1One of Frank Ramsey’s crucial contributions to philosophy is his theory of belief. His premature death, however, prevented him from finishing it. Ramsey deals with the notion of full belief in “Facts and Propositions” (1990 [1927]; FP, henceforth), as well as that of degrees of belief in “Truth and Probability” (1990 [1926]; TP, hereafter). These essays inspired different kinds of theories: FP led to theories of truth, specifically the modern deflationary theories, and TP laid foundations for modern theory of subjective probability. Moreover, in his posthumously published manuscript On Truth (1990; OT, henceforward) Ramsey analyses beliefs and emphasizes the essential role of agent’s actions in his theory. In this paper, I follow Ramsey’s thoughts as they developed in consecutive essays all evolving around the concept of belief. I show how Ramsey considers partial and full beliefs, distinguishing between full, certain and true ones. His final project was to be titled Truth and Probability which means Ramsey was considering these issues simultaneously. I examine the strong influence pragmatism has on Ramsey’s thoughts to finally show that even though Ramsey is working with both these doxastic states his rejection of true beliefs for his final theory of belief becomes clearer with every essay.
- 1 See Mellor 1978 and Sahlin 1990, as well as numerous Ramsey’s obituaries written by distinguished C (...)
2Frank Plumpton Ramsey is rightly considered the brightest star on the philosophical sky at the beginning of the xx century, not only in Cambridge.1 He wrote about 15 essays, on various topics, which all share Ramsey’s pragmatic method of analysis (cf. Sahlin 1990). In some of the essays Ramsey approaches similar issues. This has become clearer in his final writings, in which he is working on a theory of belief and truth. We know that in his celebrated TP employing the notion of partial belief, or degrees of belief, he develops a theory of subjective probability. In FP, published a year later, Ramsey mentions the issue of truth before focusing on the goal of this paper which is the analysis of full beliefs or judgements. This essay provided an inspiration to all modern deflationary theories of truth. They mistakenly present what is now known as Ramsey’s redundancy theory of truth as Ramsey’s complete view of this concept. This is, however, only a part of Ramsey’s view. In his final notes of an unfinished manuscript, which was printed only in 1991 as On Truth, Ramsey deals with the same issues – belief, truth, judgement. In all of these writings, agent’s actions play a central, unifying role.
3Ramsey is clearly investigating full and partial beliefs in different essays. His aim is to present a theory of belief. He titles his final project Truth and Probability, which allows for the assumption that he is considering how these two concepts work together. This indeed seems to have been his goal, however, throughout his essays Ramsey’s rejection of full (true) beliefs for his theory becomes decisive. There is no place for true or certain beliefs in Ramsey’s pragmatist universe of discourse. Therefore, Ramsey’s final theory of belief is a theory of partial belief.
- 2 The order in which I discuss the essays corresponds to the order Hugh Mellor chose for his book F.P (...)
4In the following paper, I will discuss Ramsey’s essays providing robust textual evidence showing that Ramsey is considering both notions: of full and partial beliefs, simultaneously, and even, that he finds connections between them. Nevertheless, I will try to demonstrate that even though Ramsey is clearly considering full beliefs, and even numerous theories of truth have been inspired through his essays, Ramsey does not aim at developing a theory of truth as a separate concept. He analyses the concept of truth in the essays discussed in this paper always in connection with other notions – judgement, belief and knowledge. He argues that even full beliefs possess a certain degree of uncertainty, for no human belief could ever be certain. I will also discuss the role Peirce’s pragmatism plays in Ramsey’s theory of belief, giving it a normative character. The aim of my paper is to show that Ramsey rejects full (understood as certain) beliefs in his final theory of belief, making it a theory of partial beliefs. My further goal is to argue that this theory is a normative theory.2
5In this essay, Ramsey’s goal is to present a logical analysis of belief and judgement which does not presuppose the concept of truth. Before proceeding with his analysis of these concepts, however, Ramsey makes a short digression to discuss the concept of truth. Ironically, this essay became known for presenting so-called Ramsey’s redundancy theory of truth, even though, Ramsey did not aim for that type of truth theory. For him, as soon as we explain the concepts of belief or judgement, we understand the concept of truth.
It is, perhaps, also immediately obvious that if we have analysed judgement we have solved the problem of truth; for taking the mental factor in a judgement (which is often itself called a judgement), the truth or falsity of this depends only on what proposition it is that is judged, and what we have to explain is the meaning of saying that the judgement is a judgement that a has R to b, i.e. is true if aRb, false if not. We can, if we like, say that it is true if there exists a corresponding fact that a has R to b, but this is essentially not an analysis but a periphrasis, for “The fact that a has R to b exists” is no different from “a has R to b.” (FP: 39)
6This quote provided an inspiration to all modern deflationary theories of truth. This is, however, only a part of Ramsey’s view. As we read further, it becomes clear that it is the theory of belief that’s crucial and that any discussion of truth depends on it. The concept of truth plays an auxiliary role in the analysis of the concept of belief, as we think in terms of the concept of truth and employ it our discussion. I do not mean to diminish the role of truth, which is crucial in all theories of belief. The point I wish to emphasise is that Ramsey is not interested in developing a theory of truth as of a separate concept. His analysis of truth is always connected to other notions, especially judgement and belief, of which truth can be predicated. He considers the theory of belief to be central and holds that as soon as we establish a theory of belief, the concept of truth will be no longer ambiguous. In the following pages, I discuss the importance of the concept of truth for the notion of belief as understood by Peirce, and hence also by Ramsey. We see the strong influence of early pragmatist thought on Ramsey’s writings. As Misak (2016) points out, two major contributions to the study of belief come from two great pragmatists: Charles S. Peirce and Alexander Bain. Peirce held that we have background beliefs against which we asses new evidence before we form new beliefs on which we act. Alexander Bain had the idea that a belief is a disposition to act. These two thoughts are clearly visible in Ramsey’s essays. He emphasizes that agent’s actions are indispensable in explaining the notion of belief. He defines belief as a disposition to act as if the believed proposition were true under certain preferable circumstances. He considers the mental factors in belief concluding that:
Their nature will depend on the sense in which we are using the ambiguous term belief: it is, for instance, possible to say that a chicken believes a certain sort of caterpillar to be poisonous, and mean by that merely that it abstains from eating such caterpillars on account of unpleasant experiences connected with them. The mental factors in such a belief would be parts of the chicken’s behaviour, which are somehow related to the objective factors, viz. the kind of caterpillar and poisonousness. An exact analysis of this relation would be very difficulty, but it might well be held that in regard to this kind of belief the pragmatist view was correct, i.e. that the relation between the chicken’s behaviour and the objective factors was that the actions were such as to be useful if, and only if, the caterpillars were actually poisonous. Thus any set of actions for whose utility p is a necessary and sufficient condition might be called a belief that p, and so would be true if p, i.e. if they were useful. [Footnote: It is useful to believe aRb would mean that it is useful to do things which are useful if, and only if, aRb; which is evidently equivalent to aRb.] (FP: 40)
- 3 Sahlin (1990: 72) presents the following matrix.
