth of the theses is guaranteed (and then what is controversial is whether there are any rational people), and uses "intact" to stress that she is concerned with anyone whose cognitive functioning is normal without prejudice to the question whether normality invests the thinker with such powers as that of being able to identify arbitrary contradictions.

A striking feature of meaning rationalism, as embodied in these theses, is that it is a doctrine about a subject’s knowledge of semantic features of thought or language. I have not found any basis for ascribing such a position to Frege. For example, in the opening pages of "On Sense and Reference" it is plain that the knowledge which interests him, and which will provide a way of introducing the distinction between sense and reference, is not knowledge of language or thought but knowledge of (non-linguistic) objects. In particular, arguing that identity is a relation between objects rather than between signs is tantamount to arguing that knowledge of identity, whether of the "a=a" form or the "a=b" form, is knowledge of objects as opposed to semantic knowledge. So my first point is that whatever the defects of meaning rationalism, we have no reason to think that they bear on Fregean sense.

However, there are many arguments in Millikan which a Fregean must address. She questions whether any identity sentences can be known a priori, whether any identity sentences are genuinely informative, and whether it is ever so much as possible to invoke semantic differences to explain ignorance of an identity. In this subsection, I want to consider an argument, which I think I detect in her work, using externalism to discredit the possibility of a priori knowledge, and hence the possibility of making the distinction between different kinds of identity sentence which Frege provides at the start of "On Sense and Reference". The use to which externalism is put blurs the distinction of the previous paragraph between the claims about semantic knowledge made by the meaning rationalist and Frege’s claims about knowledge of various other matters (identity, heavenly bodies).

Given semantic externalism, whether or not an expression has meaning depends upon whether it has various causal/historical/social properties. It is not knowable a priori whether any expression has such properties. Hence it is not knowable a priori that any sentence is meaningful. Since a sentence can be true only if it is meaningful, it cannot be known a priori whether any sentence is true. Applied to Frege’s distinction, we can condense the argument into the following form: given that it is not a priori that the sentence "a=a" has sense, it could not be a priori that a=a, or that the sentence "a=a" is true.

The objection brings out the care we must take in the present discussion over use/mention distinctions (a care which is salient in Frege’s own writings). I will stipulate that a sentence is knowable a priori iff the knowledge involved in understanding it forms a sufficient basis on which to work out that it is true; and that it is knowable a priori that p iff the knowledge involved in thinking that p forms a sufficient basis on which to come to know that p. The definitions are connected by the following: if sentence s means that p then: s is knowable a priori iff it is knowable a priori that p. I will refer to the first as "sentence a priority" and to the latter as "fact a priority".

If we rephrase the objection in terms of sentence a priority, it runs: given that the sentence "‘a=a’ has sense" is not a priori, how can the sentence "a=a" be a priori? The answer is obvious: in the first sentence ("‘a=a’ has sense"), "a=a" is mentioned, not used, so understanding it does not involve understanding "a=a". In the second sentence, "a=a" is used, not mentioned, so anything involved in understanding it is available as input to reasoning whose output may count as knowable a priori. Understanding "a=a" is possible only if "a" has sense. If externalism is true, "a" has sense only if it has various causal/historical/social properties. The condition for sentence a priority, namely that it be understood, ensures that every expression used in the sentence in question has sense; so, given externalism, ensures that every expression used in the sentence and which has externalist semantics has the appropriate causal/historical/social properties. So there is nothing inconsistent in combining the claim that the sentence "‘a=a’ has sense" is not knowable a priori with the claim that the sentence "a=a" is knowable a priori. An analogous point can be made if we keep to fact a priority throughout.

In general, externalism does not threaten a priori knowledge. Rather the opposite: since understanding a sentence, or being able to think that p, are givens for a priori knowledge, the richer the account of understanding or thinking the greater the input, and so the greater the potential output. This shows that a priori knowledge is not to be identified with environment-independent knowledge. A priori knowledge can be extracted from what is necessarily involved in understanding. If this is environment-dependent, then what is extracted may likewise be environment-dependent.

