Nominalism and Realism – Maverick Philosopher

The Hatfields and the McCoys: A Challenge to Reists and Extreme Nominalists

Top of the Substack pile.

One-Category Trope Bundle Theory and Brentano’s Reism

This morning's mail brought a longish letter from philosophy student Ryan Peterson. He would like some comments and I will try to oblige him as time permits, but time is short. So for now I will confine my comments to the postscript of his letter:

P.S. Just as crazy as one category trope bundle theory is to me, is the later Brentano’s attempt at a different one category ontology, ‘reism’, where “For example, ‘Socrates is wise’ and ‘Socrates is Greek’ are made true, respectively, by wise-Socrates and Greek-Socrates, where wise-Socrates and Greek-Socrates are two coinciding but numerically distinct concrete particulars (which also coincide with Socrates)” (from Uriah Kriegel’s Thought and Thing: Brentano’s Reism as Truthmaker Nominalism). I like to rigorously understand all the different views put forth by intelligent philosophers on a topic but I do like to spend the most time understanding the more plausible seeming views first.

Leaving trope theory to one side for the moment, I am happy to agree with Peterson's assessment of Brentano. While not literally a product of insanity, Brentano's view I find to be incomprehensible. (And I don't mean that to be a merely autobiographical remark.)

I assume what to me seems to be well-nigh self-evident: some, but not all, truths need truth-makers. (I am not a truth-maker maximalist.) A truth is a true truth-bearer. The primary truth-bearers — the primary vehicles of the truth-values — are propositions. An assertive utterance at a particular time by a particular person of the declarative sentence 'Socrates is wise' expresses the proposition Socrates is wise. I will assume that propositions are abstract in the Quinean, not the trope-theoretic, sense of 'abstract.' (You can hear an asserted sentence and see a written sentence; you cannot hear or see a proposition.) A truth-bearer is not a truth-maker, except in some recherché cases I won't mention. (And don't confuse a truth-maker with a truth condition.)

There has to be something in the world of concreta (the spatiotemporal realm of causal reality) that makes it true that Socrates exists. To avoid the word 'makes,' we can say that the sentence and the proposition it expresses need an ontological ground of their being-true. Now you either get it or you don't. There are those who don't have a clue as to what I am talking about. Such people have no philosophical aptitude, and must simply be shown the door. A contingent truth cannot just be true, nor can it be true in virtue of someone's say-s0: a contingent truth requires something in reality external to the truth-bearer and its verbal expression that 'makes' it true, where this 'making' or grounding is neither narrowly logical nor causal. (Its not being either the one nor the other sensu stricto is what prejudices some against it. I kick them off my stoa as lacking philosophical aptitude.)

Now what in the world could function as the ontological ground of the contingent truth of 'Socrates exists'? The obvious answer is: the concrete particular Socrates. (Aristotle makes this very point somewhere in The Categories.) A particular may be defined as an unrepeatable entity by contrast with universals (if such there be) that are by definition repeatable.

There is an obvious difference between 'Socrates is wise' and 'Socrates is Greek,' on the one hand, and 'Socrates exists' on the other. It is the difference between predicative and existential sentences. Now we come to the nub of the issue. It seems blindingly evident to me that the two predicative sentences (and the propositions they express), if they need truth-makers at all, need concrete states of affairs (STOAs) as truth-makers, and that these truth-making states of affairs must be numerically distinct. I have no objection to saying that wise-Socrates makes true the first sentence and Greek-Socrates the second if 'wise-Socrates' and 'Greek-Socrates' refer to concrete states of affairs (not to be confused with Chisholmian abstract states of affairs).

But that is not what Brentano is saying. His reism cannot allow for concrete states of affairs of the form a's being F. For the predicate 'F' either picks out an abstract particular, a trope, or it picks out a universal. But on reism, all you've got are things, concrete particulars, which, moreover, cannot be assayed as concrete states of affairs along either Bergmannian or Armstrongian lines.

On reism one must therefore swallow the absurdity that "wise-Socrates and Greek-Socrates are two coinciding but numerically distinct concrete particulars (which also coincide with Socrates)." So they are one and the same and yet numerically different?? A question for Peterson: Is Kriegel defending truth-maker nominalism? I hope not. For it makes no bloody sense. For one thing it implies that the putatively two but at the same time one concrete particular(s) are property-less and are thus 'bare,' though not in Gustav Bergmann's precise sense. They are property-less if there are no properties, and there are no properties if there are no tropes nor any universals. A predicate is not a property.

'Red,' 'rot,' 'rouge,' and 'rosso' are four different predicates in four different languages. If Tom the tomato is red, as we say in English, he is not red only in English or rosso only in Italian. That way lies an absurd linguistic idealism. The predicates are true of Tom because there is something in or related to Tom that makes the predicates true of him, that grounds their applicability to him. This something in Tom is either the trope in him (assuming he is a complete bundle of tropes) or a universal that he instantiates. Nominalism makes no sense. The reality of properties is non-negotiable. But of course they needn't be universals. Trope-nominalism makes sense. 'Ostrich' nominalism does not. The same goes for van Inwagen's 'ostrich realism.'

Here is another argument. Socrates, while essentially Greek (Cf. Kripke's essentiality of origin), is only accidentally wise: had he lived long enough he might have gone 'Biden.' At every time at which he exists, our man is Greek, but only at some times is he wise. (He wasn't wise when he peeped his head out from between the legs of his mother, inter faeces et urinam nascimur.) So if he is one and the same concrete individual over time, then there has to be a distinction between him and real properties (not predicates!) that are either in him as tropes or related to him as universals.

Referring to Two Things

Ed writes,

Does ‘these two things’ refer to two things, or not? (Suppose the things are shoes.)

