I have written about nominalism quite a number of times, both here at the blog and in my books (most recently in Did God Create the Universe from Nothing? Countering William Lane Craig’s Kalam Cosmological Argument). For those of you unfamiliar with the topic, let me briefly explain:

Abstract Objects

Abstract objects are incredibly important aspects within the context of philosophy. They include all of the labels and categories of things (tokens). These types are abstract. So, for example, a chair is both the token (actual chair) and the type (an abstract labeling as such). This can include numbers, universal ideas like redness, ideas like courage and justice, and even individual humans, such as Jonathan Pearce.

Because of their very nature, in being abstract, they can cause headaches for physicalism (and naturalism) and causality. Ever since the Greek times, there has been the famous problem known as the Problem of Universals. This deals with the problem in defining what the properties of objects are, ontologically speaking (i.e., what existence they have). Universals are common (universal) properties contained by more than one object. Two cars and a ball being red – what is redness? How can these different objects have an identical property and is that property real or in the mind of the conceiver, or indeed, contained within speech? Are these abstract objects and universals causally potent? Can redness take a position in a causal chain or relationship?

Platonism (realism)

Realists claim that these abstracta are real – that they exist in some tangible way. Plato, from whom the term came, believed that universals, like redness, existed separately from the particular objects (particulars) which contained said property. Platonic realism states that such entities exist independently from the particular, as opposed to Aristotelian realism states that the universals are real but dependent on the particulars.

Some arguments propose that, in order to have truth value in statements, universals must exist, such that “This apple is red” implies that the universal of redness exists for the proposition to be truthful.

One fundamental issue for such theories is: where is the locus of these universals? Where can they be found and what is their ontology?

Nominalism

Nominalism stands in stark contrast to realism in that the adherents state that only particulars exist, and not universals. Properties of particular objects can account for eventual similarity between objects (such as the green of grass and the green of a painted wall). Universals do not exist.

Conceptualism is sometimes called conceptual nominalism, such that universals and abstracts exist, but only in the individual minds of the conceivers (as concepts). (German) Idealism is close to this (think Kant, Hegel and Schelling) in believing universals to be in the minds of rational beings.

Nominalism can become VERY in-depth and confusing (when talking about the different types such as trope theory and resemblance theory). My opinion is that the discussions are crucial to the rest of metaphysics; it is just unfortunate that the discussion can be quite dry and dull. Here is an excerpt from the wiki entry on nominalism:

Nominalism arose in reaction to the problem of universals, specifically accounting for the fact that some things are of the same type. For example, Fluffy and Kitzler are both cats, or, the fact that certain properties are repeatable, such as: the grass, the shirt, and Kermit the Frog are green. One wants to know in virtue of what are Fluffy and Kitzler both cats, and what makes the grass, the shirt, and Kermit green.

The realist answer is that all the green things are green in virtue of the existence of a universal; a single abstract thing that, in this case, is a part of all the green things. With respect to the color of the grass, the shirt and Kermit, one of their parts is identical. In this respect, the three parts are literally one. Greenness is repeatable because there is one thing that manifests itself wherever there are green things.

Nominalism denies the existence of universals. The motivation for this flows from several concerns, the first one being where they might exist. Plato famously held, on one interpretation, that there is a realm of abstract forms or universals apart from the physical world (see theory of the forms). Particular physical objects merely exemplify or instantiate the universal. But this raises the question: Where is this universal realm? One possibility is that it is outside of space and time. A view sympathetic with this possibility holds that, precisely because some form is immanent in several physical objects, it must also transcend each of those physical objects; in this way, the forms are “transcendant” only insofar as they are “immanent” in many physical objects. In other words, immanence implies transcendence; they are not opposed to one another. (Nor, on this view, would there be a separate “world” or “realm” of forms that is distinct from the physical world, thus shirking much of the worry about where to locate a “universal realm”.) However, naturalists assert that nothing is outside of space and time. Some Neoplatonists, such as the pagan philosopher Plotinus and the philosopher Augustine, imply (anticipating conceptualism) that universals are contained within the mind of God. To complicate things, what is the nature of the instantiation or exemplification relation?