7This very simple and straightforward sort of belief leads the agent, here the chicken, directly towards its actions. In the situation described above, we have two possible states of the world – in one the caterpillar is poisonous in the other edible. Likewise, we have two possible actions the chicken can take, it can either eat the caterpillar or refrain from eating it. There are four possible outcomes, depending on the actual state of the world and on the action taken. If the caterpillar is poisonous and the chicken eats it, it may end up having an upset stomach, or avoids an upset stomach if it refrains from eating it. In the case the caterpillar is edible, the chicken either gets a good meal or remains hungry. In all situations, whatever the agent decides to do, she should act so as to maximise the expected utility of her action.3
8Such simple and direct example of a belief illustrates best the central role of the agent’s actions in determining of the truth conditions of her beliefs. It should be noted that this quote provided an inspiration to another modern development called success semantics. Ramsey, however, states clearly in the following sentence that this is not the kind of beliefs he wishes to discuss. He wants to examine beliefs which are expressed in words, or images, which are consciously asserted or denied. At the same time we should remember that any mental state which we actually act on is considered by Ramsey a belief. Nevertheless, he is well aware of the matter being far more complicated. There are many unforeseeable factors which can get in a way of an agent acting on her belief, as well as there are more beliefs moving to one action, which itself is usually complex. Moreover, the beliefs we hold and which move to a certain action can be of different degrees. Ramsey emphasizes the complexity of this situation in the above quote, by calling a belief “any set of actions.” Hence, beliefs are sets of actions. Ramsey never had time to finish his investigations, however, he was convinced of the central role of the agent’s action in his theory. According to him, the equivalence of disbelieving p and believing ¬p is only seen through our actions, more specifically, through their effects. As Ramsey emphasizes,
[i]t is evident that the importance of beliefs and disbeliefs lies not in their intrinsic nature, but in their causes and effects. (FP: 44)
9In FP, Ramsey deals with full beliefs, which he defines as “a set of actions for whose utility p is a necessary and sufficient condition.” Our actions are the combining force in Ramsey’s investigations into belief and truth. He suggests that whatever characterises the feelings we might have, only the attitude leading to action may be called a belief. Hence, he defines the meaning of a sentence via reference to action.
The essence of pragmatism I take to be this, that the meaning of a sentence is to be defined by reference to the actions to which asserting it would lead, or more vaguely still, by its possible causes and effects. Of this I feel certain, but of nothing else. (FP: 51)
10This is another reflection of Bain’s idea of beliefs being dispositions to act in Ramsey’s writings. As Misak holds, Peirce was convinced of this moderate dispositionalist statement.
While Peirce did not accept the metaphysics of mind that some dispositionalists adopt, he did maintain that we believe, judge, and assert a proposition only if we are disposed to act on it. The disposition to act is necessary, just as it is necessary, on Peirce’s view, that a belief must have practical consequences for it to have content. As we shall see, Peirce thought a belief’s consequences for action as central not only to constituting it but also to determining its normative status. For the fundamental norm of belief is truth, and, for Peirce, roughly, beliefs are true if they would lead to successful action and false if they would not. (Misak 2016: 26)
- 4 See a detailed exposition on this topic by Dokic & Engel 2002.
11These thoughts are reflected in Ramsey’s ideas quoted above, which in turn inspired the idea of success semantics.4 Peirce’s famous dictum that “Our beliefs guide our desires and shape our actions” (Peirce 1877: 14) is very simple and yet powerful. It is also clearly visible in Ramsey’s essays discussing beliefs, wishes and actions. But there is yet another characteristic of belief Misak shows was essential to Peirce. On Peirce’s account belief has to have practical consequences, he attributes truth to belief, as its fundamental norm. This means that if we act on a true belief we are to be successful. Ramsey embraces also this idea wholeheartedly. The following quote in which Peirce describes how we attain beliefs emphasizes their normative role.
Images pass rapidly through consciousness, one incessantly melting into another, until at last, when all is over – it may be in a fraction of a second, in an hour, or after long years – we find ourselves decided as how we should act under such circumstances as those which occasioned our hesitation. In other words, we have attained belief. (Peirce 1878: 39)
12After our hesitation ceases we find ourselves decided as how we should act, we have arrived at our belief and now we know what to do, how we should act. This complexity involving our wishes, desires, beliefs and actions has been anticipated by Peirce as well as by Ramsey. It has been reflected only much later in modern decision theories. Ramsey laid foundations for Bayesian decision theory in TP published in 1926. However different the modern interpretations of it may be, they all agree that
there are two main types of factors determining our decisions. One is our wants or desires. These determine the values or utilities of the possible outcomes of our decisions. The other is our information or beliefs about what the world is like and how our possible actions will influence the world. The beliefs determine the probabilities of the possible outcomes. The main aims of a decision theory are, fist, to provide models for how we handle our wants and our beliefs and, second, to account for how they combine into rational decisions. (Gärdenfors & Sahlin 1988: 1)
- 5 E.g. Mellor 2012, Sahlin 1990.