Perhaps not. For there are the two things, but also the plurality of them. The plurality is one thing, identical with neither the first thing, nor the second.

So the phrase ‘these two things’ actually refers to three things? Makes no sense to me.

BV: Perhaps it makes no sense to you because you think that 'thing' can only mean 'material thing.' We agree that 'these two shoes' refers to exactly two shoes, each of which is a material thing, and that there is no third material thing of which they are members. So if that is what our nominalist means when he denies that the two shoes form a plurality, then we agree.

Here is a slightly more complicated example. You have a bolt B and a nut N that fits the bolt, i.e., N can be screwed onto B. Now there is clearly a difference between B, N unconnected and B, N connected. But even here I will grant that there is no third material thing wholly distinct from B and wholly distinct from N when B, N are connected. There is no third material thing 'over and above' the connected bolt and nut. Here is exactly what you have and no material third thing in addition:

Disagreement may begin to set in when I point out that the weight of the object depicted above is strictly greater that the weights of the bolt and the nut taken separately. The total weight is additive such that if the nut weighs 2 ounces and the bolt 16 ounces, then the weight of the object depicted is equal to 2 + 16 = 18 ounces. The predicate '___weighs 18 ounces' is not true of the nut, and it is not true of the bolt, and it is not true of any material third thing 'over and above' the object depicted, and this for the simple reason that there is no such third material thing.

So what is the predicate '___ weighs 18 ounces' true of? I say that it is true of the plurality the sole members of which are N and B. I am not further specifying the nature of this plurality. Thus I am not saying that it is a mathematical set, nor am I saying that it is a mereological sum. I am saying that there is a distinction to be made between a plurality of items and the items.

Note that if our nominalist were to say that a plurality is exhausted by, or reduces to, its members, then will have given up the game by his use of 'its.' So he has to somehow avoid that locution.

Our nominalist will grant that the predicate '___weighs 18 ounces' is not true of the nut, not true of the bolt, and not true of any third material thing wholly distinct from the bolt and the nut. But he might say that it is not true of anything. The predicate is flatus vocis, a mere word, phrase or sound to which nothing extramental and extralinguistic corresponds. I reject this view. It implies that the nut threaded onto the bolt has in objective reality no weight that is the sum of the objective weights of the nut and bolt taken separately.

Our nominalist seems committed to an intolerable linguistic idealism. Suppose all language users were to cease to exist. It would remain that case that the weight of our nut-bolt combo would equal 18 ounces. It would remain the case that Earth is spheroid in shape and has exactly one natural satellite.

But why is he a nominalist in the first place? Is it because he thinks that only material particulars exist? If that is true then of course there cannot be a plurality of two material particulars. Hilary Putnam: "Nominalists must at heart be materialists . . . otherwise their scruples are unintelligible." (Phil Papers, vol. I, 338)

Is he a nominalist because he is an empiricist who thinks that only sensible particulars exist? I see the nut, I see the bolt, I see the nut threaded onto the bolt; but I don't see any plurality of material particulars. Is our man restricting what exists to that which is empirically detectable via our senses and their instrumental extensions (e.g., microscopes, telescopes, etc.)?

Is he both a materialist and an empiricist? How do those two positions cohere?

Pluralities

To what does the plural referring expression, 'the cats in my house,' refer? Not to plurality, but to a plurality. A plurality is one item, not many items. It is one item with many members. 'The guitars in my house' refers to a numerically different plurality. It too refers to one item with many members. It follows that a plurality cannot be identical to its members. For if it were there would be no 'it.'

I am not saying that a plurality is a mathematical set. I am saying that a plurality is not just its members. I am rejecting Composition as Identity. If the Londonistas do not agree with the Phoenician on this one, then I fear that there is little point to further discussion. We are at the non-negotiable. We are at bedrock and "my spade is turned."

Occam’s Razor: Its Use and Abuse

I am not historian enough to pronounce upon the relation of what is standardly called Occam's Razor to the writings of the 14th century William of Ockham. The different spellings of his name will serve as a reminder to be careful about reading contemporary concerns into the works of philosophers long dead. Setting aside historical concerns, Occam's Razor is standardly taken to be a principle of theoretical economy or parsimony that states:

OR. Do not multiply entities beyond necessity.

It is sometimes formulated in Latin: Entia non sunt multiplicanda praeter necessitatem. The principle is presumably to be interpreted qualitatively rather than quantitatively, thus:

OR*. Do not multiply TYPES of entity beyond necessity.

Thus it is not individual entities that are not to be multiplied, but types or kinds or categories of entity. To illustrate. Some criticized David Lewis' extreme modal realism on the ground that it proliferates concreta: there are not only all the actual concreta, on his view, there are all those merely possible ones as well. He responded quite plausibly to the proliferation charge by pointing out that the Razor applies to categories of entity, not individual entities, and that category-wise his ontology is sparse indeed.

'Multiply' is a picturesque way of saying posit. (Obviously, there are as many categories of entity as there are, and one cannot cause them to 'multiply.') And let's not forget the crucial qualification: beyond necessity. That means: beyond what is needed for purposes of adequate explanation of the data that are to be explained. Hence:

OR** Do not posit types of entity in excess of what is needed for purposes of explanation.

So the principle enjoins us to refrain from positing more types of entity than we need to explain the phenomena that need to be explained. It is obvious that (OR**) does not tell us to prefer theory T1 over theory T2 if T1 posits fewer types of entity than T2. What it tells us is to prefer T1 over T2 if T1 posits fewer types of entity AND accounts adequately for all the data. So there is a trade-off between positing and accounting.