The argument just considered sought to make the possibility of a priori knowledge in general rest upon the possibility of a priori semantic knowledge. Once this is seen as groundless, we can reinstate the previous distinction. Whereas Millikan’s meaning rationalist is concerned with specifically semantic knowledge, the knowledge with which Frege was concerned in introducing the sense-reference distinction was certainly not semantic. We must distinguish between the following kinds of claim:

A priori knowledge of semantic fact:

If a and b are (singular) expressions with the same sense and one knows the sense of each, one can know a priori that they have the same sense.

A priori knowledge of non-semantic fact:

If a and b are singular expressions with the same sense, one can know a priori that p, where aö"="öb says that p.

A Fregean is certainly committed to a priori knowledge of identities, non-semantic facts. But I see no reason for him to be committed to a priori knowledge of semantic facts. Believing in Fregean sense does not involve being a meaning rationalist.

2.2 Identity and folders

Millikan says that

[Frege’s argument] assumes that if some sentence "A is B" is to effect a change in one’s cognitive processes, this could only occur because it effects a change in one’s bank of information (Millikan 1993c, p. 335).

She is surely right to attribute to Frege the presumption that sentences "a=a" and "a=b" can express different items of knowledge even when there is no difference at the level of reference, a presumption for which he felt no need to argue. She challenges this presumption in two ways: by offering a folder-merging account of identity, designed to make one think that identity sentences do not contain information; and by suggesting that the identity phenomena can be accommodated without sense. The first of these strategies, to be considered in this subsection, would undermine Frege’s claim that a sentence of the form "a=b" can be informative (of considerable cognitive value), and so would undermine Frege’s contrast with sentences of the form "a=a".

One might see value in the folder-merging metaphor without abandoning a Fregean conception of sense, for it would be consistent, given only what has so far been said, to combine the views. To prevent combination would require some principles relating folder operations to the presence or absence of information in sentences. Suppose we represent the simplest contents of folders using open atoms and their negations, counting different sentences as corresponding to distinct pieces of "folder-information". Perhaps the a-folder contains Fx and Gx and the b-folder contains Fx and not-Gx and Hx. Coming to accept that a=b is then represented by the formation of a new a/b-folder. All pieces of folder-information from both the a-folder and the b-folder are moved to the new one (which in the example will accordingly contain all of Fx, Gx, not-Gx and Hx), and the now empty old folders are removed. Without directly contravening any Fregean view, we can suggest that coming to accept an identity as such never involves adding or deleting any piece of folder-information across the system. (Of course, in cases like the one imagined the system requires adjustment to restore consistency, but this could be seen as coming after the acceptance of the identity.) Finally, we could suggest that a sentence expresses information only if coming to accept it could essentially involve adding or deleting some piece of folder-information. This rules all identities uninformative, while leaving standard examples of informative sentences as informative.

The existence of the model shows at most that we could take this line about the informativeness of identities. We must take this line only if we must not only accept the model, but must also accept its use to define informativeness on the basis of the notion of folder-information. For the first requirement, we would need a reason for not reckoning as changes in folder information those which result from restoring consistency within the new folder (the deletion of one of Gx or not-Gx in the example above). For the second necessity, we would need a reason for not reckoning as informative any sentence the new acceptance of which involves some change in the system of folders. This might satisfactorily rule tautologies uninformative (supposing for a moment that these are held to be unproblematic examples of the uninformative), but it would rule identities informative. Millikan’s case against Frege on the basis of the folder model has not even got off the ground.

This does not show that the case could not be made out, but optimism is diminished by the reflection that the identity phenomena are reproduced rather than annihilated in the folder metaphor: since every folder is merged with itself, there can be no question of coming to accept that a=a, whereas there can be such a question with respect to a=b.

2.3 Identity, recognition and the a priori

Millikan challenges Frege’s views about identity on another front, claiming that our inability to see that a=b should be grouped with our less than perfect capacities for recognition, and needs no explanation in terms of anything distinctively semantic. Perhaps, she suggests, the difference between "a=a" and "a=b" is "merely notational". Even if they are entirely alike in point of meaning, we might in the latter case fail to recognize the same meaning again. But this need no more raise a semantic issue than our inability on occasion to recognize our acquaintances.