Conceptualists hold a position intermediate between nominalism and realism, saying that universals exist only within the mind and have no external or substantial reality.

Moderate realists hold that there is no realm in which universals exist, but rather universals are located in space and time wherever they are manifest. Now, recall that a universal, like greenness, is supposed to be a single thing. Nominalists consider it unusual that there could be a single thing that exists in multiple places simultaneously. The realist maintains that all the instances of greenness are held together by the exemplification relation, but this relation cannot be explained.

Finally, many philosophers prefer simpler ontologies populated with only the bare minimum of types of entities, or as W. V. Quine said “They have a taste for ‘desert landscapes.’” They attempt to express everything that they want to explain without using universals such as “catness” or “chairness.”

As ever, the Stanford Encyclopedia of Philosophy entry on nominalism is great – here.

As is the SEP entry on abstract objects – here.

As is the superb SEP entry on properties found here.

Other useful SEP entries are Challenges to Metaphysical Realism, Platonism in Metaphysics, and the wiki entry on the Third Man Argument (an argument from Plato that shows an incoherent infinite regress in relational universals, which can be found in the SEP here).

How the area is relevant to the philosophy of religion – Craig and the Kalam

I have written in the aforementioned book that largely deals with the idea of nominalism and how it affects the Kalam Cosmological Argument. As I set out in a post a few weeks back, this excerpt starts to set out the importance of nominalism/realisn to the debate:

Firstly, the only thing, it can be argued, that “has begun to exist” is the universe itself (i.e. all the matter and energy that constitute the universe and everything in it). Thus the first premise and the conclusion are synonymous—the argument is entirely circular.

So how do I establish that the only thing which has begun to exist is the universe? We may think that things like tables, chairs, humans, rocks, lemmings and so on exist. Well, they do in one sense (an arrangement of matter/energy), but in the sense of the abstract labels of “rock” or “chair”, they are exactly that, abstract labels. Their existence, in Platonic terms, as some kind of objective entity, requires the philosophical position of (Platonic) realism. Platonic realism, in simple terms, is the position that universals such as redness or doghood and abstractions (kinds, characteristics, relations, properties etc.) are not spatial, temporal or mental but have a different ontology, existing separately from the objects which instantiate such properties.^[ii] The opposite position to this is nominalism, which can mean the denial of the existence of these abstract labels in some sense.

For example, in order for the statement “John Smith is a gardener” to hold a truth value, there must be some existence property defined by “gardener” such as “gardenership”. This universal is different from the instance of the universal property found in John Smith. This is not a position that Craig adheres to. All we have on a nominalist or conceptualist worldview (as opposed to realist) is a transformative coming into existence. What this means is that what makes the chair, the molecules and atoms, already existed in some form or other before the “chair” came to be. So the matter or energy did not “begin to exist”. This merely leaves the label of “chair”.

The nominalist, as stated, adopts a position which denies the existence of universals, such as redness or gardenership, and claims that only individuals or particulars exist. Conceptualism or conceptual nominalism, on the other hand, is a position which claims that universals only exist within the framework of the thinking (conceiving) mind. Most philosophers agree that abstract objects are causally inert, by definition. This means that, at best, the abstract label is unable to have causal power anyway (regardless of its ontology).

To illustrate this, let’s now look at the “label” of “chair” (in a very cogent way, all words are abstractions that refer to something or another, but nominalists will say that these abstractions, or the relationship between them and the reference points, do not exist, out there, in the ether). This is an abstract concept, I posit, that exists, at most, only in the mind of the conceiver. We, as humans, label the chair abstractly and it only means a chair to those who see it as a chair—i.e. it is subjective. The concept is not itself fixed. My idea of a chair is different to yours, is different to a cat’s and to an alien’s, as well as different to the idea of this object to a human who has never seen or heard of a chair (early humans who had never seen a chair, for example, would not know it to be a chair. It would not exist as a chair, though the matter would exist in that arrangement). I may call a tree stump a chair, but you may not. If I was the last person (or sentient creature) on earth and died and left this chair, it would not be a chair, but an assembly of matter that meant nothing to anything or anyone.^[iii] The chair, as a label, is a subjective concept existing in each human’s mind who sees it as a chair. A chair only has properties that make it a chair within the intellectual confines of humanity. These consensus-agreed properties are human-derived properties, even if there may be common properties between concrete items—i.e. chairness. The ascription of these properties to another idea is arguable and not objectively true in itself. Now let’s take an animal—a cat. What is this “chair” to it? I imagine a visual sensation of “sleep thing”. To an alien? It looks rather like a “shmagflan” because it has a “planthoingj” on its “fdanygshan”. Labels are conceptual and depend on the conceiving mind, subjectively.

