Anti-Abstractionism and Philosophy of Language
Berkeley’s rejection of abstract ideas is developed specifically in his Introduction to the Principles, indicating that the anti-abstractionist thesis has a very special place in his over all philosophy. Consequently, one issue that has occupied commentators concerns the role that this thesis plays in advancing his immaterialist and idealist doctrines (alas, the role has not been especially clear!). Throughout my exposition of Berkeley’s arguments over the course of this book, I will attempt to point to his most important uses of this thesis. In this specific chapter, however, I want to merely underscore the considerable role that thesis plays in advancing Berkeley’s overall project (regardless of its relevance to the specific doctrines designed to advance that project). Berkeley writes:
In order to prepare the mind of the reader for the easier conceiving what follows, it is proper to premise somewhat, by way of introduction, concerning the nature and abuse of language. But the unraveling this matter leads me in some measure to anticipate my design, by taking notice of what seems to have had a chief part in rendering speculation intricate and perplexed, and to have occasioned innumerable errors and difficulties in almost all parts of knowledge And that is the opinion that the mind has a power of framing abstract ideas or notions of thing. (PHK Intro 6)
Since the issue of abstraction arises within the context of a general discussion of the “nature and abuse of language,” I will embed the discussion of abstract ideas within the larger context of Berkeley’s philosophy of language. My intention is to explain the role that Berkeley’s philosophy of language plays in framing his overall project.
Before I proceed, however, I should mention some issues of controversy. While Berkeley clearly has John Locke in mind throughout most of the Introduction (and to a lesser extent the Scholastics), he also discusses abstraction elsewhere, and it would seem that his attack is supposed to include other philosophers such as Descartes. Caution is needed, however, since while both Locke and the Scholastics endorse a process of abstraction whereby abstract conceptions are formed from particular ones, Descartes centralizes innate ideas which while possibly “abstract,” are not formed by any process of abstraction, pre-existing in the soul from inception. Thus, there are important questions how far Berkeley’s anti-abstractionism is supposed to extend; what exactly he is supposed to be denying; whom, exactly, he is supposed to be criticizing.
For the purposes of this chapter, I focus largely on Berkeley’s rejection of Lockean abstraction (although I consider other views from time to time). I focus mostly on Berkeley’s published Introduction to the Principles, and to a lesser extent on his discussion of language and abstraction in Alciphron (VII). Berkeley also (more briefly) argues against abstraction in his Essay Toward a New Theory of Vision (§122-8), Three Dialogues (I 192-4), De Motu (§2-7); and A Defense of Free-Thinking in Mathematics (§45-8), and I will draw on some of his remarks there from time to time. There also exists an earlier manuscript draft of the Introduction which differs in salient ways from the published version. I don’t explore that here.
I: Philosophy of Language
The Chief Function of Language
According to Locke, the chief function of language is to communicate ideas (E. 3.2.1, 405). Berkeley, however, denies this. Instead, he allows that language has many functions including guiding actions as well as stirring passions and forming dispositions (PHK Intro 20). Now on the face of it, Berkeley’s position seems questionable. Even if I were to say to someone “Please, hand me my keys!” thereby aiming to elicit an action, it is clear that I still mean something by the words, the person to whom my discourse is directed understands something by those words, and I have intended such communication to be successful by those words. Even in the case of demanding an action, communication is clearly essential. So how is Locke wrong?
At stake is a dispute about how words become meaningful and what it is to understand them. According to Locke, words become meaningful through their use as signs for “internal conceptions” (i.e. ideas). A speaker who uses a term without any such internal conception she is attempting to convey is no better off than a parrot who does not understand her own words. Thus, the significance of a term is given by a prior (i.e., pre-linguistic) internal conception (idea). Successful communication involves using such terms to excite similar ideas in the auditor. Thus, a communication is understood only on the condition that a similar internal conception is excited in the mind of the auditor.
In denying that words are always used in order to communicate ideas, Berkeley is not denying the trivial point that an exchange of words between two interlocutors involves successful communication. Rather he is denying that this always involves conveying a pre-linguistic mental conception from the speaker to the hearer. Sometimes a speaker may use words without prior ideas backing them up, and still speak meaningfully and with understanding; sometimes an auditor may understand words without having pre-linguistic ideas excited in her mind and still have full comprehension of what was said.
