It is by following clues that we make discoveries, not by reasoning inductively (see previous essays). Now some people would accept this view but nevertheless argue that in science we cannot avoid reasoning inductively. For , they say, suppose we have discovered a law of nature--let us say the law that all metals expand when heated. Now in saying that this is a law of nature we are saying that it holds not only in the past but also in the future. If it is a law of nature that all metals expand when heated, then metals will expand when heated not just today but also tomorrow. But how do we know they will expand tomorrow? Tomorrow has not yet come. If we know, we can only know by reasoning inductively (they say). The law has held in the past; therefore it will hold in the future. Reasoning from the past to the future is inductive reasoning.
In this paper I want to respond to this argument. My point will be, there is no need to reason inductively even in science. To help make my point I will draw on three examples.
Suppose you crack ciphers. You have been intercepting messages from a radio station which you have called Station A. The messages transmitted by Station A are encrypted by a cipher which you have already broken, a cipher which for your own convenience you have called Cipher X. Because you have already broken Cipher X, for the past six months you have been able to read every single message sent out by Station A. This morning you have intercepted another message. You have not deciphered it yet ...
How are you going to decipher your new message? Are you going to decipher it by using Cipher X, the cipher you have broken and which Station A has been using these past six months?
I think you are likely to say, 'Of course! '
So you will decipher the new message using Cipher X, as I too if I were in your position.
Let us now go over the situation again. You have broken Cipher X. You have been deciphering all messages from Station A using Cipher X. You are now about to decipher this newly intercepted message by using Cipher X.
Now considering what you have done and what you are about to do, can we infer that you are reasoning inductively? Is your reasoning the following?
Station A has been using Cipher X in the past six months. Therefore Station A will use Cipher X today.
Is this the reasoning behind the action you are about to take? Is this why you will use Cipher X to decipher the newly intercepted message?
I do not think this is your reasoning at all! True, you will use Cipher X to decipher the newly intercepted message but you will not be reasoning inductively. Instead, part of you reasoning is likely to be the following:
Station A has been using Cipher X in the past six months. Therefore Station A is not likely to be using Cipher X today.
Why will you reason this way? Why, if you are going to use Cipher X to decipher the newly intercepted message? If you are going to use Cipher X to decipher the newly intercepted message should it not mean that you think Station A is likely to use Cipher X today? If you think Station A is not likely to use Cipher X today why will you use Cipher X to decipher your newly intercepted message?
It seems irrational to try to decipher your newly intercepted message by using Cipher X when you think it is not likely that Station A is using Cipher X today. In fact of course it is not irrational at all. First, it is not irrational to think that the new message is not likely to be encrypted by Cipher X. As a cryptanalyst you know that the longer a cipher is in use the greater the chance it will be changed. By changing a cipher often you prevent it from being broken. Or, if it is broken you contain the amount of damage. Changing a cipher from time to time is a way of increasing security by those who use ciphers. The more often a cipher is changed the greater the security. Now six months is a long time. Station A should have changed their cipher a long time ago. Since they have not, today may well be the day on which they change their cipher. Therefore it is not likely that they will be using Cipher X today.
But if this is the case; if you expect the cipher to change; why will you still use Cipher X to decipher your newly intercepted message?
The answer is simple, as every one can tell. You will try Cipher X first. If it doesn't work you can then think of something else. Trying Cipher X is easy. The something else is difficult. If Cipher X works; if you can decipher your newly intercepted message using Cipher X; you will find out what the message says quickly. If Cipher X does not work; if you cannot decipher your newly intercepted message using Cipher X; you will have a new cipher to crack and cracking a cipher is difficult. Better to take the simpler route first before trying the harder. If the simpler route is the right one there is no need to try the other at all.
In your situation it is rational to use Cipher X to decipher your newly intercepted message. True, you do this with the knowledge that Station A has been using Cipher X the past six months, but your reasoning is not inductive. Rather, it is simply a matter of not crossing a bridge until you have to. It is not easy to crack a cipher. Why make the attempt if there is no need?
From the above we can see that there are situations in which we appear to be reasoning inductively when in fact we are not. When you use Cipher X to decipher your newly intercepted message you appear to be reasoning inductively. In fact you are not.