While I agree that it is right to press this line against Frege, the anti-Fregean needs to have a positive doctrine about the possibility of a priori knowledge of identity. In Millikan’s terms, the question is how the "notation" involved in "a=a" can guarantee access to a piece of knowledge, whereas the notation involved in "a=b" may obstruct access to what is supposedly the very same knowledge.

I shall take it for granted that Frege is right to think that some identities are knowable a priori and that some are not. It seems to me that if one is to attempt to explain this contrast without invoking the notion of sense, one will most likely appeal to the notion of logical form, claiming that a=a is knowable a priori in virtue of its logical form, whereas a=b, is not. In ¤3 below, I argue that an appropriate notion of logical form requires Fregean sense. But first I will address one more anti-Fregean consideration adduced by Millikan.

2.4 Psychology and semantics

Millikan rightly points out that different psychological modes of presentation cannot be assumed to be different semantic modes of presentation. I am on her side in this discussion, but, again, we draw different morals. Whereas her aim is to throw doubt on the very idea of a semantic mode of presentation, I see in such considerations reasons for not using the notion of mode of presentation as anything more than a quick initial guide to Fregean sense. As her discussion makes plain, the very phrase suggests the possibility of a kind of reduction that I think is unavailable. It suggests that a sense is contingently a sense: it is a kind of psychological state which, in general, could exist whether or not it happened to be linked with some expression in such a way as to constitute its sense. Once this approach is allowed to dominate, it becomes hard to find modes of presentation which have the intersubjective nature required for Fregean senses.

My preferred approach, by contrast, is to see senses, or more exactly the same-sense relation, as essentially linked to the description of language, with no assumption that there is a reduction to entities or relations which have a place in the description of non-linguistic phenomena. If asked to distinguish the sense of "Phosphorus" from that of "Hesperus" I would rely upon the kind of answer given by John McDowell (1977): that the senses are different is shown by the fact that one expression may be used in a correct specification of what someone said where it would be incorrect to use the other. If asked to specify the sense of "Phosphorus" I have no better simple answer than: the sense of "Phosphorus".


3. Logic and guaranteed sameness of reference

"If p then p" is supposedly a "valid logical form", from which it should follow that every instance is true, indeed, is valid, is a truth of logic. However, the alleged instance "if John is sick then John is sick" may not be true if "sick" is understood in one of its meanings on its first occurrence, another on the second. Logical forms presuppose a pattern of recurrence: they assume that for each schematic letter, each token of it is to be understood as making the same contribution to logical truth and validity. If we are to recognize a genuine instance of a logical form as valid, we must be able to recognize that replacements of equiform tokens of schematic letters make equal contributions. Hence the concept of logical validity requires the notion of a relation between tokens which obtains only on condition that they make the same contribution to validity, and whose obtaining can be manifest to reasoners. In this section, I argue that one constraint upon sameness of sense among singular tokens is that it should make sameness of reference, and thus sameness of contribution to validity, recognizable.

The phenomenon at issue has not received much attention, in part because logic operates under the assumption that expression types are the prime bearers of logically relevant properties, and that for tokens to be of the same type is a merely spatial issue, raising no epistemic problems. Even if the last claim were true, which is doubtful, this paper runs on the assumption that sense is in the first instance a property of tokens. This makes room for the observation that if one counts anything an instance of "a=a" if it has equiform tokens either side of the identity sign, not every instance is true. Moreover, even if the tokens have the same reference, this is not enough for the identity sentence to be knowable a priori, as "Paderewski" examples demonstrate. We have a priori knowledge in such cases only if something in the understanding of the sentence guarantees its truth. Hence a priori knowledge requires that something in the understanding of the sentence guarantees that the tokens have the same reference. I use "sense" to mark this relation between tokens. The conclusion is that logical notions such as "logical form", "logical truth", "logical validity", cannot be understood in the way they are intended without presupposing a notion of sense. Hence one does not avoid sense by claiming that the distinction between the a priori knowability of a=a and the non a priori knowability of a=b is based on their distinct logical forms.

