Early Moderns and "Thinking Around"

I am taking a brief break from grading to make a few notes about something I’ve become increasingly interested in recently, which I’ve been labeling for myself as “thinking around” (to be contrasted with “thinking about”).

I’m going to start with two examples, one from Hume and one from Berkeley.

On my reading of Hume, there is a sort of mental activity one can engage in towards that which is strictly and literally inconceivable.  This activity is supposition.  In one part of my dissertation, I attempt to show that Hume can embrace this form of mental engagement without abandoning his commitment to analyze all mental activity (of the understanding) in terms of conception (i.e. ideas).  At any rate, there are a few passages which are naturally read as Hume allowing that some things can be supposed which cannot be conceived.  This type of mental engagement, I argue, allows a response to a Reidian objection which charges Hume as unable to account for reductio ad absurdum reasoning.  So, while you cannot, on my reading of Hume, think of or about an even prime greater than 2, for example, you can think around such a prime, allowing you to reason your way to its non-existence.

Berkeley, like Hume, has a view of conception bound up with what ideas one possesses.  Consequently, Berkeley deploys arguments about the nature of ideas to show that certain things are inconceivable.  But, as is somewhat explicit in the third Dialogue between Hylas and Philonous, and fully explicit in Alciphron VII, Berkeley introduces a way to defend the meaningfulness of discourse in which meaningful terms to not signify ideas (rejecting a straightforward Lockeanism about language), with something I’ll call “notions” (though I don’t know if Berkeley consistently uses the “idea”/”notion” terminology to track this distinction).  Having a notion of something does not require having an idea of it.  Thus, even though I cannot have an idea of immaterial susbtance, I still have a way to engage with propositions about immaterial substances (whether we are speaking of me or god).  This too is a sort of thinking around, as I understand it.

Resources which allow a philosopher to permit our thinking around something which we cannot (on their view) properly think about or of are important elements of their views for two reasons.  First, they can give us important insights about other aspects of their views.  For instance, noting that Berkeley must appeal to some such resource in the third dialogue, to explain how we can believe in immaterial substance helps us exclude some (seemingly natural) interpretations of the first dialogue arguments against material substance.  While it might appear that Berkeley is offering a straightforward inconceivability argument against belief in material substance there, it is clear from his own later admission that we cannot strictly conceive of immaterial substance that the dialogue one argument must be more complicated than it at first seemed.

Second, however, they are important for allowing us to see how powerful objections to those philosophers wind up being.  Take Hume, who embraces the view that we cannot conceive of anything which is impossible.  Given that various philosophers have appeared to sincerely defend views which, for Hume, turn out to be impossible, there is the objection that Hume cannot be right, because we could not then make sense of such apparently sincere defenses.  A natural sort of reply is to invoke some sort of verbal confusion underlying the dispute.  But that line of reply is not always satisfying, and does not always do a good job of addressing the behavior of his opponents.  On the other hand, Hume’s resource of supposition-without-conception permits him a more robust way to understand his opponents as engaging with these impossible views (apart from merely “mistakenly defending that the sentences which express those impossibilities actually express truths”).

I’m sure that similar sorts of resources crop up in the views of other philosophers, but I don’t want to just start casting around randomly. If anyone has suggestions of places to look (especially in terms of early modern figures other than the “canonical” British empiricists), please let me know.

Monday Mill Blogging (#006)

Monday Mill blogging makes its triumphant return to Tuesdays, apparently.

Today’s post covers book 1, chapter 2, section 3.

§ 3.  General Names and Singular Names


Section §3 is largely focused on the distinction between general and singular names.  Mill’s infamous doctrine about singular names won’t be put forward until two sections later, but there are some interesting elements to this discussion nonetheless.  The section opens:

All names are names of something, real or imaginary; but all things have not names appropriated to them individually. For some individual objects we require, and consequently have, separate distinguishing names; there is a name for every person, and for every remarkable place. Other objects, of which we have not occasion to speak so frequently, we do not designate by a name of their own; but when the necessity arises for naming them, we do so by putting together several words, each of which, by itself, might be and is used for an indefinite number of other objects; as when I say, this stone: “this” and “stone” being, each of them, names that may be used of many other objects besides the particular one meant, though the only object of which they can both be used at the given moment, consistently with their signification, may be the one of which I wish to speak. (p. 27)

