Could two identical objects occupy the same space?

Kirby asked:

What is wrong with this statement:

PII (standard definition):

If X and Y share ALL their properties (indiscernible), they are identical.

It is generally held that this definition is trivially true, so PII is redefined as:

If X and Y share all QUALITATIVE properties, they are identical.

I do not understand why the original definition is trivially true rather than just true, and I do not see any justification for the redefinition. This seems to be a case of taking a perfectly good principle, unjustifiably redefining, then arguing that the principle, as redefined, is false.

When PII is re-defined, a major argument for its falseness is that we can conceive of there being two, therefore nonidentical, objects that are qualitatively indiscernible. So spatial and/or temporal dispersal becomes a good argument against redefined PII. But, if we stay with the original definition of PII, the spatial and/or temporal dispersal argument is a major argument in favor of PII. Under the original PII, perceiving two objects in different regions of space is prima facie evidence of nonidentity; if they are in different regions of space at a time, they are not identical.

Answer by Geoffrey Klempner

The principle in question, for those who are not familiar with this issue is known as the Identity of Indiscernibles. It was one of the major components of Leibniz’s theory of monads, as elaborated in Monadology and other works.

The story goes that Leibniz amused the courtiers at the House of Hanover by challenging them to find two leaves that were identical, thus disproving the principle. You will not be surprised to learn that no-one ever did. The chances of discovering two leaves that appear the same even to the closest examination are very tiny. And yet, provided the courtiers weren’t allowed to use microscopes, just the naked eye, it is perfectly possible that two such leaves could have been found.

Would it have disproved Leibniz’s theory? No. Because difference in spatial position — for example, being held in your left hand and your right hand — would according to Leibniz suffice to establish non-identity. But here’s the finesse; according to Leibniz, there is no such thing as ‘space’ as we understand it. All that exists, in ultimate reality, are ‘subjects’ of varying degrees of consciousness, ‘monads’, each representing a world from a unique point of view. All spatial relations, according to Leibniz reduce to non-spatial properties.

Your intuition, which to many people seems plain common sense, is that space is something real. Two objects, say, two leaves, which are physically identical down to the atomic level can occupy different positions in space. That’s what makes them two and not one. Spatial ‘dispersal’, as you call it, of two otherwise indistinguishable objects is both necessary and sufficient for their non-identity.

However, one consequence of this intuitively attractive view, which perhaps you hadn’t thought of, is that it becomes logically true that two objects, say, two leaves or two pennies, cannot occupy the same space. Well, we know that that’s contrary to the laws of physics. But that wasn’t the question. The Identity of Indiscernibles isn’t a law of physics. It’s meant to be a law of logic, true even in possible worlds where physics is different from what it is in the actual world.

Well, here’s another experiment. I first heard about this in a lecture given many years ago by David Wiggins (author of Identity and Spatio-Temporal Continuity, later expanded to Sameness and Substance). I have two identical pennies, one in each hand. I move them together until they touch, then I press hard and, to my amazement, the pennies start to merge into one another. I pull the pennies apart again. Then I push them into one another, further this time, and pull them apart. After several goes, I have forced the pennies to occupy the same space. I now hold a single ‘penny’ which weighs twice as much as a normal penny. Or do I? When I give the ‘heavy penny’ a sharp tap, in separates into two pennies again. Why isn’t this a case of two identical objects occupying the same space? Remember, that this is a question about logic, not physics!

If you feel the slightest temptation to say that the law that two objects cannot occupy the same space is only a law of physics, not a law of logic, then you have to question the validity of the Principle of the Identity of Indiscernibles, re-defined, as suggested, to include spatio-temporal properties.

As a footnote, Wiggins’ own theory of identity as ‘spatio-temporal continuity under a covering sortal concept’ required, he claimed, that we reject the conclusion of the penny thought experiment. As a matter of logic, according to Wiggins, two objects cannot occupy the same space at the same time. There are good reasons for a philosopher wanting to hold this, and I appreciate those reasons. But I am not fully convinced.


Role of philosophy in the postmodern era

Ez asked:

What is the role of philosophy in the postmodern era?

Answer by Craig Skinner

I am no expert in postmodernism. I will take the relevant thesis to be that progress is a mirage, search for objective truth fruitless, all accounts of reality, including science and philosophy, ‘narratives’ on an equal footing with none in a privileged position, reality constructed by us.

