Language and Logic

Language and certainty
A key question for the study of language is 'verification'. How can you show that a statement is true?

• Do you set out bits of evidence that correspond to each of the words used? (An empiricist might encourage you to do that. A reductionist might say that your statement was nonsense unless you could do it!) This assumes that language has a picturing or pointing function.
• Do you point to the internal logic of what you have said? If so, such truth does not depend upon evidence.

The distinction between synthetic and analytic statement has already been made. But language is complex: an average line of poetry, a joke, a command, a piece of moral advice or the whispered endearments of lovers can quickly dispel any simple theory of verification. We need to move on from 'Is it true?' to the broader issue of 'What, if anything, does it mean?' In examining the quest for certainty in Chapter 1, we looked at Descartes (who starts from himself as a thinking being) and at the empiricist approach. We saw the way in which Kant identified the contribution of the mind to our process of understanding the world, and also went back to Plato, noting the way in which, for him, the world of appearances is but a shadow play, and that reality is in the world of 'forms'. If we do not know exactly what the world is like, how can we know if our language reflects it accurately? Probably the greatest influence in shaping modern life is science, which (as we saw in Chapter 2) is based on observation of the world, and that it uses empirical data from which to form hypotheses. With the obvious success of science, it was very tempting for philosophers to see science as in some way a paradigm for the way in which knowledge as a whole could be gained. As science is based on observation, each claim it makes is backed up with reference to data of some sort. Without data, there is no science. The language used by science is therefore justified with reference to external objects. It 'pictures' them. A statement is true if it corresponds to what has been observed, and false if it does not so correspond. But can this test be applied to all language?

Logical positivism
Ludwig Wittgenstein (1889-1951), an Austrian who did most of his philosophy in Cambridge and studied under Bertrand Russell, was deeply impressed by the work done in mathematics and logic by Gottlob Frege (1848-1925), Russell and A N Whitehead, with whom Russell had written Principia Mathematica, a major work attempting to establish the logical foundations of mathematics. These thinkers had argued that logic and mathematics were not subjective; that is, they described features of the world, rather than simply showing ways in which the mind worked.

Wittgenstein suggested that philosophical problems would be solved if the language people used corresponded to the phenomenal world, both in terms of logic and the evidence for what was being said. In the opening statement of his hugely influential book, Tractatus (1921), he identifies the world with the sum of true propositions: 'The world is all that is the case.' But he has to acknowledge that there are, therefore, certain things of which one cannot speak. One of these is the subject self: 'The subject does not belong to the world; rather it is a limit of the world.' Another is the mystical sense of the world as a whole. Whatever cannot be shown to correspond to some observable reality, cannot be meaningfully spoken about. Wittgenstein's early approach to language presented it as a precise but narrowly defined tool for describing the phenomenal world.

His ideas were taken up by the Vienna Circle, a group of philosophers who met in that city during the 1920s and 30s. The approach they took is generally known as logical positivism. Broadly, it claims that:

• Analytic propositions tell us nothing about the world. They are true by definition, and therefore tautologies. They include the statements of logic and mathematics.
• Synthetic propositions are dependent upon evidence. Therefore there can be no necessary synthetic propositions.
• Metaphysics and theology are literally 'meaningless -since such statements are neither matters of logic (and therefore true by definition - a priori) nor are they provable by empirical evidence.
  

Moritz Schlick, one of the Vienna Circle, argued that the meaning of a statement is its method of verification. This became known as the Verification Principle.

Logical positivism was promoted by the British philosopher A J Ayer (1910-l989) in an important book entitled Language, Truth and Logic (1936). In that book he asks: 'What can philosophy do?' His answer is that is certainly cannot tell us the nature of reality as such - in other words, it cannot provide us with metaphysics. If we want to know about reality we have to rely upon the evidence of our senses. Philosophy cannot actually give new information about anything, but has a single important task: analysis and clarification. It looks at the words people use and analyses them, showing their logical implications. By doing so, philosophy clarifies otherwise muddled thought.

Ayer set out two forms of the Verification Principle.

