Friday, April 28, 2017

Sober on Essentialist Explanations in Science

"My suggestion is that the gas's kinetic energy explains what it is for the gas to have the temperature it does. It does not explain why the gas has the temperature at the time in question. The relationship here is much like the one between a dispositional property and its physical basis. If zebras differ in fitness because of their leg structure, then there is a sense in which leg architecture explains fitness relationships. The relationship is not causal; it does not explain why those fitness values came into existence. Science not only explains why certain states of affairs and events come into existence; it also seeks to explain the nature of those events."

--Elliott Sober, The Nature of Selection, p. 75.

Note that explanation is hyperintensional, and that not just any necessarily coextensive term would work equally well in place of 'the gas's kinetic energy' here.

Wednesday, April 26, 2017

Laplace and Mereology

"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes." -- Laplace

My understanding is that Laplace's demon was primarily intended as a heuristic for understanding microphysical determinism. But there is a serious question (noted by or implicit in the work of a number of philosophers of science, e.g., Sober, Loewer, Albert) as to whether, in fact, "nothing" about the physical universe would escape the demon's knowledge. There is some ambiguity in what is meant by "submit these data to analysis," but intuitively it seems that the demon's abilities would only allow him to know all of the facts describable in microphysical terms. There is a real question then about whether this would amount to knowledge of all of the facts, including about mereologically composite objects, let alone about minds.

Would we need to add to the demon's capacities, then, some sort of additional "translation manual" to tell him which macro-states are being realized by the micro-physical states? And would this amount to a problem for a reductionist picture of the world? Maybe, maybe not.

Monday, October 3, 2016

Thomistic Moderate Realism Reduces to Armstrongianism or Platonism

I've always had difficulty understanding Aquinas's "moderate realist" view on universals, at least as that view is expounded by his interpreters. It seems that they want to have their cake and eat it too: Thomists both believes that universals are "objective" and "extramental" in some sense. But they also are not extreme realists, i.e., (modern) Platonists. They also seem to say things that make it sound as if universals are merely conceptions; if taken at face value, that reduces to conceptualism or nominalism of some sort.

Here's one way of bringing out the problem.

Assuming there are universals, then:

  • 1. Either (a) universals exist extramentally or (b) they do not exist extramentally.
  • 2. If (b), then nominalism or conceptualism, QED.
  • 3. If (a), then either (i) they only exist in the objects that have them, or (ii) they sometimes exist outside of the objects that have them.
  • 4. If (i), then that is Armstrong's view.
  • 5. If (ii) then that is Platonism.
  • 6. So if (a) is true, then either Armstrong's view or Platonism is true, and so moderate realism either reduces to Armstrong's view or Platonism.
6 already seems to disambiguate the Thomistic view in a way that makes it unacceptable, and does not let it have all of the desirable qualities it is supposed to have.


  • 7. If Armstrong's view holds, then universals depend on the objects that have them, and therefore cease to exist if the objects do.
  • 8. But if the universals cease to exist, then statements about non-existent things, like "dinosaurs are big creatures", do not require universals to be true, and so universals are superfluous.
  • 9. So if Armstrong's view holds, then universals are superfluous.


That only leaves Platonism, and there are huge problems with Platonism.

To be fair, I am leaving much unsaid here, and I am not making any distinctions within "Platonism." But ultimately I think this is basically correct; the way Platonism is construed in modern times basically just is the view that there are non-mental, objective, necessarily existent, universals.

Thursday, August 18, 2016

Naturalness vs. "Arbitrariness" and "Simplicity" in Mereology

There are three answers one can give to the question: "When does composition occur?"

(1) Always.
(2) Sometimes.
(3) Never.

The first view is something like David Lewis's view: Any plurality of objects composes a third. Hence, for example, there is an object consisting of Barack Obama, my left leg, an orange, and half of the beach in Santa Monica. (We could call it the BLOB.) This is the view encompassed in classical mereology.

The third view is something like Peter Van Inwagen's view in 'Material Beings'. This view holds that (with maybe a few very specific exceptions), there are not, literally, any composite objects. There are just "simples" -- atoms in the void, physically proximate to each other and arranged in various ways.