13There is no consensus among philosophers regarding the interpretation of decision theories based on Ramsey’a theories. Many claim that Ramsey’s theory is purely descriptive, telling us merely how an ideal agent will act in a given situation.5 Given Peirce’s influence, however, and Ramsey’s own statements, I believe that his theory is a normative theory. Our beliefs guide our actions, and the truth of a belief is a norm showing us the right way to act. This thought is clearly visible in Ramsey’s writings. At the end of his short life, Ramsey leaves certain ideas behind and adopts new ones. More specifically, in his latest writings we witness Ramsey’s abandonment of logicism for a finitistic view of mathematics and in 1929 his move towards intuitionism (Sahlin 1990: 102ff.). The reason for this was Ramsey’s dissatisfaction with the axiom of infinity of set theory. These changes, however, were not restricted only to mathematics, they influenced also Ramsey’s philosophy. I believe that along with these changes came a decisive shift, motivated by Peirce’s pragmatism, towards a normative reading of his theory of belief. In his final writings, in the introduction to his lates project On Truth, written between 1927-29, Ramsey makes a statement supporting this hypothesis.
It is a commonplace that Logic, Aesthetics, and Ethics have a peculiar position among the sciences: whereas all other sciences are concerned with the description and explanation of what happens, these three normative studies aim not at description but at criticism. To account for our actual conduct is the duty of the psychologist; the logician, the critic, and the moralist tell us not how we do but how we ought to think, feel, and act. (OT: 3)
14And Ramsey does: he attributes truth, understood as accordance with facts, to opinions, statements or propositions. It is not however, the task of a logician to criticise them, but that of an expert in the field which they refer to. The logician is concerned with how the opinions are formed, with inferences, and these are not true or false, but sound, valid or rational. Nevertheless, since “the whole purpose of argument is to arrive at truth, there must be some relation between the soundness of arguments and the truth of opinions” (OT: 3-4). This relation is no doubt complex. The logician deals with rationality of the argument not its truth, nevertheless his contribution is substantial. Also here Peirce’s influence could not be clearer. Peirce is well known for identifying three normative sciences: ethics, logic and aesthetics (CP 1.191, 1903). This idea finds a precise reflection in Ramsey’s writings. Hence logic, in particular decision theory following from Ramsey’s theory of belief, tells us how we should act, therefore it has to be read normatively.
15If we read TP (written in 1926) carefully, we will notice that Ramsey is considering certain intersections between full and partial beliefs. The first two sections of TP are devoted to the frequency theory and Ramsey’s felicitous critique of Keynes’ theory. In the third one he develops his superb theory of subjective probability. In the fourth, called The Logic of Consistency, Ramsey notices the inner connection between full and partial beliefs.
16There is no doubt that our knowledge, as well as full and partial beliefs are part and parcel of human discourse and decision making. Ramsey observes, however, that if we accept full beliefs into our discourse there can be no justification for having partial beliefs.
We may agree that in some sense it is the business of logic to tell us what we ought to think; but the interpretation of this statement raises considerable difficulties. It may be said that we ought to think what is true, but in that sense we are told what to think by the whole of science and not merely by logic. Nor, in this sense, can any justification be found for partial beliefs; the ideally best thing is that we should have beliefs of degree 1 in all true propositions and beliefs of degree 0 in all false propositions. But this is too high a standard to expect of mortal men, and we must agree that some degree of doubt or even of error may be humanly speaking justified. (TP: 80)
- 6 See OT (56-7), as well as this paper’s section on Knowledge and Opinion.
- 7 I’d like to point out that in TP Ramsey uses the notions “full” and “certain” of beliefs as synonym (...)
- 8 More on this in the section on Knowledge and Opinion.
17It is clear that the beliefs we hold are of different degrees. We also act on well grounded full beliefs, which are no doubt true. Even though Ramsey is well aware that also full beliefs are involved in our process of decision making, he emphasizes that his theory of subjective probability involves only degrees of belief.6 This theory involves partial beliefs and lays down rules for a rational agent to follow in making her decisions. To act only on full beliefs would be “too high a standard to expect of mortal men.” An essential observation is that, if we introduce true full beliefs into our universe of discourse, there will be no justification for having any partial beliefs and wanting to act on them. This ideal situation is of course very distant from our reality since most of our beliefs are partial. Therefore, even though we have true, full or certain beliefs they seem to have a different ontological status than partial beliefs.7 To be sure, Ramsey doesn’t deny that we act on true beliefs, or even on our knowledge. He seems, however, to distinguish between certain and true beliefs and knowledge on one side and partial or even full beliefs on the other. All beliefs we have, which are not knowledge are subjective, only knowledge is objective.8 There is a difference between a belief which has probability 1 and a true belief. Every true belief has a probability 1, but not every belief of probability 1 is a true belief:
p is true –>Prob(p) =1, but not Prob(p)=1 –> p is true.
18For Ramsey, all kinds of belief, even full beliefs involve a certain amount of uncertainty. There is a crucial reason for this distinction, which we will discuss shortly. At the end of this section, we will answer another important question regarding acting on partial beliefs.
19Ramsey criticizes Keynes fo“ holding that “valid deductive and inductive arguments are fundamentally alike” (TP: 81), and instead, adopts the distinction ‘into two radically different kinds” of arguments made by Peirce in the “Fourth Paper: The Probability of Induction” of his celebrated Chance, Love and Logic. Here Peirce writes: “All our reasonings are of two kinds: 1. Explicative, analytic, or deductive; 2. Amplifiative, syntetic, or (loosely speaking) inductive” (Peirce 1923: 92). In explicative reasoning, certain facts are first laid down in the premises. This allows us, through analytic inference, to arrive at a conclusion. All mathematical demonstrations are counted among this sort. The synthetic arguments are of a different kind. The facts composing the conclusion are not given in the premises, and hence these are the only inferences which actually increase our knowledge, as opposed to rearranging it. Ramsey considers the arguments of the second type to be much closer to memories and perception than to deductive arguments. Memory, perception and induction, he says, are the three fundamental ways of gaining knowledge. Immediately thereafter, Ramsey emphasizes that this distinction does not coincide with the one between certain and partial beliefs, which he explains as thus.