It is a premise to this argument that we are sometimes completely justified in affirming a truth of logic or using a logical pattern of argument. I claim that this is possible only if we are, in those cases, completely justified in unthinkingly taking it for granted that recurring tokens of a given type make the same contribution to truth (in the case of singular terms, have the same reference). When this happens, I say that the similar tokens have the same sense. This does not explain how we are justified, but merely marks the fact that we are. There may be no general explanation of how we are justified in such cases.

To illustrate this conclusion, consider an argument (that is a series of genuine—interpreted—sentences) of the following form:




On a standard reading, we just assume that tokens of equiform expressions make the same contribution to validity. However, when we consider that pairs of equiform tokens may differ in meaning, in a way that would undermine the validity of an otherwise valid argument, we appreciate that this assumption does not do justice to the realities. Let us mark distinct tokens of the same type with a different number of dashes. Then a more illuminating presentation of the argument form would be something like:




This way of putting it makes it plain that there is a real question about whether the occurrence of "a˘" on the first line has the same reference as the occurrence of "a˘˘" on the second; and likewise in the other cases. My claim is that sometimes this identity is guaranteed by what is involved in understanding; in these cases, we say that the relevant tokens have the same sense.

Some identities are never fully expressible without semantic ascent. Suppose that, in the above example, we try to express what, in the previous paragraph, I expressed metalinguistically, by writing: a˘=a˘˘. This is strictly nonsense, for these marks are supposed to be tokens, and the first token of "a", marked by appending just one prime, occurred in the first line of the argument whose form was displayed a few lines up, and it can never recur anywhere else. I can refer to that token, and say that it has the same reference as the second token of "a", the one on the line below the first, but it is impossible to say this by re-using these tokens: they have been used up. This means that we cannot regard arguments like the one under consideration as enthymatic, needing but a further (object-language) sentence to be made completely valid; there is no evading unthinking reliance on sameness of reference. It also gives us a deeper understanding of the low cognitive value of a sentence of the form "a=a", in our terminology, "a˘˘˘=a˘˘˘˘" Every identity sentence has distinct tokens, so unless identity of reference has already been made available, no identity can be "true in virtue of form".

The phenomenon is entirely general. Consider, for example, modus ponens reasoning, of the form "p; if p then q; so q". If we are ever justified in using such reasoning, we must be justified in supposing that the various occurrences of p and q make the same contribution to validity. We are sometimes thus justified. The Fregean theorist I envisage will mark such cases by counting the relevant tokens of p as alike in sense; likewise for the tokens of q.

As I see it, the theorist begins by finding cases in which reasoning is indisputably both justified and correct. Acknowledging this justified correctness at the theoretical level involves seeing reasoners as justified without further ado, and also correct, in treating tokens as having the same reference. The theorist is to record this fact by counting the tokens as alike in sense. In the first instance, there is no need to think of this record as explanatory. It gains explanatory status if the same-sense relation has other work to do in the theory (as I believe it has): in describing indirect discourse, for example. Then the explanation is not so much: "the same-sense relation obtained between these tokens; so the reasoner was justified and correct", but rather "the reasoner was justified and correct, so the same-sense relation obtains, a relation whose role and working connect this case of correct reasoning with other phenomena (like indirect discourse)".

Sense is not the only possible guarantor of sameness of reference. Anaphor also plays this role. If we try to use this notion to give a representation of our sample inference, we might write:

a is F

ita= b   

itb has that propertyF.

Here the subscripts serve to make explicit the anaphoric heads of the expressions to which they are attached. However, in inference we need transportable conclusions, ones which can be placed in other contexts from which the relevant head may be absent. This involves our using further inferential steps, for example, turning the above conclusion into "b is F", and these further steps raise the same issues as before, requiring that it be legitimate for a speaker to take it, without evidential support, but merely on the basis of his understanding of the expressions, that two tokens have the same reference. So we cannot use anaphora to dispense with recognizing the phenomenon of guaranteed sameness of reference; that is, of sameness of sense.