The second view encompasses all other possibilities. One of these possibilities is "common sense" ontology, or something like it. One such view might hold that things like physical organisms, tables and chairs, rocks, planets, stars, maybe even galaxies, etc. are composite objects. But not just any plurality of things constitutes an object on this view; for instance, there is definitely no object such as the BLOB.

One argument (I think due to Van Inwagen) says that (2) can be ruled out rather easily because it is arbitrary and/or overly complicated. Hence, we must choose between (1) and (3).

However, it seems to me that people who hold to (2) might argue that their ontology only encompasses what is natural; just as there is a distinction between natural properties (like 'having mass') and gerrymandered properties (like 'being Barack Obama-or-my leg-or-an orange-or-half of Santa Monica Beach'), there may well be a distinction between natural composites and gerrymandered composites. And just as one might choose to privilege the natural properties by saying they are the only ones that exist (as D.M. Armstrong does), so one might choose to privilege the natural composites by saying they are the only ones that exist.

Obviously more needs to be said than this and this view would need to be fleshed out. But I'm more interested in the methodological question, and all I need granted is that it is a distinction one could coherently use so as to avoid (1) or (3).

Now, people like Van Inwagen might (probably, would) respond to this view by claiming that it is arbitrary, that it multiplies distinctions, that the notion of "naturalness" is mysterious and vague, and so on.

But I think it is worth noting here an "arbitrariness" in this objection: Claiming that some entity is more natural than another (or, by extension, that one's theory is more natural) is no more mysterious than claims that that (2) is arbitrary and complex, and that (1) and (3) are non-arbitrary and more simple. Defining the sense in which (1) and (3) are "non-arbitrary" and "simpler" is no easier than defining the sense in which (2) is "more natural."

Frankly, simplicity and arbitrariness, as used in this way, seem to me to be just as bad off as the other notions that anti-hyper-intensionalists use as criteria of theory choice; they are themselves hyperintensional notions in fact. That's not to say that they are bad off -- I do think there is an intuitive sense in which theories can be "simpler" and "less arbitrary" than other theories. But it is arbitrary to use "arbitrariness" and "simplicity" as criteria for selecting between metaphysical theories, and then pretend you don't know what it means when one says that his theory is more "natural" than others or, relatedly, posits entities that are "more natural."

Friday, July 29, 2016

Appreciating Mistaken Art Like Mistaken Philosophy

It is a fact -- however much a given artist may deny it -- that works of art often express a narrative and a moral point of view. This fact is sometimes (subversively) underplayed and de-emphasized. But there is no doubt that Dadaism and Bauhaus in some way express different ideals than, say, Romanticism or the Baroque.

Indeed, one might argue that certain movements in modern art -- together with higher education, the law, and the media -- bear a large portion of culpability for the general moral degradation of Western society.

At the very least the point clearly makes sense, since obviously one could argue the other way too: That certain forms of art are inherently "traditionalistic" or "reactionary," and should be "supplanted" or "opposed" by more progressive forms of art.

Still, it seems reasonable to think that, at least up to a certain point, there is value even in art that expresses a false narrative, a skewed moral viewpoint, or an improper ideal.

I think a nice analogy can be made with philosophy. On the one hand, I think that Nietzsche is entirely wrong, that his arguments fail, and that we should produce arguments to counter his viewpoint. On the other hand, clearly in some sense Nietzsche is a genius, and it would be a shame never to read him or interact with his thought. Life would certainly be far less interesting anyway.

I tend to attribute this value in Nietzsche's work to its cultural significance and influence, its excellent technical execution, and even to some extent the power of the arguments (arguments can be powerful in a way even if, ultimately, they fail). There may be other factors involved too. In short, there can be much value in a piece by Nietzsche even if that value does not lie in its truth.

Now, if we think of works of art as analogous to arguments or maybe philosophical pieces (and their authors as being like philosophers, their movements as being like philosophical "isms", and so on), then it begins to make sense how one can appreciate even art that one "disagrees" with. It is quite easy to recognize in a piece of art its cultural significance, its technical brilliance, and even the "force" of its "argument", even when one "disagrees" with it or considers it ultimately to be a (philosophical) failure.

