Why not be a Nominalist?

0. This post is a sequel to Truthmaker Maximalism Questioned.

1. On one acceptation of the term, a nominalist is one who holds that everything that exists is a concrete  individual.  Nominalists accordingly eschew such categories of entity as: universals, whether transcendent or immanent, Fregean propositions, Castaneda's ontological operators, mathematical sets, tropes (abstract particulars, perfect particulars), and concrete states of affairs.  Nominalists of course accept that there are declarative sentences and that some of them are true.  Consider the true

1. Peter is hungry.

Nominalists cheerfully admit that the proper name 'Peter' denotes something external to language and mind, a particular man, which we can call the 'ontological correlate' of the subject term.  But, ever wary of "multiplying entities beyond necessity," nominalists fight shy of admitting an ontological correlate of  'hungry,' let alone a correlate of  'is.'   And yet, given that (1) is true, 'hungry' is true of Peter.  (In a simple case like this, the predicate is true of  the the referent of the subject term iff the sentence is true.) Now philosophers like me are wont to ask:  In virtue of what is 'hungry' true of Peter?  Since 'hungry' applies to Peter in the way in which 'leprous,' 'anorexic,' and other predicates do not, I find it reasonable to put the same question as follows:  What is the ontological ground of the correct application of 'hungry' to Peter?

2. In answering this question I introduce two posits that will enrage the nominalist and offend against his ontologcal parsimoniousness.   First of all, we need an o-correlate of 'hungry.' I admit of course that 'hungry' in our sample sentence functions differently than 'Peter.'  The latter is a name, the former is what Frege calls a concept-word (Begriffswort).  Nevertheless, there must be something in reality that corresponds to 'hungry,' and whatever it is it cannot be identical to Peter.  Why not?  Well, Peter, unlike my cat, is not hungry at every time at which he exists; and for every time t in the actual world at which  he is hungry, there is some possible world in which he is not hungry at t.  Therefore, Peter cannot be identical to the o-correlate of 'hungry.' 

We are back to our old friend (absolute numerical) identity which is an equivalence relation (reflexive, symmetrical, transitive) governed by the Indiscernibility of Identicals and the Necessity of Identity.

3. But why do we need an o-correlate of 'hungry' at all?  I asked: in virtue of what is 'hungry' true of Peter?  One sort of nominalist, the 'ostrich nominalist,' will say that there is nothing in virtue of which 'hungry' is true of Peter.  For him is is just a 'brute fact,' i.e., an inexplicable datum, that 'hungry' correctly applies to Peter.  There is no need of an ontological ground of the correctness of this application.  There is no room for a special philosophical explanation of why 'hungry' is true of Peter.  It just applies to him, and that's the end of the matter.  The ostrich nominalist of course grants that Peter's being hungry can be explained 'horizontally' in terms of antecedent and circumambient empirical causes; what he denies is that there is need for some further 'philosophical' or 'metaphysical' or 'ontological' explanation of the truth of 'Peter is hungry.'

If a nominalist says that 'hungry' is true of Peter because Peter is hungry, then I say he moves in a circle of embarrasingly short diameter.  What we want to understand are the ontological commitments involved in the true sentence, 'Peter is hungry.'  We need more than Peter.  We need something that grounds the correctness of the application of 'hungry' to him.  To say that 'hungry' is true of Peter because Peter is hungry presupposes what we are trying to understand.  Apart from this diversionary tactic, the ostrich nominalist is back to saying that there is nothing extralingusitic that grounds the correct application of 'hungry' to Peter.  He is denying the possibility of any metaphysical explanation here.  He is saying that it is just a brute fact that 'hungry' applies to Peter.

4.  As for my second posit, I would urge that introducing an o-correlate for 'hungry' such as a universal tiredness does not suffice to account for the truth of the sample sentence.  And this for the simple reason that Peter and tiredness could both exist withough Peter being tired.  What we need is a concrete state of affairs, an entity which, though it has Peter and tiredness as constituents, is distinct from each and from the mereological sum of the two. 

5.  Now one can argue plausibly against both posits.  And it must be admitted that both posits give rise to conundra that cast doubt on them.  But what is the alternative?  Faced with a problem, the ostrich sticks his head in the sand.  Out of sight, out of mind.  Similarly. the ostrich nominalist simply ignores the problem.  Or am I being unfair?