What I mean by this is that I may see that a “hero”, for example, has properties X, Y and Z. You may think a hero has properties X, Y and B. Someone else may think a hero has properties A, B and X. Who is right? No one is right. Those properties exist, in someone, but ascribing that to “heroness” is a subjective pastime with no ontic reality, no objective reality.

This is how dictionaries work. I could make up a word: “bashignogta”. I could even give it a meaning: “the feeling you get when going through a dark tunnel with the tunnel lights flashing past your eyes”. Does this abstract idea not objectively exist, now that I have made it up? Does it float into the ether? Or does it depend on my mind for its existence? I can pass it on from my mind to someone else’s using words, and then it would be conceptually existent in two minds, but it still depends on our minds. What dictionaries do is to codify an agreement in what abstract ideas (words) mean, as agreed merely by consensus (the same applies to spelling conventions—indeed, convention is the perfect word to illustrate the point). But without all the minds existing in that consensus, the words and meanings would not exist. They do not have Platonic or ontic reality.

 Thus the label of “chair” is a result of human evolution and conceptual subjectivity (even if more than one mind agrees).

If you argue that objective ideas do exist, then it is also the case that the range of all possible entities must also exist objectively, even if they don’t exist materially. Without wanting to labour my previous point, a “forqwibllex” is a fork with a bent handle and a button on the end (that has never been created and I have “made-up”). This did not exist before now, either objectively or subjectively. Now it does—have I created it objectively? This is what happens whenever humans make up a label for anything to which they assign function etc. Also, things that other animals use that don’t even have names, but to which they have assigned “mental labels”, for want of better words, must also exist objectively under this logic. For example, the backrubby bit of bark on which a family of sloths scratch their backs on a particular tree exists materially. They have no language, so it has no label as such (it can be argued that abstracts are a function of language). Yet even though it only has properties to a sloth, and not to any other animal, objectivists should claim it must exist objectively. Furthermore, there are items that have multiple abstract properties which create more headaches for the objectivist. A chair, to me, might well be a territory marker to the school cat. Surely the same object cannot embody both objective existences: the table and the marker! Perhaps it can, but it just seems to get into more and more needless complexity.

When did this chair “begin to exist”? Was it when it had three legs being built, when 1/2, 2/3, 4/5, 9/10 of the last leg was constructed? You see, the energy and matter of the chair already existed. So the chair is merely a conceptual construct. More precisely a human one. More precisely still, one that different humans will variously disagree with.

Let’s take the completed chair. When will it become not-a-chair? When I take 7 molecules away? 20? A million? This is sometimes called the paradox of the beard / dune / heap or similar. However, to be more correct, this is an example of the Sorites Paradox, attributed to Eubulides of Miletus. It goes as follows. Imagine a sand dune (heap) of a million grains of sand. Agreeing that a sand dune minus just one grain of sand is still a sand dune (hey, it looks the same, and with no discernible difference, I cannot call it a different category), then we can repeatedly apply this second premise until we have no grains, or even a negative number of grains and we would still have a sand dune. Such labels are arbitrarily and generally assigned so there is no precision with regards to exactly how many grains of sand a dune should have.