It seems to me that the Razor as I have just described it ought to be in every philosopher's tool box. But how useful is it? Not very. For it tells us not to posit more than we need, but it does not tell us what we need. For example, do we need mathematical sets? Given Manny, Moe, and Jack, do we need to add to the ontological inventory the set {Manny, Moe, Jack}? It is not obvious that we do. But it is also not obvious that we don't. There are arguments on both sides which I won't go into now.

Here's the punch line: simply brandishing the Razor has no tendency to show that there are not such abstract objects as sets. That would be an abuse of the Razor. It would be the mistake of thinking that T1 is to be preferred to T2 solely on the ground that T1 posits fewer types of entity.

Note that I presupposed above that philosophy is an explanatory enterprise. Is that obvious? As Hilary Putnam says somewhere, "It ain't obvious what's obvious."

Nominalism Presupposes What it Denies

What makes a pair of shoes a pair and not just two physical artifacts? Nominalist answer: nothing in reality. Our resident nominalist tells us that it is our use of 'a pair' that imports a unity, conventional and linguistic in nature, a unity that does not exist in reality apart from our conventional importation. We are being told that out there in the world there are no ones-in-many, let alone any ones-over-many. If that is right, then there are no sets. For a set is a one-over-many in this sense: it is one item distinct from its many members. (Let's not worry about the null set, which has no members and unit-sets or singletons which have exactly one member each. Here lies yet another rich source of aporiai, but one problem at a time.)

If there are no sets, then there are neither finite sets nor infinite sets. There are just pluralities, and all grouping, collecting, subsuming under common rubrics, unifying, etc. is done in language by language-users. What I will try to show is that if you think carefully about all of this you will have to make distinctions that are inconsistent with nominalism.

My aim is purely negative: to show that the nominalism of the resident nominalist is untenable. If you have read a good amount of what I have written you will recall that I am a solubility skeptic, which in this instance means that I am not endorsing any realist solution of the problem. I am not pushing an opposing theory.

I will start with some data that I find 'Moorean,' i.e., rationally indisputable and pre-theoretical. (Unfortunately, one man's datum is another man's theory.) The phrase 'a pair' has a sense that remains the same over time and space, a sense that is the same for all competent speakers of English whether here or abroad. The same holds for ein Paar in German, and similarly for all languages. The sense or meaning of an expression, whether word, phrase, sentence, etc. must be distinguished from the expression. An expression is something physical and thus sensible. The sensible is that which is able to be sensed via one of our senses. I hear the sound that conveys to me the meaning of 'cat,' say, or I see the marks on paper. Hearing and seeing are outer senses that somehow inform us or, more cautiously, purport to inform us of the existence and properties of physical or material things that exist whether or not we perceive them. But I don't hear or see the meaning conveyed to me by your utterance of a sentence such 'The cats are asleep.' The sentence, being a physical particular, is sensible; the meaning is intelligible. That's just Latin for understandable. I hear the words you speak, and if all goes well, I understand their meaning or sense, thereby understanding the proposition you intend to convey to me, namely, that the cats are asleep. Note that while one can trip over sleeping cats, one cannot trip over that the cats are asleep.

There are two distinctions implicit in the above that need to be set forth clearly. I argue that neither is compatible with nominalism

A. The distinction between the sense/meaning of a linguistic expression and the expression. Why must we make this distinction? (a) Because the same sense can be expressed at different times by the same person using the same expression. (b) Because the same sense can be expressed at the same and at different times by different people using the same expression. (c) Because the same sense can be expressed in different languages using different expressions by the same and different people at the same and at different times. For example the following sentences express, or rather can be used to express, the same sense (meaning, proposition):

The cat is black.
Il gatto è nero.
Die Katze ist schwarz.
Kedi siyah.
Kočka je černá.

So the sense of a word or phrase or sentence is a one-in-many in that each tokening of the word or phrase expresses numerically the same sense. A tokening, by definition, is the production of a token, in this case, a linguistic token. One way a speaker can produce such a token is by uttering the word or phrase in question. Another way is by writing the word or phrase down on a piece of paper. (There are numerous other ways as well.) This production of tokens therefore presupposes a further distinction:

B. The distinction between linguistic types and linguistic tokens. In the following array, how many words are there?

cat
cat
cat

Three or one? Is the same word depicted three times? Or are there three words? Either answer is as good as the other but they contradict each other. So we need to make a distinction: there are three tokens of the same type. We are forced by elementary exegesis of the data to make the type-token distinction. If you don't make it, then you will not be able to answer my simple question: three words or one?

You see (using the optical transducers in your head, and not by any visio intellectualis) the three tokens. And note that the tokens you now see are not the tokens I saw when I wrote this entry. Those were different tokens of the same type, tokens which, at the time of your reading are wholly past. Linguistic tokens are in time, and in space, which is not obviously the case for linguistic types. I said: not obviously the case, not: obviously not the case. You see the three tokens, but do you see the type of which they are the tokens? If you do, then you have powers I lack. And yet the tokens are tokens of a type. No type, no tokens. So types exist. How will our nominalist accommodate them? He cannot reduce types to sets of tokens since he eschews sets. No sets, no sets of linguistic tokens. Linguistic types are multiply instantiable. That makes them universals. But no nominalist accepts universals. Nominalists hold that everything is a particular. I grant that the rejection of sets and the rejection of universals are different rejections. But if one rejects sets because they are abstract objects, one ought also to reject universals for the same reason.

Now glance back at the first array. What we have there are five different sentence tokens from five different languages. Each is both token – and type-distinct from the other four.

To conclude, I present our nominalist with two challenges. The first is to give a nominalist account of linguistic types without either reducing them to sets or treating them as ones-in-many or ones-over-many. The second challenge is to explain the distinction between the sense or meaning of an expression, which is not physical/material and the expression which is.

