a) When we assert that something is possible we are asserting that it may or may not be the case, that and nothing more. In order to do this we must have a quite clear idea of what would count for us as its being the case and what would count for us as its not being the case - which is why logical categories are so important. We could not, for instance (see above), have a clear idea of what would count as the answer to a question being blue or not blue.

Now, sitting here at my desk I do not know whether or not a bird is, at the moment, flying over my house - plainly it is possible; I know, in terms of what I would see, hear etc., what it would be like but I don't know whether it is happening because I happen to be indoors.

b) Now, supposing I go outside and there before me is a bird flying over my house; what I called a possibility has become (for me) an actuality, an instance of what is the case. But this does not mean that something about the bird's flight has changed, that it was one of these, a possibility, and now it is one of those, an actuality. All that it means is that this possibility happens to be an actuality. It might not have been, that is why it is a possibility - but we are now satisfied that it is also an actuality. Here compare: He has a dog; it may be a spaniel; yes, by Jove, it is a spaniel. There is no suggestion here that it thereby ceases to be a dog. If it were not a dog it could not be a spaniel. And, by the same token, if it were not a possibility, it could not be an actuality. So, let us be quite clear that actualities are simply those possibilities which happen to be the case. We say `happen to be' because, clearly, they did not have to be; the dog could have turned out to be a Labrador.

This is important to grasp: actualities are not exclusively different from possibilities, they are a sub-class of possibilities. We could express this in Aristotelian logical terms as: All actualities are possibilities but only some possibilities are actualities.

c) But you may have spotted a problem here. The idea of what would count as a pig flying over my house is just as clear to me as that of what would count as a bird flying over - so, by the rule put forward for what counts as a possibility, the one is just as much a possibility as the other. After all, it is simply our experience of the world which leads us to be confident that pigs never fly; we may be quite sure that in fact they never could but remember that a hundred years ago nearly everyone was pretty sure that a clear vision of what is going on could not be projected electronically across the world. There is nothing in what-counts-as-being-a-pig that precludes one flying and we do know what it would look like though it is a possibility which, I think, none of us would expect to happen to be an actuality. But note here that an infant with no experience of either pigs or geese would find a flying pig no more or less surprising than a flying goose.

This alleged problem has led many people who should know better to claim, and alas to teach, that either:

Some possibilities are more possible than others - or

We should make a distinction between actual possibilities (like that a bird is flying over) and merely logical possibilities (like that a pig is flying over).

Before we go any further, I want to get rid of both these bits of nonsense.

d) If you have a concept of fatness, and I am sure you do, one of the things you will realise it makes sense to say, is that one chap is fatter than another. If you have a concept of deadness, and again I am sure you do, then you will recognise that it does not make sense to say that one chap is deader than another; `Is he dead? - Yes, very' is intended to be a joke. There are degrees of fatness but not degrees of deadness; either you are dead or you are alive (not dead).

Now think about possibility - all it amounts to is that a given situation may or may not pertain. How could there be any more or less, any degrees of difference about this? We are not saying it is or it isn't, only that it could be. So the suggestion that something is more possible than something else is plainly just as silly as the suggestion that a colour might be unfriendly or an answer bright red.

So, lets have no nonsense about one possibility being more possible than another possibility and now - let's look at the other furphy, the alleged distinction between actual and `merely logical' possibilities.

e) The first point is that possibility is essentially a `logical notion'. It is not `part of the world'; it is part of our understanding of the world. We cannot distinguish logical possibilities from some other kind (illogical possibilities?). To say that X is a possibility is merely to say that X might or might not be the case - logical analysis. Indeed, in elementary formal logic there is even a standard symbol for it; a Vb indicates that either a is the case or b is the case, that either is possible; what is not possible is that neither is the case. This being so, talking about a logical possibility is a bit like talking about a feline tiger. But, to the extent that `logical' can be attached to `possibility' at all it can be attached to all possibilities.

Now consider actuality again. If X is a fox, X is an actual fox; there are no unactual foxes (they would not be foxes). We can use terms like `actual' to distinguish between imitations and the `real thing' - but if X is an imitation fox, then it is an actual imitation fox.

So- when we say that X is a possibility we are not implying that X is an actuality - it might not be; that is what being a possibility amounts to. But we are saying it is an actual possibility; there are no more unactual possibilities than there are unactual foxes!

Nor can we talk intelligibly of `merely possibly possibilities' - if X is possible it is possible, not possibly possible; that is plainly nonsense. There just could not be an impossible possibility.

Now, if in order to be a child, one must be human and must be young, we cannot make an intelligible distinction between human children and young children. If it it be a young child it must be human and if it be a human child it must be young.

