In Russell’s ‘An Inquiry into Meaning and Truth’ he discussed how we apply propositions involving ‘negation’ and the relation of these propositions to experience. Russell’s primary concern was how experience could show that a proposition is false. He noted that while negative propositions seem to have an immediate relation to experience they in fact involve not immediate experience; but perceptual judgements. Thus suppose we are told that the fridge contains cheese and butter. When we look in the fridge we immediately see the cheese, however when we look in the fridge we also discover that there is no butter. Russell thinks that discovering that cheese is in the fridge and discovering that butter is not in the fridge are not of the same logical type.
When we look in the fridge we do not see the absence of butter, rather we see a series of products. We then judge that these products are not butter, and as they are only products in the fridge, we judge that there is not butter in the fridge. Russell also notes that to make a negative judgement involves linguistic capacities. If a non-linguistic creature peered into the larder and just looked at what was there and made arbitrary judgements about what was not there; the creature could make an infinite amount of judgements as to what was not in the larder. There are a potential infinite amount of objects that are not in the larder at any given moment. He argues that when one involves linguistic communication this potentially infinite amount of negative judgements gets paired down. Thus, if someone will says ‘there is butter and cheese in the fridge’, this will make it more likely that the other person will make the judgement that there is ‘no butter in the fridge’ when they do the relevant search.
Russell’s discussion of negative propositions is admirably done in relation to concrete examples. He asks us to consider a very simple negation: ‘This is not white’. We are to imagine that we said the above statement in response to a judgement about laundry (An Inquiry into Meaning and Truth p. 77). So we have in our minds eye the proposition ‘this is white’ but your direct experience elicits the proposition ‘this is grey’. The question is how do we go from the proposition in our minds eye, the proposition elicited by our direct experience to the negative judgement ‘this is not white’?
Russell offers two possible ways to arrive at the negative proposition:
(1) You know the general proposition ‘what is grey is not white’, and from this together with ‘this is grey’ you derive the proposition ‘this is not white’.
(2) You confront the word ‘white’ with what you see and perceive an incompatibility. (ibid p. 77)
Russell notes that from the point of view of pure logic (1) or (2) must be the correct answer. As from you cannot logically derive conclusions that are negations from premises which don’t contain negations (ibid p. 77) So if we are to have negative propositions they need to either be basic propositions, either pure negations as in (2) or derived from implications of the ‘form p and not q’ as in (1). Logic allows no other possibility.

The Case of Incompatible Colours
“…Two different colours cannot coexist at the same place in one visual field. Position in the visual field is absolute, and may be defined by relation to the centre of the field by means of two angular coordinates which we may call ⱷ, ⱸ. I am saying that we know the following proposition: ‘at a given time and in a given visual field, if the colour A is at the place ⱷ, ⱸ, no other colour B is at this place’. More simply: ‘this is red’ and ‘this is blue are incompatible.” (ibid p.78)
Russell argues that the above generalisation is one that we intuitively know to be true but how we know it to be true is difficult to ascertain. According to Russell it isn’t a logical truth as Red and Blue are not logically incompatible, nor does it appear to be a truth which is derived from experience.
Russell notes that there are many other sensible qualities which we immediately recognise to be incompatible, he gives a variety of different examples such as ‘hard’ and ‘soft’, ‘hot’ and ‘cold’, ‘sweet’ and ‘sour’ etc (ibid p. 78).The important point about the preceding examples is that they are not examples of logical incompatibility. He argues that if we take these incompatibilities as basic propositions, they must be grounded on the basic general proposition (which is a more abstract version of (1) above):
(3) “For all possible values of x, ꬿx implies not ꬸx. Here ‘ꬿx’ may be ‘x is blue’, and “ꬸx’ may be ‘x is red’.” (ibid p. 78)
Russell argues that with the help of the general proposition above we can infer from seeing that ‘x is red’ that ‘x is not blue’. The important point to note here is that the inference ‘x is not blue’ is derived from a non-empirical proposition (3) above. Russell is not very happy with the above conjecture as to how we arrive at our negative proposition ‘x is not blue’. However he is not very clear on why he is unhappy with his conjecture he merely vaguely claims that the conjecture is not very plausible or satisfying. He then moves on to a different attempt to solve the problem which he also finds unsatisfactory. However before delving into his second attempt to solve the problem of negation I will critically evaluate Russell’s first attempt to solve the problem of negation.
