BASIC RULES OF REASON
by I. A. RICHARDS
KEGAN PAUL, TRENCH, TRUBNER & Co., Ltd. LONDON, 1933
Psyche Miniatures, General Series No. 62

DIVISION OF PAGES
To The Reader7
I . A  LANGUAGE MACHINE9
II .THEORY OF KNOWLEDGE 1 - 822
III.THEORY OF CONNECTIONS 9 -1165
IV .THEORY OF INSTRUMENTS12-1889
List of the Chief Senses of Some Key Words in Discussion  130

IV . THEORY OF INSTRUMENTS

    The space and time connections of things are special examples of the connections of parts in systems, and the questions which come up with them, for the detail of winch we have to go to mathematics, are outside the range of these pages. But the senses of name and of the other words which may take its place are part of Logic. With the discussion of them we come to the third division of this book, the Theory of Instruments.
    The reader will have taken note of a number of words which have been used at important points without any special account of their sense being given. Among them have been agreement, same, different, property, quality, relation, general, special, degree, sort and is. What comes now is an attempt to put our uses of these words in a clear light. I take them together in a separate division under the name of Theory of Instruments because -- more, it may be, than with any other words -- we have to take care not to put the wrong questions about them. All words are instruments with winch we keep control of their senses : but these words are instruments with whose senses in addition to this we keep control of the senses of other words. It will be best to make a start with Property.

Property
    12-1 . In the simple everyday sense, a property is that of which some man is the owner, that which some man has.
    12-2. In a sense taken from 12-1, anything which anything (see thing, 2-2) may be said to be or to have (see is 13-1). For example : mountains are high -- have the property of being high; 6 is greater than 5 -- has the property of being greater than 5 ; men are not plants -- have the property of not being plants. No limit is necessary to the things we may, truly or falsely, say are properties of things. Everything is what it is -- has the property of being the same as itself. The moon has the property of having the property . . . of not being made of green cheese. This last is only another way of saying that the moon is not made of green cheese.
    But there is a danger of our taking properties as something more than other ways of saying what may be said without them. Experts in mathematics have said, for example, that "even if there were no things at all, there would still be the property of being seven in number -- though nothing would have this property". This danger may be overcome by keeping in mind that all properties are like this property of the moon -- that it is not made of green cheese.
    In other words a property is an instrument for making comparisons between statements, between thoughts, between the senses of words. But we commonly make use of properties as if they were something more, part of the structure of what we are having thoughts about or making statements about. ' X is green ' and X has the property of being green do not say different things -- the second is not a fuller account than the first. But they say the same thing in ways which are of use for different purposes, and these purposes for which the word property is of use have now to be taken into view.
    Here comparison may be made with our use of the words being and existence. To say. ' There are cats and dogs ' and to say ' There are beings which are cats and dogs ' or to say ' Cats and dogs have existence ' or to say ' Cats and dogs are things (2-1) ', or to say ' Cats and dogs have the property of having existence ' are only different ways of saying the same thing. Things, beings, existences, are words of use when we have a need to put into words thoughts which are not only about cats or only about dogs, or only about any limited sort of thing, but are about anything. In the same way property is a word of use when we have to do with thoughts not about green things only, or about coloured things only or about limited sorts of things, but about the ways in which things are in sorts. The danger is that we make use of property when there is no need for it, and so get the idea that ' X is green ' and ' X has the property of being green ' say different things.
    This will be the best place in which to take the word is. It has three chief senses.

Is
    13-1 . Existence . To say ' A is ' or ' There is an A ' is the same as saying ' A has existence ' or ' A has being ' or ' Something is A '.
    13-2 . Part and Sort . The is of connection. To say ' A is B ' puts A into the greater sort B. This connection between A and B may be taken in two ways
    13-21 . A is a part of the sort B. For example, ' Gold is a metal ' -- gold is part of the sort, metals : or
    13-22 . The properties common to B are part of the properties of A. Gold has the properties common to all metals and some more -- those which make it different from all other metals. These two ways of taking ' A is B ' are of use for different purposes.
    13-3 . Completely the same (in Logic ' identity '). To say ' A is B ' is the same as saying ' A has all the properties which B has and no others '. When this is so completely, and A and B are not different in any way, then they are not two things, but one thing. ' A ' and ' B ' are two names for one thing, and the statement ' A is B ' then becomes a bad way of saying this, because it is hard to keep in mind that A and B are not names for different things. We will see (pp. 101,119) some of the dangers which come from this.
    It is clear from this that same has two important and different senses ; one in which to say that two things (or groups of things) are the same is to say that in certain ways they are not different, another in which we are only saying that one thing, or group of things, has two names, or is being taken in two sorts.
    The three words property, sort and same, it will be noted, do almost the same work. So does the word general, to which we may now go on-coming back later to the discussion of the forms of properties.