This eases a certain tension in my soul: I find certain forms of modern art to be fascinating; however, I know that the "point" they are trying to make is often entirely wrong, and that it ought to be "counteracted" by art that is both sufficiently modern yet does not express nihilistic, relativistic, or hedonistic passions.

But separating the "message" of a piece of art from the other components of its value makes both of these sentiments to be entirely reasonable and consistent. If we can make the distinction between a work's message and its value in philosophy, then it seems we can make it in art too.

Tuesday, July 19, 2016

Pragmatics at Home

Here's an interesting case of implicatures I noticed the other day when discussing what movie to watch with my wife. (>> means "pragmatically implies" and *>> means "does not pragmatically imply")

Case One:
W: Do you want X?
H: Only if you want it.
>> I don't want it.
*>> I do want it.

Case Two:
W: Do you want X?
H: Not if you don't.
>> I do want it.
*>> I don't want it.

What is strange about this case is that, presumably, the husband H's responses in both cases are logically equivalent to each either; assuming I'm parsing them right, they both say "I want X only if you want X" or, equivalently, "I do not want X if you do not want X." (***See bottom of page for an explanation, if this isn't clear.)

But the response in Case One (at least sometimes) implies something different than the response in Case Two.  (I say 'at least sometimes', because, as with many implicatures, it may depend somewhat on the sonic properties of one's utterance too -- i.e., the way one pronounces the words.) But this seems to imply that the implicature is "detachable" in Grice's sense (see the bottom of p.57 and ff., here).

However, according to classical Gricean pragmatics, conversational implicatures are non-detachable; hence, if these were conversational implicatures, they would both imply the same things (which they don't). So it seems that they must be conventional implicatures. (See here on that distinction.) That's sort of weird though, because conventional implicatures are usually associated with syncategorematic expressions that do not contribute any additional truth-conditional meaning to the sentence (for instance, "however," "but," "even though," "nevertheless," etc.).

Also, these implicatures seem to be more like conversational implicatures than conventional ones, since they do seem to sort of follow from something like Grice's Maxim of Manner (or, better, Levinson's M-Principle); i.e., saying something in an equivalent but roundabout way implies a non-standard meaning. For depending on whether one uses the double negation form or not you get a different implicature. However, it doesn't *quite* fit this rule I think, because it doesn't seem like either of the response from Case One or Case Two is more "roundabout" than the other; in other words, the responses in both cases seem to be symmetric as far as the "oddness" of their phrasing goes.

Anyway, kind of an interesting case. FYI, in the actual situation, I *did* want it, but I didn't want it if she didn't. : - )

***
To see the equivalence, note that all of the following are equivalent:

  • I want it only if you want it.
  • I only want it if you want it.

(These are clearly equivalent. For consider the following:
x goes to the store only if x is hungry.
x only goes to the store if x is hungry.)

  • If you do not want it, I do not want it.
  • I do not want it if you don't want it.

Wednesday, June 29, 2016

Modernizing (and Medievalizing) Analyticity

A project I've been hoping to do eventually is to re-work the concept-containment notion of analyticity. Something has always seemed to me intuitive about it, at least in the "Bachelors are unmarried" sorts of cases. (From the 19th century onward, for various reasons, the analytic truths seem to have become equated with the logical truths; this seems wrong to me.)

I'd also like to see whether the notion of analyticity comes up at all in medieval philosophy, and whether any of the tools of medieval philosophy could be of use for this project (or, what would be just as interesting, whether they would find the concept-containment notion of analyticity hopelessly confused).

There are several problems for the concept-containment approach, but a big one is this:

1. Forms of Analytic Judgments: Kant (sometimes) defined analyticity in terms of conceptual containment, roughly as: A judgment of the form 'A are B' is analytic iff the concept B is contained in the concept A.