Perhaps the issue comes down to this:  Must we accept the truth of sentences like (1) as a 'brute fact,' i.e. as something insusceptible of explanation (apart, of course, from causal explanation), OR is there the possibility of a philosophical account?

6. Finally, it is worth nothing that the nominalist blunders badly  if he says that Peter is hungry in virtue of 'hungry''s applying  to him.  For that is a metaphysical theory and an absurd one to boot: it makes Peter's being hungry depend on the existence of the English predicate 'hungry.'  To avoid an incoherent, Goodmanaical, linguistic idealism, the nominalist should give no metaphysical explanation and be content to say it is just a brute fact that Peter is hungry.

Comments

[William Woking]

>> a nominalist is one who holds that everything that exists is a concrete individual.

In which case I am an 'Ockhamist': one who is cautious of multiplying entities according to the multiplicity of terms. There can be degrees of Ockhamism. The term we are cautious about in the present case is 'fact'. An Ockhamist is not sure whether a fact is a 'thing'.

>>him is is just a 'brute fact,' i.e., an inexplicable datum, that 'hungry' correctly applies to Peter.

I don't understand the idea of 'brute fact', or why it is an 'inexplicable datum'.

>>The ostrich nominalist of course grants that Peter's being hungry can be explained 'horizontally' in terms of antecedent and circumambient empirical causes; what he denies is that there is need for some further 'philosophical' or 'metaphysical' or 'ontological' explanation of the truth of 'Peter is hungry.'

Yes, correct. What further explanation is needed other than lack of food, and Peter's nervous system?

>>If a nominalist says that 'hungry' is true of Peter because Peter is hungry, then I say he moves in a circle of embarrasingly short diameter.

An Ockhamist would not want to say that Peter is hungry because Peter is hungry. So this is a bit of a straw man.

Here are some reasons why facts are not things.

1. Negative statements. Negative statements - denials - revoke everything that was posited by the corresponding affirmative statement. Nothing has to exist in order for a negative statement to be true. In which case, it seems to follow that no fact corresponds to a negative statement. Yet I think all the arguments you give above, if valid, would validly apply to 'negative facts'. For example, suppose you argue "If a nominalist says that *it is not the case that* 'hungry' is true of Peter because *it is not the case that* Peter is hungry, then I say he moves in a circle of embarrassingly short diameter". If that argument is valid, it 'proves' there are negative facts. But it is not valid: the antecedent can be true, when the consequent is false. It can not be the case that p, without any thing or entity existing that makes it not the case that p.

2. General statements. 'There is a mouse in the house'. What thing is required to make this statement true? Not just a mouse, not just a house, clearly. But any concrete fact corresponding to the statement being true, involves other 'facts': the mouse is in the attic. Or the mouse is in the kitchen. The mouse may be running or sitting. It may be moving North, East, West and so on. All of these facts in turn involve other facts. But the fact that 'makes the statement true' can be none of these more detailed facts. A queer kind of 'thing', then.

3. Regress. We have discussed this before. We have Peter, and hunger. The existence of these 'things' is not enough. We need the existence of a certain relation between Peter and hunger. But is that relation a thing, or a brute fact? If the latter, then 'habeo propositum', my case rests. If a thing, what relation now holds between, Peter, hunger and the thing-relation, et sic proceditur in infinitum.

>>Must we accept the truth of sentences like (1) as a 'brute fact,' i.e. as something insusceptible of explanation (apart, of course, from causal explanation), OR is there the possibility of a philosophical account?

Since there is nothing that needs explaining, the expression "insusceptible of explanation" suggests a greater mystery than there actually is.

[aresh v.]

...the lack of food is not a concrete thing tough. And if you interpret lack of food in function of the concrete thing food, then negative facts can be explained in function of positive facts.

[William]

>>the lack of food is not a concrete thing tough

You have a very interesting point there, which was much discussed in medieval times. The medievals would have regarded a 'lack' of anything (such as hunger, blindness) as a 'privation'. A privation is when a thing which is "naturally suited" (aptus natus) to have something, doesn't have it. Thus privative negation requires a subject, and so is existence implying. It 'posits a subject' as the medievals said. There are further distinctions they made (and which are also made in modern philosophy of language) such as between predicate negation and sentential negation. Predicate negation is when e.g. we say 'Socrates is non-white'. This implies the existence of Socrates. Sentential negation, which the medievals called 'extinctive' or 'destructive' negation is when absolutely everything posited by the affirmation, is taken away. Thus 'It is not the case that Socrates is white', understood in a sense that does not even imply the existence of Socrates. It is the final sense that I was talking about. In the destructive or extinctive case of negation, nothing has to remain at all. Thus there cannot be a negative fact corresponding to such negation. Destructive negation covers every case from a minor infringement of the truth conditions of a statement, to a complete annihilation of everything. Since complete annihilation of everything is a case where nothing exists at all - not even a 'negative fact' - it follows that there cannot be negative facts.