General
    This word has one very important sense -- and some others which in different ways have come from it but are now almost opposites to one another. This makes it a very interesting example of the ways in which senses become changed.
    First take a look at these marks on the paper.     14-1. They are all marks. What they all are is what is general about them -- a general property of them. In addition to being marks they are all marks-used-in-printing. This is another general property of them, equally general in this sense. It comes from the sense of all -- which is all of a sort. But in another sense it is less general because marks-used-in-printing axe only a part of all marks. In the same way marks which are not marks used in printing may be on paper. To be a mark- on-paper is a more general property than to be a mark-used-in-printing and to be a mark-on-something is more general than to be a mark-on-paper. So, to be coloured is more general than to be green. This is a more general (14-11) sense of general, but one which comes from 141, for marks on paper are a part only of all marks.
    14-11. A thought (or a statement) which is about a greater group of things (having a group G as part of it) is more general than a thought about the things in group G or the things in a part of G.
    14-12. A thought of anything as being of a sort is a general thought : it is more or less general as the sort is greater or less.
    14-2 . Most of these marks here are full stops. We frequently say that something is generally so, when the sense of general is in most, but not all examples. This sense is an opposite of 14-l, where all examples have to be so for the statement to be< i>generally true.
    14-21. A statement about a great number of a group of things is a more general statement than one about a smaller number of them.
    14-22. Even more loosely generally may have the sense of frequently only. Some of these senses of general are taken by the word common. What is common to a group is what all the things in the group have (14-1). A property common in a group is one frequent in it (14-22). But common has two other important senses. A number of persons have something in common (a property 12-1) when no one of them is the owner, but they all taken together are the owner. And, a thing is said to be common when it has no special value, when it is so frequent that to have it does not make a man different from other men.
    The word used as an opposite to general is special. As some is to all, so special is to general in this first root sense. Special goes with general in 14-11. To be marks on paper is a more special property than to be only marks. So with 14-2 and 14-21. A special example is one which is different in some way from* most examples ; in this sense special is frequently used to give a suggestion of value. A special statement it may be noted is frequently one made for a special purpose.
    We saw in the discussion of sense 2-2 of thing, and in connection with the word ' abstract ' that a thing without its properties and a property without its things are equally incomplete, and that there are two ways of taking parts of the sense of a word from the other parts of its sense. An 'abstract' thought is (i) of a quality or property taken from the thing which has it ; or (ii) it is of a thing without the properties which it has. For example it may be a thought (A) of a leaf of a tree, as being green, soft, full of holes or folds, from a certain branch, and now in my hand and so on ; or we may have a thought (B) of it as being only a leaf, as having only the properties which are necessary if it is to be a leaf. To have a thought of it of the (in comparison) complete sort (A) is to have a ' concrete ' thought. A thought like (B) is of the opposite sort : it is an ' abstract ' thought.
    A ' concrete ' (or taken together) thought of a thing puts it with a great number of sorts. It puts this leaf here into the sort of green things, the sort of soft things, the sort of here-things, now-things, from-a-certain-branch-things, in-my-hand-things -- and so on. Every one of these sorts may be more or less general, 14-11. In place of taking it as a green thing, I might have taken it as a coloured thing, or as an able-to-be-seen-thing, for example, or as an apple-green thing, to go the other way and put it in a small special sort. And so with the other sorts I put it in. Now if the sorts I put it in are like the picture, so that it is the only thing which may be in (or of) these two lines or sorts, then we get an account of it
    [ diagram of an 'X'.]
which is as special as possible.
    The simplest way of making a thought special is by using the sorts here and now, or then and there -- by giving the thing which the thought is of a position in time and space, because our knowledge of the order of the positions of things in time and space is so complete that we are certain that one thing and only one thing has a given position. In Logic a thing of which we have a thought which is completely special -- that is, which is not a thought of any other thing in addition -- is sometimes named a 'particular', but there are other senses given to this word. Our only way to have a 'particular' is to put it into a number of sorts which have no other example in common.
    This and That, the most frequent names of particulars get their power by putting the things they are used for into groups of sorts which have only one example in common.
    From a completely ' concrete ' thought of a thing we may go in two ways, (i) to a thought of one or other of the sorts if is in, the properties it has, -- for example, to a thought of green or soft or thin, (ii) to a thought of it as something which has properties (see 2-2).