First off, I am not sure, but it sounds like Mill might be going in for a quasi-Meinongian view, given that opening claim.  There might be a way to cash it out that doesn’t involve quantifying over non-real entities, but it seems like Mill is suggesting that, while not every object has a proper name, every name has a proper object.  This sort of commitment is relevant to evaluating, for instance, what we can take Mill as having to say, if anything, about Frege’s puzzle and/or other puzzles for the Millian view of proper names.  For instance, if Mill is positively committed to imaginary objects as being denoted by meaningful terms, this provides him with something of a response to at least one problem arising from “empty” names.  Actually, it might be apt to call it a “presponse”, since it looks like Mill recognized that not all meaningful names correspond to real objects, and offered a view about those cases antecedent to a specific challenge being issued.

So, Mill thinks that putting together general names into complexes can supply us (perhaps only incidentally and temporarily) with names for objects that don’t have their own proper name.  This is a pretty plausible thesis, I’d say.  However, this is not the only purpose for general names.  Mill suggests that if all general names were for is to allow ad hoc construction of names for objects that don’t have their own proper names, they “could only be ranked among contrivances for economizing the use of language”.  There is a parallel here between Mill and Locke on the role of general terms/names.  Both recognize that a language where every objects possesses only a proper name would be unmanageable, and accept some sort of argument from the practical necessities of language in favor of general terms.

As noted, Mill does not think this is the only role of general terms:

But it is evident that this is not their sole function.  It is by their means that we are enabled to assert general propositions; to affirm or deny any predicate of an indefinite number of things at once. The distinction therefore, between general names, and individual or singular names is fundamental; and may be considered the first grand division of names. (p. 27)

Mill then defines a general name as a name that is capable of being truly affirmed, in the same sense, of each of an indefinite number of things.  Individual or Singular names, then, are capable of being affirmed, in the same sense, of one thing only.  Mill’s example of a general name is “Man” and his example of a singular name is “John”.  Mill is not concerned about the fact that lots of people are named “John”, because he thinks that “John” in “John Lennon” has a different sense than “John” in “John Fitzgerald Kennedy”.  Here is the interesting part.  In defending this claim, we get a preview of Mill’s famous claim about proper names:

For, though there are many persons who bear that name, it is not conferred upon them to indicate any qualities, or anything which belongs to them in common; and cannot be said to be affirmed of them in any sense at all, consequently, not in the same sense. (p. 28)

I am not sure how to make sense of this claim made here, that “John” cannot be affirmed of people named “John” at all, and the earlier claim that “a singular name is a name which is only capable of being affirmed, in the same sense, of one thing.”  The definition seems to suggest that singular names are affirmed of individuals, while the latter remark seems to suggest that (some) singular names are not affirmable at all.  Now, Mill goes on to say that “The king who succeeded William the Conquerer” is a singular name, and presumably that can be affirmed, so some singular names would still be affirmable.  However, Mill’s point that the propriety of calling someone “John” does not depend on their antecedently possessing some feature that is designated by “John” seems right.  Intuitively, the dependence goes in the other direction, the quality of “going by the name ‘John'” is had in virtue of being called “John”.  Mill’s reason for taking “The king who succeeded William the Conquerer” to be singular is this: “that there cannot be more than one person of whom it can be truly affirmed, is implied in the meaning of the words.”  In other words, there is a sort of semantic guarantee of the term applying to at most one object, and this suffices for it to be singular.

I have not mentioned revisions or amendments to the text, though the Liberty Fund edition of the text I am using has ample detail about changes to the text between the manuscript and different editions.  I do want to make mention of an interesting revision to the passage I’ve just been discussing.  The earlier text had, as the example definite description, “The present King of England” and in the explanation of it qualifying as singular, he said, “never can be more than one person at a time of whom it can be truly affirmed”.  This revision is interesting to me because I think Mill would still want to count “The present king of England” as a singular name, but it seems that it is a messy example to use, since it can, at different times, be affirmed truly of different people.  I suppose one could say that it is being used in different senses at different times, but then to explicate this, one would have to suggest that the word “present” undergoes a continual change of sense.  While this might, ultimately, be the best thing to say about it on Mill’s view, it would make things much messier to lay all this out when trying to explain the division than to treat of the quirkiness of the example later, when more of the machinery is in place.