Similarly, since all possibilities must be both logical and actual, we cannot make an intelligible distinction between logical possibilities and actual possibilities. So we are left with the simple and consistent identification: the possible is the thinkable.

But this leaves us with two questions to answer:

If whatever is thinkable is possible, what are we contrasting possibility with; what is the unthinkable? - and

Since there plainly is some kind of distinction between the possibility that a bird is flying and the possibility that a pig is flying, how can we explain this difference without descending into nonsense?

We'll look at the second one first.

3.The Concept of Probability (Likeliness)

a) As acknowledged - there is a difference between flying bird and flying pig. It cannot be a difference of possibility (there are no degrees of possibility; both are equally thinkable) - so the difference can only be of probability. Things are more or less probable; probability does `have degrees'. Nothing can be `a little bit possible' any more than a woman can be a little bit pregnant - but things are slightly or highly probable.

b) Probability is not a `logical notion' (in the way that possibility and actuality are); it is a `psychological notion'. It is intelligible only in terms of our expectations of what will occur.

We can, therefore think of the probability of X being so (in somebody's view) as ranging from .001% to 99.999%. We do not want to say 100% because to assert 100% probability would be to assert an actuality - and it is at least odd to call the actual `probable'.

Nor can we say it ranges from NIL. Every possibility must have some degree of probability - or it would not be possible. We cannot assert both that it might be the case and that there is no probability that it is the case.

We can and do, however, regard some probabilities as so low that they can be wholly discounted - as we would (I think) the probability of a pig flying over the building - or as so high that they can be accepted as actuality - as I do with the probability that my name is Smith.

But it must be understood here that, in assessing probabilities, we are resting on experience, not on conceptual analysis.

c) Consider what counts (for me) as an X% probability that Y will occur (or that Y is so). I identify (this as) a Z situation and I recall that, in X % of all Z situations I am aware of, Y has occurred (or been so). It is most important to realise that, provided I am right in my identification and my recollections, there is (by my experience) an X% probability of Y - and this would not be altered by the fact that Y did not occur in the particular case under consideration. To say that X is very probable is not to say that X is so. Thus it makes quite good sense to assert that, due to the condition of the car a breakdown was very probable, though no breakdown occurred. It would be incorrect, or at least misleading, to say that it seemed probable.

This does not imply that the assertion `a breakdown is very probable' cannot be false. But it is false if, and only if, conditions of cars similar to those noted have not in fact led to breakdowns in a high proportion of cases.

d) So, it is really very simple. The important, and only, difference between the possibility of the bird flying overhead and the possibility of the pig flying overhead is that the first is deemed to be extremely probable and would, therefore, occasion no surprise whilst the second is deemed to be extremely improbable and would, therefore, cause astonishment. It should be born in mind, however, that an infant with no experience of the world at all would not find one any more surprising than the other; our deeming of probabilities is essentially experience-conditioned.

4. The Concept of Necessity (Essentialness)

a) Which brings us, very appropriately, to our other problem, what is the unthinkable, because here we are dealing, not with our conditioning by experience, but with that reasoning capacity (which, for the present at least, we shall call intuitive) that enables us to gain and to order our experience of the world about us.

Unfortunately, in everyday speech people often say things like `The Pope would never renounce Catholicism; that would be unthinkable.` But plainly this must be untrue because, if it were unthinkable, they would have no idea what they were saying and no reason, therefore, to deem it very, very improbable; they must have a clear idea of what it would be like (i.e. have thought it) to make the remark at all. In philosophy we need to take `unthinkable' seriously - that which of necessity defies thought. Here is a simple illustration: It is quite possible, albeit very rare, for a man to be older than his uncle but it is not possible (impossible, unthinkable, necessarily-not-so) for a man to be older than his father. To realise this we do not need to rush round the world interviewing chaps and their uncles and fathers, we need simply to consider what counts as being an uncle and what counts as being a father to realise that any man must be younger than his father.

b) To say that X is possible is to say that X might or might not be so. We could, therefore, say that the concept is might-ness. When we turn to necessity the concept ismustness. We are saying that X must be so (or must be not so).

A very common confusion is between necessity and actuality, To say that X is so is not to say that it must be. This paper is white - but it could have been green (that is quite thinkable).

It must(!) be understood that the actual is a sub-division of the possile (mightness) - and a `might' cannot be a `must'. Thus, when we say such things as `I simply must get this job done` we are misusing `must'; my getting it done is a possibility (with whatever degree of probability it has).