I disagree profoundly with all this, and suspect it will be a passing phase. I certainly hope so.

I side with Aristotle, Thomas Reid, and David Lewis (among many others both ancient and modern) in thinking that there is a mind-independent, structured reality, and we can, and do, know quite a bit about it through our senses and our powers of reason. In short, I am a Realist. Furthermore I think our concepts do not divide reality up arbitrarily, as Nagarjuna has it, with reality existing only conventionally and things having no ultimate existence, being just bits of the flux arbitrarily picked out as meaningful for us. On the contrary, I feel our concepts largely match the real structure of the world, they ‘carve nature at its joints’ as Plato said.

Thus, as regards mind-independent reality, I think electrons, dinosaurs and stars are natural kinds which existed long before we came on the scene. Of course they weren’t named ‘electrons’, ‘dinosaurs’ and ‘stars’ till we appeared, but we simply named natural categories that were already there. As regards carving nature at its joints, our concepts and names are not arbitrary: ‘electrons or trees’ is just not on the same footing as ‘electrons’ or ‘trees’ as a natural kind or category.

So, having stated the framework within which I view the world and philosophy, I can move on to the role of the latter.

Although there is no sharp division between science and philosophy, the latter concerns problems within a larger framework, problems with no agreed method of solution, problems involving conceptual issues.

First, here are two things that won’t happen to philosophy:

1. Swallowed by science (as suggested by Stephen Hawking for instance).

2. Made redundant because all problems solved.

It will become clear as we proceed why I think these won’t happen.

Once upon a time all systematic intellectual inquiry was philosophy. If conceptual clarification and agreement as to systematic methods of dealing with a problem occur, the relevant area of philosophy buds off as a science. First, physics, with Galileo and Newton. More recently, biology after Darwin. And when the latter became a science, all the old wrangles about vitalism and how life could possibly arise from inert matter just evaporated. In my view the same thing is now happening with consciousness studies — wrangles about panpsychism, how consciousness could possibly arise from inert matter, conceivability arguments etc, and all the while cognitive neuroscience is in process of taking it over.

Another area is philosophy of language. After the mixed blessing of the 20th century ‘linguistic turn’ in analytic philosophy, most of semantics and syntax is now studied in the science of linguistics, whilst pragmatics has been absorbed by social science. Finally epistemology is becoming naturalized, and centuries of emphasis on scepticism may thankfully now be over, as well as the fruitless industry of trying to make the Justified-True-Belief notion of knowledge Gettier-proof. Instead we are making progress on how humans actually acquire knowledge, how the brain (‘Plato’s camera’) captures universals, forming maps of reality (conceptual frameworks), indexing and linking them.

All this talk of parts philosophy budding off as separate sciences might tempt us to think that eventually philosophy will disappear. But there are three good reasons to think otherwise:

1. Many of the old problems have not been solved

2. As the sciences develop, and technology advances, new philosophical problems arise.

3. The fact that an area of inquiry is a science doesn’t mean it’s all ‘done and dusted’.

Let us deal briefly with each.

1. Old problems unsolved.

Examples include: time; causation; free will; meaning; truth; the nature of justice, of the good life, of moral values; the a priori (is it even a coherent notion?).

2. Physics has already provided philosophers with relativity and quantum mechanics. and no agreed philosophical account of QM is in sight. It’s unclear whether string theory and loop quantum gravity are science or philosophy. Biology/ medicine has thrown up problems relating

to transplantation, euthanasia, abortion, and genetic engineering for example, indeed whole new fields of bioethics and neuroethics. Other examples include animal ‘rights’ and climate change.

3. A popular view of science is that it deals in facts (‘scientifically proven’, ‘clinically tried and tested’ etc), in certainties. But this is not so. At the limits of all areas of enquiry, philosophical, mathematical/logical, scientific, we encounter uncertainty, incompleteness, ambiguity, paradox, maybe even inconsistency (true contradictions), and these are not just due to our ignorance. Think of Godel’s Incompleteness Theorem; Turing’s Halting Problem; Chaitin’s Omega; Heisenberg’s Uncertainty Principle; quantum superposition and entanglement; Liar Sentences, Set Paradoxes and Paraconsistent Logic. And more to come I suspect. Enough to keep metaphysicists, ethicists, philosophical logicians, philosophers of science, and social and political philosophers busy for a long time.

