Philosophy 101 (philpapers induced) #2 – Abstract objects: Platonism or nominalism

Philosophy 101 (philpapers induced) #2 – Abstract objects: Platonism or nominalism February 18, 2013

So having posted the Philpapers survey results, the biggest ever survey of philosophers conducted in 2009, several readers were not aware of it (the reason for re-communicating it) and were unsure as to what some of the questions meant. I offered to do a series on them, so here it is – Philosophy 101 (Philpapers induced). I will go down the questions in order. I will explain the terms and the question, whilst also giving some context within the discipline of Philosophy of Religion.

The second question, having covered a priori in the last post, the next question in the survey was:

Abstract objects: Platonism or nominalism?

Accept or lean toward: Platonism 366 / 931 (39.3%)
Accept or lean toward: nominalism 351 / 931 (37.7%)
Other 214 / 931 (23.0%)

So what are abstract objects? What are Platonism and nominalism?

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 briefly deals with the problem in defining what the properties of objects are, ontologically speaking (ie, 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 the 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.

The problems for such theories are 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.

I am unsure as to whether the philpapers survey included conceptualism in the ‘other’ category or not, since 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 anstract 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 a 20,000 word paper on the Kalam and its problems, mainly concerning this area of philosophy. I have produced a post here and here detailing a small area of this. Here is a portion:

Authors of the KCA, such as Craig, see the argument as dealing with the beginning of existence of all discrete objects as being the set described by the term “everything”. In other words, a chair, a marble, a dog and a mountain all begin to exist and have causes for their respective existences. This would be, admittedly, the common sense understanding of the ontology of these objects – that they begin to exist at a particular point in time from having not existed at a previous point in time. What I am going to set out is very similar to one of Adolf Grünbaum’s objections that he set out in his 1990 essay “The pseudo-problem of creation in physical cosmology “.

The problem for the KCA is the definition of “everything”. My claim is that everything is in fact ‘the universe’ itself. As Grünbaum (1990) states:

…consider cases of causation which do involve the intervention of conscious fashioners or agents, such as the baking of a cake by a person. In such a case, the materials composing the cake owe their particular state of being in cake-form partly to acts of intervention by a conscious agent. But clearly, the very existence of the atoms or molecules composing the cake cannot be attributed to the causal role played by the activity of the agent. Thus, even if we were to assume that agent-causation does differ interestingly from event-causation, we must recognize that ordinary agent-causation is still only a transformation of matter (energy).

Even for those cases of causation which involve conscious agents or fashioners, the premise does not assert that they ever create anything out of nothing; instead, conscious fashioners merely TRANSFORM PREVIOUSLY EXISTING MATERIALS FROM ONE STATE TO ANOTHER; the baker creates a cake out of flour, milk, butter, etc., and the parents who produce an offspring do so from a sperm, an ovum, and from the food supplied by the mother’s body, which in turn comes from the soil, solar energy, etc. Similarly, when a person dies, he or she ceases to exist as a person. But the dead body does not lapse into nothingness, since the materials of the body continue in other forms of matter or energy. In other words, all sorts of organization wholes (e.g., biological organisms) do cease to exist only as such when they disintegrate and their parts are scattered. But their parts continue in some form.

We can, here, start to see an issue with the idea, in the first premise, of things beginning to exist with the notion of transformative creation as mentioned previously. We have already discussed how all causes can be reduced to a single cause. Now I will set out, as Grünbaun hints at, to show that “everything” is a term which also refers to a singular object.

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 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[1]. 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 other 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 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 the part of the definition of abstracts is that they are causally inert. This means that, at best, the abstract label is unable to have causal power anyway (regardless of its ontology).

Let’s now look at the ‘label’ of ‘chair’. 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 – ie it is subjective. 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 on earth and died and left this chair, it would not be a chair, but an assembly of matter that meant nothing to anything. 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. These properties are arguable and not objectively true themselves. Thus the label of ‘chair’ is a result of ‘subjectively human’ evolution.

