Michael Loux & Philip Goff Discuss Nominalism About Universals

 

[Although the quotations in this piece have page numbers, I can't remember the books or papers from which they were taken. Some readers may know.]

Nominalist Primitivism

The realist as regards universals believes that many particulars exemplify a particular universal and that this is a ‘primitive’ or ‘basic’ fact about the world. The nominalist, on the other hand, thinks more or less the same about the fact that “different objects agree in attribute by all being triangular” (1).

The question now is: What do they mean by ‘primitive’ or ‘basic’?

Is anything in the world that is truly primitive? What is the ‘exemplification’ of universals in things? What do the nominalists mean by ‘agree’ in ‘different objects agree in attribute’? Perhaps Michael Loux will explain:

“… we are to take agreement in attribute to be a fundamental or unanalysable feature of the world… There are no prior facts that serve to explain these facts; they constitute the primitive materials out of which we construct our story of the world.”

Of course the notion of fundamentality or unanalysability has been used many times before in the history of philosophy. For G.E. Moore, for example, the property goodness was deemed to be unanalysable. For Wittgenstein (in the Tractatus), simple objects were seen in the same way. In addition, truth is seen this way by many philosophers.

There must be a reason (or reasons) why we “take agreement in attribute” between different particulars. Surely we can't get away with simply saying that this agreement is ‘fundamental’ or ‘unanalysable’ – why should anyone else accept these predicates at all? Aren’t they cop-outs or neat sidesteps of the issue? Just to argue that “every ontological account must take some facts as primitive or basic” (or that physics does the same) is simply not enough of a reason or answer. We need to ask why and how they are primitive or unanalysable. There may, for example, be an argument that such things halt some kind of infinite regress. However, we still need to know why we have chosen the agreement in attributes between objects - or the exemplification of universals as properties - as such primitives.

Just as the nominalist takes the Platonic position "one step earlier" by taking “the original fact that certain things are triangular as basic” rather than relying on the basic fact of the exemplification of universals in particulars, why can’t we also take the nominalist position one step earlier by giving a more substantive and descriptive account of agreement, resemblance or whatever?

Nominalist Reformulations

The problem is linguistic, according to the nominalist. That is, we believe in the existence of universals because sentences like

“Sphericity is a shape.”

have a property (or attribute) as the subject-term (or noun-phrase) of a subject-predicate sentence. And because the name ‘Tony Blair’ in

“Tony Blair is a liar.”

refers to the person Tony Blair, we assume that the ‘sphericity’ in “Sphericity is a shape” must refer to a universal – or at least to something.

Some philosophers (including Michael Loux) believe that nominalists “deny the existence of properties” (1). If that's indeed the case, then the nominalist

“is obliged to offer analyses of all sentences which contain words apparently referring to properties in terms of sentences which contain no such words” (1).

For a start, do nominalists really deny the existence of properties or do they simply think that they're not the instantiations of universals and are thus only found in objects?

In any case, how will a simple reformulation of a sentence alone get rid of universals or properties? If I choose never to refer to God (or use the word ‘God’), that won't take God out of existence. If no one used the word ‘God’, and if everyone reformulated all the sentences which refer to God in a bona fide atheistic manner, that alone wouldn’t get rid of God (as it were).

Loux goes on to explain the nominalist position thus:

“… the sentences appear to express claims about universals, but are really just disguised ways of making claims about familiar concrete particulars… For every sentence incorporating an abstract singular term, it is possible to identify a sentence in which the term does not appear but the corresponding general term does, such that the latter sentence gives the meaning of the former.” (1, Loux, 2002: 65-66)

Of course to the layperson the sentence “Sphericity is a shape” doesn't “appear to express [a] claim about [a] universal”. It simply makes a claim about spherical objects (or, less likely, about the property being spherical). However, if ‘sphericity’ is a noun (or an abstract singular term), then this may not be logically or philosophically acceptable.

In any case, perhaps the layperson is tacitly or implicitly referring to the universal. In that case, both the realist and the nominalist are offering us (or discovering) the true logical form of the aforementioned sentence. The nominalist is arguing that the sentence is a disguised way of making a claim about a universal. The realist is saying that the logical form is apparent; though not (as it were) taken literally when it's not taken as a claim about a universal.

More technically, Loux makes a distinction between the nominalistically-unacceptable abstract singular term (‘sphericity’) and the nominalist general term which will be its substitution. What would that general-term substitution of the abstract singular term ‘sphericity’ be?

What is the substitution of

1) “Sphericity is a shape.”

that's given by the nominalist? This:

2) “All spherical things are shaped things.”

Prima facie, it's very hard to accept the latter as an analysis (or anything else) of the former! There are many differences between the two.

For a start, 2) is about spherical things. 1) isn't about things at all. In fact 1) is about a shape, not about a thing or things. 1) attributes or predicates something to the property sphericity; whereas 2) predicates something to things. We can even say that 2) is analytic (or partly analytic) in that the subjects (‘spherical things’) are by definition ‘shaped things’. 1), on the other hand, seems to offer us information about sphericity itself – that it ‘is a shape’. However, we can say that this is partly analytic too; though not in the direct manner of 2).

The bizarre thing is that 2) still contains what can be taken as references to universals anyway. Spherical things and shaped things are themselves universals, aren’t they?

Philip Goff writes that

“analysing all sentences which make reference to properties into sentences which do not make reference to properties is a tricky business”.