In order to support this claim, Berkeley provides some examples. First, he points to the use of symbols in algebra to stand for particular quantities. In Alciphron he also mentions counters (or chips) used during card games to denominate specific sums. In both cases, Berkeley points out that one can use these devices perfectly well without, on every occasion of use, having an internal conception of the sum or the quantity before one’s mind. Nor is the point of such deployments in algebra or during cards to convey internal conception from speaker to auditor. Instead, symbols can play a significant role in guiding one’s behavior.
Consider, for example, a traffic light. The signal green, although significant, needn’t convey into one’s mind the internal conception of driving a car forward; one need only step on the gas upon seeing the signal. Similarly symbols and counters play a role in guiding mathematical and game-playing practice. Nonetheless, it seems wrong to say that the manipulator of the symbols and counters, or the driver responding to traffic signals, does not understand what she is doing or that she is merely behaving like a parrot.
Berkeley also argues that terms such as ‘good,’ ‘rascal,’ and ‘danger’ may be used without any idea before the mind of the speaker; without any idea being excited in the mind of the auditor. At first, such terms may indeed suggest specific ideas to an auditor. For example, in first learning to use the word ‘good’, an idea of some pleasure (such as food) might be suggested. However, Berkeley argues, once a person is familiar enough with the words, a passion may be excited upon hearing a word without any specific conception being conveyed. Thus, upon being promised some good thing, I might experience desire for that thing without having any specific conception of what it is. For example, when I am promised a good reward in the afterlife, instead of imagining singing in a heavenly choir, I may simply experience an intense longing for the promised reward (without having a clear sense of what is in store for me). According to Berkeley’s view, one can understand the word ‘good’ without receiving an internal conception of some specific good. And certainly this seems right: A person who reacts in this way is scarcely in the same boat as a non-native speaker of English who has never heard the word ‘good’ before and doesn’t know what it means. Surely, the passion of intense longing for the unspecified divine reward to come in the afterlife demonstrates comprehension of the word ‘good’ rather than a lack thereof, despite the fact that no internal conception of that good has been excited.
Berkeley believes that the doctrine of abstract ideas emerges partially as a consequence of the belief that the main function of language is to convey ideas from speaker to auditor. For when terms are used which do not excite any ideas of particular things at all, one who maintains that the function of language was always to convey ideas, will be tempted to postulate the existence of abstract ideas.
The Meaning of General Terms
For Locke, the difference between a general name which applies to many items (such as ‘human’) and a proper name which refer to only one (such ‘Socrates’) is that the latter has a particular idea for its meaning, while the former has an abstract, general one. That is to say: Names become general by standing for abstract ideas. In effect, abstract ideas (as pre-linguistic internal conceptions) constitute the meaning of a general term.
According to Locke, simple ideas come into the mind experientially – either through sensation or through reflection (a kind of internal sensation of one’s own mental actions). However, the understanding can subject these simple ideas to various processes including compounding, comparing, and abstraction. Abstract ideas are formed by proceeding with particular ideas (which may either be simple and complex). For example, one proceeds with ideas of Peter, Paul, and Mary and then retaining what is similar, and leaving out the difference, yields an abstract idea of human.
For Berkeley, by contrast, terms are general simply because they apply to a range of particular ideas. Thus, the term ‘human’ is significant not because it has an abstract idea assigned to it, but because it indifferently denotes many ideas of particular human beings. Berkeley writes: “Whereas, in truth, there is no such thing as one precise and definite signification annexed to any general name, they all signifying indifferently a great number of particular ideas” (PHK Intro 18).
One of Berkeley’s departures from Locke, beyond this rejection of abstract ideas, is the view that the significance of a general term can be roughly fixed independently of some specific use. For Locke, the meaning of a term is principally constituted by the idea of the speaker who uses it on any given occasion. However, one cannot simply use a general term to convey all the particular ideas at once (as one could so use it to convey an abstract idea). So how is it that the general term connects with this range of particular ideas?
Berkeley’s view is that terms can suggest ideas to auditors (although they needn’t), depending upon their use. For example, from my praising the dog as the philosopher’s best friend, a particular idea of a dog may be suggested to you (e.g., your childhood companion). What makes the term general is that any idea of a dog can be suggested by it– it doesn’t matter which. In this way, the significance of a general term is determined by the range of particular ideas it is apt to suggest.
