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Compiled by Anthony Harrison-Barbet
RUSSELL
CRITICAL EMPIRICISM/ LOGICAL ANALYSIS
Bertrand Russell (Lord Russell) was born at Trelleck, Monmouthshire, the second son of Viscount Amberley. His parents died when he was very young, and he was brought up by his grandparents (John Stuart Mill was an informal guardian). He was educated at home by private tutors and then at Trinity College, Cambridge, where he studied mathematics and philosophy. He gained his degree in 1894 and was a Fellow of Trinity 1895-1901. After travelling in the U.S.A. and Germany he became a lecturer at the London School of Economics and then at Trinity College, Cambridge. Throughout his life Russell was active in politics — he was imprisoned in 1918 for writing allegedly libellous articles and in 1961 in connection with the Campaign for Nuclear Disarmament. He also stood for Parliament (unsuccessfully) on three occasions. From 1927-1934 he ran an experimental school he had established, and thereafter taught at the Universities of Chicago and California, Los Angeles. In 1931 he succeeded to the Earldom. He was elected Fellow of the British Academy and appointed to the Order of Merit in 1949. Russell was an outstanding rationalist, humanist, and socialist, and a champion of free speech, and was a prolific writer not only in philosophy (of which he was a great populariser) but also on social, political, and educational issues.
PHILOSOPHY OF MATHEMATICS, LOGIC AND LANGUAGE
[1] Russell was initially interested in the nature of mathematical truth. He came to reject both empiricist accounts of number and the view of geometry as grounded in a priori intuitions. He argued that mathematical propositions must be true necessarily (analytically), and he sought to reduce mathematics to formal logic (which he came to regard as consisting of tautologies). Taking numbers as mathematically basic and as applicable to classes, he defined a cardinal number of a given collection as the class of all equally numerous collections, that is, what such collections have in common. This illustrates Russell's (and Whitehead's) 'construction' of mathematical entities out of 'simpler' ones [in Principia Mathematica] [a].
Russell's work on logic and mathematics led to a number of paradoxes.
(1) Is the class of all classes which are not members of themselves a member of itself? We seem to have a contradiction whether it is or is not a member. Russell claimed to have resolved the paradox by his theory of types. Suppose we have a propositional function, 'x is y', where y is some property, say 'mortal'. For x we can substitute appropriate values, for example, Russell, Socrates, belonging to a particular class (man). The propositional function is made true when 'Russell' is substituted for x. What we cannot do is to substitute, say, 'class of men' for x; for this includes an element defined in terms of the function. Russell said it belongs to a different order or type. He later argued that different types constitute different syntactical functions in a sentence; and that if classes themselves are no more than incomplete symbols they can be dispensed with as 'real' entities [b].
(2) A second paradox arose out of a particular view of word meaning, namely that words acting as grammatical subjects of sentences have meaning by virtue of their denoting some entity. Thus the meaning of 'cat' is the furry animal it refers to. But then what do we say of words such as 'unicorn', 'happiness', 'class', or of self-contradictory expressions like 'round square'? In his earliest period Russell would seem to have believed that there are actual entities, albeit not 'existing' in the way that tables and chairs do, which are the denotata of such names. However, he soon came to reject this view; and to deal with the problem of non-denoting terms and phrases he devised the Theory of Descriptions ['On Denoting']. This can be explained as follows.
Names whose job it is simply to denote some simple object and whose meaning is the object denoted Russell calls 'logically proper names'. All other names are really implicit or disguised descriptions that function only as names, for example, 'the author of Waverley' and 'the King of France'. Now, suppose we say 'The King of France is bald'. If there is no such existent entity denoted by the phrase 'the King of France', is the statement as a whole false or meaningless? It certainly seems to be about something. To avoid this problem Russell in effect paraphrased the sentence to read (roughly) 'There exists some thing x such that it is King of France; and to say that anything is King of France entails that it is identical to x; and that that thing is bald'. Translated into the symbolism of formal logic this becomes: (∃x)[Fx ∙ (y) (Fy → y = x) ∙ Gx]. The non-denoting name is thus eliminated in the restructured formulation of the original sentence; and the truth of the sentence is now determined by whether or not the 'x' in '∃x' is or is not instantiated. Definite descriptions are incomplete symbols (like classes), not the real logical subjects of sentences, and have meaning only by virtue of the role they play in the logical structure of those sentences [c]; they have no meaning in isolation. Moreover they cannot mean the name they describe, Russell said, for this would produce tautologies. To say 'Scott is the author of Waverley' would be to say no more than 'Scott is Scott'. If the description had any other meaning, the sentence would be false. So the phrase on its own does not mean anything. It is thus clear that Russell placed much emphasis on logical analysis to uncover the logical structures underlying what he saw as potentially philosophically misleading grammatical forms of sentences [d].