    Whichever way we go we come in the end to having a thought of it only as a thing (2-1). For example, from a thought of a bit of chalk as a white, powder-covered, dry, used-for-writing, in-my-hand, here, now, thing we may go on to thoughts of it as :--
    only a bit of chalk
    a bit of calcium carbonate (CaCO3)
    a bit of a chemical substance
    a substance (that is, a thing 2-1)
Or we may go off to thoughts of it as :--
    white
    coloured
    able to be seen
    able to be sensed (8-2)
    -- that is, a thing, 2-1
So ways of ' abstracting ' which seem at the start to be going in opposite directions come in the end to the same completely general thought.
    Sometimes it is not hard to see that one thought is more 'abstract' than another. But with 'This is green' and 'This is coloured', for example, no answer is at present possible. Our knowledge of how the mind does its work is not complete enough. We are able, on the other hand, to say that 'This is green' is less general than 'This is coloured' because green things are a part of coloured things. And this question 'How general is a thought ?' is much more important than the question 'How abstract is it ?'
    It is not hard to make completely general true statements : 'At all times something is going to take place' is an example. Equally it is not hard to make completely special true statements : 'This is quite this green'. What is hard is to make true general statements about special examples, statements true of all of a certain limited sort of things. In this attempt one danger is so common that an account of it may be of value. It is the danger of sorting things in the same way with two different forms of words, and then taking ourselves to have said something which is important about them -- not only about the senses of our words.
    For example, a number of writings may have some effect upon us which is the same. By this they are sorted. They are the writings which have the effect X on us. We then give them a name. They become, say, Poetry for us. We then put the question, ' What have these examples of Poetry in common? ' We tightly say, 'If they have no property in common then we have no reason to give them a common name'. But in saying this we frequently do not keep in mind that they have in common the property of causing-the-effect-X-in-us, and that this property has been used in sorting them. We go on to make attempts at the discovery of another common property. After much time and trouble and work we may be able to come upon some other common property which they all have, and which no other things have. But with most groups of writings to which we give the name Poetry this is not very probable. The only common property which they will probably have is the one we have used in sorting them at the start -- that of causing the effect X. Great numbers of serious persons have given this property two different names and said 'All poetry is beautiful ', or 'All poetry has form ', with an idea that they were saying some- thing more than ' What gives the effect X, gives the effect X '.
    But, someone may say, ' They would not be the cause of the effect X without having some other common property by which they give it. For the same effect to take place there has to be the same cause !' This is the point at which the danger comes in. There is a common belief that for the same effect there has to be the same cause, but this is false, if we take cause and effect in the only sense in which it is possible to take them here. That is, in sense 9-11, -- events which will be widely separate in time and space. Much takes place between the writing of a verse and its effect in the mind. A very great number of chains of events come in from other directions. For a parallel example, take as an effect, Death. What property is there which all things which are causes of death have in common? Poison, blows, knives, not enough air, falls, . . . ? Or what is the common property of all the causes of pleasure? Or of angry or delicate feelings ? We will be in agreement that the causes (9-11) of these will frequently be as different from one another as a smell from a noise.
    Only very simple persons make this error with Death or Pleasure, but numbers of persons who are not at all simple (or only simple in their ideas of logic) have made it with Poetry, Art, what is Beautiful, what is True and such things. The parallel with Death they do not see ; but they do see a parallel with the examples of Red, Sweet, Sharp and Long. Red things have a common effect upon us, and they have a common property (in almost all examples) by which they have this effect. The time and space distance between cause and effect is here very small. So it is with and Sharp and, in less degree, with Long. So here the argument from a common effect to another common property as the cause is a good one. But it is a very bad one with Beautiful Things or True Things' or Poetry or Art, because the chains of causes in between the things we say are Beautiful, are Poetry or Art, the other causes, and the effects in us are so long, complex and delicate. Generally (14-2) the properties which we take as the causes in works of art of their effects of this sort in us, are more probably these same effects themselves put by us back into our picture of the things. They are effects in us which we see as properties in them.
    With this we come back to property, quality and relation. Property is the general word. Under it may be put a division between qualities and relation-properties, though quality is frequently used in the same sense as property.
Quality
    15-1 . A quality is a property of which a complete account may be given naming any other thing (2-2) than the one which has the quality. A picture of a quality is Ab. Examples of Qualities : A is Red, A is Beautiful, A is Wise....