The worry is that there are many judgments that do not seem to have this form, but where they seem to also be true in virtue of 'meaning' or 'concepts' (or something close). Some examples, taken from SEP:
(11) If Bob is married to Sue, then Sue is married to Bob.
(12) Anyone who's an ancestor of an ancestor of Bob is an ancestor of Bob.
(13) If x is bigger than y, and y is bigger than z, then x is bigger than z.
(14) If something is red, then it's colored.
Other examples, from Jerrold Katz:
(15) Mary walks with those with whom she herself walks.
(16) Mary walks with those with whom she herself strolls.
(17) Poor people have less money than rich people.
(18) Rich people have more money than poor people.
It's not totally clear how all of these examples can be analytic (assuming they all are) if we take analytic truth to mean that the predicate-concept is contained in the subject-concept.

I don't have a worked-out answer to this yet, but I suspect that some of the work in cognitive linguistics might be helpful. In fact, Katz' own work might be helpful here, though from what I understand Katz is a Platonist (rather than a "conceptualist") about meaning, and so it would have to be properly adapted.

In addition to these strategies, where medieval philosophy might be useful here is in seeing how we might, in fact, be able to reformulate all "basic" sentences and then parse them out so that they technically obey the constraint of "subject-copula-predicate" form.

As Terence Parsons points out, medieval scholastic Latin is unique in that it is a natural language and yet there is no distinction between a sentence's ordinary surface grammar and its logical form.

Now, if one had a close enough association between words and mental concepts, one might then be able to get a nice conceptualist-type semantics going. And it seems certain medieval thinkers did have precisely this sort of close association between mental concepts and meaning, viz., in the theory of "subordination" (I'm thinking of Buridan and Ockham right now).

This suggests that we could translate basic ordinary-language sentences into medieval subject-copula-predicate sentences, and the concept-containment idea could become more useful again.

I'm not sure it will be as simple as that or that this will solve everything, but I suspect it will make things easier.

There are some other issues for a conceptual containment theory of analyticity too:

2. Conceptual Containment: There are really at least two problems here: (a) a theory of concepts, and (b) a notion of containment. Can we give a plausible and clear theory of both? (And, what would be even better: Can we give a theory of both that is mathematizable and subject to rigor and computation once we are given a case?) And how neutral can we be here with respect to different theories of concepts and containment?

How can medieval philosophy help here? Medieval philosophy certainly contains much discussion of concepts, and that should certainly be useful.

As for the notion of containment, I can't help but think of Scotus' theory of "repugnance" and "non-repugnance" by which he assesses the modal status of basic propositions -- the kinds of propositions concept-containment seems to be after (see page 162, here). What's interesting is that Scotus seems to define repugnance as a relation holding between terms. That seems to make it a semantic relation rather than a conceptual relation for Scotus; moreover, the relation's holding is said to be grounded in "notae," which are in some sense objective features of the external world.

So this isn't exactly concept-containment analyticity; but still, in terms of its formal/logical properties, non-repugnance/repugnance behaves similarly to concept-containment/exclusion. (This seems to be an instance of a more "externalist," metaphysical picture of containment and exclusion relations; I get the sense that this sort of externalism is the norm in medieval philosophy, especially pre-Nominalism, though even after that as well.) Moreover, like repugnance-relations, concept-containment relations are supposed to ground the modal status of propositions, and moreover, they both seem to deal with the same sorts of propositions. So I can't help but think Scotus will be helpful here, even if he probably wouldn't have a view of analyticity like Kant's.

3. Rigor: How would a rigorous conceptual semantics go? Can we make it as formal, precise and mathematical as the non-conceptualist semantics have been? Some work has already been done on this sort of thing, but there's more to be said. Again, I wonder if the medieval logic might help us here, since Parsons and others have shown it to be entirely rigorous and fit for mathematical treatment. Medieval logic at its height was generally far more sophisticated than anything after it -- certainly more sophisticated than anything Kant did on logic -- and so I can only imagine it will make this project easier.

4. Externalism: Although the conceptual-containment approach seem plausible in certain cases, so does semantic externalism. Gillian Russell, a professor here at UNC, has done some brilliant work on updating analyticity to take these post-Kripkean insights into account. However, she tends toward the more externalist side of things, and I'd like to see whether we can salvage more of the connections between meaning, analyticity and concepts than she does, while still giving a reasonable account of the externalist insights (something I worry cognitive semantics a la Peter Gardenfors hasn't quite done -- see 4.1 here, for instance).