During this early period Russell supposed truth and falsehood to be attributes of propositions — these being understood as timeless existent complexes of terms, objects of 'intentional acts of belief' or of thought. Truth belongs to true propositions in consequence of the internal relationship between their constitutent terms [e]. He distinguishes between material implication and formal implication [see Principia Mathematica]. The former relates propositions (as when we say 'it is not the case that p is true and q is false). The latter relates propositional functions (such as 'x is a man' formally implies 'x is mortal'). However, Russell maintained that 'p materially implies q' means the same as 'q is deducible from p'. And he also claimed that the relation of formal implication can be subsumed under the class of material implications (just as pure mathematics is seen as the class of all propositions of the form 'p implies q'). It is on the basis of implication that inferences are made. But inference for Russell is not a psychological activity; formal logic is not a 'theory of enquiry' [f]. True propositions are identical with facts: false propositions are non-factual 'complexes'. Russell came to regard as unsatisfactory the supposition that false propositions actually have being in the same sense as non-factual entities, so he proposed a multiple-relation theory of judgement [Problems of Philosophy]. Take, for example, 'Othello believes that Desdemona loves Cassio'. In this judgement or propositional 'act' the subject or mind (Othello) arranges the elements or objects (1) Desdemona, (2) loving, and (3) Cassio in the particular order 1 to 3, thereby forming a complex unity. The judgement is true if the objects actually exist as a unity, a factual complex, separate from the judgement and in the same order as the corresponding terms in the judgement. The existence of all the objects guarantees the meaningfulness of the judgement even if there is no complex — in which case the propositional judgement is false (and does not have abstract 'being'). Russell later ['The Philosophy of Logical Atomism'] moved to the view that the intentional objects constituting propositions are now complex 'images' in the mind, which are true if they 'correspond' to the facts, false if they point away from the same facts. Correspondence seemed to be understood by him in terms of picturing or resemblance [g].
Both Russell's account of truth and his views of meaning underwent further modification in a 'behaviourist' direction and came to be linked with his theory of a 'hierarchy of languages' — though he continued to hold to the correspondence theory [An Inquiry into Meaning and Truth, ch. 21]. He postulated a fundamental language consisting of object words (nouns, verbs, adjectives) by the meanings of which extra-linguistic events could be expressed, albeit crudely. In order to say that any statements made in this basic language are true or false a 'second-order' language is needed, because the basic language does not contain such semantic terms. Thus a language's form might be described — though through a metalanguage [h]. If an indicative statement is to be regarded as true or false, it has to be meaningful. (Imperatives and interrogatives are also meaningful but cannot be said to be true or false.) Russell now distinguished between the meaning of object words and the significance of sentences. Meaning depends on reference: a word 'means' an object if when the (sensible) presence of the object causes the utterance of the word, and the hearing of the word produces effects analogous to that experienced when the object is present [IMT, ch. 1]. Significance, however, depends on the meanings of the object words in the context of a syntactically correct sentence. Strictly speaking, the significance of a sentence is that which is common to sentences which make the same assertion ('It is raining', 'Il pleut'). [See IMT, ch. 13.] Russell said this significance is now the 'proposition', which he considered to be a logical construction out of a class of sentences having the same meaning [ch. 12]. It is also the expression of the belief of the person who expresses it, identifiable with his internal physiological state — his implicit tendency to respond, behave in appropriate ways [ch. 13] [i]. If the belief, through the assertion, relates successfully to a fact, it is true; otherwise it is false. In Human Knowledge [Pt II, ch. XI] he called the facts 'verifiers'; and he made it clear that such relations between empirical beliefs and verifiers may hold even though we may not know it. The mere possibility of verification makes the statement meaningful. However, non-empirical, that is, 'analytic' propositions (of logic and mathematics, for example), are true by virtue of the form of the sentences asserted. And Russell accordingly rejects 'warranted assertibility' and coherence theories of truth [IMT, chs 10, 21, 23] [j].