Logic must then fall very definitely into two parts: (excluding analytic logic, the theory of terms and propositions) we have the lesser logic, which is the logic of consistency or formal logic; and the larger logic, which is the logic of discovery, or inductive logic.
What we have now to observe is that this distinction in no way coincides with the distinction between certain and partial beliefs; we have seen that there is a theory of consistency in partial beliefs just as much as of consistency in certain beliefs, although for various reasons the former is not so important as the latter. The theory of probability is in fact a generalization of formal logic; but in the process of generalization one of the most important aspects of formal logic is destroyed. If p and ¬q are inconsistent so that q follows logically from p, that p implies q is what is called by Wittgenstein a “tautology” and can be regarded as a degenerate case of a true proposition not involving the idea of consistency. This enables us to regard (not altogether correctly) formal logic including mathematics as an objective science consisting of objectively necessary propositions. It thus gives us not merely the ἀνάγκη λέγειν, that if we assert p we are bound in consistency to assert q also, but also the ἀνάγκη εἶναι, that if p is true, so must q be. (TP: 82-3)
20Ramsey argues that this interpretation implies not merely ἀνάγκη λέγειν – the necessity to assert but also ἀνάγκη εἶναι – the necessity to be true. This means that if we assert p we are bound in consistency to assert q, but more importantly if p is true, so must q be. Only when dealing with full true beliefs both necessities – to assert and to be true – occur simultaneously. This crucial correlation between necessities, however, is lost in the case of partial beliefs for “if we believe pq to the extent 1/3, and p¬q to the extent 1/3, we are bound in consistency to believe ¬p also to the extent of 1/3” (TP: 83). This is the necessity to assert, but there is no corresponding necessity to be true: “But we cannot say that if pq is 1/3 true and p¬q 1/3 true, ¬p also must be 1/3 true, for such a statement would be sheer nonsense.” (Ibid). The necessary distinction Ramsey makes in this beautiful exposition is between probability theory, involving partial beliefs which are always subjective, and formal logic dealing with the facts, which are always objective. In the case of partial beliefs, even in beliefs of P(p) = 1 we need to make sure that the evidence we have is obtained by a reliable process. If, on the other hand, we know that our belief p is true, the evidence is irrelevant, p is true because it is a fact. The degrees of belief, even a belief of degree 1 are always subjective and Ramsey is ontologically equally committed to them. A true belief is a fact, hence it is objective and on a different ontological level.
21In addition to this impressive elucidation, it is impossible to overlook the equivalence Ramsey draws between asserting p and p being true. Formal logic deals with facts, hence with objective true beliefs. As soon as we assert such a fact we are bound in consistency to state its truth. Asserting a fact is equal to stating that it’s true. This statement is definitely a forerunner of the redundancy claims made by Ramsey a year later in FP. It is so obvious for him that he doesn’t elaborate on it any further. To be fair, even in FP Ramsey only makes a page and a half digression into the problem of truth while discussing the main issue of his paper which is the analysis of belief. To be accordant with Peirce’s and also Ramsey’s thought, it is only consequent to add that asserting a fact, hence a true belief means being prepared to act on it. Therefore, truth has a normative function in Ramsey’s theory of belief.
22TP is about measuring agent’s degrees of belief, subjective probabilities, decision making, rational agents following a set of axioms (rules), being successful and other issues giving rise to numerous theories throughout the years. What became known as Ramsey’s Redundancy Theory was a part of the analysis of beliefs published only one year later in FP, but we saw that it was on Ramsey’s mind already in TP. We all know that we base our decisions on both full and partial beliefs; these are, however, all subjective no matter what degree of belief we have in them. Ramsey knows that too. He discusses full beliefs in a paper on probability theory because ontologically they are not different from beliefs of other degrees. Ramsey’s ontological commitment is equal in regard to full and partial beliefs. Truth, however, is something else. It is objective, and hence there is no point in having “degrees of belief” in it. Since it is a fact, we can just act on it.
23Ramsey goes back to considering the general conception and the goal of logic in the last, fifth part titled The Logic of Truth. He explicitly mentions both calculi – the formal logic, dealing with objective facts, as well as the calculus of probabilities, which as we know deals with subjective degrees of beliefs.
Let us therefore go back to the general conception of logic as the science of rational thought. We found that the most generally accepted parts of logic, namely, formal logic, mathematics and the calculus of probabilities, are all concerned simply to ensure that our beliefs are not self-contradictory. We put before ourselves the standard of consistency and construct these elaborate rules to ensure its observance. But this is obviously not enough; we want our beliefs to be consistent not merely with one another but also with the facts [footnote omitted]: nor is it even clear that consistency is always advantageous; it may well be better to be sometimes right than never right. Nor when we wish to be consistent are we always able to be: there are mathematical propositions whose truth or falsity cannot as yet be decided. (TP: 87)
24Therefore, both calculus of probabilities and formal logic have the same goal – to provide us with means necessary to make sure that our subjective beliefs, whether full or partial, are consistent with one another and with the objective facts, with the world. Full and partial beliefs are both to follow mathematical calculi to ensure their consistency and so to guide our actions. For Ramsey, these arguments show clearly that “human logic, or the logic of truth, which tells men how we should think, is not merely independent of but sometimes actually incompatible with formal logic” (TP: 87). Still, many philosophers tried to reduce human logic, especially induction, to formal logic. Consistency can lead to truth, but not on its own, it has to be applied to observation and memory. Ramsey assigns human habits a central role in forming beliefs. Inspired by Peirce, Ramsey holds that the human mind works according to general rules, or habits. Assessing new information against our fixed beliefs allows us to act consistently and not randomly. Induction plays an important role in this process. Applied to our memories and our background beliefs, it assures arriving at truth.
