With respect to universals nominalists maintain that there are no universals and only particulars exists. Conversely, realists says that there are universals. Here is a sketch of an argument against universals based on the common assumption that their must be a causal relation between a knower and the object of knowledge (causal theory of knowledge).

  1. If universals exist, either they have a spatio-temporal location or they do not.

  2. If universals do not have a spatio-temporal location, then it seems that it's impossible for them to be causal relata.

  3. If universals do have spatio-temporal location, then either we take them to be abstract entities or not.

  4. If we take them to be abstract entities then again it seems that it's impossible for universals to be causal relata.

  5. If we don't take them to be abstract entities, then their causal relation to us reduces to physical causation between particulars. In that case, we have no need for universals.

Given then above, it's hard to accept the existence of universals.

So, my questions are: If universals do not have a spatio-temporal location then how do realists explain their causal interaction with us and particulars? If they do then how do they manage to remain abstract entities, and why are they necessary?

  • 2
    Why should only exist what can be explained by physics? Complex behaviour and concepts like "love"surely exist (although not in a material way), but physics do only have very limited access. You seem to presuppose a reductive materialism which is philosophically hard to maintain.
    – Philip Klöcking
    Commented Apr 6, 2016 at 9:27
  • @PhilipKlöcking It is not what I say that there exists what can be explained by physics, but that If universals are in space and time as particulars are, then It could be explained by physics since it is physical thing. Also, if love is a kind of mental state, most of contemporary philosophers, at far as I knew, accept reduction to physical things by supervnience or other ways.
    – Darae-Uri
    Commented Apr 6, 2016 at 10:33
  • Penelope Maddy addresses both the issue of spatio-temporal location and causal relation of universals to us in the context of (non-Platonic) mathematical realism jstor.org/stable/2184647 and jstor.org/stable/27902842 Some knowledge is by inference, so causal relation can be indirect, for elementary universals like finite sets and numbers she asserts their presence in the content of perception of sets of physical objects, in other words she rejects "sense data" theories that reduce perception to sensation of particulars (this is supported by cognitive science studies).
    – Conifold
    Commented Apr 7, 2016 at 20:41
  • @Conifold Thanks for editing and answering. But what I want to ask is not just arguments against so-called "the knowledge argument" but universals as being of causal power, i.e., argument for not just universals-individuals(or cognitive one) causation but including universals-universals causation, e.g., the basicity of the solution and bluness of litmus paper. So, it is not about theory of knowledge.
    – Darae-Uri
    Commented Apr 8, 2016 at 1:57
  • That did not come through for me in any of the versions. I do not recall anyone defending universals-on-universals causation though, it seems they require a very special kind of recipient to be causally efficacious. But you could ask a new question about that, which would be clearly distinct from this one. I am curious, why would realists want that?
    – Conifold
    Commented Apr 8, 2016 at 3:21

2 Answers 2


Answering your 5 step argument:

  1. Universals do not have location, nor time.
  2. Your point 2 seems to assume Leibniz's approach to causation, that something needs to have proximal contact to be causal. That assumption was refuted by Newton, who showed that fields can act over distance. Additional work after Newton showed that superposition is a feature of much of the world, so solidity and non-congruency are also not valid assumptions. Your "it seems that" is just an unjustified assumption.
  3. N/A
  4. Your "it seems that" is just an unjustified assumption.
  5. N/A

OK, to your questions:

"How do abstract universals causally interact with us"

Karl Popper offered an answer -- abstract entities cannot directly interact with matter. But consciousness can. And consciousness can interact with abstract entities. He postulated that consciousness was an unexpected emergent phenomenon of early life, which allowed life to use abstract entities as hypotheses. A living thing can ask -- "what happens if I do X". And evaluate the hypothesis -- that X will likely lead to death -- without having to actually DO X and find out -- that X leads to death. Consciousness, by providing a means to make causal use of abstract entities, provided a massive survival advantage.

Answering the follow on questions: "how do they manage to remain abstract entities, and why are they necessary?" Abstract entities remain abstract, and they are necessary to do hypothesis formation and testing.