Suppose he responds to the second challenge by embracing conceptualism according to which meanings are mental. Conceptualism is concept-nominalism, as D. M. Armstrong has maintained. My counterargument would be that the meaning/sense expressed by a tokening of 'The cats are asleep' is objectively either true or false, and thus either true or false for all of us, not just for the speaker. Sentential meanings are not private mental contents. Fregean Gedanken, for example, are not dependent for their existence or truth-value on languages or language-users.

A Nominalist Walks into a Bar . . .

. . . looking sad.

Bartender: "What's the matter, pal?"

"My girlfriend says we have nothing in common!"

Bartender: "But you are a nominalist! Isn't that the way it's supposed to be?"

This short video is sloppy, but will give you some idea of what nominalism is if you don't have a clue.

Why Not be a Nominalist about Sets?

The resident nominalist comments:

Nominalists say that the conception of an actual infinity of natural numbers depends on there being a set of all such numbers. But Ockhamists do not believe in sets. They say that the term ‘a pair of shoes’ is a collective noun which deceives by the singular expression ‘a pair’. Deceives, because it means no more than ‘two shoes’, and if there is only a pair of shoes, then there are only two things. But if a ‘pair’ of two things is a single thing, there are three things, the two things and the pair. Ergo etc.

I agree that there cannot be an actual infinity of natural numbers unless there is a (mathematical as opposed to commonsense) set of all such numbers. But of course this holds for all numbers, rational, irrational, transcendental, etc. Indeed, it holds for any category of item that is actually infinite. If there is an actual infinity of propositions, for example, then there must be a set of all propositions. I would point out however that there is nothing nominalistic about our friend's opening remark.

Nominalism kicks in with the claim that there are no sets. What there are are plural referring devices such as 'a pair of shoes' which fools us into thinking that in reality, i.e., extralinguistically, there are three things, a left shoe, a right shoe, and the pair, when there are only two things, the two shoes. The same goes for the following seemingly singular but really plural phrases: a gaggle of geese, a pride of lions, a parliament of owls, a coven of witches, etc.

This all makes good sense up to a point. When I put on my shoes, I put on one, then the other. It would be a lame joke were you to say to me, "You put on the left shoe and then the right one; when are you going to put on the pair?" To eat a bunch of grapes is to eat each grape in the bunch; after that task is accomplished there is nothing left to do. The bunch is not something 'over and above' the individual grapes that I still need to eat.

Consider now the Hatfields and the McCoys. These are two famous feuding Appalachian families, and therefore two pluralities. They cannot be (mathematical) sets on the nominalist view. But there is also the two-membered plurality of these pluralities to which we refer with the phrase 'the Hatfields and the McCoys' in a sentence like 'The Hatfields and the McCoys are families feuding with each other.'

If, however, a plurality of pluralities has exactly two members, as in the case of the Hatfields and the McCoys — taking those two collections collectively — then the latter cannot themselves be mere pluralities, but must be single items, albeit single items that have members. They must be both one and many. That is to say: In the sentence, 'The Hatfields and the McCoys are two famous feuding Appalachian families,' 'the Hatfields' and 'the McCoys' must each be taken to be referring to a single item, a family, and not to a plurality of persons. For if each is taken to refer to a plurality of items, then the plurality of pluralities could not have exactly two members but would many more than two members, as many members as there are Hatfields and MCoys all together. Compare the following two sentences:

1. The Hatfields and the McCoys number 100 in toto.

2. The Hatfields and the McCoys are two famous feuding Appalachian families.

In (1),'the Hatfields and the McCoys' can be interpreted as referring to a plurality of persons as opposed to a mathematical set of persons. But in (2), 'the Hatfields and the McCoys' cannot be taken to be referring to a plurality of persons; it must be taken to be referring to a plurality of two single items.

Or consider the following said to someone who mistakenly thinks that the Hatfields and the McCoys are one and the same family under two names:

3. The Hatfields and the McCoys are two, not one.

Clearly, in (3) 'the Hatfields and the McCoys' refers to a two-membered plurality of single items, each of which has many members, and not to a plurality of pluralities. And so we must introduce mathematical sets into our ontology.

My conclusion, contra the resident nominalist, is that we cannot scrape by on pluralities alone. (Man does not live by manifold alone! He needs unity!) We need mathematical sets or something like them: entities that are both one and many. A set, after all, is a one-in-many. It is not a mere many, and it is not a one 'over and above' a many. The nominalist error is to recoil from the latter absurdity and end up embracing the former. The truth is in the middle.

What I have given is an argument from ordinary language to mathematical sets. But there are also mathematical arguments for sets. Here is a very simple one. The decimal expansion of the fraction 1/3 is nonterminating: .33333333 . . . . But if I trisect a line, i.e., divide it into three equal lengths, I divide it into three quite definite actual lengths. This can be the case only if the the decimal expansion is a completed totality, an actual infinity, not a merely potential one. An even better example is that of the irrational number, the square root of 2 — it is irrational because it cannot be expressed as a ratio of two numbers, the numerator and the denominator of a fraction as in the case of of the rational 1/3. If the hypotenuse of a right triangle is ${\sqrt {2}}$

REFERENCES

Max Black, "The Elusiveness of Sets," Review of Metaphysics, vol. XXIV, no. 4 (June 1971), 614-636.

Stephen Pollard, Philosophical Introduction to Set Theory, University of Notre Dame Press, 1990.

The Hatfields and the McCoys

Whether or not it is true, the following has a clear sense:

1. The Hatfields outnumber the McCoys.

(1) says that the number of Hatfields is strictly greater than the number of McCoys. It obviously does not say, of each Hatfield, that he outnumbers some McCoy. If Gomer is a Hatfield and Goober a McCoy, it is nonsense to say of Gomer that he outnumbers Goober. The Hatfields 'collectively' outnumber the McCoys.

