To: Gordon F.
From: Geoffrey Klempner
Subject: Abstract and concrete, time and motion
Date: 31st March 2008 12:28

Dear Gordon,

Thank you for your email of 16 March, with your essay for the ISFP Associate Award, 'Abstract and Concrete', and your email of 27 March, with your Associate essay, 'Time as motion and motion as time' which is the second version of an essay which you originally submitted on 4 March.

I am very glad that you are now focusing your attention on getting through the Associate. It has been quite a while since we have been able to add good material to the Pathways Essay Archive.

Abstract and Concrete

I can definitely see scope for an essay along the lines of, e.g., 'Is there a useful distinction to be made between concrete and abstract objects? evaluate different views about the nature and explanation of this distinction.'

The main difficulty with this question, as indeed illustrated by your essay, is that it overlaps with a number of other questions, the most important of which is the traditional distinction between particular and universal, as well as the Fregean distinction between 'complete' and 'incomplete' expressions ('objects' and 'concepts' -- see Frege 'On Concept and Object') and their corresponding referents.

Do we need to recognize the existence of abstract objects? For example, the set of all movable objects on my desk weighing more than 10 grams is an abstract object. However, it differs in a significant way from the set containing the null set together with the set containing the set containing the null set together with the null set. The latter might be called a 'pure' abstract object by comparison with the former 'impure' abstract object. A pure abstract object does not require the existence of concrete objects.

Talking of sets also makes clear that the issue we are addressing is not the same as the question of the nature of universals.

Is a person a concrete object or is it (as Lewis holds) a set of person stages? On Lewises theory, two such sets can in principle overlap, e.g. if I put you into a person duplicator and out come two GFs. Then GF1 is the set of all person stages from your birth up until the moment when GF1 appears as 'the one on the left' while GF2 is the set of all person stages from your birth up to the moment when GF2 appears as 'the one on the right'.

On this view, a 'person' would be an 'impure' abstract object rather than a concrete object.

Bernard Williams, in response to thought experiments about person duplication has gone one stage further in suggesting that one day we might view a 'person' such as GF or GK not as an object but a universal or predicate, like, 'Ford Corsair' or 'Pontiac Firebird'. An example of 'GF' is any object displaying the characteristic attributes of GF-ness, and there could be lots of such examples, all of whom are in a sense conscious of possessing the 'personal history of GF'.

This illustrates the importance of distinguishing 'universal' from 'abstract object'. To say that a person is a universal (as in Williams) is, prima facie, different from claiming that a person is a kind of abstract object (as in Lewis).

Are there pure abstract objects or only impure abstract objects? It has been long recognized that you can do arithmetic 'without numbers' in the sense of analysing numerical statements using only first-order predicate calculus and identity, without going on to make to the further stage of identifying numbers with sets. This is a view in the philosophy of mathematics. Opposing views would be that numbers do 'exist' as either impure, or as pure abstract objects. In Z-F set theory, numbers are defined as pure abstract objects, while, by contrast, the definition of n as 'the set of all n-membered sets' would be consistent with the view that numbers would not exist if no concrete objects existed.

If there are pure abstract objects, how does the human mind succeed in making 'contact' with them? Is that even a sensible question to ask? This seems to be the issue you are gesturing at towards the end of your essay. If no conscious beings existed numbers would still exist -- or would they?

Time as motion and the motion of time

As it stands, I have more difficulty seeing this as a potential essay for the Associate. The point Aristotle is making is admittedly philosophical. Time and motion, in the sense of the motion of an object through space, are interdefinable. This tells us something about time. Yet it also in a sense leaves the mystery of time unaddressed.

The explanation which you offer seems truistic. Measurement of time is the comparison between one movement and another. In the time it took me to walk down to my office today, the minute hand of my watch traversed 192 degrees, i.e. it 'took me' 35 minutes.

The strong temptation, of course, is to see passage through time as itself a kind of 'motion'. But this is strictly speaking nonsensical. An object 'moves' when it occupies different places at different times, and all the places in between the start and end point of its journey. That assertion, however, would fully consistent with the claim, e.g. that time is ultimately unreal, a mere 'fourth dimension' like space.

By contrast, philosophers who insist on the 'reality of temporal passage' want to say that there is something extra or additional which Aristotle's claim about time and motion does not capture. Motion is 'real' and not analogous to the occupation of different places by an extended object.

Indeed, Aristotle himself held a view which is inconsistent with the static view of time: in his discussion of 'the sea battle' he denies that there is a meaningful sense in which we can describe the world as already containing (as it were, from a standpoint outside of time) an answer to the question whether there will be a sea battle or not. The future is open, still to be decided.

In terms of Aristotle's point about time and motion, is it possible to raise any interesting philosophical questions without going into the clash between different views on the reality/ unreality of time? I think there is. You could look, for example, at the question whether it makes any *sense* to hypothesize the possibility of an 'empty time', i.e. a period of time where nothing in the universe changes or moves. This is one of the questions addressed by Richard Swinburne in his excellent book 'Space and Time'.

All the best,

Geoffrey