Quality has other senses:
    15-11 . It is used to give a suggestion of value -- as short for 'good quality'. In addition it is used in judging paintings and music when we have nothing more special to say -- as a sort of space in our statements into which we let other persons, if they are able, put something.

Relation
    16-1 . A relation is a property which puts two or more things (2-2) into connection with one another.
    Pictures of relations are A -- B
           B           B
    A<       A --<     B -- A -- C
           C           C

    Examples of Relations : A is greater than B ; A is the father of B. A is between B and C. A is later than B. A is better than B.
    A has much knowledge,
    A does the right thing at all times.
    By comparison of the last examples, and . . . others like them, with ' A is wise ', we see that the question, 'Is this a quality or a relation-property ?' is frequently one which may be answered in the two ways. The history of the language frequently makes us take a sense as a quality when a little more attention would make it clear that it is better to take it as a relation- property. Sometimes this has very serious effects upon thought. Most of the troubles which made the theory of relativity1 so slow in coming, and so hard for the general public to take in, came from the way in which position and time were taken to be qualities of things, not relations which they had to other things. A great number of dangers to thought of this sort are still strong and damaging in the present day theories of the mind. Young boys and girls before they are 7 years old generally take right and left (hand) as qualities. They have trouble in seeing how of three things :--
        A ----- B ----- C
    B is right of A and left of C. If B is right how may it not be right ? In the same way some experts in the theory of the Beautiful have great trouble in seeing how anything may .be beautiful and not beautiful. It seems probable that qualities are a special form of fiction whose purpose is to give us stronger feelings for things and keep us from wasting time unnecessarily.
    -----
    1  The theory that things are not in fixed times and places in a fixed time and space but that all things may only be measured in their relations to one another.
    -----

    An interesting and natural question comes up here. May the same fact be looked on as a quality and as a relation- property ? May Ab and A--B be the same as facts ? May they be two ways of taking one fact, or are they such that one has to be false if the other is true ? The answer seems to be that, if we are not attempting to say something about the structure of the fact, but are only sorting facts then they may be the same. If we are going into the structure of the fact, our question becomes one about fictions -- that is, about the use of our language machine. But a statement using qualities frequently seems very different from one using relation-properties. For example, 'X is beautiful' may sometimes seem very different from ' X has certain effects in certain minds'.
    Relations between relations are an important group of relations. For example, take A B C.
    (1) B is between A and C..
    (2) B comes before C and after A.
    (3) B is the son of A and father of C.
    Between these three -- a space, a time, and a cause relation -- there is a relation of being the same in one way. Let us make a comparison between these relations and A == B. The comparison gives us a different relation between relations. Relations, like other properties, may be general or special , being in a box, being in a certain part of a box ; they may be simple or complex: being the father of A, being the hated father of A , they may be ' abstract' or ' concrete' (see in comparison, pp. 34, 97) : being in a space relation to A, being in A. The detailed theory of relations has important developments in Logic and Mathematics.