Isn’t it the case that in

“All spherical things are shaped things.”

the predicates ‘spherical’ and ‘shaped’ do indeed “make reference to properties”? It's just the case that ‘spherical’ and ‘shaped’ are adjectival terms; whereas ‘sphericity’ is an abstract singular term or a noun. Does that difference alone make the above fully nominalist or even nominalist at all? Surely adjectives like ‘spherical’ and ‘shaped’ are just as parasitical on universals as the abstract singular term ‘sphericity’ is!

I would say that

“All spherical things are shaped things.”

proves Goff’s point that there

“are true sentences containing reference to properties which are not analysable into sentences which do not contain reference to properties” (2).

Yes, the above ‘analysis’ is proof of this. Goff calls this the principle of semantic irreducibility (PSI). The “reference to properties” is unavoidable in the nominalist analysis. Thus it's semantically irreducible.

Despite the problem for such nominalist reductions, Loux argues that such reductions or analyses are “essential for avoiding a commitment to properties” (2). That is, not properties per se; but property-terms which are abstract singular terms which themselves can’t help but refer to universals. Thus we can ask if Loux is against both ‘sphericity’ and ‘spherical’ (or ‘shaped’) or only against the nominalist use of ‘sphericity’. It must be both because in

“All spherical things are shaped things.”

the nominalist does get rid of the predicate ‘sphericity’. The question is, is it an acceptable analysis (or reduction) and is it the case that the predicates ‘spherical’ and ‘shape’ don’t refer to properties and therefore to universals? According to Goff, then, Loux is committed to the principle of the necessity of reduction (PNR). Or, rather, Loux thinks that the nominalist must, or should, be committed to this principle and thus be able to formulate an acceptable reduction of all the questionable sentences which include references to universals. If the nominalist can't carry out such a reduction, according to Loux, “then properties exist” (2).

Isn’t all this very linguistic in nature? That is, even if the nominalist can’t successfully offer us reductions or analyses of the suspect sentences which include references to universals, does that automatically mean that universals must therefore exist? Similarly, if the nominalist can (or could) carry out such reductions, would that automatically mean that universals don't exist? Surely what we can and can't do with our sentences (or with our grammar) doesn't affect the existence or non-existence of universals. People use the predicates ‘God’, ‘Pegasus’ and even ‘the round square’, Quine uses the word ‘meaning’ and Paul Churchland uses the word ‘belief’. These people don't believe that these things exist. So why should the sentence “Sphericity is a shape” bring the universal sphericity into existence (as it were)? Likewise why should the sentence

“All spherical things are shaped things.”

stop universals from existing or even prove their non-existence (even if the above is an acceptable analysis or reduction)? Perhaps, then, such concerns are normative and grammatical in nature. That is, if you think that universals don't exist, then say

“All spherical things are shaped things.”

and that will be fine. On the other hand, if you think that universals do exist, then say

“Sphericity is a shape.”

and that too will be fine. Your particular formulation will show other people your ontological commitments. It will neither prove nor disprove the existence of universals, just as Bertrand Russell's

“There is at least one thing, such that this none thing is king of France.”

didn't prove (or even show) that the king of France did not in fact exist. It showed us, instead, that the formulator himself doesn't believe that the king of France exists. (Perhaps the formulation alone doesn't show us that the king of France doesn't exist.) And neither does

“All spherical things are shaped things.”

show us that the universal sphericity doesn't exist, just as

“Sphericity is a shape.”

doesn't show us that the universal sphericity does exist.

Basic Elements of Ted Sider's Metaphysics

 

The following is a commentary of various sections of the book Riddles of Existence: A Guided Tour of Metaphysics (2007), by Ted Sider and Earl Conee

i) Possibilities as Ghosts

ii) Natural Laws and Universals

iii) Absolute Necessity & Natural Necessity

iv) Why We Need Possible Worlds

v) Possible Clintons & De Re/De Dicto Necessity

vi) On Conventionalism

vii) Ted Sider the Platonic Essentialist

viii) Why is an Apple an Apple?

ix) On David Armstrong’s Sparse Theory of Universals

x) Universals as Sets

xi) Nominalist Reformulations

xii)The Conceptualist View of Universals

Possibilities as Ghosts

Ted Sider offers us an interesting argument against the existence (or being or non-obtaining) of possibilities in certain ontologies.

Certain philosophers believe that possibilities (such as unicorns or Tony Blair’s being a serial killer) have some kind of being even though they aren't actual. Are these possibilities ‘ghostly things’? Not really. Because, in a sense, ghosts exist. They just have a ghostly existence of, say, intangibility. Or, as Sider puts it:

“Rather than making it the case that unicorns are possible, the existence of a ghostly unicorn would just mean that ghostly things are actual.”

Is Sider saying that a belief in the being of possibilities is also a commitment to their actuality – even if that actuality is a little ghostlike? Or is he saying that we shouldn’t see possibilities as ghostlike entities at all?

How should we see possibilities? In Sider’s words, “if possibilities are not ghostly entities, then what are they?” (183). If possibilities, such as Blair being a serial killer, are not ghostlike or anything else, what are we talking about when we talk about them? What is Tony Blair the serial killer or, for that matter, Pegasus or even the round square?

Natural Laws and Universals

We can make sense of natural laws and their necessary nature by bringing in universals.

Ted Sider says that according to the universals theory “laws of nature are from connections between universals” (188). Is there literally a connection-universal between universals as they are instantiated in individual particulars – whether objects or events?

