John Smith asked:

If abstract objects are non-causal and human brains are just physical objects how are we able to know about things like numbers, sets, ethical properties, etc.?

Suppose at t1 I do not know about some abstract object x, then at t2 I come to know about x through intuition or whatever method for acquiring non-inferential knowledge of abstract objects the anti-nominalist has in mind. How exactly is X not causal, if it can bring about changes in the physical world; e.g. in my brain?

Answer by Geoffrey Klempner

A meaty question in metaphysics. I could see this in quotes followed by ‘Discuss’ on a Sheffield University BA Metaphysics exam paper. (I once gave a Metaphysics course at Sheffield, although this would not an exam question I would have personally chosen.)

By a remarkable coincidence, you share your name with the philosopher and theologian John Smith (1618-1652) who along with Henry More, Ralph Cudworth, and Benjamin Whichcote formed a group of Plotinus enthusiasts who were known as the ‘Cambridge Platonists’. This is relevant to your question, which concerns the platonist-nominalist debate, still in various guises a live topic among contemporary analytic philosophers.

One thing often lacking, unfortunately, in the analytic approach is a sense of history, so I am going to sketch briefly what it means to be a Platonist — a true Platonist rather than someone who merely dislikes the ‘nominalist’ idea that the physical world of concrete particulars is all that really exists, everything else being a more or less artificial ‘construction’.

When we talk about ‘numbers, sets and ethical properties’ we are not really referring to any entity, according to the nominalist. There is nothing ‘out there’ beyond the physical realm for our words to ‘name’. These are just words that we use according to rules.

As you correctly note, causality is the crucial notion. But how do you know that causality necessarily involves physical objects or events? That’s something that Plato would have strongly denied.

In a seminal article ‘Causation in Perception’ (in ‘Freedom and Resentment’ 1974), P.F. Strawson makes the case for a necessary link between perception and causation which does not involve the traditional, and questionable Lockean idea of a causal link between public ‘things’ in the world and private ‘ideas’ in the mind. It is essential to perception, Strawson argued, that there are ways and means by which we come to perceive objects, that, for example, perception requires light, and that it can be distorted or obstructed by things getting in the way.

Plato, in his dialogue Phaedo makes the remarkable claim that the soul is ‘akin’ to the Forms, as one of his arguments for the existence of a non-physical soul. We could not have, e.g. the idea of equality (the Form of Equals) if our soul was not of a similar nature as the Forms. There has to be a causal link there, albeit a non-physical kind of causality. In the Republic, he tells a story about how the philosopher comes to know the Form of the Good, which like the sun in the physical world provides the necessary illumination by means of which the other Forms are perceived by the soul.

Goodness plays a crucial role here, because ‘virtue’ as Plato conceives it just is aligning our souls with the order of the universe, which necessarily involves right action because you could not know, e.g. the Form of Justice without being motivated to act justly. Wrong action is a form of misalignment of the soul, obstructing intellectual perception of the Forms.

Contemporary ‘platonists’ so-called (with a small ‘p’) won’t have any of that. They may or may not think that ‘ethical properties’ are real (you can be a platonist about mathematics and a subjectivist or nihilist about ethics). Gottlob Frege (whom I mentioned in a previous answer) strongly believed that numbers ‘exist’ in their own right, despite giving, in his brilliant Foundations of Arithmetic (1984), an effective recipe for parsing away reference to numbers in favour of the logic of quantification.

So what was Frege’s story about ‘intuition’ or ‘perception’? He was a mathematician, and like many mathematicians could testify to the powerful experience of ‘seeing’ logical and numerical relationships. Unlike computers, human beings rely on their capacity for ‘vision’. Is this just metaphor? What is its cash value?

I don’t have any problem with saying that numbers are real, nor do I feel the need to ‘define’ them in terms of some other abstract objects such as sets. A number is what it is and not another thing (if you go down the definitional route you are faced with more or less arbitrary choices, so why bother?).

Are tables and chairs real? They are and they’re not. Lacking Locke’s ‘microscopical eyes’ we are forced see aggregations of atoms and molecules as single ‘objects’, which they are not ‘really’. But then neither are atoms, etc.

Why not just say, that anything you can talk about has the kind of ‘reality’ that is appropriate for the thing in question. Corresponding to this, there are any number of different notions of causality. We chunk things in different ways according to the topic. Causality and perception are everywhere and at every level (you can ‘perceive’ with the aid of an electron microscope). There is such a thing as intellectual perception, even if it does not have the metaphysical baggage that traditional Platonists or Neoplatonists gave it.

Is there no solid ground for our conceptual scheme? Why does there need to be? When Ronnie O’Sullivan strikes the white snooker ball with his cue so as to pocket the red into the center pocket, then ricochet off the black to come back into the perfect position for the next shot, his action has ’caused’ this to happen, through his exquisitely refined judgement that has no correlate in the mechanics of rebounding snooker balls. You will look in vain for an explanation on the level of physics — the ‘causation’ isn’t there, or rather there are too many ’causes’ and ‘effects’ but none of them are relevant in explaining what just took place at the snooker table.