It therefore seems that there must be something in addition to the individual Hatfields (Gomer, Jethro, Jed, et al.) and something in addition to the individual McCoys (Goober, Phineas, Prudence, et al.) that serve as logical subjects of number predicates. In

2. The Hatfields are 100 strong

it cannot be any individual Hatfield that is 100 strong. This suggests that there must be some one single entity, distinct but not wholly distinct from the individual Hatfields, and having them as members, that is the logical subject or bearer of the predicate '100 strong.'

So here is a challenge to Ed Buckner the nominalist. Provide truth-preserving analyses of (1) and (2) that make it unnecessary to posit a collective entity (whether set, mereological sum, or whatever) in addition to individual Hatfields and McCoys.

Nominalists and realists alike agree that one must not "multiply entities beyond necessity." Entia non sunt multiplicanda praeter necessitatem! The question, of course, hinges on what's necessary for explanatory purposes. So the challenge for Buckner the nominalist is to provide analyses of (1) and (2) that capture the sense and preserve the truth of the analysanda and yet obviate the felt need to posit entities in addition to concrete particulars.

Now if such analyses could be provided, it would not follow that there are no 'collective entities.' But a reason for positing them would have been removed.

Nominalism and Being

Ed Buckner is threatening to write a book on the history of philosophy from the perspective of nominalism. I encourage him to do so for his sake and ours. One of the things he will have to do early on is to define 'nominalism' as he will use the term given its varied use in the history of philosophy. The following redacted re-post from over ten years ago (7 March 2012) may help him focus his thoughts.

……………………………………

Today I preach on an old text of long-time commenter and sparring partner, London Ed:

Nominalism is the doctrine that we should not multiply entities according to the multiplicity of terms. I.e., we shouldn't automatically assume that there is a thing corresponding to every term. Das Seiende is a term, so we shouldn't automatically assume there is a thing corresponding to it. Further arguments are needed to show that there is or there isn't. A classic nominalist strategy is to rewrite the sentence in such a way that the term disappears.

My first concern is whether this definition of 'nominalism' is perhaps too broad, so broad that it pulls in almost all of us. Does anyone think that every term has a referent? (No) Don't we all hold that there can be no automatic assumption that every occurrence of a term in a stretch of discourse picks out an entity? (Yes) For example, one would be hard pressed to find a philosopher who holds that 'nothing' in

1. Nothing is in the drawer

refers to something. (Carnapian slanders aside, Heidegger does not maintain this, but this is a separate topic about which I have written a long unpublished paper.) Following Ed's excellent advice, the apparently referential 'nothing' can be paraphrased away:

2. It is not the case that there is something in the drawer.

This then goes into quasi-canonical notation as

2*. ~(∃x)(x is in the drawer).

In (2*) the tilde and the particular quantifier are syncategorematic elements. On the face of it, then, there is no call to be anything other than a nominalist about 'nothing,' using 'nominalism' as per the suggestion above.

Whether there is call to be a nominalist about 'being' is another matter. Before proceeding to it, consider the following example:

3. Peter and Paul are blond

which could be parsed as

3*. Peter is blond and Paul is blond.

Now I rather doubt that anyone maintains that every word in (3*) — or rather every word in a tokening of this sentence-type whether via utterance or inscription or some other mode of encoding — has an entity corresponding to it. This suggests a taxonomy of nominalisms:

Mad Dog Nominalism: No word has an existing referent, not even 'Peter' and 'Paul.' (I write 'existing referent' to disallow Meinongian objects as referents. The waters are muddy enough without bringing Meinong into the picture — please pardon the mixed metaphors.)

Extreme Nominalism: The only words that have existing referents are names like 'Peter' and Paul'; nothing in reality corresponds to such predicates as 'blond.' And a fortiori nothing corresponds to copulae and logically connective words such as 'and' and 'or.'

Nominalism Proper: Particulars (unrepeatables) alone exist: there are no universals (repeatables). This view allows that something in reality corresponds to predicates such as 'blond.' It is just that what this predicate denotes is not a universal but a particular, a trope say, or an Aristotelian accident. I am using particular to refer to any unrepeatable item, whether concrete or abstract. Thus Socrates is a particular while his whiteness is an abstract particular, where 'abstract' is being used in the traditional as opposed to the new-fangled Quinean way. Both are particulars because neither is repeatable in the way in which a universal is repeatable. Thus the whiteness of Socrates is numerically distinct from the whiteness of Plato.

Methodological Nominalism: This is just Ed's suggestion that we not assume that for each word there is a corresponding entity.

I hope no one is crazy enough to be a mad-dog nominalist, and that everyone is sane enough to be a methodological nominalist. The two middle positions, however, are subject to reasonable controversy. What I am calling Extreme Nominalism has little to recommend it, but I think Nominalism Proper is quite a reasonable position. There has to be something extralinguistic (and extramenal) corresponding to the predicate in 'Peter is blond,' but it is not obvious that it must be a universal.

If I understand Ed's position, he holds that all reference is intra-linguistic. That makes him a linguistic idealist. Is that a 'mad dog' position?

Now let's think about whether we should be nominalists with respect to words like das Seiende, that-which-is, the existent, beings, and the like. Heidegger has been known to say such things as Das Seiende ist, or

4. That-which-is is. (Beings are.)

Now is there anything in reality corresponding to 'that-which-is' and 'beings'? Well of course: absolutely everything comes under 'that-which-is.' There is nothing that is named by 'Nothing.' And if I met nobody on the trail, that is not to say that I met someone named 'Nobody.' But absolutely everything falls under 'a being,' 'an existent,' ein Seiendes, das Seiende.