Suggestion, for Berkeley, is a technical notion which (as we shall see) does considerable work in his philosophy. According to Berkeley, upon experiencing x and y consistently together on multiple occasions, one can come to suggest the other. This is possible, by Berkeley, as a consequence of habit. For example, upon experiencing the word ‘dog’ spoken while a dog is present, one can come to associate the two, so that when somebody says ‘dog,’ an idea of a dog is suggested. One can think of this habit as a tendency or inclination to imagine a dog when the word ‘dog’ is uttered in the appropriate context. Which dog one imagines, however, is undetermined.
Appreciating this can help us understand how Berkeley might begin to reply to an important philosophical challenge: If one does not possess a prior (abstract) idea of a triangle, how can one identify any particular triangle as a triangle? Doesn’t one first need to know what a triangle is in order to then see whether the object in question possesses the right characteristics? In Berkeley’s view, this does not seem to be a problem. If I see a new human that I have never seen before, there is no reason that she may not suggest the term ‘human’ to me (if she resembles at least another human already associated with the term ‘human’). Nor is there any reason why I might come to imagine a new person, simply on basis of hearing the term ‘human’ and being inclined to think of humans.
In such an account, to be sure, some room needs to be allowed for imperfect resemblance. For example, there will be phenomenal differences in contrasting utterances of ‘dog’ when rendered by different voices at different times. Similarly there are differences among different ideas of dogs produced by the imagination. Habituation and suggestion would therefore have to work in cases of sufficiently similar resemblance. Certainly one problem is that this many not be an easy line to draw. However, it is a problem which Berkeley feels is reflected in the imprecision of common linguistic practice.
Berkeley’s positive account of general terms helps us understand why he fingers the doctrine of abstract ideas as a key promoter of perplexity. For consider philosophical questions such as this: “What is a human being?” and “What is goodness?” Insofar as such questions aim at a specification of what all humans or all good things have in common, such questions admit of no answer. And they admit of no answer not because such answers are beyond human access, but because there is no one similarity shared by all particulars subsumed under a general term.
To be sure, Berkeley admits that many general terms can have definitions. Thus a triangle may be defined “a plain surface comprehended by three right lines” (Intro 18); and this appears to specify a single commonalty. The point, however, is that these definitions themselves include further general terms (such as ‘surface’ and ‘line’) and ultimately there will be terms such as ‘colour’ and ‘extension’ which indifferently denote a range of particular colours and particular extensions. In such cases there will be only degrees of similitude. For example blue is more like green than it is like red; six feet is closer to five feet 11 inches than five feet 2 inches. Yet there is no one similarity in which all equally participate (such as colour or extension) since there is no such abstract idea.
As a consequence a term such as “good” cannot be understood “abstracted” from various ideas of good things which it indifferently denotes. To be sure, it may be used and understood without the excitement of an idea of some particular good thing (as when it is used to excite desire and the appropriate behavior which attends such desire). However, the view that such a use involves an abstract idea is predicated on the false view that the term is used to convey an internal conception of abstract goodness rather than its actual use – namely to excite passion and thereby to entice to action. Thus we see Berkeley’s negative and positive project articulated in his very conception of language: The doctrine of abstract ideas (which yields perplexed philosophical questions) is built upon a misconstrual of the true function of language which often has less to do with the exchange of internal conceptions of things and more to do with incitement to action.
II: Arguments against Abstraction (Standard Worries)
Traditionally, Berkeley’s rejection of abstract ideas has been found wanting. One of the reasons for this is that Berkeley doesn’t seem to provide much argument for the position. In the Principles, he merely alleges that he cannot engage in this process of abstraction; in Alciphron he simply denies that he can find any such abstract ideas at all. Obviously Berkeley is not pointing to some idiosyncrasy on his own part. Rather, he believes that nobody can frame such ideas. The question is why.
The Imagist Reading
One traditional concern about Berkeley’s professed inability to form an abstract idea is that he is assuming that ideas must be imagistic in nature. That is: He is assuming that ideas are either sensory or produced by imagination (as one might, with some focus produce the idea of a particular unicorn upon closing one’s eyes). In this view, the reason that Berkeley finds he cannot produce the abstract general idea of a triangle or a human is that imagination only ever involves imagining particulars things (such as particular triangles, particular humans). It isn’t possible to imagine human without imagining some one particular human.