There are other lessons we can draw from this example about Station A, but I will leave them till later. In the meantime let us consider a second case.
Our second example has to do with Station B. Station B is more careful than Station A. Station B changes its cipher frequently. However, in order to make things simpler for themselves and for those with whom they are corresponding, they change their ciphers according to a scheme; that is, they have a formula which tells them when to change their cipher and what the new cipher should be, so that if you know this formula and one of the ciphers they have used you can work out all the ciphers they have used or will use. Of course you would not know about this scheme beforehand but since the change in cipher is structured; since it follows a formula; it is possible that in time you will catch on.
You have caught on. You have broken some of their ciphers and, after a time, you have broken their scheme as well. As a result of all this hard work you now know every cipher Station B has used and will use … until, of course, they change their scheme.
Whether or not Station B will change their scheme you will not be reasoning inductively with regard to the ciphers they will use. You will not say, because Station B has been using Cipher Y the past ten days Station B will use Cipher Y tomorrow. You will not reason this way because tomorrow may well be the day on which, according to their scheme, Station B changes its cipher.
Again, there will be other lessons to be learnt from this example but I will leave them till later. In the meantime, let us go on to the third example.
In this example we are dealing with Station C, a station, from all that we can tell, set up by amateurs. Station C, like Station B, changes its cipher frequently. In fact it changes it everyday. But every time Station C changes its cipher it does not do so completely. Most of the old cipher remains; only small parts are changed. As example in one instance, in the old cipher S stands for T and B for H. In the new cipher, S stands for H and B for T. The rest of the new cipher is exactly the same as the old.
Clearly the way Station C changes its cipher gives them no added security whatsoever. If you have broken their cipher today you can break their cipher tomorrow. The reason for this is simple. When Station C changes a cipher it only changes small parts of the cipher. Since most of the old cipher remains unchanged any new message you have intercepted can be deciphered in large part by using the old cipher. Once this is done context will tell you where the minor changes have occurred and what they are.
Professionals will not change their ciphers the way Station C changes theirs. Station C, however, may have reasons for doing things the way they do, or perhaps, as we have suggested, they are simply amateurs.
It is worth noticing that in this third case Station C, by introducing minor changes every time, could eventually end up with ciphers that are very different from those they originally use. But while this could happen once you have broken one of their ciphers you will have no trouble tracking them from that point onwards. Every new cipher they use you will be able to crack, doing so without too much difficulty.
There are lessons we can learn from our three examples, I have said. I want now to spell out some of these and apply them, by and by, to the way we think about the laws of nature. My main point is we can, and should, look at the laws of nature in such a way that no inductive reasoning is required.
One lesson that we have already learnt from our examples is that we could appear to be reasoning inductively when in fact we are not. We would keep on deciphering messages from Station A using Cipher X even though it grows less and less likely that Station A will use Cipher X. In that we will keep on using Cipher X we appear to be reasoning inductively. In fact we are not. We will keep on using Cipher X not because Station A has been using Cipher X the past six months and therefore likely to be using Cipher X again, but because we do not want to cross a bridge until we have to. Cracking a cipher is difficult; why make the attempt if there is no need?
One of the advantages in having knowledge is that we can be 'ahead' instead of being 'behind'. Station B changes its ciphers according to a formula; they have a scheme. When we have found out about this scheme we can tell ahead of time what their ciphers will be. In this case we know ahead of time what will happen. But the scheme can change; we have no control over the scheme. We can tell ahead of time what ciphers Station B will use only as long as their scheme remains in place. If they abandon their scheme we will stop having advance knowledge. In looking for knowledge we can be ahead sometimes, but not always.
We can tell ahead of time what cipher Station B will use because Station B adheres to a scheme: the changes in cipher occur according to a formula; they participate in a structure. Events participating in a structure can be predicted once the structure has been uncovered.
But Station B can abandon its scheme. Now if this abandonment is part of some structure it again can be predicted after the structure has been known. But if the abandonment is not part of some structure; if it is simply the result of a decision Station B makes; it cannot be predicted. Events not participating in some structure cannot be known ahead of time.
There can be structures within structures. Station B uses ciphers that are breakable. A breakable cipher is structured. These ciphers that Station B uses are governed by a scheme which is also structured. In the same way that there could be layers of structures in the case of ciphers there could be layers of structures in the universe. This is to say, there could be laws of nature at different levels. Laws at a deeper level could govern those on the level above. The scheme Station B uses governs the ciphers they use. The scheme is deeper than the ciphers.