This is a kind of pragmatism: we judge mental habits by whether they work, i.e. whether the opinions they lead to are for the most part true, or more often true than those which alternative habits would lead to. (TP: 93-4)
25Our beliefs have to “work,” and this we can only determine by acting on our beliefs. Once again Ramsey discusses the logic of truth, expressed in full beliefs in the last section of his paper on probability theory. Since we also base our action on our subjective full beliefs they fit into the theory of rational decision making just the same as partial beliefs. Ramsey’s theory of subjective probability works equally for beliefs which we hold to a probability of 1/3 and for full beliefs of probability 1. We act on our beliefs according to the principle of maximizing expected utility. In that way we make our beliefs work. What Ramsey doesn’t explicitly mention here, is the objective factor, i.e. the world in which we act on our beliefs. He introduces this concept in FP, published a year later. As we have seen, however, Ramsey states clearly that the goal of logic is to ensure that our beliefs are consistent not simply with one another, but also with the facts – with the world, with the objective factor.
26In the following section, I will present some further arguments from Ramsey’s essays, hoping to show that for him the connection between full and partial beliefs has been there all along, at the same time emphasizing his rejection of true beliefs for his theory.
27At the very beginning of this paper, Ramsey admits that the defect of his TP was that “it took partial belief as a psychological phenomenon to be defined and measured by a psychologist” (TP: 95). This, of course, no science can accept, since the notion of a belief of degree 2/3 is useless to anyone except to the speaker herself. Also, any indefinite degree of belief in a proposition is useless to an outside observer unless the speaker acts on her belief. We must be able to assign numbers to our beliefs in an intelligible way. Hence, Ramsey wonders:
Now what is the point of this numerical comparison? How is the number used? In a great many cases it is used simply as a basis for getting further numbers of the same sort issuing finally in one so near 0 or 1 that it is taken to be 0 or 1 and the partial belief to be full belief. But sometimes the number is used itself in making a practical decision. How? I want to say in accordance with the law of mathematical expectation; but I cannot do this, for we could only use that rule if we had measured goods and bads. But perhaps in some sort of way we approximate to it, as we are supposed in economics to maximise an unmeasured utility. The question also arises why just this law of mathematical expectation. The answer to this is that if we use probability to measure utility, as explained in my paper, then consistency requires just this law. (TP: 95)
- 9 For a detailed presentation of decision theories see Decision, Probability, and Utility edited by G (...)
28Here, Ramsey suggests an obvious thing, namely that the agent wants her beliefs to be as certain as possible before she acts on them. Hence, we approximate our partial beliefs as closely as possible onto full ones. In that way we can make as certain a decision as possible. We cannot use the law of mathematical expectation because it only works for goods and bads, hence for true or false beliefs. But as Ramsey says we can approximate our partial beliefs onto full ones, just as in economics to maximise an unmeasured utility, here we can use Ramsey’s principle of maximising expected utility introduced in his theory of subjective probability. This principle is at the bottom of every modern decision theory. They all agree that there are two main factors determining our decisions: our wants and desires determine the utilities of the possible outcomes of our decisions; and we all have information about the world and based on it we form our beliefs which determine the probabilities of the possible outcomes. The principle of maximizing expected utility (MEU) simply states that if we consider the utilities of the outcomes and the probabilities of the states we are able to calculate the expected utility of different alternatives.9 Also, keeping Peirce’s influence in mind, we should say that we must adhere to “the body of our background beliefs” and asses the new ones against it. As we see, this procedure is rather complex, but Ramsey finds a way to measure our partial beliefs and compute their expected utilities. In a given decision situation we should always choose the alternative with maximal expected utility.
29Also in this essay Ramsey considers the notion of belief, specifically he inquires how to understand “reasonable degree of belief.” In order to define this notion, he employs the concept of truth, hence of full belief.
When we pass beyond reasonable = my, or = scientific, to define it precisely is quite impossible. Following Peirce we predicate it of a habit not of an individual judgement. Roughly, reasonable degree of belief = proportion of cases in which habit leads to truth. (TP: 97)
30Consistently with his previous investigations, also in 1928, Ramsey regards partial beliefs as approximating onto the full ones. His analysis of a “reasonable degree of belief” encounters numerous difficulties leading him to a conclusion that a precise meaning of “reasonable” isn’t relevant. Nevertheless, his intuitive decision is to approximate degrees of belief onto full beliefs. It is important to notice that Ramsey rejects the concept of truth in the case of “regular” beliefs. Following Peirce, he only allows habits to be true, because they have been previously proven and acted on successfully.
31Further, in the part on Logic as Self-control Ramsey refers to Peirce once more and brings the two notions, of full and partial belief, together again. He holds that they both are to be understood as acts of decision making. In one case while forming a judgement I decide to have a full belief that such and such is the case, and consequently I am prepared to act on it. Similarly, a partial belief is a decision to have a belief of a specific degree, i.e. to act in a certain way (cf. TP: 99-100). In both cases I make a decision based on my subjective beliefs of different degrees.
32It is interesting to refer to Bernard William here. For him, when deliberating what belief is, we must consider the connection between belief and decision. Specifically, he means the connection between full-blown belief and our decision whether to say or not what we believe, our decision is only about whether to express in words what we believe. “This is, however, a decision with regard to what we say and do; it is not the decision to believe something.” (Williams 1973: 147). For Williams belief is only connected with decision to say or do what the belief is about, not with decision to believe. He argues that if we could choose what to believe this would imply that beliefs could be contingent. The reason beliefs cannot be contingent is because they aim at truth. “If I could acquire a belief at will, I could acquire it whether it was true or not; moreover I would know that I could acquire it whether it was true or not.” (Ibid.: 148). This takes us, however, off our tracks trying to follow up on Ramsey’s investigations. The point here is that Williams’ criticism does not apply to Ramsey for two reasons. The first is that for Ramsey belief is always connected with action. He even says that only a mental state upon with we act can be called a belief. He argues that “we shall however find it impossible to give any satisfactory account of belief or even of thought without making any reference to possible resulting actions” (OT: 45). So if we decide to have a certain belief, we simply decide to act in a certain way. The second reason is that Ramsey’s beliefs are definitely not arbitrary. They are proceeded by a reliable process, not only in the case of knowledge, as we will see in the following section. Before we come to hold a belief we assess it against our background beliefs which we have already acted on and were successful.