If this reading is correct, it would seem that Berkeley is merely begging the question. To see this, consider that Descartes distinguishes between imagination and pure understanding. It doesn’t seem possible to imagine a chiliagon specifically (as opposed to a myriagon). Yet one may nonetheless have an understanding of what a chiliagon is. This understanding, for Descartes, is not based in imagination but consists in pure intellection (Sixth Med CSM II 50-51). If Descartes is correct that we possess ideas of pure intellect (such as the idea of a chiliagon), then Berkeley’s rejection of abstraction based on the fact that he can imagine no such thing entirely neglects pure understanding rather than arguing against it.
I think, however, that Berkeley’s denial that he can frame abstract ideas needn’t be based on his inability to imagine something that is not particular. Instead, we ought to bear in mind the important relation between Berkeley’s rejection of abstract ideas and his philosophy of language. What Berkeley is rejecting are ideas which are prior to language. They are the entities that are alleged (by Locke) to constitute the significance of general terms. Thus, we can fine-tune the challenge: If such abstract ideas exist, then it ought to be possible to form an abstract idea or internal conception without using language at all. The challenge, as I understand it, is to formulate an abstract idea without using words. Can you do it? Take “the Berkeley-challenge.”
That said, there is also a suggestion in the Principles that Berkeley goes beyond maintaining the psychological impossibility of framing abstract ideas, to the view that abstract ideas are themselves inconsistent and therefore impossible. At § 13 he cites from Locke’s Essay:
. . . does it nor require some pains and skill to form the general idea of a triangle . . . for it must be neither oblique, nor rectangle, neither equilateral, equicrural, no scalenon, but all and none of these at once. If effect, it is something imperfect that cannot exist, an idea wherein some parts of several different and inconsistent ideas are put together. (E. 4.7.9, 596)
Berkeley goes on to ridicule this inconsistent idea of a triangle; and this suggests that Berkeley rejects abstract ideas not only because of his psychological ability to form then, but on the basis of the view that they are themselves inconsistent.
The concern, however, is that while Locke seems to say in this passage that abstract ideas are formed by both leaving out the differences and by retaining the differences of particular ideas, this is not Locke’s actual view (abstraction merely consists in leaving out the differences). It might consequently seem that Berkeley has, with a little too much youthful eagerness, overemphasized this passage while misunderstanding Locke’s actual view. In such a view, Berkeley seriously blunders in reading Locke.
The difficulty with this rather uncharitable interpretation of Berkeley, however, is that at § 9 of the Principles (and elsewhere) Berkeley accurately represents Locke’s account of abstraction as the process of merely leaving out the differences. Moreover, it is really quite implausible that Berkeley could have made such an elementary error in characterizing Locke’s view. A more tempting position is that in belaboring this passage, Berkeley is merely exploiting the rhetorical opportunity that it provides.
However, some commentators have also suggested that there is more going on here than that. For Berkeley additionally appeals to an impossibility argument against abstract ideas in other works (such as Alciphron), and it may well be that this is what he is alluding to in making fun of Locke’s absurd triangle. This is the argument:
The Impossibility Argument
(1) If a thing includes a contradiction in its definition, then it is impossible to form an idea of it
(2) Any thing allegedly represented by an abstract idea includes a contradiction in its definition.
(3) So: It is impossible to form an idea of any thing allegedly represented by an abstract idea (by 1 and 2).
(4) So: Abstract ideas are impossible (by 3).
Now in formulating an argument of this type, an influential commentator, Kenneth Winkler, has proposed that the relevant impossibility be understood in terms of the impossibility of objects of abstraction existing separately from that which they are abstracted. For example, in proceeding with a diversity of particular triangles, one leaves out the differences and retains the similarity (i.e., triangularity) – a universal which is exemplified in all particular triangles. Both Locke and Berkeley agree that only particulars exist (and presumably agree that independently existing universals cannot exist). And Berkeley is supposed to conclude from this, and premise (1) that abstract ideas are impossible.
In Winkler’s view, however, there are a least two difficulties with Berkeley’s argument. First, it is hard to see how Berkeley can explain the inconsistency. It is clear that ‘Bachelors are married’ involves a contradiction. The idea of a bachelor should include the idea of being unmarried, so the idea of an unmarried bachelor would have to include both the idea of being unmarried and the idea of being married. But in the case of triangularity, every idea of a particular triangle should include the sub-idea of triangularity. Yet if particular ideas of triangles are consistent, how can an inconsistent idea be obtained merely by abstracting the triangularity-part from those ideas?