Back to the main text: Mill observes that even an incomplete definite description, such as “the king”, can, in the right context, count as an individual name.  Like the point about “the present king of England”, this looks to open the door to all sorts of complications, at least if one tries to reconcile the official definitions of singular and general names with a willingness to allow context to dictate the singular/general nature of a name.

The last two things Mill does in this section are: a) complain about use of the word “class” to define “general name” and b) distinguish between collective singular names and general names.

On (a):  Mill says that it is common for people to define general names by saying general names are names of classes.  “But this, though a convenient mode of expression for some purposes, is objectionable as a definition, since it explains the clearer of the two things by the more obscure.”  Mill goes on to propose that the definition be reversed, seemingly insensitive to the fact that this would rule out unnamed classes.  I don’t know if that is a major issue, but it seemed worth observing.

On (b): Here Mill is essentially telling us that general names are predicated distributively, collective names predicated jointly.  “The 76th regiment of foot in the British army” is a collective singular name for a group of soldiers.  There is only one group (at a given time) of whom you can properly affirm that name, and you can’t affirm it of each of the individual members.  “Regiment” is Mill’s example of a collective general name, since it can be affirmed of a lot of different groups in the same sense.  Mill suggests that it is “general with respect to all individual regiments, of each of which separately it can be affirmed: collective with respect to the individual soldiers of whom any regiment is composed.”  This last line suggests that collectivity is type-relative.  This is good, because it means we don’t have to decide all questions of collectivity in our basic semantics.  “Mt. Everest” can be non-collective with respect to the category mountain, but still turn out to be collective with respect to the category particles of matter.

Next time on Monday Mill Blogging: §4, “Concrete and Abstract Names”


Monday Mill Blogging (#005)

Monday Mill blogging on a Thursday? Why not.

Today’s post covers book 1, chapter 2, section 2.  All this focus on naming is making me want to take some time to re-read part III of Carnap’s “Meaning and Necessity”.  But for now I am sticking with the Mill.

§ 2.  Words Which are Not Names, but Parts of Names


Mill ended §1 by indicating the need to outline a taxonomy of names.  But before he will give us his taxonomy of names, he feels it is necessary to discuss words that are not properly considered names, but which are parts of names.  Mill shares the conventional wisdom of which words those are:

Among such are reckoned particles, as of, to, truly, often; the inflected cases of nouns substantive, as me, him, John’s; and even adjectives, as large, heavy.  These words do not express things of which anything can be affirmed or denied.  We cannot say, Heavy fell, or A heavy fell; Truly, or A truly, was asserted; Of, or An of, was in the room. Unless, indeed, we are speaking we are speaking of the mere words themselves, as when we say, Truly is an English word, or, Heavy is an adjective. (p. 25)

Mill’s view here seems to be that words, in addition to their customary uses, can be used to denote “the mere letters and syllables of which [they are] composed”, and in that usage, words like “of” and “heavy” are names.

Ultimately, Mill is going to remove adjectives from this list, and treat them as names.  He explains his reasoning as related to the fact that it is a mere grammatical accident of English that we cannot say “A heavy fell”.  Mill marshalls some cross-linguistic evidence from Greek and Latin in support of this point, and then reaffirms that adverbs and particles can’t ever denote terms in a proposition (except when being used as names for the words themselves).

Mill then puts the views he has just been outlining in scholastic terms.  What he is calling names are what the scholastics called Categoremic terms, the words that are not names, but only parts of names, are the scholastics’ Syncategoremic terms.  Rather than have a third class for compound terms (“A court of justice”), Mill treats these as many-word names, and classes them as Categoremic.