We will find, in addition, that the universals theory of the laws of nature is essentially coached in terms of causality or the causal forces of natural chemicals. Sider gives us an example of a chemical law:

Methane and oxygen must react to produce carbon dioxide and water.

This means that methane, oxygen, carbon dioxide and water are treated as (or are) universals. More specifically,

“these universals are related to one another in such a way that any instances of the first two [methane and oxygen] react to produce instances of the second two [carbon dioxide and water]. In short: the universals methane and oxygen necessitate the universals carbon dioxide and water”. (188)

It's clear that universals, on this account, are like (or simply are) natural kinds. Or, again, perhaps natural kinds are universals. More relevantly, it's said that certain universals, when found together, will necessitate other universals. Thus we have a necessary causal relation between universals as these universals are found in natural kinds.

All the above are examples of necessitation. However, they don't explain what necessitation actually is. This is like Quine's case of explaining analyticity by giving examples of analytic statements.

Sider asks:

“What does it mean to say that methane and oxygen ‘necessitate’ carbon dioxide and water?”

We can now ask:

How do they necessitate? Why do they necessitate?

Absolute Necessity & Natural Necessity

There's a difference between natural necessity and what Ted Sider calls absolute necessity. Clearly, absolute necessity is stronger, as it were, than natural necessity.

Interestingly, we can say that “even violations of the laws of nature are absolutely possible, for example” (191). Here again we have a definition of necessity in terms of possibility. More accurately, we can say that natural necessity isn't absolute necessity because it's absolutely possible that natural necessity can be violated. In other words, our natural laws could have been different. And if they were different, perhaps a “dropped stone hovering in mid-air” is an absolute possibility. However, a married bachelor or “a person who is taller than himself” is an absolute impossibility.

Sider then defines absolute necessity, again, in terms of possibility:

“The only things that are absolutely necessary are things whose falsity is not absolutely possible. It is absolutely necessary that all bachelors are unmarried, and that it is raining if it is raining.” (191)

(Wittgenstein’s tautologies.) It's not possible for necessary things to be otherwise or to be false. It's absolutely impossible for absolutely necessary things to be otherwise or to be false. If you deny an absolute necessity you get something that is logically contradictory; such as a married bachelor or a male who is also female or someone who is both 5ft 9 and 6ft 2.

Interestingly enough, Sider seems to accept and take for granted a de re or essentialist account of necessity. In other words, that bachelors are unmarried has nothing to do with the analyticity of the statement ‘All bachelors are unmarried’; or the fact that ‘bachelor’ and ‘unmarried man’ are synonymous terms. Instead a bachelor not being married man is necessarily a fact about the world and not a fact about our language. Its truth is de re, not de dicto. Surely if we say that “If it is raining it is raining” that isn't a de dicto or analytic necessary truth. It's a fact about the world. However, we would say that if someone says

“If it is raining, it is not raining.”

we would simply say that he or she is misusing language; though not necessarily misunderstanding the true nature of the world. However, perhaps both misunderstandings can't be disconnected. We use language because of the way the world is. And we can also say that the way we understand the world (at least to some degree) is a product of our language. These two realities of understanding the world can't be disunited.

Why We Need Possible Worlds

Ted Sider talked earlier about possibilities being ‘ghostly entities’. It's because philosophers thought of possibilities (as well as necessities) this way that David Lewis took away the ghostly aspect of possibilities and made them real (or gave them being) at possible worlds. According to these possible worlds, our possibilities are sometimes their actualities:

The best thing about Lewis’s theory is that it thoroughly demystifies absolute necessity and possibility. Lewis has no use for ghostly possibilities. He firstly confines flying pigs and other possibilities to their own possible worlds; so that they don't infest ours. Then he removes their ghostly status by claiming that they are just as real as the objects in our world.

We certainly had a problem with defining and explaining possibility and necessity without possible worlds. Where are they? Now, in a sense, we can tell people where they are. Necessities and possibilities are at possible worlds. Necessities are the case (or true) at all possible worlds (or at least at the worlds to which they apply). And possibilities are the case (or are true) at at least one world. Thus necessities and possibilities are in some cases concrete and in others abstract. Thus it's acceptable according to quantificational logic, of which it can be seen as its extension. Perhaps we can now also see modal logic as fully extensionalist – at least in certain cases. What this means is that flying pigs and other possibilities are real according to the worlds which contain them. To our world, they are mere possibilities. According to the possible worlds in which they exist, they are actualities.

To reiterate. According to Sider's David Lewis,

“we do have a reason to believe in his possible worlds: only by believing in them can we demystify necessity and possibility” (193).

In that case, Lewis might have argued that Hume and other empiricists were right to have rejected necessities (and possibilities) – after all, they didn't believe in (or know about) possible worlds. Without possible worlds, necessity and possibility wouldn't have made any sense.

Despite all that, Sider still has his own qualms about possible worlds. However, if they are seen as theoretical constructs or posits (as it were), then we can see where Lewis is coming from. That is, “it is sometimes reasonable to postulate things for theoretical reasons” (193). For example, “no one has ever directly perceived an electron”; though physicists “postulate electrons to explain the results of the experiments they perform” (194). Of course, to Lewis himself possible worlds aren't theoretical constructs – they are real. To Lewis, in order to work and explain things, possible worlds must have real existence; not just theoretical or even pragmatic existence.

Possible Clintons & De Re/De Dicto Necessity

The concept [essence] is then directly broached by Ted Sider by thinking in terms of possible Bill Clintons or of Bill Clinton’s counterparts.