1. A proposition is said to be verifiable if and only if its truth is conclusively established in experience (a strong form).
2. A proposition is verifiable if it is possible for experience to render it probable or if some possible sense experience would be relevant to the determination of its truth or falsehood (a weaker form).
   

Of course, other statements can have meaning, but Ayer is concerned with statements which have 'factual meaning' - in other words, if experience is not relevant to the truth or falsity of a statement, then that statement does not have factual meaning.
He argues that every genuine proposition, capable of being either true of false, should be either a tautology (in other words, true by definition) or else empirical hypothesis (something which makes a claim that can be verified by experience). For this reason, all metaphysics is regarded as nonsense for it claims to make statements that are outside empirical verification, but also not true by definition.

An example of the strong form 'There are three people in the next room.' Meaning: If you go into the next room, you will see three people there.

Of course, it is not always possible to check information that easily. Where the evidence is not available, it was thought important to be able to specify what sort of evidence would count for or against a statement.

An example of the weaker form 'Within the universe there are other planets supporting life.' Meaning: if you were able to examine every planet in the universe, you would find others with life on them. Although we have not been able to detect signs of carbon-based life like our own as yet, such a discovery would be able to show that the statement is true. The statement is therefore 'meaningful'.

Statements are meaningless if there is nothing that would count for or against their being true. On this basis, much of what passes for religious language, or aesthetics, or morality, would be categorised as 'meaningless', because none of these things can be specified in terms of concrete facts that can be checked by observation. It is a way of limiting the meaning of any statement to the scientific and empirical way of examining the world. if the only meaningful statement is one that make an empirical proposition, there is really nothing more to say. Ayer accepts that statements may be emotionally significant for him, but not literally significant - but it is literal significance which is taken to be the basis of certainty. Logical positivism encounters two main problems:

1. How do I know that what I think I see is actually there? I could ask other people to look, checking if they see the same thing. But that would never actually prove that the object was there - for there is no way of getting beyond the sense experiences to the thing-in-itself. However many bits of evidence I get, I can never have absolute proof that there is an external thing being observed: we could all be mistaken.
2. How do we verify the statement: 'The meaning of a statement is its method of verification?' Is it synthetic? if so what is the evidence for it? What evidence could count against it? Or is it analytic? If so then the word 'meaning' is logically the same as 'method of verification' and the theory doesn't say anything.
   

Showing the logical inconsistency within a theory is one way to discredit it, but it does not thereby render it of no further interest. The important thing about logical positivism is that it represents a particularly strong form of empiricism and a particularly narrow form of language. The service is has rendered philosophy is that, by showing what a wide range of propositions it considered 'meaningless', it required philosophers to revise and broaden their understanding of language, so that statements that are meaningless in simple 'picturing' terms take on meaning in other areas:
expressing feelings; giving commands; stating preferences. This whole range of linguistic uses therefore serves to illustrate the flexibility of communication, and the need to get beyond simple empiricism.

That said, the Verification Principle is a valuable check, to make sure that statements about personal preferences or commands do not parade themselves as though they were straightforward empirical statements of fact.
Interestingly, towards the end of his life (as illustrated by the interview extract on p. 34), Ayer was to admit that his thought had moved on since the time of writing Language, Truth and Logic (accepting that one might communicate aesthetic experience, for example), but it remained an important touchstone for a particular way of examining philosophy.
Few, today would want to take on the bold claims of meaning and certainty of the logical positivists or Ayer, since philosophy has in general recognised the far more flexible nature of language and of the meaning of statements, but they came from a period when science and mathematics were seen to provide suitable images of clarity and precision, and therefore became models of an approach to which ordinary language was pressed to conform.
But where does that leave general statements about the way the world is?