Philosophy is becoming more naturalistic. Obsession with scepticism will fade, although the old sceptical puzzles will live on as exercises for the novice. Close links with science, maths, logic and politics will continue, as well as the traditional links with art and literature in the Continental tradition. Common themes in Eastern and in analytic philosophy will be further explored. Philosophy of religion remains vigorous but the emphasis has shifted to empirical study of religious belief/practice as a feature of human nature, rather than exposition of the divine attributes and justifying the ways of God to man.

I have had to be brief since this is an answer to a question, not a treatise, but I hope I have said enough to convince you that philosophy is alive and well in the postmodern era and has a rosy future.


Do laws actually make a difference?

Christopher asked:

Do laws really make a difference? Don’t we basically behave the same way regardless? I know laws can make a difference by punishing people who threaten the welfare of society, but do they deter those actions? If not, then could a society ‘work’ if it had no laws?

Answer by Shaun Williamson

This is not a question for philosophy. It is a question for psychology to answer. The proven answer (proven by experiment) is that laws do make a difference. Most people will obey the law as long as other conditions exist. One of these conditions is that they must have a reasonable expectation that the law will be enforced.

I know this from my own experience. In the 1980s when there were few parking wardens in central London it became obvious that some drivers would park anywhere. They parked on the pavements, they parked on yellow lines because they had little expectation that they would be penalised for it.

The situation got so bad in certain areas that vigilante groups of residents started gluing notices over the windscreens of cars that were blocking their pavements.

People are complex and different. There are people who will obey the law just because it is the law (unless they think the law is unjust). There are people who will only obey the law if they have an expectation of being penalised if they break the law. Then there are people who will not obey the law (sociopaths or psychopaths). Then there are the protesters who refuse to obey laws that they think are unjust.


Descartes’ argument for God’s existence in the 3rd Meditation

Sam asked:

Lay out the structure of Descartes argument for God’s existence in Meditation 3. What is the crucial premise in the argument, and what evidence does Descartes provide for it? How might we object to the argument?

Answer by Craig Skinner

Descartes doesn’t set out his arguments explicitly listing premises and conclusions. He antedates predicate logic and was no fan of syllogistic logic. He seems to think that God’s existence is pretty well self-evident, and arguments mere heuristic devices for the more slow-witted meditators.

He may therefore have been disappointed that his arguments were criticised rather than acclaimed by theologians (and others), as detailed in the Objections together with his Replies which Descartes published along with his Meditations.

His Causality Argument in Meditation 3 is a bit different from the Design Argument or the usual Cosmological Arguments; and from the Ontological Argument, his version of which is in Meditation 5. But we need to dip our toe into the waters of scholastic philosophy to grasp it.

A fair reconstruction is:

P1: I have the clear and distinct idea of God (a most perfect being: infinite, eternal, omnipotent, benevolent).

P2: A cause must be at least as great (real) as its effect.

C: This idea of God (P1) can’t be from (imperfect) me (P2). Its cause must be God or (impossibly) greater. So God exists.

The argument is valid. But it is sound only if P1 and P2 are true. Both can be challenged.

You ask what is the crucial premise.

All premises in an argument are crucial in the sense that if any one is false, the argument is unsound. Let’s count P2 as the crucial one because it looks a bit obscure, and was the one more criticized at the time. I will say something about P1 later.

Premise 2:

The relevant discussion is couched in technical scholastic terms. Two types of reality (being) are distinguished regarding ideas. The existence of an idea (its formal reality) and the content of an idea (its objective reality). Here ‘objective’ refers to the object contained in the idea, rather like the modern use of ‘subjective’ – it refers to the tree (say) in my mind, not the tree in the garden. The notion of degrees of reality is the introduced. Ideas all have the same degree of formal reality, all being states of mind, but differ in degrees of objective reality – lowest is a ‘mode’ (a property of a thing eg shape), intermediate is a finite substance, highest is an infinite substance.

P2 therefore expresses the ‘Causal Principle’: the degree of formal reality of the cause must be at least as great as the objective reality of the effect. Hence an idea whose content (objective reality) is infinite (my idea of God) can’t have its cause in a finite being (with less than infinite formal reality) such as me, only in God, so God exists.