As references, here is Popper's Tanner Lecture, spelling out his 3-worlds theory: https://www.thee-online.com/Documents/Popper-3Worlds.pdf

And here is Popper outlining the development of consciousness in a 3-worlds model, see in particular section 4: http://www.informationphilosopher.com/solutions/philosophers/popper/natural_selection_and_the_emergence_of_mind.html

  • I made some edits which you may roll back or continue editing. You can see the versions by clicking on the "edited" link above. I did not understand the phrase "Additional world after Newton". This might be worth a further edit. Also if you have a reference for Popper that would strengthen your answer. Also any other reference would strengthen your answer and give the reader a place to go for more information. Welcome to this SE! Commented Sep 30, 2018 at 20:49
  • Thank you for the clean-up of spelling errors! "World" was another, now corrected. I have added two links.
    – Dcleve
    Commented Oct 2, 2018 at 1:16

Penelope Maddy addresses both the issue of spatio-temporal location and causal relation of universals to us in the context of (non-Platonic) mathematical realism see Perception and Mathematical Intuition and Mathematical Epistemology: What is the Question. First, causal theory does not require direct causation, some knowledge is by inference, including inductive inference from simple cases, which may well apply to universals. So causal relation can be mediated by an inferential link to direct interaction, and elementary universals, like finite sets and numbers, are present, she claims, in the content of perception of sets of physical objects. In other words, she rejects the "sense data" theories which reduce perception to sensation of particulars (this is supported by cognitive science studies, see Metaphysically, what comes before the cognitive ability to make distinctions?). Here is her response on causal efficacy and spatio-temporal location of universals:

Consider the following case: P needs two eggs for a certain recipe, reaches into the refrigeratorf or the egg carton, opens it, and sees three eggs there.... the various numerical beliefs acquired on this occasion are perceptual, and I further claim that they are beliefs about a set, that is, I claim P acquires the perceptual beliefs that there is a set of eggs before P, that it is three-membered, and that it has various two-membered subsets...

I must agree that many sets, the empty set or the set of real numbers,f ore xample, cannot be said to have location, but I disagree in the case of sets of physical objects. It seems perfectly reasonable to suppose that such sets have location in time-for example, that the singleton containing a given object comes into and goes out of existence with that object. In the same way, a set of physical objects has spatial location insofar as its elements do. The set of eggs, then, is located in the egg carton - that is, exactly where the physical aggregate made up of the eggs is located.

It is interesting that Maddy's only credited source of inspiration is Gödel, who suggested that abstractions in our experience appear due to "another kind of relationship between ourselves and reality... [other than] the action of certain things upon our sense organs". But it is well known (from Gödel himself) where he got this idea. It was Husserl's categorical intuition/ideation, see In what fundamental ways, if any, does Husserl break with Kant? And indeed Maddy's theory of ideal perception is largely a redux of Husserl's, but with explicit realistic commitments.

  • 1
    Maddy is an interesting writer, but the passage you quoted is plainly absurd. There's a world of difference btween perceiving 3 eggs and perceiving a set of 3 eggs. "Set" was not even a first-class concept until the last half of the 19th century; her argument is perfectly circular. The move from perception of individuals to conceptions of groupings is for scientists (developmental psychs, cog scientists, etc.) to investigate, not philosophers of mathematics. And what does "perceptual belief" even mean?
    – user20153
    Commented Apr 13, 2016 at 22:31
  • 1
    @mobileink Half of Maddy's paper is a review of developmental psychology and cognitive science on perception of objects as unities, she then sketches how similar mechanism works for sets, her description is essentially right as psychology. I am guessing historical timing of concept's introduction is irrelevant under mathematical realism, presumably she refers to the "reality" it describes. Perceptual belief is a belief directly acquired from perception or "any belief acquired on a given occasion which influences and is influenced by perceptual beliefs acquired on that occasion".
    – Conifold
    Commented Apr 14, 2016 at 21:34
  • 1
    I think that the eggs example is somewhat strained (if not scrambled). People function largely on automatic, with just a bit of look-ahead. Animals do not look ahead so much. If a weasel happened on a nest with 3 eggs, it might eat one, eat another, become full and scamper off. A person making a recipe would get the carton, grab two eggs and move on, they would not think about set theory. (It is hard enough to get my students to do that when I teach SQL, let alone thousands of generations of cooks.) Humans could see if there was only one egg in the carton and visualize there not being enough.
    – user16869
    Commented Apr 23, 2016 at 18:04
  • @user16869 When we look at bushes at a distance they appear as a green blur, if we pay attention and focus we might discern individual leaves, or even the contour of a rabbit hiding there. Perception of ideal unities may not be "on" often, but it is enough for Maddy that the ability is there, mathematicians then develop it purposefully.
    – Conifold
    Commented Oct 2, 2016 at 3:11

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