The second difficulty is that (2) seems true only if we suppose that abstract ideas represent impossible objects (such as independently existing universals). However, it is hardly clear why this needs to be the case. In order to see this, let’s distinguish between two different types of procedures. In what I shall call division, one is supposed to conceive of the abstracted feature separated from the features that are left out; viz., one is supposed to conceive of a feature existing actually separated from the rest.
By contrast, in the case of consideration, one only attends to certain features without attending to the others. Thus, one might think of the triangularity of a particular triangle without thinking of any of the specifics which makes it unique. But in focusing only on triangularity (to the exclusion of the other features), one needn’t actually conceive of triangularity as existing separately.
In Winkler’s view, Berkeley is assuming that Locke endorses a division model of abstraction. And Berkeley’s point is that division is only possible in case the object divided is something that can legitimately exist on its own. One cannot divide something in thought that cannot be divided in reality: One cannot conceive of triangularity as existing on its own, if it is impossible that it do so in reality. Instead, Berkeley himself proposes a consideration model of abstraction as if it were his own discovery.
The difficulty, according to Winkler, is that it is far from obvious that Locke himself actually endorses a division model of abstraction. There is good textual evidence that Locke recognizes consideration as a mental activity, and some commentators have argued plausibility that this is precisely the model that Locke adopts in his account of abstraction: One attends to the similarities and ignores the differences. But this is not to divide those similarities off from the differences; it is not to conceive of those similarities as existing separate from the differences. If this is right, then Berkeley’s position is closer to Locke’s than he supposes. Indeed, he is guilty of a misreading of Locke, that while considerably less egregious than an over emphasis on the ‘absurd triangle,’ nonetheless undercuts the force of his argument.
III: Arguments against Abstract Generalizing (An Alternative Interpretation)
One of the difficulties with the preceding interpretation is that it leaves unexplained why Berkeley and Locke propose significantly different semantic accounts of general terms. According to Locke, the meaning of a general term is an abstract idea; according to Berkeley a general term indifferently denotes a range of particular ideas. If abstraction for Locke is mere consideration, then the meaning of a general term is given when one selectively attends to the retained similarities found in any one particular idea. Given that Berkeley likewise believes in consideration (in this interpretation), why does he not appeal to it in his semantic account of general terms? Instead of maintaining that a general term merely applies to a range of particular ideas, Berkeley could maintain that the meaning of a general term is given by considering the relevant aspects of similarity (i.e., the abstract idea yielded through consideration). But he doesn’t. While consideration does some work in other areas of his theory, it plays no role at all in Berkeley’s account of meaning. What explains this difference?
Before I offer what I think is a deeper reading of Berkeley’s anti-abstractionism, I want to pause to further develop some intricacies of Berkeley’s position that I have thus far neglected. First, I have represented abstractionism only in terms of abstract general ideas (i.e., the ideas which give general terms their content). However, in addition to abstract generalizing, at § 7 of the Principles Berkeley also recognizes another kind of abstraction, that we can call singling out. Consider for example, an idea of a blue circle. The idea has features of both colour and shape. Singling involves abstracting one of those features from the other. Here, however, in abstracting the determinate blue from the determinate circle, one does not yield a general idea that could provide a general term with content.
Second, Berkeley distinguishes abstract generalizing into two different types. At §8 he recognizes abstract generalizing with regard to properties (i.e., determinate colours such as red and blue to colour in general, particular extensions to extension in general). At §9 he recognizes generalizing with regard to more complex things that possess properties (such as humans, animals, and bodies). The division roughly corresponds to a Lockean distinction between simple and complex ideas.
Now one of the striking things about Berkeley’s rejection of abstract generalizing from complex ideas is that he consistently points out that such ideas must include ideas of certain properties. For example, the idea of human must include colour (since all human beings have some complexion or other), the idea of a triangle must include shape (since all triangles have some shape or other). The difficulty, Berkeley claims, is that the idea cannot include a specific colour or a specific extension. So why is this a problem?
Rather surprisingly, Locke himself actually denies that one can form an abstract idea of colour. The reason for this is that ideas of colours (such as blue, red, and yellow) are simple ideas. With respect to complex ideas, abstraction involves the retention and omission of ideas which are part of compound particular ideas. With respect to simple ideas such as the idea of white, abstraction involves the retention of the simple ideas and omission of ideas which are related to that idea. For example, the simple idea of white may be included within the compound idea of milk as well as related to the idea of some specific time; and it may also be included within the compound idea of chalk and related to the idea of some other time: Abstraction involves retaining only the idea of white.