In treating of these many worded names, Mill also presents a view on non-restrictive relative clauses (though he doesn’t call them that):

Thus, when we say, John Nokes, who was the mayor of the town, died yesterday—by this predication we make but one assertion; whence it appears that “John Nokes, who was the mayor of the town,” is no more than one name.  It is true that in this proposition, besides the assertion that John Nokes died yesterday, there is included another assertion, namely, that John Nokes was mayor of the town. But this last assertion was already made: we did not make it by adding the predicate, “died yesterday.” (p. 27)

I say this is a view, even though it seems a bit cursory in terms of detail, because it, in a sense, helps us figure out what Mill would want to say about the truth or falsity of a sentence of the form, “n, who was G, is H”, when the referent of ‘n’ has the property designated by ‘H’, but not the property designated by ‘G’.  The use of that sentence, it seems, makes the proposition, of the referent of ‘n’, that they have the property designated by ‘H’, so the primary assertion made in uttering the sentence is true.  However, in the subject term of the sentence “there is included another assertion”, the assertion, about the referent of ‘n’, that they possess the property designated by ‘G’, which is false.  It isn’t clear whether this gives us a satisfactory answer about how to classify the sentence “n, who was G, is H”, relative to a circumstance of evaluation, but it does shed some light on how Mill thinks about the relationship between sentences and assertions.

Next time on Monday Mill Blogging: §3, “General and Singular Names”


Monday Mill Blogging (#004)

In this week’s Mill Blogging, we’re actually going to start getting to the meat of some of Mill’s views on language. Today’s post covers Book 1, Chapter 2, section 1.

§ 1.  Names are names of things, not of our ideas


As the chapter opens, Mill approvingly quotes Hobbes on the definition of “name”:

“A name” says Hobbes, “is a word taken at pleasure to serve for a mark which may raise in our mind a thought like to some thought we had before, and which being pronounced to others, may be to them a sign of what thought the speaker had before in his mind.”  This simple definition of a name, as a word (or set of words) serving the double purpose of a mark to recall to ourselves the likeness of a former thought, and a sign to make it known to others, appears unexceptionable. Names, indeed, do much more than this; but whatever else they do, grows out of, and is the result of this. (p. 24). (Mill cites the Hobbes work “Computation and Logic” as the source of this quote)

Mill then goes on to ask whether names are “more properly said to be the names of things, or of our ideas of things?”  Mill suggests that common usage is on his side in answering that names are names of things, and not names of our ideas of things.  Mill charges Hobbes with taking the contrary opinion, though I don’t think I see it, at least, not from the passage he quotes:

The eminent thinker, just quoted, seems to countenance the latter opinion. “But seeing,” he continues, “names ordered in speech (as is defined) are signs of our conceptions, it is manifest that they are not signs of the things themselves; for that the sound of this word stone should be the sign of a stone, cannot be understood in any sense but this that he that hears it collects that he that pronounces it thinks of a stone.”

Now, I grant that this passage appears to commit Hobbes to the view that the word ‘stone’ is a sign of the conception/idea STONE (to adapt a notational convention from contemporary philosophy of mind).  However, Mill’s question was not whether names were signs of things or signs of our ideas, but whether they were names of things or names of our ideas.  This may seem to be a nit-picky point, but I think it is important to be careful about the various semantic (or quasi-semantic) relations invoked on various theories of language.  Absent something like the assumption that, for any term t and any object o: t names o just in case t is a sign of o, Hobbes’s view about what names are signs of doesn’t (for all that has been said) directly bear on the question of whether terms name things or ideas.

I am taking some time to dwell on this because it seems clear that various approaches to theorizing about language will differ with respect to which semantic relations they take to be central or primary, but often, will propose definitions or accounts of other semantic relations in terms of their favored semantic relation. For instance, someone could adopt the Hobbesian view that ‘stone’ is a sign of STONE, and then analyze the naming relation as obtaining between a term and the object or content of the idea that term is a sign of.

So, without having read “Computation and Logic”, I am inclined to think that Mill has undersold the case that Hobbes is committed to the wrong answer about whether terms name things or ideas.

