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So I am reading Loux's contemporary introduction to metaphysics, and he starts by giving two broad ideas about universals.

Do realists and nominalists actually disagree about what really is? For example, it feels like all the arguments for realism could be saying either 'universals exist in some platonic way' or 'it is more convenient to extend the word exist to include universals'

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  • Good question. I'm more of a nominalist, and essentially I say the world is some specific mathematical object, and things that are part of that object "exist" and things that are not part of it "don't exist." The way to find out whether something is part of that object is via induction. Induction isn't telling us integers are part of the object, so the most parsimonious hypothesis is that integers are not part of it. Essentially the real world is only that which we can discover things about via induction from sensory input. – causative Feb 8 at 20:03
  • when you say the 'real world is only that which we can discover things about via induction from sensory input' you could be saying two things: 1) The things I can discover by my senses I will call the real world (and leave any claims about the rest of reality to another sentence) 2)All that exists is the real world and this is what can be discovered by the senses – Toby Peterken Feb 8 at 20:18
  • It's "the things that can be explored by my senses through induction I will call the real world and existent and reality." "Real world" and "existent" and "reality" are all defined in reference to the mathematical object that can be investigated through the senses via induction. I don't take any of those three terms as privileged or different from the others. Also I don't restrict the real world to what I myself may discover in my lifetime - I am only one person. The real world is whatever may in principle be discovered by applying induction to sensory data. – causative Feb 8 at 20:25
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    They do disagree what "really is" - realists say abstract objects exist and are part of the real world's "furniture", and nominalists say they do not, they are just convenient verbal fictions. The disagreement here is over whether the universals (some of them, anyway) are objective items in some sense, or just linguistic artifacts that serve our human purposes. – Conifold Feb 8 at 20:29
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See the SEP article on nominalism:

[T]here are (at least) two kinds of Nominalism, one that maintains that there are no universals and one that maintains that there are no abstract objects. Realism about universals is the doctrine that there are universals, and Platonism is the doctrine that there are abstract objects.

So there definitely is a difference. The problem is that while you can be a realist about many things, nominalists are rejecting the existence of certain objects. So basically, if you are a realist about everything but universals or abstract objects, you are a kind of nominalist.

On the other hand, someone who is a realist about universals or abstract objects says that they are a real part of the world. A Platonist does not simply say that we should extend the meaning of the word exist to include abstract objects as well because it is more convenient or a use of language important to our way to talk about the world. It's not like they'd agree with nominalists regarding ontology and suggest a little exception for the use of the word 'exist'. A Platonist says that every understanding of the word 'exist' which excludes abstract objects (like what nominalists do) is plain and categorically wrong because things like THE table or pure tableness really exist so that they can and must be meaningfully referred to by saying that they exist. That is what makes them Platonists.

The reason why this is a substantial disagreement is that realists do assume the reality of a given object

independent of anyone’s beliefs, linguistic practices, conceptual schemes, and so on (from the second link)

Thus, words are merely the means with which they argue about the world independent of these words. They argue about how to correctly refer to this world. This means that in some sense, they do indeed argue about which objects could correctly be referred to by 'to exist', but they both hold that the correct use is not to be decided by us, but determined by the core of their disagreement: by what there really is.

As you may understand now, most people who label themselves as (metaphysical) Platonists probably do not understand what the term really means.

(Disclaimer: Out of epistemological reasons, I myself hold that metaphysical discussions about correct (eternal) ontology are meaningless, but that is not what nominalists and realists think. That's why the disagreement is substantial for them.)

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    Well, he's asking whether the difference between nominalists and Platonists is only a difference in how they define the word "exists." Or "really exist" or "is real" etc. What do such words mean? It's possible to simply define the word "exists" to also include what I'd call fictional objects, like Harry Potter's wand, or mathematical triangles. Indeed this is what is done in mathematics (in my estimation) when we say things like "there exists a real number such that..." – causative Feb 8 at 23:09
  • @causative Added a bit of clarification. Realism thinks of ontologies being independent from our minds and the meaning of 'to exist' involving a correct reference to these objects, therefore arbitrary redefinitions like you describe are - for them - simply wrong. The mathematical use of the word is very different from that. – Philip Klöcking Feb 9 at 7:41
  • I interpret the mathematical "exists" as "would exist, if counterfactually the axioms we're using held." And the fictional "exists" as "would exist, if counterfactually the rules of this fictional story held." These counterfactuals are independent of our minds. – causative Feb 9 at 8:09
  • @causative Firstly, that is basically Lewis' view and not widely accepted. One problem is that there is no epistemic justification for the underlying assumption that the formal relations we make out in our thought are independent from our way to think. And if we say "but if counterfactually this was true, then if counterfactually XY is true then..." we still have not positively said anything about what actually is true, ie. we cannot, within the theory, consistently assert that counterfactuals indeed are independent of our minds. – Philip Klöcking Feb 9 at 9:53
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    Let us continue this discussion in chat. – causative Feb 9 at 17:29
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Of course, their only difference is how they define the word "exists". If two equal saints meet and argue about something, most likely u should bet they're both honest, smart and wise guy, just confused about each other's definition. This universal confusion caused so many unnecessary conflicts throughout history. As Socrates once hinted that debate is not to defeat anyone's judgement, but is an efficient way to sort out each other's confusions and quickly lead to the always-escaping elusive truth...