So I see no reason to have any nominalist scruples about the latter expressions. I don't see any problem with forming the substantive das Seiende from the present participle seiend. But you will be forgiven if you balk at the transformation of the infinitive sein into the the substantive das Sein and take the latter to refer to Majuscule Being.

Against Ostrich Nominalism (2021 Update)

Cyrus asked me whether being an ostrich indicates a moral defect. He is invited to repeat his question in his own words in the Comments. Logically prior question: what is an ostrich? The entry below is a redacted version of one from January 2013.

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As magnificent a subject as philosophy is, grappling as it does with the ultimate concerns of human existence, and thus surpassing in nobility any other human pursuit, it is also miserable in that nothing goes uncontested, and nothing ever gets established to the satisfaction of all competent practitioners. (This is true of other disciplines as well, but in philosophy it is true in excelsis.) Suppose I say, as I have in various places:

That things have properties and stand in relations is a plain Moorean fact beyond the reach of reasonable controversy. After all, my cat is black and he is sleeping next to my blue coffee cup. ‘Black’ picks out a property, an extralinguistic feature of my cat.

Is that obvious? Not to some. Not to the ornery and recalcitrant critter known as the ostrich nominalist. My cat, Max Black, is black. That, surely, is a Moorean fact. Now consider the following biconditional and consider whether it too is a Moorean fact:

1. Max is black iff Max has the property of being black.

As I see it, there are three main ways of construing a biconditional such as (1):

A. Ostrich Nominalism. The right-hand side (RHS) says exactly what the left-hand side (LHS) says, but in a verbose and high-falutin' and dispensable way. Thus the use of 'property' on the RHS does not commit one ontologically to properties beyond predicates. (By definition, predicates are linguistic items while properties are extralinguistic and extramental.) For the ostrich nominalist, predication is primitive and in no need of philosophical explanation. On this approach, (1) is trivially true. One needn't posit properties, and in consequence one needn't worry about the nature of property-possession. (Is Max related to his blackness, or does Max have his blackness quasi-mereologically by having it as an ontological constituent of him?) And if one needn't posit properties, no questions need arise about what they are: sets? universals? tropes? mereological sums? and so on.

B. Ostrich Realism. The RHS commits one ontologically to properties, but in no sense does the RHS serve to ground or explain the LHS. On this approach, (1) is false if there are no properties. For the ostrich realist, (1) is true, indeed necessarily true, but it is not the case that the LHS is true because the RHS is true. Such notions as metaphysical grounding and philosophical explanation are foreign to the ostrich realist, but not in virtue of his being a realist, but in virtue of his being an ostrich. Peter van Inwagen is an ostrich realist.

C. Non-Ostrich Realism. On this approach, the RHS both commits one to properties, but also proffers a metaphysical ground of the truth of the LHS: the LHS is true because (ontologically or metaphysically speaking, not causally) the concrete particular Max has the property of being black, and not vice versa.

Note 1: Explanation is asymmetrical; biconditionality is symmetrical.

Note 2: Properties needn't be universals. They might be (abstract) particulars (unrepeatables) such as the tropes of D. C. Williams and the abstract particulars of Keith Campbell. Properties must, however, be extralinguistic and extramental, by definition.

Note 3: Property-possession needn't be understood in terms of instantiation or exemplification or Fregean 'falling-under'; it might be construed quasi-mereologically as constituency: a thing has a property by having it as a proper ontological part.

Against Ostrich Nominalism

On (A) there are neither properties, nor do properties enter into any explanation of predication. Predication is primitive and in need of no explanation. In virtue of what does 'black' correctly apply to Max? In virtue of nothing. It just applies to him and does so correctly. Max is black, but there is no feature of reality that explains why 'black' is true of Max, or why 'Max is black' is true. It is just true! There is nothing in reality that serves as the ontological ground of this contingent truth. Nothing 'makes' it true. There are no truth-makers and no need for any.

I find ostrich nominalism preposterous. 'Black' is true of Max, 'white' is not, but there is no feature of reality, nothing in or at or about Max that explains why the one predicate is true of him and the other is not!? This is not really an argument but more an expression of incomprehension or incredulity, an autobiographical comment, if you will. I may just be petering out, pace Peter van Inwagen.

Can I do better than peter? 'Black' is a predicate of English. Schwarz is a predicate of German. If there are no properties, then Max is black relative to English, schwarz relative to German, noir relative to French, and thus no one color. But this is absurd. Max is not three different colors, but one color, the color we use 'black' to pick out, and the Germans use schwarz to pick out. When Karl, Pierre, and I look at Max we see the same color. So there is one color we both see — which would not be the case if there were no properties beyond predicates. It is not as if I see the color black while Karl sees the color schwarz. We see the same color. And we see it at the cat. This is not a visio intellectualis whereby we peer into some Platonic topos ouranios. Therefore, there is something in, at, or about the cat, something extralinguistic, that grounds the correctness of the application of the predicate to the cat.

A related argument. I say, 'Max is black.' Karl says, Max ist schwarz. 'Is' and ist are token-distinct and type-distinct words of different languages. If there is nothing in reality (no relation whether of instantiation or of constituency, no non-relational tie, Bergmannian nexus, etc.) that the copula picks out, then it is only relative to German that Max ist schwarz, and only relative to English that Max is black. But this is absurd. There are not two different facts here but one. Max is the same color for Karl and me, and his being black is the same fact for Karl and me. Copulae as bits of language belonging to different languages are token-distinct and type-distinct. But they pick out the copulative tie that is logically and metaphysically antecedent to language. Or will you say that reality is language all the way down? That way lies the madness of an absurd linguistic idealism.