We can change the nature of Clinton a lot. However, there are certain things which we can't do to him (as it were). That is, we can't take away what is essential to him. Sider writes:

“He might have had electric blue hair. But now: could he have been a flower?” (194)

Why couldn’t Clinton have been a flower? I suppose it depends on what or who Clinton actually is. What, or who, is Clinton? He’s a politician. Surely Clinton would still be Clinton if he weren't a politician. In fact, at this moment in time, for all I know, he may not be a politician anymore. That wouldn’t mean that he has cased to exist as a man or, indeed, as Bill Clinton. Ah! As a man. Could Clinton be Clinton if he weren't a man? Possibly. Cut off his bollocks and drain out his testosterone and see what we get. Perhaps it’s what’s in his head that matters.

Must he be a human being in order to be Clinton? Could a flower or a stone be Clinton (or vice versa)? Clearly not. What about an elephant? Again, it depends on what or who Clinton is. Either that, or it depends on how we define Clinton (or that which Clintonizes). Sider, however, settles for Clinton’s being a human being:

“In short, Clinton could not have been anything other than a human being. That is, it is an absolutely necessary truth that Bill Clinton is a human being.” (195)

Why couldn’t Clinton “have been anything other than a human being” (195)? Why is it “an absolutely necessary truth that Bill Clinton is a human being”?Sider gets his point across by rejecting the analytic or de dicto account of necessity. For example,

“All bachelors are unmarried.”

is necessarily true because it is analytically true. This isn't the case with

“Bill Clinton is necessarily (or essentially) a human being.”

The above isn't analytically true. As Sider explains:

“… the sentence ‘Bill Clinton is a human being’ does not seem to be true by definition, for unlike the word ‘bachelor’, which carried a definition (unmarried male), the name ‘Bill Clinton’ has no definition. It just stands for Bill Clinton. We all know that Bill Clinton is a human being, but this isn’t built into the meaning of the name ‘Bill Clinton’ by definition.” (195)

So if

“Bill Clinton is a human being.”

is necessarily true, it's not true analytically. It's not true by definition. The definition ‘human being’ is not built into the proper name ‘Bill Clinton’. Indeed the name ‘Bill Clinton’, according to Sider, doesn't have any definition (or sense!). So either it's necessary that Clinton is a human being (non-analytically necessary); or it's not necessary that Clinton is a human being. It seems, intuitively, to be necessary in some way.

The questions is, then: What kind of necessity would this be?

It must be something about Clinton himself that makes it necessary that he is a human being. That is, it is part of his essence that he's a human being. He has the essential property: being a human being.

We can also conclude (or infer) from this that if the name ‘Bill Clinton’ has no definition (or sense), and thus can't be a part of a necessarily true analytic statement, then the name ‘Bill Clinton’ must refer, instead, to Clinton’s essence. It must directly refer to his essence; not indirectly via definitions, concepts, or Fregean senses. It “just stands for Bill Clinton” the physical and psychological being. It stands for a res, not a dicto.

On Conventionalism

Ted Sider then attacks conventionalism’s own attack on de re (as it were) modalities.

He argues that if we accept conventionalism, at least on this issue, then we “demystify philosophy itself” (196), not just modality:

“If conventionalism is true, philosophy turns into nothing more than an inquiry into the definitions we humans give to words. By mystifying necessity, the conventionalist demystifies philosophy itself. Conventionalists are typically up front about this: they want to reduce the significance of philosophy.” (196)

This is strong stuff! Is conventionalism really that extreme? Is Sider’s account of conventionalism fully correct? At first blast, this does seem like a certain kind of conventionalism – viz., logical positivism!

Do conventionalists say that philosophy is “nothing more than any inquiry into the definitions we humans give to words” (196)? Or do they simply stress the importance of our words when it comes to philosophy? In any case, surely to the conventionalist it's not just a question of word-definition; but one also of our concepts. That is, how do our concepts determine how we see or interpret the nature of the world? If it were all just a question of word-definition, then conventionalists would be nothing more than linguists or even lexicographers.

Perhaps conventionalists don’t give up on the world at all. They simply say that our words and concepts, and indeed our definitions, are important when it comes to our classifications, etc. of the world.

When Sider writes that by “demystifying necessity, the conventionalist demystifies philosophy itself” (196) he implies that philosophy is nothing more than the study of necessity! In that case, it's no wonder that the conventionalist “wants to reduce the significance of philosophy” (196) if that's really the case. This seems to be a thoroughly Platonic (or perhaps also partly Aristotelian) account of philosophy in its obsession with necessity, and according to Sider again (on the previous page), with essence. Is that really all that philosophy is concerned with – essence and necessity? Again, this was true of Plato, and to a lesser degree of Aristotle; but what about 20th century philosophy? Indeed what about Hume and many other pre-20th century philosophers?

Ted Sider the Platonic Essentialist?

I've just mentioned Ted Sider’s Platonic notion of philosophy’s role, and now we can see yet more evidence of this.

What is philosophy? Sider answers this question thus:

1. it ‘investigates the essences of concepts’.
2. It ‘seek[s] the essence of right and wrong’.
3. It ‘seek[s] the essence of beauty’.
4. It seek[s] the essence of knowledge’.
5. It ‘seek[s] the essences of personal identity, free will, time, and so on’. (195)

However, according to conventionalism, “these investigations ultimately concern definitions” (195). Not only that: Sider claims that according to the conventionalist, it “seems to follow that one could settle any philosophical dispute just by consulting a dictionary!” I would like to know if there is such a conventionalist animal who really believes this. As I said earlier, Sider’s account of conventionalism really seems like an account of 1920s and 30s logical positivism. And no philosopher is an old-fashioned logical positivist today.