However, when it comes to abstracting from ideas of blue, yellow, and white there is now nothing left to omit. The ideas of the colours are simple, and all extraneous ideas related to them have already been omitted. If one attempts to generalize now, nothing will be left over (E. 3.4.16, 427-8). And whether abstraction for Locke involves division or consideration is irrelevant. For if the latter, then Locke’s point is that once one considers a colour (such as blue), there is nothing be focused on while ignoring something else. One cannot focus merely on colour while ignoring blue, for in focusing on colour one must thereby consider the blue. That is: There is only one aspect for consideration left.
This leads to some immediate consequences. First, as Locke himself recognizes, his own account of general terms cannot apply in the case of colour since there is no abstract idea of colour (ibid.). Second, since there is no such abstract idea, there is no idea to be included within the complex idea of human that isn’t itself specific. But since an abstract idea of colour is supposed to be included in the abstract idea of human, the fact that such an idea cannot be formed means that the abstract idea of human cannot be formed.
With this in mind, we can begin to better understand Berkeley’s Impossibility Argument. Consider the notion of an indeterminate colour. For Berkeley the expression “indeterminate colour” is an oxymoron. And this has some plausibility. If it is part of the notion of colour that colours be determinate, then the notion of an indeterminate colour is inconsistent in the same way that the notion of a married bachelor is inconsistent. Suppose, however, that one may selectively consider colour while ignoring anything determinate. Then the term ‘colour’ could have minimal content (provided by the abstract idea of colour) leaving it entirely consistent to speak of a colour that was neither red, nor white, nor blue, nor anything determinate at all.
To be sure, if abstraction is viewed as consideration, then one can maintain that view that an indeterminate colour is nonetheless inconceivable (i.e., that one cannot conceive of an indeterminate colour by dividing colour off from the determinacy). But this, by itself, does not yield the view that ‘indeterminate colour’ is a contradiction in terms. Suppose, for example, that one cannot conceive of colour existing separate from having a particular extension. Even if this is inconceivable, it doesn’t follow that an extensionless colour is a contradiction in terms or that extension is included within the idea of colour.
Berkeley, by contrast, offers an account of the meaning of general terms which can accommodate this inconsistency. In moving from particular ideas to something more general in the case of colour, one is left with no content at all. This is to say: Without reference to particular colours, the term ‘colour’ has no content. Instead, the term ‘colour’ is supposed to indifferently denote a range of ideas of particular colours. Thus, to deny of a colour that is red, white, yellow, or anything else is to deny that which gives it content. This is: The denial is self-contradictory.
IV: Arguments against Abstracting Singling (Alternative Interpretation)
The account that I have provided already sheds some light on Berkeley’s rejection of abstract general ideas. However, in order to be successful in needs to be likewise shown that other general terms referring to properties such as ‘extension,’ ‘figure,’ and ‘motion’ are similarly problematic. Consequently, as it stands this is more of an illuminating proposal than it is a well defended interpretation. I will move on, however, by addressing a more serious weakness of it: It doesn’t accommodate Berkeley’s rejection of abstract singling. Notably, Berkeley’s explicit formulations of the Impossibility Argument only ever take aim at abstract generalizing. This may suggest that the argument isn’t intended for singling. But if so, why does Berkeley reject it?
While Locke himself does not call singling a form of abstraction (he only recognizes generalization), singling seems very much like the type of procedure Locke needs in order to engage in abstract generalizing. Since generalizing involves retaining similarities while excluding differences, the capacity to single out certain properties from others would be especially useful in that regard. For example, suppose one proceeds with a round patch of blue and a square patch of blue. In order to form the abstract idea of blue, one must leave out the extraneous features which are related to the simple idea of blue (such as particular shape). This requires that one be able to single out the colour from the shape.
Now recall Winkler’s interpretation. Berkeley, who himself endorses consideration, rejects the possibility of dividing properties which cannot exist separated in nature; and he mistakenly takes Locke to fall prey to this flawed conception of abstraction. But there’s another possible interpretation. To understand it, distinguish between two types of consideration: Mental and Discursive. In the case of discursive consideration, one simply mentions certain aspects while failing to mention others. For example, one might mention the colour of a patch without mentioning its shape. By contrast, in the case of mental consideration, one focuses upon certain aspects of an idea to the exclusion of others without using language at all. In the proposed interpretation, in rejecting abstract singling, Berkeley is thereby rejecting mental consideration. While Berkeley does allow for discursive consideration, he takes Locke to more strongly and wrongly require the mental kind. One advantage of this interpretation is that Berkeley need not be represented as in any way misunderstanding Locke.