Finally, 'Max is black' is true. Is it true ex vi terminorum? Of course not. It is contingently true. Is it just contingently true? Of course not. It is true because of the way extralinguistic reality is arranged. It is modally contingent (possibly false if true; possibly true if false), but also contingent upon the way the world is. There's this cat that exists whether or not any language exists, and it is black whether or not any language exists.

Therefore, I say that for a predicate to be contingently true of an individual, (i) there must be individuals independently of language; (ii) there must be properties independently of language; and there must be facts or truth-making states of affairs independently of language. Otherwise, you end up with (i) total linguistic idealism, which is absurd; or (ii) linguistic idealism about properties which is absurd; or (iii) a chaos, a world of disconnected particulars and properties.

The above is a shoot-from-the hip, bloggity-blog exposition of ideas that can be put more rigorously, but it seems to to me to show that ostrich nominalism and ostrich realism for that matter are untenable — and this despite the fact that a positive theory invoking facts has its own very serious problems.

Metaphilosophical Coda: If a theory has insurmountable problems, these problems are not removed by the fact that every other theory has problems. For it might be that no theory is tenable, while the problem itself is genuine. If I argue against a position, that does not make me for its opposite. So when I argue against presentism in the philosophy of time that does not make me for eternalism, even if eternalism is the contradictory opposite of presentism.

One cannot exclude a priori the existence of genuine aporiai or insolubilia. Curators of logic museums take note.

Nominalism, Existence, and Subsistence

Here are five versions of nominalism by my current count:

Mad-Dog Nominalism: No word has an extra-linguistic referent, not even proper names such as 'Peter' and 'Paul.'

Extreme Nominalism: The only words that have existing referents are proper names like 'Peter' and Paul'; nothing in reality corresponds to such predicates as 'blond.' And a fortiori nothing corresponds to copulae and logically connective words such as 'and' and 'or.'

Nominalism Proper: Particulars (unrepeatables) alone exist: there are no universals (repeatables). This view allows that something in reality corresponds to predicates such as 'blond' as in 'Peter is blond.' It is just that what this predicate denotes is not a universal but a particular, a trope say, or an Aristotelian accident. What I am calling nominalism proper also allows for abstract particulars where an item is abstract just in case it is non-spatio-temporal and causally inert. Mathematical sets, for example are abstract particulars. The set: {x: x is a prime number and x is less than 1o} is abstract because it has no spatiotemporal location and is causally inert. It is particular because it is unrepeatable which is equivalent to saying that it is not possibly such as to be instantiated. Sets have members — the null set aside — but no instances. (Quiz for the reader: tell me the cardinality of the set just mentioned.)

Reistic Nominalism: Attach the codicil 'There are no abstract items' to nominalism proper and the result is reistic nominalism. On this view only particulars exist, and all particulars are concrete (non-abstract). Franz Brentano is his later years was a reist. See the SEP entry, Reism.

Methodological Nominalism: This is the view that we ought never assume that for each word there is a corresponding entity.

I hope no one is crazy enough to be a mad-dog nominalist, and that everyone is sane enough to be a methodological nominalist. The three middle positions, however, are subject to reasonable controversy. They are not obviously false and they are not obviously true. What I am calling extreme nominalism has little to recommend it, but I think nominalism proper is quite a reasonable position. As it seems to me, there has to be something extra-linguistic (and extra-mental) corresponding to the predicate in 'Peter is blond,' but it is not obvious that it must be a universal.

Thomas Beale sent me to a blog post of his that begins as follows:

Nominalism is a philosophical doctrine usually understood to entail a rejection of universals, in favour of the belief that only the concrete exists. Universals are understood as instantiable entities, i.e. something like types. Another flavour of nominalism involves rejection of abstracta, such as mathematical entities, propositions, fictional entities (including possible worlds).

I personally think that most nominalist arguments are straightforwardly wrong, but not for the usual reasons that universals and/or abstracta are said by realists to exist, but for the opposite reason: types and abstracta are just there, even if they don’t ‘exist’, in the sense of being spatio-temporally concretised. The real problem is that we misuse the word exists at least half the time in philosophy. The way we should talk is to say things like: there are universals . . . .

So that’s why nominalists are wrong. There are universals, but they don’t exist.

First of all, it is no misuse of 'exist/exists' to use these expressions interchangeably with 'is/are.' It is standard English to use them interchangeably. Examples: I am; I exist. God is; God exists. Island volcanoes exist; there are island volcanoes. Unicorns do not exist; unicorns are not; there exist no unicorns; there are no unicorns. Scollay Square once existed; Scollay Square once was. Socrates would never have come to be had his parents never met; Socrates would never have come to exist had his parents never met. And so on.

Nevertheless, we are not the slaves of ordinary language and one is free to distinguish between existence and being as Bertrand Russell did in Principles of Mathematics.

Now if existence is the mode of being enjoyed by all and only spatiotemporal items, then abstracta and transcendent universals do not exist. (A transcendent universal is one that needn't be instantiated to be. An immanent universal is one that cannot be unless it is instantiated.) If transcendent universals are, but do not exist, then they enjoy the mode of being called subsistence. This seems to be what Mr Beale is telling us.

Here is an interesting question. Suppose with David Armstrong that universals are immanent –ones-in-many, not ones-over many — and that first-order immanent universals are constituents of thick spatio-temporal particulars. Would not these universals be "spatio-temporally concretised" in Beale's words? Suppose universal U is a constituent of a, b, and c — concrete existing spatiotemporal particulars — and is wholly present in each without prejudice to its unity as a universal. Would U then not be "spatio-temporally concretised" and therefore existent?