One thing I worry about in trying to find analyticity in medieval philosophy is that medieval philosophy seems to tend much more toward externalism about semantic content (though this is only a hunch I get -- I can't point to anything specific). But maybe I'm wrong and there is room for analyticity in medieval philosophy; and even if not, the project may still be worthwhile, since maybe we will find new reasons to either abandon or revise our conception of analyticity in interesting ways we've never thought of.

So I plan to do some research on medieval logic and semantics in the next few weeks, and maybe this will help my concept-containment project. Moreover, I think it is an interesting historical project in its own right to see whether something like analyticity can be found (or reformulated) in terms of medieval semantic categories.

Sunday, March 20, 2016

Perceptual Representation: Pictures and Sounds, Seeing and Hearing

Perceptions are representations. What representations are can be cashed out in several ways.

First, they are about something.

Second, they represent the world as being a certain way.

Moreover, they have satisfication notions associated with them (and corresponding satisfication conditions, i.e., conditions that must obtain for them to be satisfied). The satisfaction notion of desires is 'being fulfilled' or not; with belief it is 'being true' or not; with volitions it is 'being done' or not; with commands it is 'being obeyed' or not; and with perceptions it is 'being accurate' or not.

Representations include words, sentences, beliefs, pictures, questions, paintings, videos, signs, diagrams, maps, hand gestures, commands, recordings, desires, and, in the case at hand, perceptions.

If a given representation has a satisfaction notion associated with it, it will also follow that it has satisfaction conditions. Giving the satisfaction conditions for a type of representation is (at least part of) giving a semantics for that type of representation.

Much work has been done on giving semantics for various sorts of linguistic representations. Whole classes of sentences have been given rigorous semantics. For instance, famously, modal language has been given a whole semantic theory, rigorously formulated in terms of mathematical models involving possible worlds.

Arguably, something similar can be done for pictures.

If a rigorous semantics can be given for pictures, this may hold some promise for giving a rigorous semantics for visual perceptions. Naively, we think of vision as giving us an "image". Think for instance of Ernst Mach's drawing of his own visual field:

Mach's picture of the visual field

With appropriate modifications for the perspective and particularities of our visual field, the naive application of pictorial semantics to visual-perceptual semantics would be to straightforwardly give the same semantics for our visual perceptions as we would for a drawing of our visual field.

This is obviously simplifying hugely and leaves a host of questions unanswered. But it allows us to get a preliminary grip on things.

What I'm interested in lately is whether, suitably modified, the semantics of auditory perception will be similar to the semantics of visual perception.

You can think of visual perception as giving you a picture, where the picture includes such properties as {OBJECT, SHAPE, MOTION, COLOR, DISTANCE, SPACE, TEXTURE, CAUSE, AGENCY}. All of these properties are represented in visual perception (and, with most of them, in pictures too, at least generally).

(Note: One of the simplifications we have to make in assuming the semantics of visual perception is just like the semantics of pictures is that, as with the semantics of pictures, visual perceptions do not have a temporal-duration aspect: A good assumption for pictures maybe, which can be thought of as "instantaneous" in some way; on the other hand, a bad assumption for visual perception, which as perceptual psychology demonstrates represents motion, and an even worse assumption for auditory perception.)

So we can think of vision as giving a picture. Can we think of hearing as giving us a picture too? If we can, then if the move from pictorial semantics to visual-perceptual semantics is relatively straightforward, then so will the move be from pictorial semantics to auditory-perceptual semantics (and maybe we can even find a better representational correlate than pictures for sound; hint: recordings maybe?).

Well, clearly, hearing doesn't immediately represent all of the same properties as vision. And neither does vision represent all of the same properties as hearing.

However, that doesn't need to stop us from thinking of hearing as presenting an auditory "picture," at least if we understand "picture" as picking out a general representational structure that is in some way common to normal, physical pictures and our mental, visual images. After all, as we said before, we can think of the visual image as a picture representing such properties as {OBJECT, SHAPE, LOCATION, MOTION, CHANGE, COLOR, DISTANCE, SPACE, TEXTURE, CAUSE, AGENCY}. But then maybe we can also think of hearing as giving us an auditory representation, structurally similar to the visual image, but instead representing such features as {OBJECT, LOCATION, MOTION, CHANGE, DISTANCE, SPACE, CAUSE, VOLUME, PITCH, TIMBRE}. We might even be able to include SHAPE and AGENCY in there in some cases (almost certainly in the case of bats), though I'd have to double-check the scientific literature.