This problem is also exemplified in the species problem which, like many other problems involving time continua (defining legal adulthood etc.), accepts the idea that human categorisation and labelling is arbitrary and subjective. The species problem states that in a constant state of evolving change, there is, in objective reality, no such thing as a species since to derive a species one must arbitrarily cut off the chain of time at the beginning and the end of a “species’” evolution in a totally subjective manner. For example, a late Australopithecus fossilised skull could just as easily be labelled an early Homo skull. An Australopithecus couple don’t suddenly give birth to a Homo species one day. These changes take millions of years and there isn’t one single point of time where the change is exacted. There is a marvellous piece of text that you can see, a large paragraph[iv] which starts off in the colour red and gradually turns blue down the paragraph leaving the reader with the question, “at which point does the writing turn blue?” Of course, there is arguably no definite and objectively definable answer—or at least any answer is by its nature arbitrary and subjective (depending, indeed, on how you define “blue”).

So, after all that, what has begun to exist? A causally inert abstract concept.

You see, once we strip away the labels and concepts, all we have left is matter and energy which is only ever involved in what has been called transformative creation, meaning it doesn’t begin to exist, but is being constantly reformed throughout time. It only began to exist at the Big Bang or similar (in Craig’s model).

So where does this leave us? The implications are twofold. Firstly, as Grünbaum illustrates, with all effects being merely transformative creations (i.e. nothing comes into existence but is transformed from already existing matter or energy), then we have an equivocation of the term cause. In Premise 1 we are talking about transformative causality, whereas in the conclusion we are talking about creation ex nihilo or creation out of nothing.

What I eventually go on to show is the further ramifications of this:

This has some fairly crucial implications for the KCA necessitating a reformulation as follows:

1) The universe that begins to exist has a cause for its existence;

2) The universe begins to exist;

3) Therefore, the universe has a cause for its existence.

If we then project the syllogistic changes from Section 3.1 over this reformulated syllogism then we get an even more tautologous and incoherent argument:

1) The universe that begins to exist has the universe as the causal condition for its existence.

2) The universe began to exist.

3) Therefore, the universe had the universe as a causal condition for its existence.

For this and other reasons, sorting out the abstracts debate is crucial as to whether the KCA holds.

Other relevant arguments

But nominalism is not restricted, in its relevance, to the KCA alone. It is pertinent to pretty much all areas of philosophy and theology that are connected to metaphysics. Let’s take morality. This is the ultimate abstract idea. Many religionists believe in an absolute, objective morality. However, if they fail to give a coherent account of objective, realist abstracta, then their account of objective morality falls apart.

This is replaying Kant’s thoughts about ding an sich – things-in-themselves. These things refer to nuomenon as opposed to phenomenon. The noumenal world may exist, but it is completely unknowable through human sensation.

We, as subjective minds, cannot access a thing-in-itself – say, a chair. We cannot know the chair since we are not the chair. We merely subjectively interpret it, its properties and its chairness. That is the best we can hope for. In this way, all experience is necessarily subjective. This has knock-on effects to truth or fact, depending on how we define them. What is the true colour of a fox? Well, it depends on who the observer is. The fox merely has properties – that much could be “objectively” (with caveats) established, at a fundamental level. But how those properties ontologically manifest is dependent on the sensor.

Even if God existed, and had some ideal moral law, it could only ever be interpreted subjectively. Moreover, there is little coherent way that it could be a  law in the Platonic sense – some floating ethereal thing out there in the ether. Objective morality fails from the very outset in that there cannot be “objective” – the metaphysical notion of these universal abstracta is flawed.

This is the case for any number of ideas, such as human rights. I have long argued that human rights don’t exist objectively, that they are conceptually constructed by human minds and codified into laws or charters. People argue over them – you only have to look at freedom of speech and hate speech to see the difficulty in defining such nebulous abstracta – and these arguments are reflective of the subjective properties of such ideas.

Any abstract notion (and there are so many) that theologians invest their time in expounding, explaining and re-jigging falls into the scope of arguments concerning nominalism. Theologians assume the building bricks and construct logical arguments therefrom. But if the building blocks literally don’t exist, then the edifices are equally fictive. Morality, atonement, and so on…

We live our lives as though this abstract reality really does exist alongside us, but that reality is inside our collective minds. The realisation of this is fundamentally terminal for much of what religion is based on – the ontic reality of metaphysics. Without a coherent case for some kind of ontic realism, then the basic foundations of religion and theology disappear, evaporating into conceptually, subjectively constructed phenomena.