What evidence does Descartes provide for P2?

None. It is simply an assertion. Philosophers like to call something a Principle — Principle of Sufficient Reason, Principle of Identity of Indiscernibles, Final Anthropic Principle etc — when they want us to swallow an idea without good argumentative support.

Objections to the argument:

P1 is questionable:

1. Descartes assumes we all have the same (God-given) innate ideas. But I can simply deny having the P1 idea. Gassendi (5th Objections) says our finite minds can’t have an idea of infinity. Descartes replies that we can – it’s our understanding that is limited, not the thing of which we have (limited) understanding. I side with Descartes here. But it doesn’t follow that I have a clear and distinct idea of God. Descartes gives no criteria for, or definition of, clear and distinct ideas, no guidance as to recognition of slightly unclear or somewhat indistinct ideas which are thereby unreliable.

2. The argument from clear and distinct ideas is viciously circular. The conclusion that God exists is based on a clear and distinct idea, but the truth of these ideas is only guaranteed by assuming the existence of God.

P2 is false: two objections (both by Mersenne, 2nd Objections)

1. The idea of God CAN come from me. Having some degree of perfection, I can posit higher and higher degrees of it.

Descartes replies that the idea does in a sense come from me. It is innate, planted by God. We couldn’t form the idea of God if God didn’t exist. But here, Descartes simply repeats the Causal Principle and begs the question.

2. Animals and plants (greater) come from inanimate causes (lesser). Descartes replies that animals lack reason and so have no perfection not found in inanimate matter, or, if they do, it comes from some other source. I find Descartes unpersuasive here, and would generalize Mersenne’s point to say that simple things plus simple rules can yield complexity eg simple initial conditions in the cosmos plus laws of nature allow atoms, compounds, galaxies, life and mind.

To say that finite minds need an infinite cause simply begs the question as to God’s existence.

In short, Descartes’ argument is unsound.

Of course neither Descartes nor anybody else has proved the existence of God. Belief in God is a matter of faith and revelation. If God existed he could show himself unequivocally (alleged revelations to date being highly dubious), but in the absence of this, no proof is possible in my view. Hence those of us unconvinced by revelation and unwilling to make leaps of faith should be, at least, agnostic.


More on ‘must everything that evolves have intelligence/ consciousness?’

Christopher asked:

This question is for Shaun Williamson:

You said in an answer to my question about ‘intelligence in evolution’ that, ‘Being conscious means having sensory awareness of the world and to have sensory awareness of the world you need sense organs and a nervous system.’ Doesn’t being aware of yourself also count as being conscious? Let’s say hypothetically that I have no way of sensing/perceiving the outside world, wouldn’t I still be conscious even without any awareness of anything except myself? Although, I can’t really imagine how I would perceive/ conceive without the external world to relate/ compare myself to.

Answer by Shaun Williamson

No, our idea of consciousness does not include just awareness of yourself. If it did we would all know that it did and you wouldn’t even have to ask the question.

Suppose the doctor says to the nurse ‘Is the patient conscious?’ and the nurse replies ‘He has no sensory awareness but still he might be aware of himself’. How is the doctor supposed to understand that. Suppose we say that a pebble on the beach has no brain and no senses but still it might have an inner awareness of itself. What can we make of that idea? It paints a picture but its not a picture we can do anything with.

You must remember that language (and therefore thought) was not invented by God. It was invented by men so that they could talk to each other about things that interest them. Now people can be self aware but they must also be conscious i.e. have awareness of the outside world before it makes sense to talk of them being self aware. If we say something like ‘He slowly became aware that he no longer loved his wife’ then we imagine that this dawning awareness could only happen when he was conscious (in the ordinary sense of that word). You can’t become aware of something when you are unconscious or asleep. You can dream that you have become aware of something but that is not the same as being aware of something.

Wittgenstein pointed out that when we are philosophizing our language has no context so we invent one for it and then it can sometimes seem that we can extend language is all sorts of interesting ways. ‘Philosophical problems arise when language goes on holiday’.


More on ‘can a perfect being create something imperfect’?

Christopher asked:

This question is a response to an answer I received from Jürgen Lawrenz about a perfect being and creation.