In other words, the perceptual "structure" could remain the same between visual perception and auditory perception, and indeed, some of the qualities that are represented in vision may be represented in hearing, and vice versa. For instance, just from what I've listed, the intersection of properties represented in hearing and vision will include such features as {OBJECT, LOCATION, MOTION, CHANGE, DISTANCE, SPACE, CAUSE). On the other hand, maybe it is unique to vision to include {COLOR, TEXTURE}, and maybe it is unique to hearing to include {VOLUME, PITCH, TIMBRE}.

But again, despite the differences in features that are represented in hearing and vision, the overall representational structure might be, generically, the same at a certain level of abstraction.

What would be interesting would be to work out a precise semantics for visual perceptions and a precise semantics for auditory perceptions and see where, in the details, the two actually differ. Obviously hearing and vision will have their accuracy conditions assigned by different systems of depiction. But it's exciting to think that the two might not be so far apart, that they may, structurally speaking, having a lot in common, and that light might be shed on both by looking at conventional, physical representations (such as pictures, recordings, etc.).

Thursday, February 18, 2016

Russell on Existence in TPLA III: The Argument from Transferability

In the last post we explained what Russell's views on existence are and how they entail a "higher-order" theory of existence according to which existence is not a feature of individuals but of some "higher-order" things, viz. propositional functions. Since this is, initially, a very counter-intuitive proposal ("Socrates exists" is meaningless on Russell's view!), Russell ought to have some arguments to defend his view. This is going to be a long series of posts, so we'll discuss several of Russell's arguments from The Philosophy of Logical Atomism, but in the next two posts we'll discuss one of his arguments in particular: What I will call the "Transferability Argument." But before that I'll briefly mention Russell's motivation for having a theory of existence like his in the first place.

In the first place, the whole notion of existence comes up in connection with what we might call “negative existential” statements. A negative existential statement is a statement saying that something does not exist: For instance, that Socrates does not exist, or that dogs do not exist. These present an initial puzzle. On the one hand, if they are true, then it seems “Socrates” and “dogs” do not refer to anything, and so it’s not clear what could make the sentences true. On the other hand, they seem to be saying that something, “Socrates” or “dogs,” has the feature of “not existing.”

Now, this doesn’t immediately support Russell’s view on existence, but it does give one impetus to develop some sort of view that would address the question of negative existentials. It is interesting to see how Russell’s view deals with the problem. In the first place, ‘Socrates does not exist’ is simply meaningless according to Russell, since it doesn’t make sense to attribute existence to an individual, and so neither does it make sense to deny existence of an individual. On the other hand, since existence is a property of propositional functions, “dogs do not exist,” is easy to deal with: it is the same as saying ‘x is a dog’ is impossible. This involves no shady references to non-existent dogs or anything of that sort. One need only say that ‘x is a dog’ is never true.

With that said, it is not enough to point out that Russell’s view gives an answer to this question. Russell’s view is still prima facie implausible, and there might also be other positions available. Hence, Russell needs to give some direct arguments specifically for his view and arguments against alternatives. We will discuss just one of the arguments that Russell gives, which I call “the Transferability Argument.” The argument is quite subtle in fact, and it is rather complicated. But I think it is worth thinking through because it incorporates several interesting assumptions from logic and the philosophy of language.

Before delving into it, I want to define what we will call a ‘transferable predicate’. Russell does not use this terminology himself, but he uses the concept, and his argument is easier to state with this terminology. Now, a predicate F is transferable in my sense just in case (i) F can  be meaningfully applied to some kind G, and (ii) for any kind G that F applies to, ‘G’s are F’ is true only if every individual x that is a G is also F. For instance, the predicate ‘green’ is transferable: It applies to a generic kind term like ‘men’, since we can say ‘men are green’, and ‘men are green’ is true only if each man is himself green. The predicate ‘green’ “transfers” to the individual men. The predicate ‘numerous’ on the other hand is non-transferable: While we can say ‘men are numerous’, it does not imply any particular man is himself numerous. Indeed, this last statement is meaningless.