Russell, Evolution and Innate apparatus
Russell found his above explanation implausible. One of the reasons for this was that he preferred to justify his speculations on empiricist grounds and was reticent to use rationalist explanations. Rationalist explanations were generally held in pretty low esteem at the time Russell was writing. There were a number of reasons that rationalism was not looked upon unfavourably at the time. Rationalists such as Descartes, Spinoza and Leibniz were at the forefront of the scientific revolution. However their rationalist explanations of the success of science came under severe pressure through arguments of the empiricist philosophers who contended that empiricist explications of the sciences explained its success better. One difficulty that empiricists had with rationalist explanations was that it was utterly mysterious how we derived our capacity of so called ‘a priori’ knowledge. Prior to the scientific revolution and the birth of rationalist tradition; philosophers such as Plato and Saint Augustine argued that humans had innate knowledge in areas such as morality, mathematics etc. However they had no convincing explanation of this a priori knowledge. Plato argued that we had innate ideas acquired in a prior life that we could remember by contemplation of the forms, while Saint Augustine claimed we arrive at this universal knowledge through a revelation from god. None of the rationalists had a more compelling explanation of how we acquire non empirical knowledge of things like mathematical truth; for example, Descartes had to bring God into the picture as a guarantor of the validity of our logical and mathematical truths.
Philosophers in Russell’s time were impressed by the empiricist criticism of rationalist epistemology; however, they weren’t convinced that the great empiricists (Locke, Berkeley, Hume) had a compelling account of mathematical knowledge etc. In ‘Inquiry into Meaning and Truth’ Russell wasn’t interested giving an explanation of how we acquired our mathematical knowledge. Rather he was trying to demonstrate how we derive our knowledge claims from basic perceptual beliefs. In his introduction to ‘An Inquiry into Meaning and Truth’ Russell noted:
“I shall, throughout this book, try to avoid the consideration of logical and mathematical knowledge, which does not raise the problems which I wish to discuss. My main problem, throughout, will be the relation of basic propositions to experiences, i.e., of the propositions that come first in the epistemological order to the occurrences which, in some sense, are our grounds for these propositions.” (ibid p. 16)
He was interested in analysing our language, and discovering how we go from simple object languages which pick out perceptual features of our environment, to a secondary language which included logical constants, true and false, and so on up the hierarchy of languages. But as we saw above when moving from the object language to the meta language Russell immediately ran into difficulties as to how we could do this based entirely on perceptual experiences. He was forced to admit the unempirical basic proposition which is necessary to form negative judgements from experiences:
(3)“For all possible values of x, ꬿx implies not ꬸx. Here ‘ꬿx’ may be ‘x is blue’, and “ꬸx’ may be ‘x is red’.” (ibid p. 78)
Russell was uncomfortable with appealing to an unempirical basic proposition but didn’t have any other compelling way to explain our knowledge in this domain. As we saw above though appeals to non-empirical knowledge had a chequered history in philosophy. An atheist philosopher like Russell, who had strong empiricist leanings, would have been extremely uncomfortable with the explanations of non-empirical knowledge that philosophers such as Plato, Augustine and Descartes provided. While Russell was prepared to countenance unempirical knowledge, he was extremely uncomfortable with doing so and only did so if he had no other choice.
An avenue available to Russell to explain non-empirical knowledge was the theory of evolution. Yet Russell, unlike later philosophers, such as Chomsky and Quine never made much use of this avenue. When Russell was considering how a human could derive negation from experience he didn’t sufficiently appreciate how important negation or proto-negation would be to living creatures in the wild.
Russell gave the example of a person looking in the fridge and forming the judgement that ‘there is no butter in the fridge’. He then tried to analyse how the person would be capable of forming the judgement and considered a variety of different difficulties with his explanations. But better question with more immediate consequences would be how could a mouse form the proposition ‘there is no cat in this field’?
If we consider the question about a mouse forming a negative proposition from an evolutionary perspective; things look much different. Russell noted that we cannot form a negative proposition purely from the fact that something is not present in the field. There are an infinite amount of possible entities that are not present in the field. So the mouse going into the field would have to make an infinite amount of judgements about what is not present in the field. Of course from an evolutionary perspective such a situation would not occur. A mouse isn’t just some blank slate who forms its judgements entirely based on empirical observation. A mouse will have particular concerns and interests that will limit the type of hypotheses it makes. A creature that couldn’t make snap judgements as to whether there were no predators in the field before entering it to eat would be culled by natural selection in no time. Animals pausing to consider the infinite possibilities of counterfactual entities before acting wouldn’t last long enough to pass on their genes in the time constrained environment that natural selection acts on.
A logician like Russell didn’t consider the time and energy constraints on a living creature trying to survive in its environment. Natural Selection builds cheap fast brains that do the minimum; i.e. try to survive long enough to pass on their genes to the next generation. Such a creature will not will not consider logical possibilities; rather they will be concerned with salient information, the salience being primarily what will get me food for energy, what will help me find a mate, and what danger may be nearby.
With this fact in mind, Russell’s question about the perceptual basis of forming negation takes on a different hue. The non-linguistic creature will have expectations of what there is in the world it is exploring and a quick glance will tell the creature that some things that it expects to be there are in fact not there. From here is a short step for the creature to form the judgement ‘there is no cat in the field’. So from an evolutionary perspective there is little reason to follow Russell in arguing that forming perceptual judgements of negation must involve linguistic capacities.
Likewise, there is little reason to follow Russell in worrying about the fact that he has to use non empirical axioms to show how we derive negative propositions. From an evolutionary point of view we would expect any creature to come to the learning situation choc o bloc with innate apparatus.