Again, Sider’s take on conventionalism seems thoroughly old-fashioned in nature. However, his Platonist account of philosophy (or its role) seems even more old-fashioned in nature. In fact it seems antiquated and ancient.

Take his view of aesthetics as just one example.

Sider claims that aestheticians “seek the essence of beauty” (195). Plato, his friend, searched for the essence of beauty; but I doubt that many contemporary aestheticians would do so (except, perhaps, philosophers like Roger Scruton).

Why is an Apple an Apple?

We may say that three red apples have nothing absolutely in common; although they may well be similar. Thus, the nominalist concludes, universals in this and all instances do not exist. These apples, however, must have at least one thing in common. Not only that: the nominalist, surely, must agree that they have one thing in common: they are all apples. Even dissimilar apples would still be dissimilar apples.

Now we can also conclude “that they have in common the property being an apple” (156). However, who says that they are all apples? The nominalist will argue that all they actually share is the name ‘apple’ – nothing more. In addition, if they're all apples, they must be so in virtue of properties other than the property being an apple. The property being an apple is surely not enough to share. They must be apples in virtue of other properties which determine the fact that they are apples.

Perhaps being an apple is a higher-order property under which fall lower-order properties such as being red, having chemical/molecular constitution X, being sweet, etc. In other words, an apple wouldn’t be an apple if it weren’t for these lower-order properties. Being an apple isn't enough. Thus if we accept the property being an apple (indeed perhaps even if the nominalist accepts this property), we must also accept other lower-level properties and thus, perhaps, other universals.

In terms of shared properties between entities of the same kind, Sider gives us the electron as an example.

Again, what do all electrons share in virtue of which they are all electrons and thus all instantiate the universal electron or the property being an electron? According to Sider:

“Physics tells us that all electrons have exactly the same charge. So according to physics the electrons have this property in common.” (156)

There is more to it than that. Because “all electrons have exactly the same charge” (156), physics concludes that it “plays a basic role in extremely well confirmed physical explanations of much of what happens in the world” (156).

So universals seem to come to the aid of elementary physics. More than that: physics actually studies universals.

And if an electron (or being an electron) is a universal, perhaps the electric charge of each electron is also a universal – after all, electrons must be more than their electric charge. In that case, perhaps many universals constitute an electron! Alternatively, the electrical charge of an electron may be its only essential property. Thus even if electrons have other properties, these properties will only be contingent in nature. If the electric charge of an electron is its only essential property, then we can say:

electron = electric charge X

That is, an electron just is [an] electric charge (or charge X).

David Armstrong’s Sparse Theory of Universals

It can easily be seen that universals seem to proliferate indefinitely in number. Especially if it's the case that there is a “different universal every time there is some apparent difference in the way of things” (169). So, according to David Armstrong, we need to cut down the inhabitants in the world of universals. How does he do this? –

“There are no negative universals, such as not being an apple and non-self-instantiation… David Armstrong, a leading contemporary proponent of the sparse universals idea, holds that only properties used in scientific explanations are genuine universals.” (169)

For a start, if there were negative universals, we would have one for every (positive) universal. For example, not red(ness), not happy, not being a book, etc. Clearly, predicates for some of these negative properties already exist.

That may mean that their universals already exist. Thus

not happy = sad

not tall = small

not heavy = light

This isn't the case for the negative properties not red or not being an apple. Clearly there's no word for not being an apple, etc.

If negations can have universals, what about the negation of a negation, such as not not being an apple or not not being a book? However, perhaps we can say that

not not being a book = being a book

not not being an apple = being an apple

Are double negations identical to positives in the world of universals? Is

not not being an apple = being an apple

the same as

true = not false?

Now for another aspect of Armstrong’s sparse universals theory. He argues “that only properties used in scientific explanations are genuine universals” (169). So what about these questions? -

1) What if science hasn't discovered certain properties yet?

2) What if science has discovered a property which is a genuine universal; though which it doesn’t accept as a genuine scientific property?

3) What if certain non-scientific properties are genuine universals even if science doesn't accept them as genuine?

For example, the properties/universals beauty, wisdom, sexiness and even truth are certainly not scientific predicates or properties. More to the point, hardly any, if any at all, of Plato’s much-loved and discussed universals would be seen as genuine scientific properties today. Yet it was Plato who discovered (as it were) universals and past them down to Western philosophy as a whole, including to David Armstrong.

Ted Sider goes on to say that the notion of negative universals is problematic as well; not just their existence. Some negative predicates seem thoroughly acceptable. Other simply don't use the negative particle ‘non’ or ‘not’. He writes:

“For instance, the predicate ‘unoccupied space’ sounds very negative. But what about ‘empty space’? That seems to mean the same thing, without being at all clearly negative. And what about ‘pure space’? That seems to mean the same thing again, while sounding positively positive.” (169/70)

I don’t think that these predicates are analogous or the same as not being an apple and the rest. In the former case, we would get

‘space’ – ‘non-space’

or

‘space’ – ‘not being space’

not

‘space’ – ‘unoccupied space’

or Sider’s

‘space’ – ‘empty space’

They don’t seem the same at all (not just because of the omission of the particles ‘not’ and ‘non’); though we can indeed say that ‘unoccupied space’ and ‘empty space’ are negative in a certain sense. They are negative without being negations. That is, ‘empty space’ is not a negation of ‘space’ and neither is ‘unoccupied space’. And ‘pure space’ certainly isn’t a negation of ‘space’.