You stated that ‘God is a theological (theoretical and metaphysical) conception. Take him out of theory and into the world and you no longer have a God.’ But, if we are even to have the concept of god and have thoughts about god, then aren’t we already taking god out of the metaphysical realm and into the world since our thoughts are necessarily of this world? If I’m following your logic correctly, then simply conceiving of god automatically contradicts gods very existence.

Also you stated that, ‘This is not even mentioning that part where you speak of creating. Pure prejudice. What makes you state this assumption as if it was selfunderstood? Why should God create anything?’ I don’t understand what you mean by ‘pure prejudice,’ by me? I was certainly not trying to discriminate in any way, my assumptions about god creating us is based on religious texts. Also, I didn’t say anything about what god should or shouldn’t do, those who are religious believe he has already done the things I attributed to him. Were you trying to say that god was prejudice by creating this, but not that? Those are the only to implications/ interpretations of your statement I can find. Could you clarify please?

Answer by Jürgen Lawrenz

Dear Christopher: With such difficult matters, it is imperative to cultivate a very clear and unambiguous language to avoid getting tangled up in a morass of confusions. If you will read your subsidiary question carefully, you may see that you have inadvertently claimed that human concepts create god — that by being thought of (and named), god exists. I doubt that this is what you wished to say.

You come closer to the mark with your remark about my logic, but then you spoil it with another careless articulation. What is ‘simply conceiving of god’? Do you really think that anyone could ‘simply’ conceive of god and have something intelligible in their mind? If you wish to follow the philosophical drift of these issues, you must go on and state the attributes of such a conception; and when you do this, you should notice before long that only human analogies and natural forces comes to mind, which this god may indeed transcend: But it is a very limited concept. Pursue this thought a little further and you will find yourself with an unintelligible concept on your hands, namely how you can state the conditions of existence of this god.

It is precisely from such difficulties that the medieval thinkers defined god as having negative attributes, in other words, all the attributes that you can think of are not of god, but only of what your puny thoughts can elaborate. The actual attributes of god would all be incomprehensible to us, because they are plainly not based in any experience we can have. Therefore if from this basis you makes claims that such an indefinable god actually exists, you have a limited god on your hands: not an actual god, but a self-contradictory bundle of notions and ideas taken from the physical world and mingled up with a confused metaphysical clutter.

As for creativity, my remark was not essentially directed to you personally. It is true that the default ‘conception’ of god assumes that god is creative. But for this to make sense, you must leave your literal understanding out of the picture and approach the matter from the symbolical angle. Creativity is a creature attribute; but god is not a creature. It is not not possible for us to conceive how god might have created the physical universe in any literal understanding of this notion. Some of the scholastics, who were very deep thinkers on these issues, also pronounced negatively on it. It is mere human naivety, indeed presumptuousness, for us to ‘conceive’ that god may be obliged to create the universe before we humans can ‘conceive’ that he must have created us and everything.

So the difference is that many (millions of) people believe in an intelligible ‘fatherly’ god because they have been taught and are not encouraged to question those teachings. Accordingly they spontaneously associate god with a vague notion of a supernatural analogue of humans. On the other hand there are thinkers who grapple their whole life long with the tangled web of self-contradictions in which they become involved the moment that words like ‘omniscience’ or ‘eternity’ come up. They are aware that words denote things, yet matters relating to god mostly do not denote, because our minds are not capacious enough to contain the required denotations. This is why religion is a matter of faith, not of belief, nor of science, nor of knowledge.


Locke on personal identity

Jim asked:

We have to write an essay on the following:

Please write an argumentative essay in response to the following. Locke: whatever has the consciousness of present and past actions is the same person to whom they both belong (278). Explain and evaluate Locke’s claim.

I don’t really understand Locke’s statement. I thought it might mean that if for example I got drunk last night then today I learned from my actions last night and am therefore a different person that I was yesterday. I really need help. I just don’t really understand how I would approach writing this essay. Thanks!

Answer by Craig Skinner

The quote ‘Whatever has the consciousness of present and past actions is the same person to whom they both belong’ is from 27.16 of the famous chapter (27) ‘Of Identity and Diversity’ in Book 2 of Locke’s An Essay Concerning Human Understanding (2nd edition 1694).