An obvious objection to my above discussion is that it relies on the unargued assumption that non-linguistic creatures use propositional attitudes when thinking. However, my argument isn’t actually reliant on this assumption. I am arguing that IF non linguistic creatures think using propositional attitudes, natural selection will have build constraints in to the possibilities the creatures will entertain when judging what is or is not in the environment, and these innate constraints will make it much easier to form negative judgements.
Russell’s Second Way of Forming Negation
We saw above that Russell had little reason to be so wary about appealing to unempirical knowledge once we adopt an evolutionary perspective. Russell offered another way we a creature could acquire negation. This way involved comparing a word such as ‘white’ and judging whether the environment contained this entity. Russell seemed to view this explanation as in competition with his first explanation in terms of non-empirical grasping of incompatibility. However, there is no reason to view these explanations as in competition they could both play a role in people acquiring the use of negation.
On difficulty with Russell’s discussion of our use of word’s was that he didn’t really appreciate the role of reinforcement shaping how language is used. To this end I think that using Skinner’s work on Verbal Behaviour would help push Russell’s explication in the right direction.
In his ‘Verbal Behaviour’ Skinner discussed the type of perceptual experiences which would work to elicit the response ‘Not Red’. While Russell was concerned with the fact that we seem to be able to form non-empirical judgements about our perceptual field:
“I am saying that we know the following proposition: ‘at a given time and in a given visual field, if the colour A is at the place ⱷ, ⱸ, no other colour B is at this place’. More simply: ‘this is red’ and ‘this is blue are incompatible.” ( An Inquiry into Meaning and Truth p.78)
Skinner was more concerned with the environmental and social contingencies which would shape our response ‘Not Red’:
“The stimuli which continue to strengthen Red and which therefore continue to produce the qualified Not Red are only those situations which are similar to red. Blue will not only not evoke Red, it will not evoke Not red. A strong reddish-orange, may however, do so. Additional verbal stimulation- for example, the echoic prompt red- may, of course evoke the response Not red in the presence of a blue object” ( B.F. Skinner ‘Verbal Behaviour p. 324)
When Skinner is discussing negation he does so in relation to what he calls a qualifying autoclitic. He defines a qualifying autoclitic as “a function that qualifies the tact in such a way that the intensity or direction of the listener’s behaviour is modified” (ibid p. 322). In this respect Skinner asks us to consider the qualifying autoclitic of ‘No’. ‘No’ can be used to qualify any tact. The tact ‘rain’, which is under the control of a particular environmental event, could theoretically be metaphorically extended to include such things as a water sprinkler and metonymically extended to a dark grey sky. If the verbal community that a speaker is a member of doesn’t reinforce such metaphorical and metonymical extensions, or even punishes it, this type of Verbal Behaviour will decrease in use.
Skinner notes that ‘no’ is used a lot of times as a mand to change behaviour. Thus if a child is playing with something dangerous the parent will say ‘no’. In this instance ‘no’ functions as a mand to change ones behaviour; to stop doing what one is doing. This use of ‘no’ as a mand also occurs with verbal behaviour. Thus if a child pronounces a word wrong or uses it in the wrong circumstances the parent will say ‘no’ and may follow the ‘no’ with an explanation of what is wrong with the behaviour. So a child growing up will pretty quickly come to understand that ‘no’ is a mand to stop or change what you are doing.
When a person is using a tact such as ‘Red’, it is possible to modify the tact by using the qualifying autoclitic ‘no’. A person who has grasped the use of no as a mand to modify behaviour could of course apply it to his own verbal behaviour. He could apply it to any statement about our perceptual experiences and modify the intensity or direction of the statement. Thus when the person sees a dog he could use the tact ‘cat’ and qualify it by saying ‘no-cat’, meaning that the tact that ‘there is a cat present’ is false. However Skinner argues that a person will only qualify a tact with a ‘no’ in certain circumstances. As we saw above he gives us the example of something red; he notes that ‘red’ is unlikely to evoke either ‘blue’ or ‘not-blue’. The rationale for this is that we wouldn’t use a qualifying negation for no reason. Something reddish may act as a stimulus for us saying ‘not-red’ as it is close enough in hue to red to be confused with it so we could use a qualifying tact to ‘not-red’ upon being presented with a redish orange object. If a person were to say ‘not-blue’ in the presence of a red object it may be in response to a query from a person who doesn’t know the colour of the object and wrongly guesses that it is blue . The important point to note is that Skinner is using both context and intersubjective communication as a key to understanding how the qualifying autoclitic ‘no’ is typically used.
Skinner’s emphasis on intersubjective communication and social reinforcement is important as a way of supplementing Russell’s account. A person may eventually learn to use the word ‘white’ and check if there are any objects in the environment matching it but and therefore derive the negative judgement ‘not white’ but this process will be reliant on two more fundamental processes. (1) Our innate biologically given expectations of what is salient in our environment (2) Shaping by our sociolinguistic group in how to appropriately use the word ‘no’.