Necessary
    Properties (qualities and relations) are of two sorts : necessary and chance.
    17-1 . A necessary property is one which a thing has under all conditions.
    17-2 . A chance property is one which a thing has only under some conditions.
    Examples :
    Necessary. Straight lines from the middle point to the limiting line of a circle are all equal. A is not not-A. What I have done I have done. The past may not be changed.
    Chance. Balfour had on a tall hat at the Versailles Conference, Clemenceau a round one. Every year millions of good apples are put in the water to keep the prices up. Death comes to all.
    The two words necessary and chance have a number of other senses which have to be kept out here, as the examples will make clear.
    17-11. We say something is necessary without which under present conditions things would not be as they are. Even when we see that it is not probable that conditions will ever be changed (as with the last example 'Death comes to all') the something is not necessary (in the 17-1 sense) if a. possible change in conditions might make things different. It is only where no change of conditions, however great, makes the property different that it is necessary in sense 17-1.
    17-12. A special and very common sense of necessary is that in which, if we have a desire to do something and there is only one way of doing it (or one way is better than any other) that way is said to be necessary.
    17-3. We say something is a chance when we have not enough knowledge of the conditions under which it takes place, or when (17-31) such knowledge as we have makes us ready for another thing to take place. But in 17-2 the degree of our knowledge of the causes of the thing does not come in. If with a change in conditions a change might come in the property, then it is a chance property.
    Another way of saying that a property of a thing is necessary in sense 17-1 is to say that it is not possible for this property of the thing to be changed. If it was changed the thing would then not be that thing. It would become another thing. So the question 'Is this a necessary (17-1) property ?' is a question about the senses of the words with which the thing and its property are being named -- that is a question about our thoughts of them.