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. For example, 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 (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 they same object cannot embody both objective existences: the table and the marker!

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 not become 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, 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 continuums (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, a large paragraph (see end), 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.

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.

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 being 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 creation out of nothing. As Grünbaum reasons:

Since the concept of cause used in the conclusion of the argument involves creation out of nothing, we see that it is plainly different from the concept of cause in the premise. And for this reason alone, the conclusion does not follow from the premise deductively. (Grünbaum 1989)

 This amounts, then, to a fallacy of equivocation whereby the author is using two distinct meanings of the same term in a syllogism. This makes the argument logically invalid.

The second ramification of this line of argument is that it means that the term “everything” is actually synonymous with “the universe”, with the universe being a set of finite energy and matter that has remained, in accordance with the Law of the Conservation of Energy, constant over time. We have agreed, then, that abstract concepts might begin to exist, but these are causally inert and do not exist objectively – only in the minds of the conceiver. So that leaves matter and energy, which has always existed because it is, in effect, the universe itself. It is not that the universe is ‘made up’ of lots of matter and energy making it something, it simply is a quantity of matter and energy. 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.

As we can plainly see, if we delve into the actual meaning of these terms and input these definitions back into the syllogism we are presented with an argument that amounts to little more than nonsense.

One could claim, however, that this argument relies at least partially on the establishment of nominalism, conceptualism or some other form of non-realism in order to work. To this we shall now turn.

RELATED POSTS:

#1 – a priori

#2 – Abstract objects – Platonism or nominalism?

#3 – Aesthetic value: objective or subjective

#4 – Analytic-Synthetic Distinction

#5 – Epistemic justification: internalism or externalism?

#6  – External world: idealism, skepticism, or non-skeptical realism?

#7 – Free will: compatibilism, libertarianism, or no free will?

#8 – Belief in God: theism or atheism?


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  • SmilodonsRetreat

    OK, let me try.  So, this is really a question of definitions and whether the definitions have any real meaning. Is that kind of it?

    Does green have a universal meaning?  I think I would fall into the realism camp (being a science type and all).  For example, green is a universal property, but by definition.  Green is defined as light between the wavelengths of 520 and 570 nanometers.  So, anything that reflects light of that wavelength is green.

    But we define green to be that way.  I would say that light is reflected at that wavelength and no matter what you call that group of wavelengths, it’s still the same.  We could call it Ford, but it is still the same color.

    On the other hand, diamonds have a unique character of being valuable.  That’s something I would think is not universal.  That valuableness is based on the characters of diamond (shiny, hard, rare) that are real, but the valuableness is dependent on perception.  We can define a dried grape as ‘diamond’, but it doesn’t have any of the
    properties that makes diamond unique.  So, the definition is
    meaningless.

    Am I even close?

    • It’s about properties, and the ontology of properties. What are properties made of, if you will? As the SEP states:

      The nominalist about universals rejects universals — but what are they? The distinction between particulars and universals is usually taken to be both exhaustive and exclusive, but whether there is such a distinction is controversial.[5] The distinction can be drawn in terms of a relation of instantiation: we can say that something is a universal if and only if it can be instantiated by more than one entity (whether it can be instantiated by particulars or universals) — otherwise it is a particular. Thus while both particulars and universals can instantiate entities, only universals can be instantiated. If whiteness is a universal then every white thing is an instance of it. But the things that are white, e.g. Socrates, cannot have any instances.
      [6]

      Realists about universals typically think that properties (e.g. whiteness), relations (e.g. betweenness), and kinds (e.g. gold) are universals. Where do universals exist? Do they exist in the things that instantiate them? Or do they exist outside them? To maintain the second option is to maintain an ante rem realism about universals. If universals exist outside their instances then it is plausible to suppose that they exist outside space and time. If so, assuming their consequent causal inertness, universals are abstract objects. To maintain that universals exist in their instances is to maintain an in re realism about universals. If universals exist in their instances, and their instances exist in space or time, then it is plausible to think that universals exist in space or time, in which case they are concrete. In this case universals can be multiply located, i.e. they can occupy more than one place at the same time, for in re universals are wholly located at each place they occupy (thus if there is whiteness in re, then such a thing can be six meters apart from itself).