One more question. If there were a good argument for either nominalism proper and/or reistic nominalism, would that not also be a good argument against universals and abstracta that are but do not exist? He who fights shy of multiplying entities beyond necessity does not care whether the entities exist or subsist.

Finally, aren't there good objections to the notion that there are modes of being?

A Realist Walks into a Bar . . .

. . . looking glum.

Bartender: "What's the matter, pal?"

Realist: "My nominalist girl friend says we have nothing in common!"

Against Ostrich Nominalism

That things have properties and stand in relations I take to be a plain Moorean fact beyond the reach of reasonable controversy. After all, my cat is black and he is sleeping next to my blue coffee cup. ‘Black’ picks out a property, an extralinguistic feature of my cat.

1. Max is black iff Max has the property of being black.

As I see it, there are three main ways of construing a biconditional such as (1):

A. Ostrich Nominalism. The right-hand side (RHS) says exactly what the left-hand side (LHS) says, but in a verbose and high-falutin' and dispensable way. Thus the use of 'property' on the RHS does not commit one ontologically to properties beyond predicates. (By definition, predicates are linguistic items while properties are extralinguistic and extramental.) Predication is primitive and in need of no philosophical explanation. On this approach, (1) is trivially true. One needn't posit properties, and in consequence one needn't worry about the nature of property-possession. (Is Max related to his blackness, or does Max have his blackness quasi-mereologically by having it as an ontological constituent of him?)

C. Non-Ostrich Realism. On this approach, the RHS both commits one to properties, but also proffers a metaphysical ground of the truth of the LHS: the LHS is true because (ontologically or metaphysically speaking) the concrete particular Max has the property of being black, and not vice versa.

Note 1: Explanation is asymmetrical; biconditionality is symmetrical.

Note 2: Properties needn't be universals. They might be (abstract) particulars (unrepeatables) such as the tropes of D. C. Williams and Keith Campbell. Properties must, however, be extralinguistic and extramental, by definition.

Note 3: Property-possession needn't be understood in terms of instantiation or exemplification or Fregean 'falling-under'; it might be construed quasi-mereologically as constituency: a thing has a property by having it as a proper ontological part.

Against Ostrich Nominalism

Can I do better than peter? 'Black' is a predicate of English. Schwarz is a predicate of German. If there are no properties, then Max is black relative to English, schwarz relative to German, noir relative to French, and no one color. But this is absurd. Max is not three different colors, but one color, the color we use 'black' to pick out, and the Germans use schwarz to pick out. When Karl, Pierre, and I look at Max we see the same color. So there is one color we both see — which would not be the case if there were no properties beyond predicates. It is not as if I see the color black while Karl sees the color schwarz. We see the same color. And we see it at the cat. This is not a visio intellectualis whereby we peer into some Platonic topos ouranos. Therefore, there is something in, at, or about the cat, something extralinguistic, that grounds the correctness of the application of the predicate to the cat.

Finally, 'Max is black' is true. Is it true ex vi terminorum? Of course not. It is contingently true. Is it just contingently true? Of course not. It is true because of the way extralinguistic reality is arranged. It is modally contingent, but also contingent upon the way the world is. There's this cat that exists whether or not any language exists, and it is black whether or not any language exists.

Metaphilosophical Coda: If a theory has insurmountable problems, these problems are not removed by the fact that every other theory has problems. For it might be that no theory is tenable,while the problem itself is genuine.

Nominalism and an Identity Theory of Predication

The Worthy Opponent comments,

We nominalists hold that 'God is good' is true when what is signified by 'God' and what is signified by 'good' are numerically one and the same thing.

I stumble over this.

Apparently, it is The Opponent's view that a sentence such 'Socrates is good' is true when what is signified by 'Socrates' and what is signified by 'good' are numerically one and the same thing. I don't understand. 'Good,' unlike 'Socrates,' is a common term: it applies to many individuals. So there cannot be numerically one thing that both 'Socrates' and 'good' signify. 'Socrates' signifies one thing; 'good' signifies many things.

If, contrary to fact, there were only one good thing, then it would make some sense to say that 'Socrates is good,' which is by its surface grammar a predication, could be read as asserting the numerical identity of Socrates with the one good thing. But if Socrates is good, or seated, or conversing with Theaetetus, this is only contingently the case. So how analyze the possibly true 'Socrates is not good' on the assumption that there is only one good thing? We would have to say that Socrates is distinct from himself — which is absurd. For if, in actuality, Socrates is good in virtue of being identical to the one good thing, then, in the possible counterfactual situation in which he — the very same individual — is not good, he would have to be numerically diverse from the one good thing, namely, himself!

The same argument goes through even if there are many good things. For the Opponent's claim is that Socrates is good in virtue of being identical to one of the many good things. Call this good thing G. The claim is that 'Socrates is good' is an identity proposition in disguise, and that its deep logical form is: S = G.

The problem is that 'Socrates is good' is contingently true. But 'S = G' is not contingently true. So the predication is not an identity proposition in disguise.

This looks to be a pretty powerful objection.

I am assuming something that is well-nigh self-evident, but which I fear the Illustrious Opponent will deny, namely, that if a = b, then this is non-contingently the case. In other words, I am assuming that if a = b, then there is no possible situation in which a and b both exist but are numerically distinct.

Curiously, the Opponent's theory works in one case and one case only. But he has to admit the divine simplicity. So assume that God exists, that God is essentially good, and that God is identical to his attributes, and that therefore God alone is good in this sense. If God is identical to his attributes, then God = the one and only good thing. (Socrates is good only in an analogical and derivative sense.) In this one case, 'God is good' is an identity proposition in disguise.