Possible
    18-1. Something is possible when its being so does not make any change in our language machine necessary (17-11).
    This has to be taken with care. Any one language machine (any one group of senses) we make puts limits to the things which may said with it. What comes outside these limits is ( in this sense) not possible. By making a change in the machine (changing the senses of some of the words) we are frequently able to take in some of these not possible things and make them possible. But there are certain limits to all language machines, certain ways of working which are necessary (17-12) for all of them, however different the details of their working may be. For example, in all language machines, A is not not-A. If a sense is A it is not possible for it to be not-A. If we do not keep this rule the working of the machine goes wrong everywhere. In the chief sense of possible, the limit between what is possible and what is not possible is put by these rules, which are necessary for all language machines But we have not at present enough knowledge about the senses used in our language machines (if, for example, some words have one sense or a number of others which we have not at present given attention to) to be certain where these limits come, so a good working sense of possible is
    18-2. That is possible which the rules of our language machine seem to let as say.
    Other senses are common :--
    18-3. That is possible which is in agreement with our knowledge of the way things are, of fact (4-2).
    In this sense it is possible for a man to be running at 20 miles an hour, but not at 30 miles an hour. We are certain of this because we take the conditions under which he is running as fixed. But with a change in these conditions (running on the moon, for example) we would not be certain. It might be possible for him to take a run at 30 miles an hour then. So we have
    18-31. That is possible which, with a change of conditions, would not be out of agreement with our knowledge.
    We are still certain that with no change of conditions would he be able to take a run at 10,000 miles an hour. To do so he would have to become some different thing ; he would no longer be a man, or no longer be running.
    With this we come to probable and some of the most troubling questions in the theory of science. We have seen (p. 100) that it is not hard to make true general statements if we do not put anything special into them. 'Something will take place now' was the example And equally it is not hard to make completely special true statements : 'This is quite so'.
    We may take these two statements as necessary -- made true by the working of the language-machine and such that it is not possible for them to be false. Taking them so and putting them as the limits of the completely general and the completely special, all statements between these limits (and all knowledge) are only probable more or less. To give an account of probable we have to go back to the conditions of thought and knowledge.
    In knowledge (5-1) effects take place in our minds and their causes are what we have knowledge of. This is cause in sense 9-5. The general form of the conditions of knowledge (in 5-1) is the same as the general form of any other conditions. And the way in which knowledge takes place is the same as the way in which any other effect takes place. See the picture after 9-1. The questions 'What is a thought about ?' and 'How is it true ?' (in the senses which go with 5-1) are the same questions in different words. The questions 'How probable is it that the thought is true?' or 'that it is knowledge?' or 'that what it is of is a fact?' are again the same. The use of the word probable, as if a quite new question was coming in is the cause of most of our trouble here. Generally (14.2) the way we have of taking up the same question in new words without seeing that the question is the same, and the way we have of not seeing when the question is changed without the words being changed are the two chief causes of our errors. It is much harder to keep these changes in control than to give a right answer, in agreement with our knowledge, to any clear question,
    Any picture of cause and effect is (for this sense of knowledge) a picture of knowledge. But our use of other senses of knowledge and other ways of putting questions about it makes this hard for us to see. What we have to do here, is to put away other theories for a time, and go to the roots of our everyday ways of saying things about our knowledge.
    Take a simple example first.
    The noise of a bell comes to your ears. Something then takes place in your mind -- a thought of the bell. Here the bell is the cause of your thought of it in a clear way. (You may have in place of this, a thought of the noise of the bell not of the bell, or the noise may come to you through the radio.) Take note here that your thought is true.
    Now take a more complex example. Someone says the word bell to you or you see the word printed on this paper. Again a thought of a bell takes place in your mind. The effect of the word in your mind is the same in some ways as the effect of the bell itself would have been. The word is a sign or representative of the bell. How this comes about is a question to which we have at present only parts of the answer. A great amount of work is being done upon it, and it may be hoped that we will before very long have much more knowledge about it.
    To say that the word is a sign of the bell is to say that when the effect of the word comes into the mind, it is joined by chains of events which come from bells. The special property of the mind is that in it these joining of chains of events some times take place. The word bell has in the past come to our ears together with the noises of bells, the seeing of bells, the touching of bells and so on. This coming together of a number of events in the mind makes it possible for the mind to go through effects (have thoughts) the cause of which is not in fact present. The other cause, here the word bell, joined with it in the past, takes its place and so is its representative. Other things than words are representatives in this way, though words are our most ready examples. Here take note again that your thought is true. There are or have been bells, that is a condition of your being able to have thoughts about them. So, because your thought says no more than this, it is true.
    This joining together of causes, so that in the future one of them becomes the representative of the other when the other is not present, only takes place under special conditions of attention and interest -- about the detail of which our knowledge (5-12) is small. It only takes place sometimes. If this were not so, we would at all times be having all thoughts -- which would be as bad as not having any at all. In addition there are certain regular forms under which causes are joined together. The seeing of a bell is joined with the seeing of the word bell ; but, with the seeing of a bell, has in the past been joined the touching of it, the touching of other things, the hearing of it and of other things all through the history of our minds and back, probably, far into the early history of man, and the animals from which he came. So there is a fixed order in the ways in which causes of thoughts are joined together and this order is what we get in our picture of the way things are. A quite small change in our interests may be able to make this picture very different, and there is some reason for the view that the picture is being changed quickly at present.
    Now take an even more complex example. You see the words ' All bells are made of metal '. This group of words has an effect in your mind which is a representative of the effects of :--
    (1) Bells
    (2) Metal things
    (3) Anything made of something
    (4) Any groups with which you have had to take note of all of the things in them.