- 10 It is true that Ramsey discusses “dispositional beliefs, opinion” and even “dispositional knowledge (...)
33All the discussed essays have been written within the last three years of Ramsey’s life. Ramsey considers either partial or full beliefs, or regards them simultaneously. Even though Ramsey has written these essays with different goals in mind, i.e. developing a theory of subjective probability, an analysis of full belief and judgement, there is a common thread in all of them. First of all, the notion of action is crucial to both full and partial beliefs. Since we act on full as well as on partial beliefs, one could see action as a combining force these doxastic states have in common. We must remember that for Ramsey, as earlier for Peirce, only the mental states upon which we actually act can be called beliefs.10 Furthermore, we want our beliefs to be true before we decide to act on them, hence we approximate partial beliefs to the full ones. We achieve this when, based on our experience and evidence, we apply the principle of maximizing expected utility to determine on which partial belief we should act if we want to be successful. Following these calculations a partial belief can become a full belief, and if, in addition to being certain and true, it is also well grounded, it becomes our knowledge. We can, however, never compare our utilities, they are very individual and subjective. We must also be careful not to confuse belief with knowledge. Even full belief isn’t knowledge if it isn’t certain, true and well grounded.
34Ramsey devotes to this topic a separate essay called Knowledge, as well as a chapter of his unfinished manuscript On Truth. In both, a belief has to be true, certain and held for good reasons, hence obtained by a reliable process or well-grounded for it to be called knowledge. On the contrary, full and partial beliefs both involve a certain amount of uncertainty or doubt, which distinguishes them from knowledge.
35Ramsey devotes a substantial part of his final, unfinished manuscript to the issue of belief and judgement. He begins the third chapter titled “Judgement” by distinguishing different mental states to be examined. The first group he calls dispositional as they are rather dispositions, something merely potential, which is manifested only when the occasion arises. These are knowledge, beliefs and opinions once formed and now remaining latent until needed again. Their characteristic is that rather than being current acts of thinking, they build a persistent background of our mind. Peirce calls them “background beliefs” against which we asses new information before forming a belief (see CP, e.g. “Theoretical Interest,” “Forms of Consciousness”). As an example of dispositional beliefs Ramsey mentions historical dates we learned once and now could give without having to actively think of them. Also certain conventions count as dispositional beliefs, for example we learn as children that we hold on the red light and move when it turns to green and now do it habitually. They resemble rather qualities of dispositions of character, as for example we call a friend loyal or stubborn not necessarily because they are displaying these qualities at the moment.
36Ramsey assigns judgements to the other group, and calls them present acts of thinking. It is important to remember that the propositional references of dispositional beliefs are derived from judgements. Even though the following quote starts with an explanation of propositional reference, the main point Ramsey makes is the central role played by the agent’s actions in determining the truth and utility of one’s beliefs, both full and partial.
Our problem is to explain propositional reference, and in connection with dispositional knowledge and beliefs, this means that we have to analyse the meaning of saying that a man has a belief that such and such is the case, for instance, that the earth is flat. This we have seen to be partly an assertion about what he would think and say and partly (if I am right) one about how he would behave. The assertion we make about his behaviour is evidently a very complicated one, for no particular action can be supposed to be determined by this belief alone; his actions result from his desires and the whole system of his beliefs, roughly according to the rule that he performs those actions which, if his beliefs were true, would have the most satisfactory consequences. [Footnote: This formula obviously requires modification to include the case of partial beliefs, and is anyhow inexact as it takes no account of the impulsive element in action.] (OT: 45ff.)
37It is again the notion of action that connects full and partial beliefs. However, Ramsey postpones a full discussion. It is important to notice that here he discusses the possibility of including partial beliefs, not in the case of dispositional states, but for the second group, namely judgements. There can be no dispositional partial beliefs, since the dispositional beliefs are not current acts of thinking but rather proven beliefs building the persistent background of our mind against which we asses new beliefs. Ramsey adopts Peirce’s view again, this time eliminating doubt from judgement. He decides not to restrict our use of the word “judgement” only to those beliefs of which, based on evidence, we can be certain, “but to include the formation of my opinion, if it is formed with sufficient confidence for us to take it as a basis for our future thought and action, and regard its truth temporarily at any rate, as a settled question” (OT: 46). At the same time Ramsey emphasizes that we must “clearly exclude those cases in which we merely decide that one possibility is more likely than another” (ibid.). He wants to include those beliefs which contributed in the process of formation of our opinions. These are beliefs we weren’t fully convinced of at some point, but through further considerations or trial and error procedure either dismissed or fully accepted. He has an important restriction, that is: we need sufficient confidence in these partial beliefs in order to accept them as basis for our thought and action. It is, however, not enough that we are more convinced of p than of ¬p. The more important conditions is that the belief doesn’t violate the Principle of Maximal Expected Utility, only then we should regard it temporarily as true. Ramsey discusses the necessary requirements for such a process of forming a conviction in the next part of the book on Knowledge and Opinion.
38In the remaining part of this chapter Ramsey determines what mental states could count as judgements. He argues that even thinking out loud or saying something to oneself should be regarded as judgement, since it is not meaningless but expresses our thoughts. Furthermore, even if we don’t have a particular thought but merely an image in our mind, as long as it leads us to action, it counts as judgement.
39As Ramsey sees it, judgement actually comprehends two different processes: knowledge and opinion. Here, he wishes to examine the relationship between judgements and knowledge in more detail. It seems that when we say knowledge, we imply that the judgement involved is infallible, hence it has to be true. The sense in which the judgement in knowledge is true is very strong. Ramsey even says that in knowledge we have a judgement which is incapable of being false. This, however, is not enough: in addition to being true it also has to be made with utter conviction, we have to be certain of it.