Sider then makes a point similar to one already made. What if “there is a fully legitimate science that turns out to be mistaken?” (170) In that case we should ask if “predicates in a mistaken scientific theory identify genuine universals” (170).

There are more problems.

We can argue that

“maybe no current scientific predicate identifies a universal, because we may not have any scientific theory that is entirely correct” (170).

The problem for Armstrong is that it is only through science (or physics) that he (or we) can identify the genuine universals. However, science is always in a state of change. So perhaps we shouldn’t accept any universals. Not because universals don’t exist; but because we don’t know which are the genuine universals – at least not yet.

Universals as Sets

Some philosophers claim that universals are simply sets. That is, “each universal is identical to a set of things” (172). More precisely, the universal being red “is the set of things that are red” (172).

Firstly, in the case of certain universals, this would mean, effectively, that universals are concrete or even extensional in nature. That is, if the universal horse is the set of horses, and horses are concrete, then the universal horse is itself concrete because it's nothing more than the members which make up the set of horses. This wouldn't work for abstract entities like numbers or properties like being blue.

For example, the set of numbers, if there is such a set, can't be concrete and therefore the universal number (or numbers) can't be concrete or even extensional.

What about being red?

We've already talked about the set of things that are red. We can say that the things that are red may well be concrete. Is the property itself, red, concrete or is it abstract? Perhaps if the universal being red is the set of red things, and if red things are both concrete and with the abstract property (i.e. red), then the universal being red must be both concrete and abstract if it's determined by the set of red things.

There may be a problem with identifying universals with sets.

If sets are all about membership, then what if a set has no members? It becomes a member of the null set. That is, the set of Devil-dealing Salem witches and the set phlogiston contain no members. Thus both are actually members of the null set; despite the different predicates ‘phlogiston’ and ‘Devil-dealing Salem witches’.

If we believe that universals aren't identical to sets, we can keep the universals being a Devil-dealing Salem witch and being phlogiston and maintain their differences even though there are no Salem witches and there is no such thing as phlogiston. In the case of sets, however, they were both null sets (or members of the null set) and thus were indistinguishable.

Surely they are distinguishable? As Sider asks: “how could there be just one universal here?” (173). Even if there were no witches of Salem, surely we can say that witches are very different from phlogiston! And yet according to set theory, they both constitute the very same class – the null class.

Nominalist Reformulations

When we say

“Blue is a colour.”

we appear to be referring to a thing or a property as it is in itself. It's the subject-term of the sentence. ‘Blue’ is a noun – if an abstract noun or an abstract singular term. Or, as the universalist would put it: the sentence “seems to be about the universal being blue” (175). Nominalists don’t like this sentence precisely because it implies, or even entails, the existence of the universal being blue. What do they prefer? This:

“Each blue thing is a coloured thing.”

Here the subject-term is not ‘blue’ but ‘blue thing’ (or ‘blue things’). So the colour blue isn't as it were separated from all blue things or itself the subject of the sentence. Instead we're talking about things (say, cats or cups) that just happen to be blue. Thus in terms of grammar, ‘blue’ is now an adjective; not a noun.

How does this solve the problem of the reference to a universal? After all, the words ‘blue’ and ‘coloured’ are still used, even if only as adjectives. How does giving a word adjectival status stop it from referring to a universal? Don’t adjectives like ‘blue’ and ‘coloured’ also refer to universals? Indeed aren’t the properties being blue and being coloured both instantiations of the universal blue and the universal colour or coloured?

No universalist ever said that universals can’t belong to other objects which are themselves universals. The blue of a cat isn’t any less of a universal because it's a property of a cat. Indeed property-universals must belong to things – they are the properties of other things.

So, again, how does the reformulation get rid of reference to universals?

Sider spots a similar problem with another nominalist reformulation. Take this:

“Sloth is a vice.”

Clearly the subject-term could refer to the universal sloth or to being slothful. Not only that: isn’t the word ‘vice’ also a reference to a universal? So what does the nominalist offer us? This:

“Every slothful thing is a vicious thing.”

How can this be a reformulation if it doesn't refer to a thing or to things at all? Its subject is sloth, not the slothfulness of things. It's telling us that every slothful thing is a vicious thing. There's no reference to things that are slothful at all in the original. Even if it is not taken as a universal, the word ‘sloth’ in the former sentence is a reference to a property; it's not a reference to things which have that property. What if every thing died, would the property or universal sloth (or being slothful) immediately cease to exist? Perhaps only God still exists. Couldn’t He still say, to Himself, that ‘Sloth is a vice’ even though there would be no persons to actually be slothful?

Sider spots his own problem with

“Every slothful thing is a vicious thing.”

He writes that this sentence “is not true”. It's not true because

“[s]omeone who has the relatively minor vice of sloth may be otherwise so virtuous that he or she is in no sense vicious” (176).

In other words, sloth is a vice; though not every slothful thing is a vicious thing. That is, sloth is just sloth; though a slothful thing is more than being merely slothful – he may be otherwise virtuous. Sloth must be a vice. Though even a slothful person is not, as it were, a vice (or a ‘vicious thing’). Another way of putting this is that vice, or even the predicate ‘vice’, can be attributed to – or predicated of – sloth or the predicate ‘sloth’. However, vice, or the predicate ‘vice’, cannot be attributed to – or predicated of – every slothful thing because some slothful things aren't vicious.