    All these are joined together in your mind in a way which you see, without trouble, is very different from, for example, the way of 'Some things are metal bells ' or ' All metal things are bells ' or ' Some bells are made of metal '. Your thought has a form, the effects the words have (effects which are representatives of other causes than the words-of bells, made-of-metal things, and groups of alls) come together in a certain way. Now, if in fact (4-4) all bells are made of metal, if, that is to say, these causes are together in the way in which the form of your thought takes them as being, then your thought is true. Here, in fact, it is false : in China and Japan some bells are made of wood !
    You have a way out. You may say that you were not taking into account any wood things with which persons may make noises. That for you a bell was a bell and a metal thing, that these wood things are only given the name bell because the right name was not at hand. In your sense of bell, ' All bells are made of metal ' is true because anything not made of metal would not be a bell.
    This is a very frequent position in arguments. The important question then is : 'Is your statement about the senses you are giving to your words or is it about the things you are having thoughts of ?' If it is taken to be about the senses of words, then it might give us knowledge and may be true or false. If if is taken to be about things, then it gives us no knowledge (the senses being fixed) and so is not true and not false. It only says again what has been said before with the word Bell. (See in Comparison pp.101-2, 'Poetry is the cause in us of the effect caused by poetry because it is Poetry ')
    All thought is sorting. We have thoughts of things only as being things of a sort. This is another way of Saying that thoughts are of their causes (9-3). When things have been sorted in one way with bells (as made of metal), if we go on sorting them in the same way only, by saying ' All bells are made of metal ' we are saying nothing. To say something we have to put them into a new sort. So, if we take bel1sto be instruments used for making certain noises for certain purposes in certain ways, and then say ' All bells are made of metal ', we are saying something because we are sorting them in a new way -- we are putting these things into the sort of things made of metal. In so doing we come into danger. What we say may not be true.
    Every statement not dependent only upon the working of the language machine (as with ' All bells (metal) are made of metal ') is in this danger, it may not be true. We may put this by saying that every statement is only probable in a high or low degree. This is again only a way of saying that the laws of cause and effect -- thoughts coming under their control -- are not certain. Probable is the word used when we are attempting to give a measure of the degree in which thoughts may safely be taken as true. Even the best tested laws of science, when they have been made separate from the rules of the language machine of science, are only probable in a high degree. And those of our thoughts which have not been taken into science and tested, are only probable in a degree which by comparison will seem very low. Most of them are general in senses 14-11 and 14-2, not in l4-1, which gives them a better chance of being true -- because any one of a number of different facts will make them true. But even so the space and time between the thoughts and their causes (what they are of) and the complex way in which the effects of different things are joined in them makes error probable. Error is the natural condition of man.
    This is the reason why the man of science, whenever he is able to do so, puts man-made instruments, whose tendencies to error he is able to keep in control, in the place of his mind. The camera for the eye, the balance for his muscles, and so on. And why, in addition, he makes use of mathematics -- much better language machine than everyday words because the discovery and control of its rules is not so hard. With the use of mathematics, the language machine for measuring, comes the tendency to put questions about degrees in place of questions about sorts.
    This division between degrees and sorts is not as important as it has seemed to some writers. It is parallel to one between amounts and qualities. Science, it is sometimes said, is only able to give accounts of those things which may be measured and says nothing about qualities. This is only true of those sciences which have been able to make statements about amounts do the work which in every-day language is done by statements about qualities. When this is not, at present, possible science makes use of qualities. Science does not put amounts in place of qualities because it has a desire (from a hate of living things and so on) to take qualities out of thought, but because statements about amounts may be made to do the work of thought better `1n some ways, though possibly not in others, Amounts are relations which are not so hard to put in order and keep in control as qualities. In the same way, degrees are a network of sorts which may be measured. A degree is a fixed amount by which examples in a general sort may be different from one another. In a general sort we put special sorts which are different by equal amounts.
    The question ' Are A and B different in degree or in sort ?' is common at certain turning-points of discussion. Put in this way it frequently seems a very deep question to which no certain answer may be given. For example, ' Is man different in sort from the animals or only in degree ?' Are the animals different in sort or degree from the plants, and the plants from the earth, red from blue, 'Communism ' from 'Capitalism ', seeing from hearing . . . and so on ? Some persons have a feeling that an answer one way will be very different In its effect from an answer the other way. These questions seem hard and deep and important because we have not first taken a decision as to what we are talking about. And we have not kept in view that a degree is one division of a sort -- a division by which comparisons between examples of the sort may be made. To make such division in a sort we have first to come to a decision as to which the sort is. A sort is a group of things with some property in common. And only when we have this property clearly in view are we able to go on to attempts to make divisions of amounts (degrees) of the property. These attempts are dependent upon our power of measuring and there are a great number of things which, at present, we have no power of measuring. Which is not to say that we will not ever have it.
    To give an answer to any question of the form ' Are A and B different in sort or in degree ?' it is necessary to have a clear idea of the properties which A and B have in common -- because it is not possible to put two things in comparison in any way if they have no property in common. (See in comparison change p. 83). Then we have to see if we have any way of measuring some property which they have in common. If we have no way, we have to say that, as far as our knowledge goes, they are different in sort and not only in degree. To say this is to say that we have not got the power, at present. We have such need of more powers in this troubled existence that this would, if we were wiser, seem a sad thing to have to say. But numbers of persons take great pleasure in saying, whenever possible, that things are different in sort and not only in degree. It is as if they had the thought that to say this makes things more free, that when a thing may be measured it is of less value. They seem to have the idea that more power over things would make our condition worse, not better ! The less foolish are probably in fear of the use to which other persons might put greater powers. The more foolish are in fear of having their thoughts about things put in better order.