When we say that a judgement is knowledge, we imply at least two things; that the judgement in question is true and that it is made with complete conviction. […] The term knowledge, then, implies both truth and certainty, and on the other hand belief and opinion imply neither truth nor falsehood, but generally imply at least a slight degree of uncertainty. (OT: 56-7)
40It is obvious then, that knowledge can only be stated of full beliefs and it requires further conditions. Full and partial belief, contrary to knowledge, both “imply at least a slight degree of uncertainty” (ibid.), even if our belief is full, hence if we assign it probability 1. We should note that “certain” as used by Ramsey here about beliefs does not mean “full” as it did in TP. It is much stronger now, for it means “incapable of being false” (OT: 56).
It is however, supposed that in knowledge we have a kind of judgement, which is infallible. This means not merely that we only call a judgement knowledge when it is true, but that there is a class of judgements, distinguishable otherwise than as true ones, which are not merely all in fact true, owing to some law of nature, but are in the nature of the case incapable of being false, since in them the mind is apprehending a fact, and were there no such fact, there would be not a false judgement but no judgement at all. (Ibid.)
41Knowledge is “not merely true” but is “incapable of being false” (ibid.), it is a fact, hence it is objective. This seems to be the major difference between the way Ramsey is using the word “certain” in TP and in OT. In TP “certain” means “full,” held to a degree of probability 1, and hence subjective. In OT it means “incapable of being false” because it is a fact. What we know are facts. Ramsey states another condition judgement must fulfill before it becomes knowledge, namely it has to be well grounded: “[T]he thinker has sufficient reason or evidence for his judgment: not merely that it is true and that he is certain of it, but that in some sense he has a right to be certain of it.” (OT: 57). It is this objective characteristic (the world giving ground to our beliefs) which allows for our subjective beliefs to become objective knowledge.
42Ramsey lists conditions corresponding to these listed above in his essay “Knowledge” (1929; K, henceforth). At first glance, this essay may seem barely like a page and a half long note, but I believe that it has been held rightly, that Ramsey’s arguments have a potential for a comprehensive and fully developed theory of knowledge (cf. Sahlin 1991). Ramsey holds that if a belief is to be knowledge it has to be (i) true, (ii) certain, and (iii) obtained by a reliable process (K: 110). The condition of belief’s truth has been analysed by Ramsey in FP and also in TP. Sahlin argues that what Ramsey understands as a belief being certain has to be interpreted simply as a full belief.
One reason for interpreting the certainty condition as ‘X has full belief in P’ is that the whole of Ramsey’s philosophy is largely derived from a conviction that it is important to formulate a human logic, a logic of rational action. His philosophy of probability is only one example of the importance he attaches to understanding the rational elements of individual decision making. (Sahlin 1991: 1401)
43The central condition for judgement or belief to be knowledge discussed in K is not certainty but being obtained by a reliable process, which requires a bit more consideration. Ramsey discusses this condition thoroughly, not paying much attention to certainty. He thinks that, perhaps, “formed in a reliable way” is somewhat clearer than “obtained by a reliable process.”
We say “I know,” however, whenever we are certain, without reflecting on reliability. But if we did reflect then we should remain certain if, and only if, we thought our way reliable […] For to think the way reliable is simply to formulate in a variable hypothetical the habit of following the way. (K: 110)
44“Variable hypotheticals” are general statements which Ramsey discusses in “General Propositions and Causality” (GPC, henceforth) published also in 1929. There, he argues, against his earlier views due to Wittgenstein, that universal statements are not simply conjunctions. The main reason why they cannot be written down as conjunctions is simply because they range over infinitely many objects, e.g. “All men are mortal” can never be fully written out. Ramsey says “A belief of the primary sort is a map of neighbouring space by which we steer. It remains such a map however much we complicate it or fill in detail. But if we professedly extend it to infinity, it is no longer a map; we cannot take it in or steer by it. Our journey is over before we need its remoter parts” (GPC: 146). Therefore, what Ramsey means by the process being reliable is “to simply formulate in a variable hypothetical the habit of following the way” (K: 110) – in this case the induction, however, casual as well as inferential processes can be called reliable processes, they all involve “sound reasoning.”
45Sahlin holds that for Ramsey the second and third condition are connected, and yet must be independently satisfied. This, in turn, leads to an important leap in understanding Ramsey’s theory of belief and knowledge, namely that knowledge leads us to success.
Firstly, this means that the certainty condition and the condition of a reliable process are not allowed to be simultaneously but independently satisfied. Whatever number of favourable and concurring pieces of evidence we might have, they are worthless if they are not obtained by a reliable process. Secondly, that full belief in p, to avoid some theoretical problems connected with the updating and dynamics of probabilities, should be interpreted as ascribing p a probability sufficiently close to 1.
By emphasizing that a reliable process is necessary for knowledge, a belief being knowledge if it is obtained by such a process and is true, i.e. always leads to success. (Sahlin 1991: 142)
46We have partial and full beliefs, and the latter can become knowledge if they satisfy the necessary conditions. Both partial and full beliefs are meant to guide our actions, and so support our decisions, and hence to help us to get what we desire. Only full beliefs fulfilling the conditions necessary for them to be called knowledge can be fully relied upon always to lead us to successful actions. If we interpret the certainty condition agreeing with Ramsey’s analysis in TP, it means that he is talking of full belief. If, however, we consider his latest writings, especially OT, we must admit that there are reasons to read it as incapable of being false. For Ramsey all beliefs, partial and full “imply at least a slight degree of uncertainty,” knowledge does not. In OT Ramsey requires knowledge to fulfill rigorous criteria: it has to be “not merely true” but “incapable of being false” for in knowledge “the mind is apprehending a fact” and the agent has “sufficient reason or evidence for his judgement.” These all are conditions supporting a much stronger reading, namely our knowledge is certain, because it is a fact.