The main ideas for the paper can be traced to Campbell 1987 and Strawson 1957.

As Keith Hossack pointed out, Frege’s own view, in the case of indexicals, is arguably that the bearer of sense and reference is a composite of an expression type and a feature of the context, e.g. a time. (Cf. also Kźnne 1992 and Harcourt 1993.) I do not think that this interpretation would call for any revision of the main argument of this paper.

There are certainly passages which appear to be inconsistent with the supposition that Frege believed in infallible knowledge of sense. For example, discussing whether one could count as a definition an attempt to explain an existing simple sign by identifying its sense with that of a complex he writes:

Let us assume that A is the long-established sign (expression) whose sense we have attempted to analyse logically by constructing a complex expression that gives the analysis. Since we are not certain whether the analysis is successful, we are not prepared to present the complex expression as one that can be replaced by the simple sign A. (Frege 1979, p. 210)

The concluding sentence of this passage provides another example:

The senses present us with something external and because of this it is easier to comprehend how mistakes can occur than it is in the case of the logical source of knowledge which is wholly inside us and thus appears to be more proof against contamination. But appearances are deceptive. (Frege 1979, p. 269)

Since Frege himself counts as a semantic externalist (if all this means is that meanings are not in the head), it might seem that a careful formulation of the relevant thesis is needed here. However, the only thing that matters to Millikan is that semantic properties should not be accessible a priori. As I will show in detail, this is something Frege has no need to deny.

In a helpful comment received after I had submitted this paper for publication, Ruth Millikan said that this section misrepresents her. She is not concerned (1993c) with knowledge of language, but with mental representations. It might be that the view here presented, in which there is Fregean sense without senses (as entities), fails to engage with Millikan’s real target. Her comment opens up avenues which I would like to explore; though this must await another occasion.

Even this may overstate the case, for perhaps coming to accept that all Fs are Gs is a matter of acquiring the disposition to add Gx to any folder containing Fx, which, if no folders contain Fx, does not involve any change in the pieces of folder-information across the system.

It may be that Millikan thinks that externalism defeats the very idea of a priori knowledge, though I showed in ¤2.1 above that there was no easy way to establish this.

Cf. Strawson, 1957; and, for an application of the point close to that made here, Campbell 1987. "Sick" is not shown to be ambiguous by the fact that one can be sick in body without being sick in mind, or vice versa, any more than "human" is shown to be ambiguous by the fact that a human can be a man without being a woman, or vice versa. But Strawson’s point is good, even if the example is a little infelicitous.

Suppose a person thinks that there’s Paderewski the statesman and also a different Paderewski, the pianist. He is wrong because in fact the statesman is the pianist: there is just one Paderewski. Yet such a person can, without obvious irrationality, believe something he could express as "Paderewski is not Paderewski".

For example, the basis for the justification of reasoning involving repeated perceptually based demonstrations of an object (cf. Campbell 1987) may be different from that involving propositionally valid reasoning.

Versions of this paper were read at Logica 1996 in the Czech Republic, at Sheffield University’s Philosophy Department Seminar, at a one day conference on Frege organized by the Philosophy Programme of London University’s School of Advanced Study, and at the Philosophy Society of Portugal in Lisbon. I would like to thank participants for the many helpful comments and suggestions I received on those occasions. I would also like to thank the following for detailed written comments which I found extremely valuable: Michael Beaney (whose book, cited above, appeared too late for me to be able to take it into account), Keith Hossack (my commentator at the London conference just mentioned), Michael Martin, Christopher Peacocke, and Tom Stoneham. After I had submitted this paper for publication, I had occasion to show it to Ruth Millikan, who thought that I had misunderstood her on various points. I have briefly addressed the claimed misunderstanding she thought most serious in footnote 5 above, but printers’ deadlines made it impossible to do justice to her comments.



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