[Bill Vallicella]

William the Ockhamist writes, >>cautious of multiplying entities according to the multiplicity of terms.<< But virtually all philosophers are cautious in this regard. Similalry, no one wants to multiply entities (or rather kinds of entity) beyond necessity. Your injunctions are somewhat empty. It's like saying, 'Do the right thing!'

You are a difficult guy to have a conversation with because you feign lack of understanding. Surely you understand that by 'brute fact' above there is no reference to the concrete facts that serve as truthmakers.

You won't even agree with me as to what the issue is. I'd say I explained it very clearly near the end of my post.

[aresh v.]

Bill,
You say: "What we need is a concrete state of affairs, an entity which, though it has Peter and tiredness as constituents, is distinct from each and from the mereological sum of the two"
Should I interpret your statement as:
1) the state of affairs "Peter is tired" is a BASIC entity constituted by 2 other BASIC entities ('Peter' and 'tired'). therefore states of affairs can't be reduced to their constituents?
or 2) the state of affairs "Peter is tired" is a DERIVED entity constituted by 2 other BASIC entities ('Peter' and 'tired'). therefore states of affairs can be reduced to their constituents?
thanks

[Clark]

Bill, what do you think of the "middle ground" of moderate realism? That is the idea there are universal concepts but that they pick out only individual things. Armstrong being the obvious example although clearly the medieval figures often adopted this position. I confess that to me it still seems like nominalism but clearly it's not nominalism as normally conceived.

[William Woking]

Well I suffered years of the 'Williams technique' of feigning ignorance so perhaps some has rubbed off.

But in this case I really do not understand. You say you explained the issue towards the end of the post. Do you mean this:

>>>Perhaps the issue comes down to this: Must we accept the truth of sentences like (1) as a 'brute fact,' i.e. as something insusceptible of explanation (apart, of course, from causal explanation), OR is there the possibility of a philosophical account?

I have already said that 'insusceptible' being a privative term automatically suggests a mystery we cannot explain. But I really don't see the mystery. There is nothing that is not susceptible of explanation. Elsewhere you say that for the nominalist "it is just a 'brute fact,' i.e., an inexplicable datum". Why should the nominalist agree with that? I.e. why should the nominalist agree that it is 'inexplicable'? It is simply true on 'horizontal' grounds, as you neatly term it. What else is there to explain?

You say "[For the nominalist] There is no need of an ontological ground of the correctness of this application. There is no room for a special philosophical explanation of why 'hungry' is true of Peter. " Yes, agree. There is no room, and no need for a special philosophical explanation. Why should there be?

You say "If a nominalist says that 'hungry' is true of Peter because Peter is hungry ..." very well, but I wouldn't say that. There is no room for a 'because' other than the horizontal one (Peter hasn't eaten for a day, e.g.).

You say "the ostrich nominalist is back to saying that there is nothing extralingusitic that grounds the correct application of 'hungry' to Peter. " I have already addressed this in a comment to an earlier post. If this is intended as the claim that nothing distinguishes the thought that p, from the fact that p, the nominalist is not claiming that. S/he is not denying 'external reality' in that sense, i.e. not denying the distinction between belief and reality, as an idealist might do, and as your statement misleadingly suggests.

Note, as I also suggested earlier, a proposition may be true because there is no external reality. Thus 'nothing exists' or, as I said earlier, any 'extinctively' negative statement, whose possible truth conditions are infinite, and which include the possible state of affairs that nothing exists. Not that the fact of nothing existing would be a state of anything, of course.

[William Woking]

AFTERTHOUGHT (I am really trying to see it your way). You begin by saying "Nominalists cheerfully admit that the proper name 'Peter' denotes something external to language and mind" . Then you say "nominalists fight shy of admitting an ontological correlate of 'hungry,' let alone a correlate of 'is.' "

OK - is the problem that while a nominalist admits an external reality corresponding to 'Peter', there appears to be a gap in reality that must correspond to Peter being hungry? In what way does reality have to 'grow' from the bare 'Peter' to 'Peter is hungry. Is that the problem?