      Thus, both on ante rem and in re realism about universals, universals enjoy a relation with space very different from that apparently enjoyed by ordinary objects of experience like houses, horses and men. For such particulars are located in space and time and cannot be located in more than one place at the same time. But universals are either not located in space or else they can occupy more than one place at the same time.

    • You can define what you like, as that is merely subjective labeling. But what is the actual existence property of greenness? Doe sit exist (somehow, somewhere)? That greenness, though, is it a particular instantiation of green, particular to each instantiation, or is it a universal property which exists outside of the instantiation?

      One argument against universals is known as Bradley’s Regress and, though you can argue for and against it, goes like this:

      There are other more specific arguments against universals. One is that postulating such things leads to a vicious infinite regress. For suppose there are universals, both monadic and relational, and that when an entity instantiates a universal, or a group of entities instantiate a relational universal, they are linked by an instantiation relation. Suppose now that a instantiates the universal F. Since there are many things that instantiate many universals, it is plausible to suppose that instantiation is a relational universal. But if instantiation is a relational universal, when a instantiates F, a, F and the instantiation relation are linked by an instantiation relation. Call this instantiation relation i2 (and suppose it, as is plausible, to be distinct from the instantiation relation (i1) that links a and F). Then since i2 is also a universal, it looks as if a, F, i1 and i2 will have to be linked by another instantiation relation i3, and so on ad infinitum. (This argument has its source in Bradley 1893, 27–8.)

      The relationship between entities and their properties is itself a universal abstract relational entity, and if these exist, then there would be a relational infinite regress, in simple terms.

      Personally, I favour that these abstracts are merely conceptual ideas which don’t exist per se (though this prompts the question of the ontology of conception and consciousness). It is certainly simpler (Ockham’s Razor favours nominalism).

      If you dare, start with reading this:
      http://plato.stanford.edu/entries/nominalism-metaphysics/

  • SmilodonsRetreat

    OK, you’ve done it.  My brain is now gibbering in the corner of my cube.  Great.  ;)

    I’m trying to wrap my head around this and failing.  If an object is white, then that is a property of the object.  So that is real.  But I can think of the property of ‘white’ with or without that object OR I think of an object being white without it being actually white OR I can think of the white object, as a model within my mind that may or may not have any connection to reality.  In those lasts, they would be non-real.

    So would that make ‘white’ a universal?  Because not only can an object be white, but it is a property in and of itself?

    I’m not sure my brain can work with this… I’m just going to have to think about it… a lot.

    • “I’m trying to wrap my head around this and failing.  If an object is white, then that is a property of the object. ”

      That is indeed the QUESTION. What is the ontology of the property? Is it merely instantiated every time you see something that is white such that every instance is a particular? Or is there something abstract which is ‘whiteness’ that the object taps into, instantiates. Do all squares exhibit squareness? If so, where does the universal of squareness exist? What is it made of?

      And we can say this for any abstract object which isn’t necessarily a universal.

      The characterisation of abstract objects as non-spatiotemporal and causally inert objects might be thought unsatisfactory to the extent that it tells us only what they are not, but not what they are. But this is not a problem for the nominalist. The business of the nominalist is to reject such objects, not to characterise them in a positive way. And for the purposes of rejecting abstract objects, their characterisation as non-spatiotemporal, causally inert objects is a reasonably clear characterisation (at least as clear as the notions of spatiotemporal object, causation, causal power, and related ones are)

  • Deep fellas, deep………

  • Well worth the effort. Thanks.  Please continue the series.

    • Thanks for the feedback. I will slowly but surely get through the philpapers survey questions!

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