Language and perception
In what sense can a proposition be known to be true? In the Introduction we considered the way in which statements could be true by definition or true by experience. The former included statements of mathematics. Once the words were known, the truth or falsity of a statement followed automatically. But as we looked at statements based on experience, we found other problems. First of all, there is the uncertainty about any experience: it might always be mistaken or interpreted differently. Second, there is the way in which we have to use general words in order to describe particular things:

• Imagine a situation in which there were no general words. How would you describe a tree without the word 'tree', or without the words 'green', 'tall' or 'thick' etc. etc.? Each of these words, unlike a proper name, has a meaning which can be applied to a whole variety of individual things - indeed, learning a language is about learning the whole range of general terms which we can put together in order to describe particular things.
• Do these general terms refer to things that exist, or are they simply 'names'. Does 'goodness' exist, or is it just a name for certain kinds of things of which I approve? We saw this reflected in differences between Plato and Aristotle, and in the realist"nominalist debate.
• In looking at logical positivism, we saw a philosophy that was based on the 'picturing' function of language. Statements only had meaning if they reflected evidence (or potential evidence) from the world of the senses.
• How far can we trust our perception?
• Is perception the same as sense data?
  

It's all a matter of interpretation
There are drawings that can be interpreted in different ways.

Do you see the profiles of two people facing one another or do you see an elegant chalice? Try switching your perception from one to the other - notice the mental effort involved. Is there any difference between the one and the other perception - difference, that is, in what is actually being seen?

Have a look at this simple example opposite. Such visual games illustrate the ambiguity of all experience. As you make the mental effort to shift from one thing to the other, you are discovering the reality of 'experience as' - that all experience requires an element of interpretation, and that seeing a whole thing in one way will influence the perception of each individual part. Here is the dilemma facing any empirical method of verification for language:

• If all experience involved 'experiencing as'
• And if two people may therefore interpret the same data differently
• How do you decide between them or verify the truth of what they say?
  

Note
It seems curious that, in logical positivism, philosophy was developing a narrow view of meaning (that of picturing items of sense data) at the very time when science was starting to realise that there can be two different and incompatible ways of viewing things, both of which can be considered correct - as with the wave or particle theories of light.

Knowledge and language
As far as philosophers in the Anglo-American tradition were concerned (see Chapter 8 for the different approach taken by continental philosophy), for much of the 20th century, philosophy was dominated by the discussion of language. indeed, there was a feeling that this was all that philosophy was about - everything else being sorted out by sciences or politics or sociology. Philosophy, rather than having any specific content, was an activity, and that activity was to do with the sorting out of words and their meaning.
Philosophy has sometimes been given a role rather like that of an indigestion tablet - something necessary in order to purify the system and enable comfort and efficiency to return. So philosophy would help every other subject, by clearing away its confusions about language.
Early in the 20th century, as we saw, the logical positivists argued that the meaning of a statement was given as its method of verification. This view attempted to purge language of all that could not be reduced to sense experience. Metaphysics was out, and ethics was little more than the expression of a preference for certain things.
By the l950s this view of language was becoming broader. Wittgenstein (who, in the earlier phase of his work had espoused this radically reductionist approach to language) broadened his view, and accepted that language could take on different functions, of which straight description of phenomena was only one. This allowed more flexibility, and recognised that the expression of values and emotions, the giving or orders and making of requests, were all valid uses of language. They were all different 'language games'. In other words, language was no longer just 'picturing' reality, but found its meaning in its many different uses.
At this point, philosophers seemed to be catching up with common sense, and abandoning the purity of the unchallengeable statement as the goal of meaning. To know the meaning of a statement, you have to see it is its context and understand what it is intended to achieve. In Chapter 6 we shall be examining different tasks that language can perform in the field of ethics. What we need to recognise at this point is that language is not simple and transparent.

In other words People (hopefully) think before they speak. They may also perceive before they think. Therefore: What they say reflects the nature of thought and of perception. Language is therefore only as simple and straightforward as the thought and perception that produced it. Add intuition, emotion, existential angst and the general confusions of human life, and the resulting language is very complex indeed: It may perform many different functions. It may play many different games. We may not even be aware of the implications of what we are saying, which is to return to Plato, who in his dialogues portrays Socrates as a man who is constantly asking people what they mean, and thereby exposing their confusions and opening up the way to greater clarity. Without language we cannot have metaphysics or epistemology: indeed, we cannot have philosophy, civilisation, culture or other distinctively human features of life.