But then I still don't see the problem. 'Peter' is a bare proper name, not a sentence. To get to the reality corresponding to it, we would have to say 'Peter exists'. So what reality is added by 'hungry'? Answer: that which is expressed by 'hungry Peter exists' (if I can put it that way). But then a nominalist does not have to fight shy of admitting an 'ontological correlate' i.e. a reality, of 'hungry'. The ontological correlate is simply the difference between the reality expressed by 'Peter exists', and the reality expressed by 'hungry Peter exists'.

[Bill Vallicella]

WW,

Do you agree with this:

1. Peter is hungry at some times but not at others.
2. If Peter is hungry at time t, this is not necessarily the case: he might not have been hungry at t.
Therefore (with the help of an auxiliary premise about the nature of identity)
3. Peter is not identical to hungry Peter.

Now I ask you: is there anything in reality that distinguishes Peter from hungry Peter? If yes, what is that?

[Bill Vallicella]

Clark,

The scholastic view should not be confused with Armstrong's. He maintains that there are universals, though they cannot exist unexemplified. I am attracted to A's view. The scholastic one never made much sense to me.

[Bill Vallicella]

aresh,

You ask a good question. A state of affairs cannot be reduced to its constituents, for it is their unity. But it cannot exist unless they exist. So it is a derived entity in your sense.

[aresh v.]

Bill,
Actually I was using the notion of derivation as a synonym of 'reduction'; and not as a synonym of 'ontological dependence'. However I think I've got your point.
Now, there is something really counter-intuitive in your proposal: a state of affairs should intuitively be the result of 2 things getting connected and not the reason of 2 things getting connected; just as the "A and B being married" is a status of A and B which results from A and B getting married and not the reason, the condition of which A and B getting married is the result (actually if the marriage of A and B had already obtained prior to getting married, they wouldn't even have needed to get married)

[William]

>>3. Peter is not identical to hungry Peter.

Disagree. In the case you have given, the person who might not have been hungry (Peter) is the same person as the one who is actually hungry (Peter).

>>Now I ask you: is there anything in reality that distinguishes Peter from hungry Peter? If yes, what is that?

I agree that the proposition that Peter exists is not identical to the proposition that hungry Peter exists. But the difference is merely that the second gives us more information. There may be no corresponding distinction 'in reality': there is nothing that distinguishes that fact that Peter exists, when hungry, from the fact that hungry Peter exists. Reality is unitary. I suppose we sometimes talk about the 'facts' (plural) of the matter. Peter is hungry, Peter is in the kitchen, Peter is looking for food, and so on. But that seems just a way of talking about propositions.

[aresh v.]

William, Bill,

It seems that your debate started from a different set of assumptions on the role of the notion of 'existence':
while William is simply assuming that "existence" is meaningfully ascribable only to concrete things, so that whatever explanation we can provide for the multiplicity of the terms in a sentence, that shouldn't imply the statement that there are other existing entities besides concrete things.
Bill is assuming that the explanation of the multiplicity of the terms should lead us in individuating what exists and what not.
And these seem to be just two incompatible ontological projects, isn't it?

P.S.
"Thus privative negation requires a subject, and so is existence implying": do you mean that lack of food implies the existence of food? What if I'm hungry because I ran out of food?

[aresh v.]

Another way to formulate the problem:
Assumed that the multiplicity of traits we attribute to a given concrete thing are really grounded in the concrete thing itself, that is indipendently from how we represent these concrete things (by means of thoughts and sentences), the puzzle is how these traits can be real and at the same time not existent themselves!
So unless you deny the assumption, it seems you have only to ways of addressing this issue:
1) these of traits (we ascribe to one and the same concrete thing) are real and at the same time they are not existent (because existence is applicable only to concrete things and not their traits)
2) these of traits (we ascribe to one and the same concrete thing) are real and at the same time they are existent (because for something to be real means to exist)

[William]

>> do you mean that lack of food implies the existence of food?

No, being hungry implies the existence of a hungry person.

[aresh v.]

...and silence?

[Bill Vallicella]

WW,

We will agree that numerically the same person can go from being hungry to being sated to being hungry again. Thus I am not questioning diachronic numerical identity. We will probably also agree that numerically one and the same person who is actually hungry at t is possibly such as to be not hungry at t. (I do not question transworld identity the way David Lewis does with his counterpart theory.)

