Tis a common observation, that the mind has a great propensity to spread itself on external objects, and to conjoin with them any internal impressions, which they occasion, and which always make their appearance at the same time that these objects discover themselves to the senses. (Hume, Treatise of Human Nature, I. iii. XIV)
(1) Mary is a brunette.
This sentence attributes a property (dark-hairedness) to Mary. The sentence is true if and only if Mary has this property. Now consider by way of contrast the sentence:
(2) Mary is beautiful.
Prima facie, (2) has much the same character as (1). It attributes a property (beauty) to Mary. It is true if and only if Mary has this property.
However, if the proverb 'Beauty is in the eye of the beholder' is true, (1) and (2) are not as similar as they might first appear. If I utter (2), I am not so much attributing a property to Mary as I am characterising my own reaction to her. I say 'Mary is beautiful' since she evokes a certain reaction in me. I find her beautiful.
Such a view might be called 'projectivist': beauty is not a property of Mary. In describing her as beautiful I am 'projecting' my reaction onto her, talking as though my reaction to her is a property of her.
Projectivism in aesthetics has already been discussed as an example. Most opponents of projectivism in aesthetics claim that beauty is a real objective property that some objects have and others lack.
Hume (Treatise on Human Nature) is perhaps the grandfather of ethical projectivism, which was philosophical orthodoxy throughout the twentieth century. It has since fallen out of favour, but has some supporters, notably Simon Blackburn (Essays in Quasi-Realism, Spreading the Word).
Optics and neurology have taught us a great deal about human colour perception. It has been claimed that modern science has undermined the naive idea that objects are coloured in the way we experience them. For example, there is no property of yellowness common to ripe bananas, lemons etc. We call all these things ‘yellow’ because they induce certain visual sensations in us, and we wrongly suppose that these experiences are properties of the objects themselves. See for example C H Hardin’s book Colour for Philosophers.
Suppose for example that somebody is hit by a hammer, and sometime later a bruise appears at the point of impact. The impact of the hammer is an observable event; the bruise too is observable. The causal connection between the two events, however, is not observed or experienced, at least according to Hume. Hume believed that whenever we can claim to know something about the world, that knowledge must be derived from experience (see Hume's fork). We do not experience the causal connection between a hammer impact and the formation of a bruise. All we observe are distinct events, occurring at the same place and time (Constant conjunction). Because we observe events of this type, we are led by induction to suppose that like causes will result in like effects, and from this we have the notion of causation. This does not mean Hume doubted that one material object was able to cause a change or movement in another material object. It means that insofar as we talk about some cause resulting in some effect, it is not something we have learned of the world we are talking about because it is not derived from experience. Rather, we are talking about a feature of our thinking which we are inclined to discuss as if it were a feature of the world.
In short: when we believe we have observed a causal connection all we have really experienced is a conjunction between two separate events. We can only know about the world through experience, so causation as a feature of the world is something unknowable to a human being.
What does it mean to say that the probability that a coin lands heads is ½? One might think that the coin will either land upward or it will not, the probability is not a feature of the world, but rather just a measure of our own ignorance.
Frank Ramsey (see his collected papers, edited by D. H. Mellor) and Bruno de Finetti, developed projectivist theories of probability in the early twentieth century. To explain their theories, the concept of degree of belief must first be introduced.
Let us say that a person has a degree of belief of 1 in a particular proposition if he completely convinced of its truth. For example, most people have a degree of belief of 1 in the proposition that 2+2=4. On the other hand, a person has a degree of belief 0 in a proposition if he is utterly convinced of its falsity; most people have a degree of belief of zero in the proposition that 2+2=5. Intermediate values are possible. A man who thinks that his dog has stolen the sausages, but is not completely sure, might have a degree of belief of 0.8 in the proposition that his dog stole the sausages.
For each person A, we can define a (partial) function CA mapping the set of propositions to the closed interval [0, 1] by stipulating that for a proposition P CA(P)=t if and only it C has a degree of belief t in the proposition P. Ramsey and de Finetti independently attempted to show that if A is rational, CA is a probability function: that is, CA satisfies the standard (Kolmogorov) probability axioms.
They supposed that when I describe an event has having probability P I am really voicing my degrees of belief. Probabilities are not real features of the world.
For example, when I say that the event that the coin lands heads up has probability ½, I do so because my degree of belief in the proposition that the coin will land heads up is ½.