Linguistic philosophy
While the logical positivists were analysing statements in terms of the their verification through sense experience, other philosophers - notably, G E Moore (1873-1958) and J L Austin (1911-1960) -were investigating the ordinary use of words. Along with the broader approach taken by Wittgenstein, this led to the view that ordinary speech was an activity that could be analysed to show its internal logic and implications, and that such analysis would clarify meanings and therefore solve philosophical problems.
This approach, known as linguistic philosophy, became a dominant feature of philosophy in the l940s and 50s. In Chapter 4 we shall see that one of the most controversial books on the philosophy of mind at the time was entitled The Concept of Mind, and offered a radical view of mind based on the analysis of ordinary language.
And here is the key to what linguistic philosophy was about: it worked on the assumption that philosophical problems came about because of the ambiguities and confusions of normal speech. Once that speech could be analysed and its confusions exposed, new insights and clarity would emerge.
Linguistic philosophy therefore redefined the task of philosophy in terms of the clarification of language. We see linguistic philosophy having a significant influence on the philosophy of mind (in asking what we mean when we use words such as 'mind' or 'person'), or ethics (where moral statements can be considered in terms of recommending a course of action, for example). It is a way of doing philosophy, and it is not the same as the philosophy of language, which asks questions about how language develops, what it does and how it relates to those things which it describes or brings about, and how it is learned.

Formal logic
Logic is the branch of philosophy which examines the process of reasoning. When you start with a set of premises and reach a conclusion from them, the process of doing so is called deductive logic. An argument is valid if it is impossible for the conclusions to be false if the premises are true. An argument can be valid even if the premises are false (and therefore the conclusion is false); just because you are mistaken, it does not mean that your reasoning is not logical. An argument where the premises are true and the logic is valid is sound.

Note Deductive logic differs from the 'inductive' method of reasoning used by science. The inductive method starts with evidence and concludes that (on the balance of probability) this or that is to be expected in the future. A conclusion reached by that method is always open to be revised if there is new evidence. Deductive logic is not about evidence; it is the formal and abstract way of looking at the structure of an argument.

Logic has a long history. In Plato's dialogues we find Socrates debating with various people. He invites them to put forward propositions, and then analyses their implications and the arguments they have used. His argument often takes the form of  'If B follows from A, and B is clearly wrong, then A must also have been wrong.' But the main influence on logic for 2,000 years was Aristotle. He set down the basic features of deductive logic, in particular the syllogism, in which major and minor premises lead to a conclusion. The most quoted piece of logic ever, has to be the syllogism:

All men are mortal.
Socrates is a man.
Therefore Socrates is mortal.

This can be expressed as:

All As are B
C is an A
Therefore C is B.

From the basic syllogism, we can go on to explore the forms of inference - in other words, what can validly follow from what. Some principles of logic appear quite obvious, but are crucially important for clarifying arguments. William of Ockham (1285-1349), a logician who commented on Aristotle, is best known for his argument that one should not multiply entities unnecessarily. In other words, given a number of possible explanations, one should incline towards the simplest. This is generally known as Ockham's Razor.
Logic is often able to highlight common errors. One of these is known as the argumentam ad ignorantiam, which is to argue for something on the grounds that there is no evidence against it, whereas to establish that something is the case, one needs to show evidence for it.

In other words There may be no evidence that someone did not commit a particular crime, but that cannot be offered as proof that he or she did commit it. If this basic feature of logic were overlooked, the justice system would be in deep trouble. Notice that an argumentum ad ignorantiam may sometimes be slipped into a popular discussion of the paranormal: there is no evidence to show that extra-terrestrials were not the cause of some phenomenon, therefore, in the absence of any other explanation, we can take it that they were!

Logic can become very complex, with parts of an argument depending on others: 'If not this, then that, but if that then something else...' Clearly, it would be cumbersome to write out all the elements of each argument in order to examine the logic involved.
To overcome this problem, formal logic uses an artificial form of language. This language uses sets of letters, A, B, C, etc., to stand for the various component premises and conclusions, and also a set of signs to act as connectives. These signs stand for such logical steps as 'and', 'or', 'it is not the case that', 'if...then' and 'if and only if'. This use of artificial languages is particularly associated with the German philosopher and mathematician Gottlob Frege(1848-1925).