47We have seen in the preceding sections that the force uniting full and partial beliefs are the agent’s actions. We act on both full and partial belies. Now the question is, what does it take for us to act on a partial belief? To what degree do we need to believe in p to be prepared to act on it? In TP, Ramsey explains what we expect from our beliefs.
This is a kind of pragmatism: we judge mental habits by whether they work, i.e. whether the opinions they lead to are for the most part true, or more often true than those which alternative habits would lead to. (TP: 93-4)
48TP is a paper on subjective probability theory, yet Ramsey talks here about beliefs leading to truth. This we have seen applies to full but also to partial beliefs of different degrees. In this case, we need to approximate our partial beliefs onto full ones, which we have already formed. Also this time, we draw from our experience and use the new evidence and so transform our yet partial beliefs into full ones. Since the factor combining our full and partial beliefs are our actions, Ramsey’s theory of belief is a straightforward decision theory.
Theories of this type are generally founded on four basic assumptions. First, the values of the outcomes in a decision are determined by a utility measure which assigns numerical values to the outcomes. Second, when determining the value of a decision alternative, the only information about the agent’s wants and desires that is used is the utilities of the possible outcomes of the alternatives. Third, an agent’s beliefs about what might happen in a given situation (about the states of the world) can be represented by a unique probability measure defined over the states. Fourth, for all states and all alternatives, the probability of the states is independent of the act chosen. Finally, it is argued that the fundamental decision rule is the principle of maximizing expected utility. In a given decision situation, the agent should choose the alternative with maximal expected utility. (Sahlin 1990: 54)
49Today’s decision theories have their roots in the Bayesian approach, first axiomatised by Ramsey. Since Bayesian theory deals with subjective probabilities, it has been often criticised for being arbitrary. The decision maker has neither full control over the factors determining the outcomes of her decisions, nor does she even have full beliefs on which she bases her decisions. Hence, in a bayesian decision theory, the agent deals with uncertainties. Nevertheless, “Bayesian theory reduces all problems to decision making under risk by assuming that the decision maker, by processing his or her partial information, can generate a unique probability distribution over the states of the world” (Gärdenfors & Sahlin 1988: 5). What is meant by making decisions under risk is simply that the decision maker knows exactly the probabilities of the states. Furthermore, based on TP, the authors formulate the fundamental decision rule of Bayesian theory, which they call
The principle of maximising expected utility (MEU): In a given decision situation the decision maker should choose the alternative with maximal expected utility (or one of the alternatives with maximal expected utility if there are more than one). (Ibid.)
50According to the authors, Ramsey develops his theory of maximizing expected utility in TP. Yet, Sahlin presents his decision making matrix using the famous chicken example, presented by Ramsey in FP, which shows how one acts or should act having full beliefs. As we have seen: “Thus any set of actions for whose utility p is a necessary and sufficient condition might be called a belief that p, and so would be true if p, i.e. if they are useful.” (FP: 39-40). And he sums up in a footnote: “It is useful to believe nRh would mean that it is useful to do things which are useful if, and only if, nRh; which is evidently equivalent to nRh” (FP: 40).
51We know that modern decision theory deals with decision making based on full beliefs as well as on partial ones. Ramsey knows it is necessary to include as basis for our actions partial beliefs, as he shows in TP, as well as full beliefs as he presents in FP. This is possible because both full and partial beliefs always include a certain amount of uncertainty and are always subjective. They are ontologically different from knowledge which is objective. The intersections between formal logic and theory of probability are indisputable. The reasons that lead Ramsey to reject true beliefs from his theory of belief are just as clear. He makes two important distinctions:
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subjective vs. objective.
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beliefs (partial and full) on one side and knowledge and truth on the other.
52Our beliefs, both full and partial are always subjective. They guide our desires and have individual utilities we assign them, influencing our actions accordingly. As Peirce (1877: 14) wrote: “Our beliefs guide our desires and shape our actions,” distinguishing beliefs from doubt. Nevertheless, guiding our individual desires remains a feature of subjective beliefs.
53Our knowledge, however is no longer purely subjective. The knowledge we arrive at is based on a long process of decision making. There are many beliefs involved in this process. Some turned out to be true and others false, hence were dispensed with. Knowledge is a judgement which is infallible. This means that there is a class of judgements, which are “not merely all in fact true, owing to some law of nature, but are in the nature of the case incapable of being false” (ibid.). We cannot claim that knowledge is belief which just happen to be true “owing to some law of nature” (ibid.). Knowledge is a judgement or a belief which is incapable of being false. In knowledge “a mind is apprehending a fact” (ibid.). If this fact did not exist, we could not make a judgement about it at all.
54Hence, our knowledge is based on our subjective beliefs which are grounded in the world which is independent of our wishes and of our thoughts. It has been pointed out that Ramsey’s subjectivism about beliefs is not incompatible with his view that beliefs are real dispositions correlated with objective facts (Engel & Dokic 2002: 13). Not only are these two notions “not incompatible”; our subjective beliefs are necessarily dependent on the objective facts. Ramsey is considering both full and partial beliefs in numerous essays, and yet due to their subjective character he regards only knowledge to be true. Moreover, he names a further condition for a full, true belief to become knowledge – it has to be obtained by a reliable process, or well grounded. We know of the strong influence Peirce’s pragmatism had on Ramsey. It characterizes Ramsey’s latest essays and it necessitates the normative reading of Ramsey’s theory of belief. It has been argued that Ramsey tells us merely what is reasonable for an ideal agent to think in an ideal situation, and hence what a reasonable action would be. We have seen, however, that this would mean for such an agent only to act on full, true beliefs; there could be no justification for partial beliefs. Most of our conduct, however, is based on partial beliefs which we hold to different degrees. To only act on full, true beliefs “is too high a standard to expect of mortal men, and we must agree that some degree of doubt or even of error may be humanly speaking justified” (TP: 80) and also “this ideal is more suited to God than to men” (TP: 89). This is why Ramsey develops a theory of subjective probability, showing us how to measure the degrees of our beliefs and thus following his principle of maximizing expected utility decide on the best possible action.