    The end of this discussion is near, but the reader may be waiting for an answer to a question which has been in his mind from the first page. What is this Agreement on which almost everything in this apparatus of divisions seems to be dependent ? It came at the start in the account given of our purpose , it came again in the senses of thought, fiction, fad, knowledge, true, sense, and in the senses of of and about. It came, but not so openly, in the chief senses of cause and law. It is at the back of all our discussion of change, same, property, general, necessary, possible and probable. No other word seems so important, but no special discussion of it has been attempted till now in these pages.
    We have seen -- with true, with sense ;, with property, general and sort ; with possible and probable -- how the same questions may be put again and again in different words ; how a way, a form, a sort, a group, a property are all ways (sorts, forms, groups, properties) of things ; and how a thing may be a law, and a law again a way. The words with which discussion goes on are more in number -- though every word has its group of senses -- than the senses they are used to put in order. And at more than one place the trouble and danger to thought which come from our way of taking an answered question as a new one have been pointed out. Is this question ' What is Agreement ?' only the other questions ' What is a sort ?' 'What is a way of being the same ?' 'What is a general property ?' 'How are thoughts true ?' 'What is knowledge ?' and 'What is a cause ?' put in another form ? As questions -- as forms of words to which, when senses for them have been fixed, answers may be given -- these are or may be made, clearly different. But the fact (4-2) about which we put them seems to be one fact -- a very complex fact, of which a number of views, of parts of it, may be taken. The part which may not be clear -- for which a separate account of the senses of Agreement might be a help -- is covered by senses of the words general, property and cause. It is possible and not hard, to give a list of them by using these words. But then, someone might say 'Ah!I you are saying what Agreement is by using cause and general, and you said what cause and general are by using Agreement ! You are moving in a circle and your account of these things is only a trick !' If, on the other hand, I took some new words, say X and Y, with which to give an account of the Agreement which has been used in talking about knowledge, then someone would say, 'Ah I he has given no account of X and Y, the senses upon which everything in his system is dependent ; so it is not complete and has no base !' These two protests would equally be signs that the purpose of these pages has not been rightly taken. As was said at the start, this apparatus of senses is to be tested by the help it gives us in putting our thoughts in order, In letting us say what we have a need to say and keeping us from saying other things which will get in the way of our purposes. If it is a help, that help is its base. What the purposes are for which the machine may be a help is only made clear by the range of its uses. We are able to give an account of a purpose only by saying in detail what it is a purpose to do. A purpose, in this sense, is not something different from the way in which it may be worked out.
    There are other purposes than those whose limits are put by the language machine of which a rough account has been given in these pages. At certain points suggestions of these other purposes have been put in the form of possible senses for some of the words (see fact 4-3, knowledge 5-3, true 7-21) senses of which I have made little use in the later pages. With a farther working out of these purposes -- and of the purposes of this language machine -- it might be possible to see more clearly into their connections. It is the hope of everyone in whom thought about thought and its ways is a strong and frequent interest that by making one language-machine more complete, more clear, more delicate, room will be made for the senses and divisions of the other language-machines which are the servants of other purposes. Every system of thought makes some attempt to take into account other and different systems. Its power to do this is limited by the errors in itself -- in addition to the errors in them. This system here, this apparatus of senses, has in it a great number of errors. Some of them I see and would put right if, in my attempts at present to do so, new errors did not come in their place. It is printed because anything which may be of help, however little, may in these years be a step to better things.

    A last word.   If you do not clearly get the sense of what I have said you will, in making the attempt to get it, have gone through a great number of the possible senses of these words in your mind. It is not very important that you get my sense and no others, and not important if what I say is true or not. And it is not important for anyone to have any belief that what has been said here is so. What is important is to see that the sense of words may be taken in groups, and that if the form of one group of senses becomes clear to us, the form of other groups of senses, which we may not ever have put in connection with them, may become clear at the same time. This gives us new chances for the control of our thought and for taking over the knowledge we have of one field into other fields. As Colegidge said, ' that only is learning which comes again as power '. And to see how any sense is in relation to any other is to get a sort of learning which comes again as power.
 
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