With that said, Russell’s Argument from Transferability can be reconstructed as follows:

  • (1’) ‘Unicorns exist’ is false, but meaningful. [Premise]
  • (2’) If there is an individual sense of ‘exists’, then ‘exists’ is transferable. [Premise]
  • (3’) If ‘exists’ is transferable, then ‘Unicorns exist’ implies ‘a exists’, for some proper name ‘a’ of some particular unicorn. [Premise]
  • (4’) So, if there is an individual sense of ‘exists’, then ‘Unicorns exist’ implies ‘a exists’, for some proper name ‘a’ of some particular unicorn. [By 2’ and 3’]
  • (5’) If ‘a’ is a proper name then ‘a is F’ is meaningful only if ‘a’ refers. [Premise]
  • (6’) So ‘a exists’ is meaningful only if ‘a’ refers. [5’, Universal Instantiation]
  • (7’) Suppose there is an individual sense of ‘exists’. [Supposition for Reductio]
  • (8’) Then ‘Unicorns exist’ implies ‘a exists’ for some proper name ‘a’ of some particular unicorn. [By 4’ and 7’]
  • (9’) If ‘unicorns exist’ is false, then ‘a’ does not refer. [Premise]
  • (10’) So ‘a’ does not refer. [By 1’ and 9’]
  • (11’) So ‘a exists’ is meaningless. [By 10’ and 6’]
  • (12’) No meaningful statement can imply a meaningless statement. [Premise]
  • (13’) So, ‘unicorns exist’ is meaningless. [By 8’, 11’, and 12’]

But this contradicts our assumption in (1’). Hence, we must reject our assumption in 7’:

  • (14’) There is no individual sense of ‘exists’. [By 7’ – 13’ and Reductio ad Absurdum]

This is an extremely interesting and rich argument. It is the best reconstruction I can give of Russell’s argument. The argument is clearly valid. It has a total of six premises: 1’, 2’, 3’ 5’, 9’, and 12’. I think it is useful to isolate the premises so that we can see precisely the principles at work here:

  • (1’) ‘Unicorns exist’ is false, but meaningful.
  • (2’) If there is an individual sense of ‘exists’, then ‘exists’ is transferable.
  • (3’) If ‘exists’ is transferable, then ‘Unicorns exist’ implies ‘a exists’, for some proper name ‘a’ of some particular unicorn.
  • (5’) If ‘a’ is a proper name then ‘a is F’ is meaningful only if ‘a’ refers.
  • (9’) If ‘unicorns exist’ is false, then ‘a’ does not refer.
  • (12’) No meaningful statement can imply a meaningless statement.

The first premise is uncontroversial I assume. The third premise seems to follow from the definition of ‘transferable’.  12’ also seems straightforward: If, by hypothesis, p is meaningful, then it does not imply anything meaningless, and this is just what 12’ says. That leaves 2’, 5’, and 9’ as the crucial premises.

I take it that the motivation behind 2’ is that if ‘existence’ is just another predicate of individuals, like ‘green’, say, then it should be transferable in precisely the way they are. After all, how could it be that ‘frogs are green’ is true but that ‘green’ does not transfer to all of the individual frogs? But if ‘exists’ is just like ‘green’ then it should behave in the same way.

5’ seems to be motivated by the fact that we are supposing ‘a’ to be a proper name in Russell’s sense. Recall that, according to Russell, a logically proper name is a word whose meaning just is a particular object; in other words, the proper name ‘a’ is meaningful only if, and because, ‘a’ refers. So if ‘a’ is meaningless, then the whole sentence ‘a is F’ will be meaningless too.

Finally, 9’ is motivated by the fact that if ‘unicorns exist’ is false then there simply aren’t any unicorns for ‘a’ to refer to, and so ‘a’ cannot have a reference.

On the face of it, there is some reasonableness about all of these premises. However, I think there are worries for all of them. In the next post I will try to raise some of those worries.