The Problem of "Universals" is such an ancient typical conflict, now I think every sensible person will agree there exists a necessary mathematical concept called "2" after seeing two seemingly identical things. The only critical insight in this simple-yet-seemingly-philosophically-deep problem is that all human concepts/definitions are relative, meaning the concept "exists" itself is relative to a certain layer of our mind... "2" is certainly more abstract than "pain" which our body can feel impressively while a number, not so much due to our biological design. While certain math genius may feel "2" more impressively than "pain", and that's why this person can surely outperforms you in solving Math number theory problems in the long run as a persistent game, unless somehow later you acquired more intuition after huge effort and struggle...The most hard part is when most people say something "exists" they implicitly assume there's an absolute background reference frame in which there's an objective yes or no binary definitive statement can be made. And most of them will be satisfied spending all their life arguing about this type of "wonderous" existence and that kind of "pitiful" nonsense, essentially much like machine, they'll keep their focus on these outward worldly existences to try to "prove" or "disprove" from their experiences as a vanity show to others. While for those rare illuminated and awaken people, inward retrospect and self-reflection is much more important than those outside existence or not. They fully understand when indulging in outward existence discussion the endgame is just to find a place for inward sentiment to attach, and they never lack any wealth to find such a place to know themselves much deeper and clearer. Neither outward realism nor nominalism is all the truth, they're just a small starting part of it to stimulate and invoke your inward "intellect memory sea", which in some religious factions it's called “the Eight Consciousnesses”. it's beyond common outward/inward perceptions, ego and comprehensions, similar to western world's subconsciousness notion. So the whole truth remains extremely hidden and mystically elusive in this vast sea of pictorial metaphors, no two persons will share exactly same images to the same clarity degree, not even nowadays super AI/GPT3 can sort out completely. Thus to understand and progress oneself accordingly is the ultimate goal and the only important truth for oneself...

By the way, most people will regard math as absolute truth, such as number 2 is real and really exists in some Platonic spiritual world apart from this imperfect material world (sounds like dualism here). But my view is contrary, number 2 (or any abstract universal concepts) resides in the same "metaphoric" realm of human mind, just happen to be located in the relatively most clear-countably-verifiable-universal layer. Again, literally written as an Arabic symbol "2", its semantic meaning can be limitless, it may be forming 2 dollars (object) in your mind, while doubling an existing action (function) in my mind, etc. When we talk about "2" in pure math context, the aforementioned concrete differences disappear, and it suddenly becomes a more clear-but-abstract notion which is still a metaphor but with much higher clarity compared to previous physical images. So in the physical context, it makes sense for nominalists to claim "2" does not exist at all (since relative to this context there're no two exactly identical leaves in this measurable physical layer), however, relative to the more abstract math layer, it also makes sense for realists to claim "2" exists in this Platonic realm... I don't opine separating the noumena from the phenomena as a serious business, its useful for some purposes, but all these concepts and separations are still man-made (fake) analogies consciously engineered to explain to a naive but confused child who is actively seeking an authoritative answer from the grown-ups. A child usually will be overwhelmed if provided too many alternative different explanations...

This world perceived by human mind is nothing but metaphors, that's why we can have several different models/theories about the same phenomena, such as the Newtonian Force Laws, Lagrangian/Hamiltonian Path Integral Minimum Action Principle, and the later Maxwell/Einstein Local Field Theory in classical physics and then applied further into QM, so far all these above 3 distinct models (metaphors) are not proved wrong while very useful and taught in every physics department around the globe. In the meantime, because our mind is constantly forming-destroying-reforming numerous metaphors as free will, most of these created images/processes/analogies are in more or less confused state. For example, if you've never been visiting a place and people around you are talking extensively about it, still in your mind you'll form some vague images from what you heard. Most of these misconceptions are like "avidya" in eastern Buddhism's nothing-but-metaphoric teachings, huge huge and thick darkness in the form of ignorant confusions is covering human mind like the "five mountains" and thus all its derived senses...

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  • Agree with much of what you said, except the use of the phrase "in some Platonic spiritual world apart from this imperfect material world". I don't think Plato was of the opinion that "forms" exist in a spiritual world apart from the material world. Rather, everything that exists, exists in the same world, but those who are used to living in a cave fail to realize that there is more to the world than the shadows with which they are so familiar. – Math Keeps Me Busy Feb 9 at 13:33
  • @MathKeepsMeBusy thx for your comment. My understanding of Platonic world vs material world is like common set-theoretic mapping concept, people believe there're certain correspondence btw them so that one application in a world can be applied/reflected into another world. However, my own philosophical preference is to view them as computer software layers, they're just layers of the whole same stack from the screen output down to hardware instruction set. So in the same stack, there're no magic mappings, just normal causality flows between these layers upon layers... – Double Knot Feb 11 at 17:35
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I think it helps to think of a concrete example of where their approach might differ, specifically the question of justice and how to be a just person.

Realists believe that justice is a real thing. They might have a different understanding of it, and they may disagree about how to achieve it. They would agree though that the conversation about what justice is to be meaningful.

In (at least some forms of) nominalism, justice isn't a thing beyond a name, or perhaps a concept that I have in my mind and you have in your mind (see e.g., https://en.wikipedia.org/wiki/Nominalism#Medieval_philosophy). In that view, debating what justice is wouldn't really make sense, because we may have two different notions of justice. I can convince you to change your notion of justice, but there is no root, real justice we ultimately are trying to figure out.

As a practical matter, the distinction can matter. Nominalism also has led to Voluntarism (https://en.wikipedia.org/wiki/Voluntarism_(philosophy)#Medieval_theological_voluntarism), the view that morality is a question of God's will (and therefore only knowable by knowing God's will), as opposed to something about God's intellect (and therefore something we can reason about even without knowing about God), and the tools one uses for reasoning about morality are therefore different. In the latter case, we can use reason, including the reasoning of people who come from different faiths, to understand morality. In the former case, we have to rely on Divine Revelation to understand morality (since we wouldn't presume to know God's will beyond what he has revealed).

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