When searching for knowledge, at the deepest level that we have reached we are always one step behind. We do not know at this time whether the scheme Station B uses is governed by a deeper scheme. If it is not and Station B abandons its scheme tomorrow we can only find out after the fact. If the scheme Station B uses is governed by a deeper scheme, since we do not know this deeper scheme at this time, we are already one step behind.
In looking for knowledge, even though sometimes we are ahead of the world, at the deepest level we are always one step behind. When we are ahead; when we can predict; we have power: the foreknowledge allows us to arrange things in such a way as to suit our purposes. But this power has a limit; we are not omnipotent: at the deepest level we are always one step behind.
We do not know that all the laws of nature will not change radically tomorrow: we cannot dictate to the world how it should behave; we are not omnipotent. But if all the laws of nature change radically tomorrow we will be in a very tight spot--assuming that we are still around. If they all change and we are still around, we will have to discover these laws all over again, which might take millions of years even if we should eventually succeed. But it is likely that we will not be around. The human organism is not such that it can remain intact whatever the laws of nature.
That all the laws of nature should change radically tomorrow is not a situation that we can make any provisions for. But we cannot predict it will not happen. A cipher in use for a long time can change overnight, so can all the laws of nature.
If it is a situation for which we cannot make any provisions does it mean then that we have to behave as though all the laws of nature will not change? In our example about Station A did we not behave as though Cipher X had not been replaced even though we knew it might?
But we did not behave as though Cipher X had not been replaced! No cryptanalyst worth her salt would. We used Cipher X to decipher our newly intercepted message only as a first step. We were aware that Cipher X might not work today. If Cipher X did not work we would have to take additional steps. Now it is possible that all the laws of nature will change radically tomorrow but it is also possible that only some of them will change while the rest remains the same. (If we think it is a contradiction in terms to speak of laws of nature changing we will have to change the definition of 'laws of nature'.) Laws of nature describe the structure of nature. Some structures change in time but not completely: the ciphers used by Station C changes with time but only in minor ways. If some of the laws of nature change but most of them do not, by paying attention we can find out (as we did with the ciphers used by Station C). Therefore, even though there is nothing we can do if all the laws change we should not behave as though none of them will change. We have to make allowances in our behaviour so that if some of them change while most remain the same we can find out.
It is possible that some laws of nature will not only change but do so according to a structured scheme--as with the ciphers used by Station B. If this is the case there should be clues. We should be on the lookout for these clues.
Suppose we have discovered a scheme according to which some of the laws of nature change. Even then there is no guarantee that such a scheme will last for ever. Station B has a scheme for the ciphers they use, but if they chose to they could abandon their scheme tomorrow. In looking for knowledge, we have said, ultimately we are always one step behind.
Suppose the structures in nature change in minor ways but not according to a scheme--as with the ciphers used by Station C; it should be relatively easy for us to track these changes through time. The emphasis here is on 'relative'. Tracking these changes will not be easy in an absolute sense. Scientists have been tracking changes in structure of some viruses. This is not a task any one can do. But it is possible--because in the time the structure of a virus is changing, most of the other structures in nature remain more or less the same. Because these other structures have not changed in a radical way we can detect the changes in viruses.
Will metals expand tomorrow when heated? We do not know that they will. We do not know that they will not either. If we had to use this law in any way tomorrow, in building bridges for example, or even in solving theoretical problems, as a first step we will use it as we have been using it. If it turns out not to hold we will then contemplate what to do next. We cannot provide for the possibility that all the laws of nature will change radically tomorrow. The most allowance we can make at any time, and this is the allowance we should make, is for most of the structures in nature to remain the same and only a small fraction to change at any one time.
Suppose tomorrow comes and we have intercepted a new message from Station C. If we can decipher most of this message using the same cipher we are using today, we know then that Station C has not changed its cipher radically, that the cipher Station C is using tomorrow is largely the same as the cipher it is using today. Similarly, if we can go about our chores tomorrow more or less the same way we can today, we know then that the laws of nature have not changed radically, that more likely than not, all metals will expand when heated.