Another advantage is that it further illuminates the difference between Locke and Berkeley with respect to the meaning of general terms. Locke needs to allow for mental consideration (or mental division). For it is this type of process which is supposed to confer meaning upon general terms. For example, in order to obtain the simple, abstract idea of blue, Locke needs to leave out all of the differences (such as shape). He needs to do this prior to language (and therefore prior to discursive consideration). By contrast, Berkeley does not need to do this. Instead, the term ‘blue’ can indifferently denote a range of particular ideas of blue (all of them with different shapes). Indeed, Berkeley can press the “I just can’t do it” argument discussed above. Proceed with a circular patch of blue. Now attempt to mentally focus on the blue without thereby focusing on the circularity; and attempt to do it without thinking in words about the blue (since this is merely a form of discursive consideration). Can you do it? If not, then Berkeley scores a point.
Here, however, great caution is required. The fact that one cannot mentally consider some blue without considering its extension, had better not lead to the stronger view that an idea of some blue patch doesn’t have at least two aspects – namely its colour and its extension. For it is quite clear that one can compare the difference between a small patch of blue and a large patch of blue. They are similar in colour, but different in extension – hence at least two aspects for comparison. What Berkeley is denying is that there are distinct aspects which one can mentally attend to inherent in any idea itself: While one can compare and contrast two patches of blue with regard to their extension, one cannot mentally attend to colour without extension given some isolated patch of blue. This means that in accepting comparison between ideas while rejecting mental consideration of single ideas, an account of general terms is required that is fundamentally one involving resemblances among a plurality of ideas. This also suggests that imperfect resemblance, for Berkeley, may involve basic relations among different ideas rather than a similitude between contrasting features inherent in each idea. For example, whether a patch is large or small depends upon what it is compared with. In Berkeley’s view, however, extension may not be abstracted from large or small and is therefore an essentially relational affair.
Now those who see Berkeley as endorsing mental consideration do admit that he endorses discursive consideration as well. However there does not seem to be especially good evidence for the position that Berkeley ever admits the former. The strongest evidence comes in a passage that was added to the Introduction in the 1732 edition of the Principles:
And her it must be acknowledged that a man may consider a figure merely as triangular, without attending to the particular qualities of the angles, or relations of the sides. So far he may abstract: but this will never prove, that he can frame general inconsistent idea of triangle. In like manner we may consider Peter so far forth as man . . . without framing the aforementioned abstract idea . . . inasmuch as all that is perceived is not considered. (PHK Intro §16)
Yet while this is good evidence that Berkeley endorses consideration, it is not evidence at all that he endorses mental consideration. This passage makes entire sense, if we understand considering in terms of mentioning. So when recognizing that ‘all that is perceived is not considered’ Berkeley may well mean that ‘all that is perceived is not mentioned.’ Indeed, if he means to reference The Impossibility Argument in referencing the ‘absurd triangle,’ then he simply cannot mean mental consideration, since the Impossibility Argument applies to abstract generalizing regardless of whether mental consideration or division is deployed.
Indeed, while a full defense of this interpretation is not called for in an introduction to Berkeley’s thought, I do want to point to a passage in the Dialogues which seems to support this reading. Philonous says:
But how does it follow that because I can pronounce the word motion by itself, I can form the idea of it in my mind exclusive of body? Or because theorems may be made of extension and figures, without any mention of great or small . . . such an abstract idea of extension, without any particular size or figure, or sensible quality should be distinctly formed, and apprehended by the mind? Mathematicians treat of quantity, without regarding what other sensible qualities it is attend with, as being altogether indifferent to their definitions. But when laying aside the words, they contemplate the bare ideas, I believe you will find, they are not the pure abstracted ideas of extension.
In Winkler’s reading, Berkeley ought to be contrasting some (or any) form of consideration with mental division; and the appeal to discursive consideration specifically as well as this issue of pulling away words is irrelevant. In the proposed reading, by contrast, this passage makes more sense. Berkeley recognizes discursive consideration while denying that there is such as process as mental consideration in these cases. To determine this, one simply lays aside the words and recognizes that no such mental abstractions can be formed. Here the connection between the appeal to discursive consideration and pulling away words is obviously essential, since Berkeley is denying that there is any such consideration prior to language.