The question concerns the nature of the distinction between Peter and an accidental property such as being hungry. That property might be a universal or it might be a particular ( a trope). Either way is it really distinct from Peter. Or so say I.

I suspect you would deny this real distinction, though. Are you saying that in reality there is no distinction between Peter and (i) HIS being hungry, and (ii) being hungry?

Are you saying that there is the predicate 'hungry' but no property that corresponds to it?

I hope you realize that people like me do not maintain that there is a property for every predicate. There is no disjunctive property corresponding to the disjunctive predicate 'anorexic or divisible by 2.'

Only an idiot would 'multiply' entities according to the multiplicity of terms. But that is not to say that in no case does something real correspond to a predicate.

[William]

I think I have already agreed that the predicate 'lives in London' involves a relation between its subject, and a real existing entity, the city London. So my position does not rule out the existence of properties such as states of the metabolic system (hunger), of the nervous system (worry) and so on.

What I deny is that there is a relation between something signified by the whole predicate 'lives in London' (which if it existed, would not be the same as London) and the subject (e.g. Peter) that makes the proposition 'Peter lives in London' true, a relation or state of affairs or complex that acts as a 'truthmaker'. This would lead to a number of absurdities. For example, we would have to suppose that if 'Peter lives in London' were false, those same two entities were connected in some different way corresponding to true denial. We would also have Frege's problem: if 'lives in London' signifies a thing, we could invent a word for any entity named by a predicate. Let's call this a 'concept'. But is the concept 'lives in London' a concept, or a concrete object like Peter?

Even if you buy into properties ('hunger'), there is still the problem of what is signified by predicates ('is hungry'). You have to solve that problem before you can have a satisfactory theory of 'truthmakers'.

[Account Deleted]

William,

See my response to some of the issues you raise in the last post in the previous thread "Truthmaker Maximalism Questioned".

[William Woking]

>>the last post in the previous thread

Wow I just saw it. It was so long (two pages of A4) that I printed it out and will read it after supper. It is a rainy and dismal evening in London.

[William Woking]

Peter, I read your comment. I hope Bill doesn't mind if I post my reply here, as it is connected with the points raised here.

1. Your first argument was that predicates exist in language because universals exist in the world. But I didn't see any argument for universals existing, beyond the fact that predicates exist, so you seemed really to be arguing that universals exist because predicates exist.

2. Your second argument, as far as I understood it, seemed similar to Bill's above. We need predicates to fully express facts about the world, ergo things named by the predicates must exist in reality. Thus, what 'is hungry' adds to 'Peter' must correspond that something in reality that if added to Bill gives a fact, or a truthmaker or something. I reply as before. 'Is hungry' is not a name, and adding it to 'Peter' to give 'Peter is hungry' does not give us two concatenated names, and hence does not give us two concatenated things in reality. That is absurd. What the nominalist is objecting to is moving from a bit of language which we must add to proper names to make a sentence, to the existence of some queer entity that is a referent for that bit of language.

Apologies if I misunderstood your comment.

[Clark]

Bill, could you comment more on Armstrong vs. Scholastic realism? I'm intrigued. Unfortunately my knowledge of the scholastics like Scotus is more superficial than I'd care to admit. My understanding though is that the moderate realists in the medieval period located universals in the mind but simultaneously in things themselves. So the scholastics accept that only particular things exist but simultaneously there is a nature to the things not reducible to the individual things. I confess I just don't see how that differs from Armstrong. Is it just that Scotus focuses in on the mind more than Armstong? (I have to confess I've not read Armstrong since college, so I might just have some poor memories here)

[aresh v.]

William,
could you kindly confirm me if you agree with the formulation of the problem I gave you in the above post (aresh v. | Tuesday, March 30, 2010 at 04:48 AM)?
thanks

[Bill Vallicella]

WW,

I said this in my main post: "I admit of course that 'hungry' in our sample sentence functions differently than 'Peter.' The latter is a name, the former is what Frege calls a concept-word (Begriffswort)." More precisely, the concept-word is '... is hungry.' Thus you shouldn't foist upon realists the view that a sentence is a concatenation of two names corresponding to a conccatenation of two objects.

I don't deny that realism leads to various conundra, e.g. the Horse paradox (if we buy into Frege's talk of the unsaturatedness of concepts) and Bradley's regress (if we don't). Perhaps realism leads to absurdities. But how is nominalism any less absurd? It strikes me as absurd to say that there is nothing in reality that makes 'hungry' true of Peter in the way 'anorexic' is not true of him.