There is another frustrating/confusing bit in §1, where Mill offers an argument against the view that names are names of ideas:

When I say, “the sun is the cause of day,” I do not mean that my idea of the sun causes or excites in me the idea of day; or in other words, that thinking of the sun makes me think of day.  I mean, that a certain physical fact, which is called the sun’s presence (and which, in the ultimate analysis, resolves itself into sensations, not ideas) causes another physical fact, which is called day.  It seems proper to consider a word as the name of that which we intend to be understood by it when we use it; of that which any fact that we assert of it is to be understood of; that, in short, concerning which, when we employ the word, we intend to give information. Names, therefore, shall always be spoken of in this work as the names of things themselves, and not merely of our ideas of things. (p. 25)

To me, it looks like Mill is offering a conflation of two arguments one of which is abysmal and one of which is spot-on.  The spot-on argument is something like:

1) If the term “sun” is the name of the idea SUN, then when I assertively utter “the sun is the cause of the day”, I am making a claim about SUN.
2) It is not the case that when I assertively utter “the sun is the cause of the day”, I am making a claim about SUN.
3) So, the term “sun” is not the name of the idea SUN.

I’m willing to get on board with that argument.  Note, however, that the wacky stuff about SUN causing DAY plays no role.  Which is for the best, since, there is no reason for the proponent of the view that ‘sun’ names SUN to suggest that ’cause’ names the relation of causing, instead of naming the idea CAUSE.  There is then an open question for the view about the difference between listing three ideas (SUN CAUSE DAY), and actually doing some assertion/predication.

Sometimes when I read this, I think it is supposed to be a slam on Hume, since, on some readings, Hume’s reductive account of causation makes it a relation between ideas, but if that’s what is going on here, it is difficult to see why Mill would include an incidental objection to Hume (which, I should add, is also not entirely charitable), in the midst of giving a general argument against the view that names are names of ideas.

At any rate, the last surprising bit in this passage is the claim that “in the ultimate analysis” the sun “resolves itself into sensations, not ideas”.  I am assuming that, when we get further into the Logic, enough about Mill’s metaphysics will be revealed for me to know what that claim amounts to.

Next time on Monday Mill Blogging: §2, “Words which are not names, but parts of names”

Monday Mill Blogging (#003)

Chapter 1 of the Logic is titled, “Of the Necessity of Commencing with an Analysis of Language”.

Mill acknowledges that it is common enough to begin a treatise on logic by discussing terms and other matters of language that there isn’t really a need to explain why he is going to start with a discussion of language, but he goes on to discuss it anyway.

Language is evidently, and by the admission of all philosophers, one of the principle instruments or helps of thought; and any imperfection in the instrument, or in the mode of employing it, is confessedly liable, still more than in almost any other art, to confuse and impede the process, and destroy all ground of confidence in the result. For a mind not previously versed in the meaning and right use of the various kinds of words, to attempt the study of methods of philosophizing, would be as if some one should attempt to become an astronomical observer, having never learned to adjust the focal distance of his optical instruments so as to see distinctly. (p. 19)

This remark from Mill is a very similar thought to one advanced by Tim Williamson in “Must Do Better“:

Philosophers who refuse to bother about semantics, on the grounds that they want to study the non-linguistic world, not our talk about that world, resemble astronomers who refuse to bother about the theory of telescopes, on the grounds that they want to study the stars, not our observation of them. Such an attitude may be good enough for amateurs; applied to more advanced inquiries, it produces crude errors. Those metaphysicians who ignore language in order not to project it onto the world are the very ones most likely to fall into just that fallacy, because the validity of their reasoning depends on unexamined assumptions about the structure of the language in which they reason. (p. 9)

I find the telescope/microscope analogy interesting, and compelling.  Note that neither Mill nor Williamson is embracing the view that questions about language are the primary target of inquiry; rather they both liken the importance of understanding how language works to the importance of knowing how to use your tools.

In the next section of Chapter 1, Mill explains, more or less, the basics of his view of propositions.  We are told that “the answer to every question which it is possible to frame must be contained in a Proposition, or Assertion” and that “whatever can be an object of belief, or even of disbelief, must, when put into words, assume the form of a proposition” (p. 20).