Sider does offer another ‘paraphrase’:

“Every slothful thing has at least one vice.”

Isn’t that analytically true or true by definition? If something is slothful, and sloth is a vice, then that slothful thing must have at least one vice – namely, sloth. And that vice is sloth or being slothful! We are back to the property being slothful and therefore the universal sloth!

The Conceptualist View of Universals

Ted Sider now considers conceptualism as an alternative to nominalism about universals. He says that a concept “is a means by which we can think of things” (177). This sounds like a Fregean take on concepts. On this account, concepts are the 'senses' of words and of truth-valued sentences. The sense determines the reference. It is the way in ‘which we can think’ of the reference. It is a ‘mode of presentation’ of a thing or a reference. Thus a Fregean concept helps us to get at (as it were) a thing (or a reference of a name or word).

Thus, on this Fregean account, the word ‘boat’ does not refer to a boat or to boats generally. According to Sider, “the word 'boat' [stands] for this concept” (177). Instead of

‘boat’ → a boat (or all boats)

we have

‘boat’ → [boat]

More specifically, if we allow the word ‘boat’ to stand for the concept [boat], rather than a boat or all boats generally, Sider says that “we give the general application to boats that the concept has built into it” (177). In other words, the word ‘boat’ becomes general because it stands for the concept [boat].

However, what exactly has [boat] built into it in order for the word ‘boat’ to have a general application to boats? How does this work? Perhaps it's a basic or brute phenomenon; or it may require a theory of reference for general terms like ‘boat’ or for concepts such as the concept [boat]. Again, why does the concept [boat] - or any other concept - have “the desired generality” of which Sider speaks?

What the conceptualist means is that what all boats share is the simple fact that the concept [boat] has a ‘general application’. This means that the conceptualist can “deny that any one entity is shared by all of the boats” (177). This seems like a simple reworking of nominalism. Instead of saying that the word ‘boat’ has a general application (as the nominalist does), the conceptualist simply says that the concept [boat] has a general application. What’s the real difference between nominalism and conceptualism besides the substitution of concepts for words? They both believe that there's no single entity shared by all boats themselves. They only share (if that’s a suitable word) either the word ‘boat’ or the concept [boat]. Isn’t conceptualism a kind of nominalism (or vice versa)? Indeed, what is the point of the word ‘boat’ or the concept [boat] having a general application if what they refer to (that is, all boats) don't share any properties? What purpose does such a general applicability serve?

This is like the predicate ‘blurg’ referred to later by Sider. That is, the only thing at the end of each act of ostension shares with other things ostended with the word ‘blurg’ is that they have been given the same name – namely, ‘blurg’. That’s it. Literally the only thing they share is the name ‘blurg’ and the fact they've all been pointed at and then named ‘blurg’. Is that the case with boats as well? Do all boats only share the word or name ‘boat’ or the fact that they all fall under the concept [boat] and that’s it? If that's the case, why are they called ‘boat’? Why do they all fall under the concept [boat]? There must be more to this than the name ‘boat’ or the concept [boat] (as well as the pointings and stipulations required in the first place).

Necessity & Possibility are Interdefinable

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A.N. Prior’s formal account of necessity and possibility within a propositional and modal context. Key: ◇ = possibly, □ = necessarily, ∨ = or, ∧ = and, P = proposition, ≡ = if and only if.

Within modal logic, necessity and possibility are interdefinable. In other words, we can define (or explain) necessity in terms of possibility, and we can define (or explain) possibility in terms of necessity.

To say that something is possible isn’t to say that it’s likely or unlikely, or that it probably will happen some time in the future. In this context at least, what is important about any given x being possible is that its (as it were) non-happeningness isn’t necessary.

So there’s nothing necessary about there being no unicorns or seven-foot-high cats.

Again, there are no unicorns. However, it’s not necessary that there are no unicorns. And there probably couldn’t be seven-foot-high cats. However, it isn’t necessary that there aren’t any, or that there won’t be any in the future.

We can kind of invert this possibility-necessity relation by making it a necessity-possibility relation. So instead of defining possibility in terms of necessity, we can now define necessity in terms of possibility.

Something is necessary if it has to be the case, or if it must happen. In terms of possibility, we can say, “that its failure to happen is not possible”. So if we drop a stone here on Earth, it must fall to the ground (i.e., if there is nothing material stopping it). It’s not possible that it would, or could, just float in the air.

This is natural necessity, and we can oppose it to logical necessity. It’s not logically necessary that a stone must drop to the ground.

Semantic Necessity?

Can we say that it is necessary that all bachelors are unmarried? After all, married bachelors aren’t possible.

However, is this simple semantics?

The word ‘bachelor’ is a synonym for ‘unmarried man’. Thus, if we say that

“John the bachelor is married.”

we’re also saying that

“John the unmarried man is married.”

Thus, with the (as Quine put it) “substitution of synonym for synonym”, we arrive at a straightforward assertion of a logical contradiction. In other words, we’re saying that John can be both unmarried and married at one and the same time. Thus, John’s unmarried status is necessary precisely because he’s a bachelor. Therefore, his being a married bachelor isn’t possible.

To repeat. The necessity of the statement

“John the bachelor is unmarried.”

being true is partly a result of the impossibility of the statement

“John the bachelor is married.”

being true.

[See note.]

From all the above, we (to use another modal term) couldn’t have necessity without possibility (or something’s impossibility). Similarly, we couldn’t have possibility with necessity (or something’s being necessary).