[Bill Vallicella]

Clark writes, >>My understanding though is that the moderate realists in the medieval period located universals in the mind but simultaneously in things themselves. So the scholastics accept that only particular things exist but simultaneously there is a nature to the things not reducible to the individual things. I confess I just don't see how that differs from Armstrong.<<

You are basically right about the medievals. Humanity, e.g., has two modes of existence, esse intentionale and esse reale, being in the mind and being in reality. So humanity exists universally in the mind, but as particularized in Socrates. In itself, however, humanity is neutral as between these two modes. See my latest post.

Armstrong says nothing like this. He maintains that there are universals in things, but they cannot exist unexemplified. Maybe what's confusing you is that the scholastics and Armstrong both reject unexemplified or 'Platonic' universals. Armstrong never says that only particular things exist in reality. Quite the contrary.

[William]

>> you shouldn't foist upon realists the view that a sentence is a concatenation of two names corresponding to a conccatenation of two objects.
I'd like to see a convincing explanation of how they avoid it. Suppose we can split the predicate into a noun plus something else. There always has to be 'something else' because the sentence is more than a list of nouns.
Now, turning to reality. Suppose the nominalist agrees that there are real objects corresponding to the list of nouns. Peter and hunger, say. Now the realist claims 'it is absurd to say that there is nothing in reality that makes 'hungry' true of Peter'. That seems to commit the realist that as well as the list of things corresponding to the nouns, there must be something else in reality corresponding to the linguist 'something else'. For a mere set of things corresponding to the list of nouns would not serve as a truthmaker. The something else would have to be something in reality corresponding to, for example, the 'is true of' in " 'hungry' is true of Peter".
But this intuitively leads to the 'concept horse' paradox. (I say 'intuitively' - I think I could construct a more formal argument around this, but will wait to see what you think).

[Account Deleted]

William,

My argument that predicates exist because universals do was intended to counter your claim that the realist simply posits universals because predicates exist. Here is a question: Do you think that individuals exist because there are singular terms in our language? Or do you have an independent argument for the existence of individuals?

Second, I argued that you cannot maintain the equivalence between 'A is red', 'B is red', and 'C is red' with 'A, B, C, are red' unless you admit word types.

Third, you said that

"So, when asked about what all Londoners have in common, an Ockhamist may be perfectly happy to admit the existence of the entity 'London' (other Ockhamists may not). However, London is not enough. The relation of 'living in London' is also required. And if asked to admit to an entity corresponding to 'living in London' to which all Londoners are related (and a possible further entity of relation to that entity, ad infinitum), any respectable Ockhamist would just say no."

Here you admit that merely listing the individuals that share something in common is not enough; you also need to list the relation? I ask you: Why? And not enough for what purpose?

If merely listing the individuals is not enough because doing so leaves out some essential aspect that is part of the facts in the world that account for the similarity, then what is this aspect that is left out? And how would this aspect that is left out by merely listing the individuals be resurrected by mentioning that there is also the predicate yet in the same breath denying that the predicate expresses anything that is part of the world?

I do not see how you answered my objection that you are committed to word, sentence types and to the objection of my last paragraph.

[William Woking]

Peter,

I think the word-type argument is a separate issue. The point of my arguments here is that whether universals exist or not is not relevant to the 'truthmaking' argument.

The truthmaking argument (as I understand it) is that there must be something in reality that brings together Peter and the referent of 'is hungry', in order to cause 'Peter is hungry' to be true.

>>Here you admit that merely listing the individuals that share something in common is not enough; you also need to list the relation?

Here is my argument again, which is closely related to Bradley's paradox. We have William, and London. The mere fact of London existing, and William existing, is not enough to make 'William lives in London' true. We need the relation '.. living in __'.

Now if we were to suppose that '.. living in __' were itself an object, the referent of a singular term, we would have three objects. William, London and the relation. Is that enough to make the statement true? No, because we still have the objects. We need to specify further relations between William and '.. living in __', and between London and '.. living in __'. Thus we have five objects. Is that enough? No, because we need still further relations to connect all these objects together, and we get Bradley's regress.

Thus no collection of objects alone can make any proposition true. But the Realist requires this, because the Realist believes a truthmaker is a thing of some kind. Or I suspect so.