Locke is not concerned here with learning from our actions or with moral improvement. He is concerned with what makes it the case that somebody is the same individual over a period of time. He is especially concerned with fair praise and blame, both in this life and at the Last Judgment, what he calls ‘forensic’ issues. Obviously praise/blame can only be fair if the individual being rewarded/punished is the SAME individual as the one who did the good/bad deeds.

So, what makes me the same individual as yesterday or last year?. Locke distinguishes between being the same Human Being (‘same Man’ as he puts it) and being the same Person. Neither depends on being the same Substance.

Being the same Human Being, like being the same plant or animal, is to be the same living, organized body, to be ‘the same continued life communicated to different particles of matter, as they happen successively to be united to that organized living body’ (27.8). In short I am the same Man as twenty years ago even although none of the atoms constituting me then is part of me now.

Being the same Person is to have continuity of consciousness – one presently remembers one’s past actions. Locke’s famous definition of ‘Person’ (27.9):

‘A thinking intelligent being, that has reason, and can consider it self as it self, the same thinking thing, in different times and places; which it does only by that consciousness, which is inseparable from thinking’

So Personal identity is not identity of Substance (one could swap one’s material body, or, Locke feels, one’s immaterial soul, without loss of identity) but identity (continuity) of consciousness.

Being the same Human Being and being the same Person needn’t always go together. Locke describes an early mind swap thought experiment. The mind of the Prince enters the body of the sleeping Cobbler (whose own mind departs). The individual who later wakes up is the same Man as was (the Cobbler), but a different Person (the Prince).

You can think of yourself as essentially a Human Being or as essentially a Person.

If you are essentially a Human Being, then you were once a zygote, then an embryo, a foetus, a child, an adult, and may sadly sustain brain damage and pass into a persistent vegetative state (PVS). If you were to get a brain transplant, you would be the same Man with a new brain, even though this brain thought as it did in the donor, just as a transplanted heart pumps blood as it did in the donor, so that the brain thinks it IS the person of the donor in a new body, like the Prince waking up in the Cobbler’s body.

If on the other hand you are essentially a Person, then YOU were never a zygote or an embryo, nor can you be a human in a PVS, for none of these has consciousness, far less continuity of consciousness. If your brain were transplanted into a new body you would think of this as YOU getting a new body rather than somebody else getting a new brain.

Each view has its counterintuitive aspect.

The Human Being view means that identity goes with the body not the brain in brain transplant/downloading thought experiments. On the other hand, the individual in the PVS is still YOU (as relatives mostly think, few take the Person view and think you no longer exist).

The Person view means that identity goes with the brain/mind in transplant/downloads. On the other hand YOU were never an embryo or a foetus, and the individual in the PVS is not YOU.

So, in short, the quotation we started with states the psychological, or memory, or continuity of consciousness criterion for being the same Person, namely you are conscious of your present actions and recall yourself doing past actions.

So in your ‘argumentative essay’, you need to:

1. Explain that the Locke quote states the condition for persisting Personal identity.

2. Distinguish between identity conditions for a Person and for a Human Being (‘Man’ in Locke’s text). Quote Locke’s definitions of (sameness) of Man and of Person.

3. Evaluate the pros and cons of Locke’s memory criterion for Personal identity.


(a) intuitive, corresponds to the common notion of a ‘self’

(b) allows fair dealing by the law and by God at the Last Judgment. At the latter (so the story goes) you may not even have a body, but are the same Person who did the deeds when embodied, and can remember doing them.


(a) what about discontinuities in consciousness (i) sleeping (ii) memory for distant events lost – Thomas Reid’s example of the Old General who remembers nothing of his boyhood – according to Locke the old man is not the same person as the boy, but he clearly is. On the other

hand is it fair to punish a person for something they can’t remember doing (she was mad, or drunk at the time; or is now demented). Locke thinks it is sometimes not fair.

(b) a big one this, the definition is circular, begging the question. How do you know that the memories you have are genuine rather than false or quasi- memories ? To suppose they are YOUR memories presupposes there is a YOU. Maybe we can say there must be an appropriate causal relation between me now and the memories I have.

(c) problems with split-brain/fission cases – which of the beings, both of which are psychologically continuous with you, IS you. Maybe neither, and what matters is survival (continuity of consciousness) not identity.

Finally, do read Locke’s Chapter 27 (or at least 27.8 to 27.29), it is one of the most important, influential, and still relevant parts of his philosophy.