Example The connective 'if. .then' is shown by an arrow pointing to the right, the conclusion (therefore) is shown as a semi-colon. Take this argument: If I miss the train I arrive late at work. I have missed the train. Therefore I shall arrive late at work. We can formalise this by using the letter 'A' for 'I have missed the train' and 'B' for 'I will arrive late at work'. Rewritten, the argument becomes: A (A® B);B

An important feature of logic is that it breaks down each sentence into its component parts and makes clear the relationship between them. So formal logic helps to clarify exactly what is and what is not valid. Arguments set out in this way become very complex indeed, and there are a large number of unfamiliar signs used for the various connectives. If you pick up a copy of Russell and Whitehead's famous Principia Mathematica or browse through the Journal of Symbolic Logic you will see page after page of what looks like advanced mathematics or complex scientific formulae. For the uninitiated, it is extremely difficult to follow!

Mathematics
Much work on logic has been done by mathematicians, and that is not surprising, since mathematics - like logic - works on premises and rules. Two philosophers already mentioned, Frege and Russell, independently came to the conclusion that the rules of mathematics could be shown to be elementary logic, and that it should therefore be possible to prove the basis of mathematics. In their work, developed by Russell in Principia Mathematica (published in three parts, 1910-1913), mathematics becomes an extension of logic, and in theory (although not in practice, because it would take far too long to set down) all mathematical arguments could be derived from and expressed in logical form.
When we looked at the theory of knowledge, we came up against Kant's distinction between things that could be known through the senses and the structures imposed by the mind to enable us to make sense of and order our experience. Later we saw that statements may be divided into synthetic (depending on experience and uncertain) and analytic (known directly and certain). But where does mathematics fit into this scheme?
2+2=4 is a classic example of an analytic statement. One does not have to check numerous examples to come to the conclusion that their sum will always be 4 and never 5. The same is true in general of mathematics; it is a matter of logical deduction and certainty. But does that mean that mathematics is true only in the mind? Is it not the case that two things, added to another two things in the external] world, will always make four things? If this is so, then things in the 'real' world can be understood through mathematics and logic; it has to do with actual relationships, not simply with mental operations.

Comment If this were not so, how is it that theories about the origin of the universe come from professors of mathematics?

Perhaps, like so many other issues, this can be traced back to Plato. He held that numbers, or geometrical shapes such as triangles or squares, were all perfect; you don't get an 'almost square' or a 'nearly 2' in mathematics. But in the real world, nothing is quite that perfect. He therefore held that mathematics is about objects known through the mind rather than the senses, objects which (like his 'forms') belonged to a world different from the one we experience. Hence, mathematics could be known a priori, with a certainty impossible with things in this world.
Predictably, Aristotle countered this with the claim that mathematical concepts were abstractions and generalisations, based on things experienced. The debate between the Platonic and Aristotelian views has been very influential in the history of mathematics, as in so many other areas of philosophy. The philosophy of mathematics is a major area of study, beyond the scope of this book. All we need to note is the close relationship between mathematics and logic. Debate continues into whether arithmetic can validly be reduced to 'set theory' and whether mathematics as a whole can fully be reduced to logic, and if so, what the value is in making such a reduction.

In defence of the illogical
Just because Frege saw that mathematics was based on logic, and logic is concerned with the structure of language, it does not follow that all language is (or should be) presented with mathematical precision - any more than the logical positivists succeeded is eliminating all statements that could not be empirically verified. At the very end of Tractatus, Wittgenstein pointed out that there were some things on which one had to remain silent. In other words, they were beyond the scope of meaningful propositions, validated with reference to sense experience. But that has not stopped people speaking of them.
Language performs a great variety of functions, and its meaning is given by its function. When we move on to examine continental philosophy - including existentialism and postmodernism - we shall be exploring questions about the meanings that do not fit the more narrow parameters of analytic philosophy. We have to be prepared to explore the fact that a statement can communicate something of importance, even if - by the standards of an Aristotelian syllogism - it is illogical. This is not to make a value judgement, simply to point out that logical argument is not the only form of meaningful language.

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