Mill goes on to characterize a proposition as “discourse, in which something is affirmed or denied of something” (p. 21), and analyzes propositions as containing three parts (subject, predicate, and copula).  Throughout this section, Mill seems to be describing what an Early Modern like Locke called “Verbal Propositions”, insofar as they are “formed by putting together two names”, and Mill tells us that propositions “consist of at least two names”.  Similarly, when we were earlier told that the answer to every question is “contained in a proposition”, or that propositions are a certain type of “discourse”, it is clear that Mill is taking propositions to be something linguistic or verbal.  Mill’s propositions diverge, importantly, from at least one major strand of use of the term “proposition” in contemporary philosophy, and this will be important to bear in mind.

Mill ends chapter 1 with an argument in favor of studying names before studying things, by appeal to the fact that language was shaped by many people:

In any enumeration and classification of Things, which does not set out from their names, no varieties of things will of course be comprehended but those recognised by the particular inquirer; and it will still remain to be established, by a subsequent examination of names, that the enumeration has omitted nothing which ought to have been included. But if we begin with names, and use them as our clue to the things, we bring at once before us all the distinctions which have been recognised, not by a single inquirer, but by all inquirers taken together. It doubtless may, and I believe it will be found, that mankind have multiplied the varieties unnecessarily, and have imagined distinctions among things, where there were only distinctions in the manner of naming them. But we are not entitled to assume this in the commencement. We must begin by recognising the distinctions made by ordinary language. If some of these appear, on a close examination, not to be fundamental, the enumeration of the different kinds of realities may be abridged accordingly. But to impose upon the facts in teh first instance the yoke of a theory, while the grounds of the theory are reserved for discussion in a subsequent stage, is not a course which a logician can reasonably adopt. (p. 22)

Here I think we see an interesting commitment on Mill’s part to a sort of qualified attention to ordinary language.  There is something like a very weak presumption that distinctions made by ordinary language are legitimate distinctions, at least to the extent that one has to show cause to disregard them, rather than having to show cause for attending to them.  This, I think, falls far short of a commitment to anything like the subsequent movement of ordinary language philosophy, but it is worthwhile to note that Mill explicitly references ordinary language (and not, say, specifically the technical vocabularies of past scholars).

Berkeley on the Molyneux Problem

In the course of “An Essay Toward a New Theory of Vision”, Berkeley considers Molyneux’s question. The question, as quoted by Locke (and Locke being quoted by Berkeley at NTV 132): “Suppose a man born blind, and now adult, and taught by his touch to distinguish between a cube and a sphere of the same metal, and nighly of the same bigness, so as to tell, when he felt one and t’other, which is the cube and which the sphere. Suppose then the cube and sphere placed on a table, and the blind man made to see: quaere, whether by his sight, before he touched them, he could now distinguish and tell which is the globe, which the cube?”

Berkeley, in agreement with Locke (who was in agreement with Molyneux), says “no”: it is not possible for someone born blind, who learned shape-names by touch, to then tell by vision alone, which of two shapes presented is a sphere, and which a cube.

Berkeley uses this opportunity to argue for the doctrine of proper sensibles—the view that there is no overlap among the ideas proper to different senses.  In other words, Berkeley maintains that there are no ideas that originally enter the mind through more than one sense.

It is easy to see what Berkeley has in mind if we put the issue this way:  Call the idea you get through touch of one side of a cube T-SQUARE (for tangible square).  Call the idea you get through one vision of one side of a cube V-SQUARE (for visible square).  Berkeley proposes that, if some ideas (such as the idea of a square) come in through both sight and touch, then T-SQUARE would be identical to V-SQUARE, and the only difference would be in the way you acquired them.  But if T-SQUARE and V-SQUARE are identical, then, Berkeley argues, the formerly blind individual should be able to identify the cube, since they know that a cube is a body terminated by squares, and they can also see some squares.*

The most interesting part of Berkeley’s discussion, though, comes in NTV 141 to 143(ish).  And what makes this interesting is the startling similarity between what Berkeley says here, and the position Leibniz takes in New Essays On Human Understanding.
Right before NTV 141, Berkeley has just responded to the worry that V-SQUARE and T-SQUARE are called by a common name (‘square’) because they are of a common species, by appeal to the view that we often use the same name for the sign as well as for the thing signified.  This, in combination with the view that V-SQUARE is a sign of T-SQUARE is intended to address that worry.  The discussion moves on, then, to another potential worry:

But, say you, surely a tangible square is liker to a visible square than to a visible circle: it has four angles and as many sides: so also has the visible square: but the visible circle has no such thing, being bounded by one uniform curve without right lines or angles, which makes it unfit to represent the tangible square but very fit to represent the tangible circle. Whence it clearly follows that visible figures are patterns of, or of the same species with ,the respective tangible figures represented by them: that they are like unto them, and of their own nature fitted to represent them, as being of the same sort: and that they are in no respect arbitrary signs, as words. (NTV 141)

The worry of this passage rests on what I’ll call the “greater fitness” claim: Some visible ideas have greater fitness than others to serve as signs of a given tangible idea. The worry attributes this fitness to a cross-modal commonality of species. In NTV 142, Berkeley responds to this worry by noting that the fitness of representation can be accounted for in terms of the complexity or simplicity of the ideas, without appeal to a common species. Importantly, Berkeley does not deny the greater fitness claim. Rather, he tries to show that a canonical instance of arbitrary representation exhibits a parallel case of differential fitness.

But it will not hence follow that any visible figure is like unto, or of the same species with, its corresponding tangible figure, unless it be also shewn that not only the number but also the kind of the parts be the same in both. To illustrate this, I observe that visible figures represent tangible figures much after the same manner that written words do sounds. Now, in this respect words are not arbitrary, it not being indifferent what written word stands for any sound: but it is requisite that each word contain in it so many distinct characters as there are variations in the sound it stands for. Thus, the single letter a is proper to mark one simple uniform sound; and the word adultery is accommodated to represent the sound annexed to it…It is indeed arbitrary that, in general, letters of any language represent sounds at all: but when that is once agreed, it is not arbitrary what combination of letters shall represent this or that particular sound. I leave this with the reader to pursue, and apply it in his own thoughts.

In the New Essays, Leibniz (through the mouth of Theophilus), answers Molyneux’s question thus:

[Y]ou will see that I have included in [my reply] a condition which can be taken to be implicit in the question: namely that it is merely a problem of telling which is which, and that the blind man knows that the two shaped bodies which he has to discern are before him and thus that each of the appearances which he sees is either that of a cube or that of a sphere. Given this condition, it seems to me past question that the blind man whose sight is restored could discern them by applying rational principles to the sensory knowledge which he has already acquired by touch…My view rests on the fact that in the case of the sphere, there are no distinguished points on the surface of the sphere taken in itself, since everything there is uniform and without angles, whereas in the case of the cube there are eight points which are distinguished from all the others. (NEHU, book 2, chapter 9)

Leibniz claims that the formerly blind person could reason their way to the right answer, if they are told that the two visual appearances are of shapes with which they are already familiar (and further, told the specific pair of shapes that the two visual appearances are of). Berkeley concedes that, taking for granted that the visual is to be a sign of the tangible, it is not arbitrary which visible figures represent which tangible figures.
To give credit where credit is due; Leibniz himself indicated that he thinks he is on pretty much the same page with people who want to give a “no” answer; he just thinks they are giving a fine answer to the wrong question.
Anyway, it was interesting for me to find out that Berkeley pushes what is essentially the Leibnizian line on Molyneux’s problem.
*Berkeley’s argument is actual given in terms of numerical and specific difference, which is good, because it avoids an issue present in my quick reconstruction, having to do with token vs. type identity.  To frame it so as to avoid this issue, we can take T-SQUARE to name a particular idea you got through touch. Then the question is whether T-SQUARE and V-SQUARE are of the same kind (i.e. intrinsically alike, for a certain sense of intrinsic), not whether they are identical.  That way of putting it captures Berkeley’s language more clearly: “upon the supposition that a visible and tangible square differ only in numero it follows that he might know, by the unerring mark of the square surfaces, which was the cube, and which not, while he only saw them” (NTV 133).