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Note:

The American philosopher W.V.O. Quine (1908–2000) critically examined this account of what can be called conceptual (or linguistic) necessity. However, it was worth noting the basics first. [See Quine’s ‘Two Dogmas of Empiricism’.]

There are No Proofs in Science

There are no proofs in science - at least not strictly speaking. There are in mathematics and logic.

In basic terms, why is that?

This is how John Horgan puts it:

“The only propositions that can be verified – that is, proved true – are those dealing in pure logic or mathematics.”

Horgan continues:

“Such systems are closed, in that all their components are based on axioms that are true by definition.” (202)

In other words, such propositions can be proved because they belong to systems which make it the case that they can be proved. Or, more formally, they can be proved because they are "based on axioms that are true by definition”. That basically means that the propositions or theorems are provable – and sometimes easily so – precisely because they're derived from axioms which are true by definition and which, in turn, belong to systems entirely created by such axioms and the following theorems; as well as by the deductive rules from which the theorems are generated. That means, in essence, that proof is possible because the axioms - which generate the theorems - were designed to be true by definition. That truth-by-definition is passed on (as it were) from the axioms to the theorems/propositions.

In a simple sense, all this makes proof easy. Or at least in makes proof dependent only on systems and their contents – nothing more.

Truths about 'external reality', on the other hand, depend on a whole lot more and that's why they can never be proven. And that's as true of scientific statements as it is of the statements of religion or politics.

However, it's proof that's being spoken of here, not truth itself. Thus some of those scientific statements can be taken to be true – just not provably true. (Indeed since Godel we have known that some 'Godel sentences' within maths and logic are true; though not provably true.)

Thus truth and proof are intimately connected in logic and maths. Though that's not the case with science; if only when taken separately from its mathematical underpinnings.

As for that 'external reality'. Horgan continues by saying that “[n]atural systems are always open”. Moreover,

“our knowledge of them is always incomplete, approximate, at best, and we can never be sure we are not overlooking some relevant factors” (202).

In other words, natural systems aren't based on axioms which are true by definition. They aren't human creations. Having said that, numbers and logical relations can be deemed to be platonic/abstract in nature; though the systems themselves are still human creations. It is the abstractions and entities they capture that are – if they are – platonic or mind-independent.

A Reductionist Analysis of Reductionism?

It can be seen that reductionism isn't only a scientific and philosophical obsession - it's actually a human obsession.

People naturally reduce things. They also seek out essences even if there are no essences to seek. Indeed the use of stereotypes and generalisations - in all walks of life - is often a result of this way of thinking. And the thing is - it's not always wrong or suspect. Sometimes there are generalisations which contain a lot of truth - if not the whole true. Stereotypes capture elements of truth. And almost everything can be reduced down to more basic elements; whether material things or problems.

Perhaps physicists and philosophers are indeed the worst offenders. As John Horgan puts it:

“They want to show that the complicated things of the world are really just manifestations of one thing. An essence. A force. A loop of energy wriggling in a 10-dimensional hyperspace.”

Then, ironically, Horgan says that the arch-reductionist - a sociobiologist - may himself argue that

“a genetic influence lurks behind this reductionist impulse, since it has motivated thinkers since the dawn of civilisation. God, after all, was conceived by the same impulse”.

Here a (possible) sociobiologist is giving a reductionist account of the reductionist impulse itself. In other words, just as a sociobiologist may boil many - or even all - (biological) things down to genes; so he may also boil the reductionist impulse (or even instinct) itself down to genes. Thus sociobiological reductionism is applied to sociobiological reductionism - as indeed it must be (if you think about it).

So it's ironic that reductionism - which is the enemy of so many religious people and many philosophers - should itself be seen (by some) as a result of a religious impulse.

As I said about generalisations and stereotypes, many reductions may be largely correct. Still, they could/can never be the whole story - though even this could be deemed a generalisation! It depends, first of all, on what's being reduced. It also depends on what, exactly, is being said about what's being reduced and what it's being reduced to. In the end, the sociobiological claim may not be as monumental and all-encompassing as one first imagines. It's often people's gut reactions to some kinds of reductionism that overstretches things rather than the reductionist himself.

In the end, most people are happy with some – or even many - reductions. This is primarily the case because many reductions don't seem to have any direct impact on human beings as such; either philosophically, morally/religiously or politically.

Earlier John Horgan mentioned that God was “conceived by the same impulse” which drives reductionism. Later he says that “[m]ost of Einstein's contemporaries saw his efforts to unify physics as a product of his dotage and quasi-religious tendencies”. However, perhaps I'm cheating here because that “dotage” was about scientific unification, not scientific reduction. Though unification and reduction often - or always - walk hand in hand.

For example, Horgan cites Einstein's own case in which he “spent his later years trying to find a theory that would unify quantum mechanics with his theory of gravity, general relativity”. This appears to be an endeavor in unification which, at the same time, would have required reductive work. After all, when you get down to the basics (or when you reduce things to quantum mechanics), then that's when you see that things are unified. The unification would come from the reduction of the separate elements. However, it can be said that quantum mechanics is in itself a reduction in that in order to get there (as it were), things/objects would have had to have been reduced to matter and forces; matter, forces and fields to molecules, forces and fields; molecules to atoms; and then atoms to sub-atomic particles.... and what have you. Knowledge of gravity and even general relativity is also the natural result of reductive work in physics and cosmology...

So what about a sociobiologist reducing love down to genes or at least to some other lower (biological) level?....