[Here note the misuse of `must' above. That people do not understand this is, regrettably, quite conceivable.]

c) We do encounter correct uses of `must' and `necessary' in ordinary discourse from time to time. For instance `Our Fred' must be taller than her Charlie because your Sam is taller than Charlie (I've seen them together) and our Fred is taller than your Sam as you can see' - - or`I know he's from the U.K. but he's not necessarily English; he may be Scottish' In these bits of conversation we have quite correct uses of `must' and ` and `necessity' and we also have examples of how people do think, do work things out. Indeed most of our (correct) uses of necessity are not in speech at all, but in our reasoning processes.

It is important to realise that Aristotle when he produced his `formal logic' (or syllogistic reasoning) did not invent anything or produce a better kind of thinking; he merely codified and indicated the `rules' by which people (and, indeed, other animals too) do in fact reason when they reason successfully. I do not particularly recommend a study of elementary, formal logic but it is worth noting that the `logical rules' are such things as: If all X's are Y, then some Y's must be X; if no X's are Y then no Y's could be X; If all X's are Y and this is an X then this must be a Y; if this is either an X or a Y, and it isn't an X, then it must be a Y. So consider: `He's a pretty learned sort of chap (and all professors are learned chaps) so he may be a professor' or `a dolphin can't be a fish because it's a mammal and no mammals are fish" or `He must have been to University because he's a dentist and all dentists have university degrees' or `It must be a female magpie because it doesn't have a white back and all male magpies do (and it must be either a male or a female)'.

d) These are just the ordinary thinking processes that we use all of our waking lives. (If there is an ornithologist in the house, he is probably pointing out that young male and female magpies look pretty well alike. This is true - but irrelevant. We are concerned here with valid reasoning, not with what happens to be the case. For instance: since all green things are cabbages and all men are green, all men must be cabbages - this is a quite sound piece of reasoning although it is built upon pretty awful observations of what possibilities are in fact actualities in the real world out there.) Note that the `rules' which these processes are applying all begin with `if'; there are no categorical necessities, only hypothetical ones. What we can say (quite categorically) is `That person is not a man so it must be a woman' but the reasoning which justifies our saying it is "If people are either men or women and that person is not a man then that person is a woman" and, for us, the probability that people are either male or female (and not hermaphrodites) is so high that we take it as a basic premise for argument that grown up people are either men or women.

So, what we utter categorically is never what must be the case. No state of affairs (actuality) can be a necessity since it must be a possibility. What we utter (categorically) is what we believe to be the case, which is why believing is the next topic for us to consider.

e) But before moving on to an examination of believing it may be as well to be familiar with some of the terminology which frequently occurs in references to possibility and necessity.

A term you may well encounter is `tautology'. A tautology is an assertion of a necessity in categorical form so that it appears to be telling us something about the state of affairs when it is not.

For example: `Having this accident was not intentional'. Plainly, once we have identified an accident as such we know it was not intentional. Not being intentional is part of what count as being an accident.

This, of course, is terribly obvious but many tautologies are less obvious. When a politician says `Unless we can export at least as much, in value terms, as we import, then our trade balance will suffer" not everyone realises immediately that he is simply asserting the self-evident.

It is important to note, however, that whereas tautologies are `rendered trivial' (i.e. not really telling us anything we didn't know) by the necessary relations between concepts, they are not (per se) assertions of necessities. `This husband is married' still assumes the possibility that this man is a husband; he might not be. `If he is a husband, he is married' tells us about how words should be used, not about states of affairs in the world. Compare: `If it is a dragon it will breathe fire'.

Two other terms which people should be familiar with are `analytic' and `synthetic'. We have considered analysis already - the `breaking down' of something (in this case, a concept) into its component parts. An analytic assertion is one which, in effect, spells this out (e.g. if he is a father he has offspring). Synthesis, on the other hand, is the joining together of two (compatible but independent) concepts to create a new (more complex) concept (e.g. pen-ness and blueness to create blue-pen-ness). So that when we say `My pen is `blue' we are telling people something they may not have known. It is plainly possible for my pen to have been red.

So - synthetic assertions deal in possibility; analytic assertions deal in necessity. And when we `write off' an assertion made as `merely analytic' we are saying that it is a tautology.

It should now be plain to you that possibility and probability and actuality all belong as it were to the object of our thought, whereas necessity belongs to the thought process itself. There are no necessities in the world; necessities are `in' argument (reasoning) about the world.

Notice how often in these notes I have used terms like `must', `have to', `whenever', `only if', `therefore', `unless', `so' ...These are `necessity words'. They refer, not to states of affairs as such, but to our intuitive realisations (thinkability) that if X is so Y must be so, that X implies Y.