Part V: Knowledge and Assent
One difficulty that Berkeley must accommodate is how universal knowledge is possible in his view. For it was standardly recognized that the sciences concerned universal (not particular) truths. How can one know that all humans are mortal? What is the object of knowledge in this case? Is it necessary that one have knowledge of each and every human being individually? This seems tedious and besides the point, since the issue isn’t knowledge that John is mortal, that Mary is mortal, and that Fred is mortal, but that all humans are mortal.
Berkeley’s solution is to admit the existence of general ideas that are not abstract. Such ideas are not formed by a process of abstraction; rather some particular idea is used as a sign to represent all other particular ideas of that sort. For example the idea of John, while particular in itself, can be made a general idea when it functions as a sign for all other ideas of particular humans. The move that Berkeley makes here is both radical and tremendously important for his philosophy. In addition to recognizing that words can be signs, Berkeley allows that all ideas can function as signs (and often do). Insofar as the sciences concern universal truths, the objects of scientific knowledge are nothing but signs. For example, while the idea of some black line is itself particular, it becomes general when used as a sign for all lines. The object of scientific knowledge is not that one idea of a black line, but rather that idea qua general idea (i.e. qua sign). According to Berkeley particular ideas can function as signs just as words can function as signs. Thus this idea of the black line must be capable of indifferently suggesting any other idea of a line. This hardly requires a stretch. Given that the word “line” is apt to indifferently suggest any idea of a particular line, it is easy to see why any one idea of a line may itself likewise be apt to suggest an indefinite range of ideas of particular lines.
One worry, however, is how it is that one can establish a universal truth once and for all. How can one show that Pythagorean Theorem holds of all right angle triangles? Just because one shows the theorem to hold of a single right angle triangle, it hardly follows that the theorem holds from of all of them. Won’t we need to run the demonstration an infinite number of times, for each individual instance? Berkeley’s answer to this question involves an appeal to discursive consideration. While one uses a particular idea of a triangle in the demonstration (as in a diagram), one only mentions those features which are relevant to the proof at hand. So when demonstrating something about all triangles, one does not avail oneself to any of the particularities of the triangle used in the diagram. For example, one does not appeal the fact that triangle is right-angled in a demonstration about the triangle in general.
Operative Knowledge and the Christian Mysteries
Berkeley’s view that the objects of the sciences are signs fits within his more general conception of knowledge. In order to understand this more clearly, it is useful to contrast it with the Lockean view that Berkeley is rejecting. Just as Locke requires that terms have ideas annexed to them in order to have meaning, Locke sees knowledge as the clear perception of the agreement or disagreement among ideas. Thus, for Locke, knowledge (as well as belief and faith) requires ideas. This Lockean position was used by free-thinkers (such as Toland and Collins) to call into question knowledge (or faith) in the Divine. For if religious terms such as ‘grace’ do not have any ideas annexed to them, then how are they significant? And if knowledge and faith require the perception of ideas, then how is it possible to even assent to a religious truth?
Just as Berkeley allows for the meaningful use of terms without any backing idea, so Berkeley conceptualizes knowledge in a way that does not require the perception of ideas. For Berkeley, assent involves acting according to general rules. And rules are given by signs. For example, signs in arithmetic such as ‘+’ and “=” play a role in determining and limited our actions with respect to other signs such as “1” and “2”. For Berkeley, then, knowledge is not the perception of agreement or disagreement among ideas, but rather the skillful management of signs. For example, to know that 1 +1= 2 is to know how to manage the signs correctly (i.e., according to rules). In this way, Berkeley allows the religious notions such as grace can be objects of faith (and even knowledge) insofar as one has appropriately mastered the sign “grace” and the rules of behavior associated with it. Note, then, that just like his theory of language, Berkeley’s theory of knowledge is deeply bound up with his agenda of critiquing disconnected speculation, and returning philosophers to everyday affairs. For knowledge does not involve the mere perception of ideas; rather knowledge is itself situated within the context of (rule-governed) action. Since science is concerned with signs, any attempt to depart from the use of such signs to navigate conduct is an attempt at abstraction – which according to Berkeley, is impossible.
 See Kenneth Winkler’s introduction to A Treatise Concerning the Principles of Human Knowledge (Cambridge: Hackett, 1982), pp. xi-xxi.