METAPHYSICS
[2] Russell's metaphysics (and his theory of knowledge — see below) are closely bound up with his views on logic and language. In his earliest period, having rejected the doctrine of internal relations and dogmatic monistic idealism, he was an extreme realist, believing in the actual existence of a plurality of external relations, universals, spatial points, instants of time, numbers, and perhaps also 'selves' [a]. But in due course he came to extend the reductive analysis he had used in mathematics to the wider sphere of philosophy, in particular to the language employed to describe the physical world [Our Knowledge of the External World]. Points, instants, material particles are now regarded as logical constructions of sets of events. Physical objects are definable in terms of actual sense-data (for example, red patches) or possible sense-data ('sensibilia'), sense-data being regarded as physical entities located in the nervous system. This is a phenomenalist theory [b]. Likewise he supposed the 'self' to be a constructed collection of states sharing the same common quality of being described as 'mental', and which are apprehended as the 'act of awareness'. But we have no direct acquaintance with this self as such [c]. Russell thus held that we use different 'languages': one to describe our ordinary everyday experiences of tables, trees, people, but translatable into another for the purposes of natural science (which makes use of such concepts as space, time, particle) and psychology (mental states) [d]. And he seemed to use his reductive analysis techniques as a means of revealing what he supposed to be the ultimate constituents of reality [see 'The Philosophy of Logical Atomism']. The ideal or 'basic' language supposedly represents in its structure ('isomorphically') the nature and structure of the 'real' world as consisting of a plurality of particulars ('logical atoms' — sense-data and universals) which are independent of each other [e]. The common sense world of everyday experience can then be understood as consisting of complexes of atomic facts, for example, 'This is white' (particular), and 'All men are mortal' (universal). Russell soon recognised that there were difficulties with his logical atomism and his postulation of isomorphism between language and 'reality'. We can never be sure we have actually reached logical ultimates; and general facts may have to be admitted as ultimate constituents if general statements cannot be shown to be functions of atomic statements.
In the next stage of his thought Russell eliminated even the 'act of awareness' he had supposed to be required to apprehend the collection of states partly constituting the mind. He now [Analysis of Mind] adopted a form of 'neutral monism'. Both mind and matter are neutral constructions or complexes of particulars which are neither mental nor material. Sense-data may be physical and psychical, depending on the way we group them with other particulars in our common sense experience of events, that is, on whether we relate them to the viewing of images from our own perspective or to the appearances in space of objects. To all intents and purposes this adds up to an abandonment by Russell of the view of sense-data as physical and extra-mental objects of awareness, and of the notion of any intentional mental act [f]. As for 'universals', he seemed later to think of these as empirically correlatable qualities common to the individual things which are collections of them (redness, hardness, and so on) [IMT, ch. 6] [g].
KNOWLEDGE
[3] Russell's theory of knowledge is in its fundamentals relatively stable and consistent. Throughout his writings knowledge tends to be presented as a relationship between the knower and 'objects'. But as to what these objects are and how they are known he offered different answers at different times — reflecting the various shifts and modifications in his metaphysics and philosophy of language.
In his earliest period [especially Problems of Philosophy] he distinguished (a) things and (b) truths. Knowledge of things he called knowledge by acquaintance; and under this heading he included sense-data, universals, and probably mental states and his own 'self' or mind. The objects of knowledge of truths are judgements, or beliefs that something is the case. Knowledge that is thus subordinated to knowledge of. Truths, he said, may be (i) self-evident — our knowledge then being 'intuitive'; or (ii) derivative — such truths being 'deduced' from self-evident truths. Examples of truths known intuitively are the principles of logic and mathematics, the principles of induction, and truths which 'correspond' to complex facts, including truths of perception and immediate memory. From our knowledge of things together with our knowledge of truths we may derive knowledge of things by description. Russell here included physical objects, other human beings, and minds [a].
Because of difficulties associated with inference to physical objects and mental selves Russell subsequently supposed such objects of knowledge to be constructions out of subjective or 'lived' immediate experience. Objects of knowledge then become constituents of atomic facts, namely sense-data and universals, expressed in atomic sentences (from which complexes can be built truth-functionally). [see Our Knowledge of the External World; Analysis of Mind] [b]. Later still [An Inquiry into Meaning and Truth, ch. 19] he came to admit that we cannot know whether atomic facts are simples, that is, ultimate entities. Having rejected sense-data, so as to avoid solipsism, he returned again to a consideration of the possibility of inference as a basis for knowledge and attempted to show how inferences to the general propositions of science might be justified [Human Knowledge, Pt III, ch. III and passim] [c]. Such inferences are not demonstrative — unlike those employed in mathematics and logic. But he recognised that there are inferences which we accept as having varying degrees of probability — though many generalizations are of course false. Can we then establish criteria for distinguishing between valid and invalid inferences in science? How far should we allow ourselves to move away from a fundamentally empiricist position? To deal with these issues Russell sketched out a number of principles, though these were neither systematically formulated nor in any sense proven. He supposed rather that they are 'justified' in that they provide the framework within which our inherently biological propensity to draw inferences can operate, and which is successful in so far as our whole system of science and everyday knowledge 'works' [d]. Five postulates were set out [HK, Pt VI, ch. IX, though he said it might be possible to operate with fewer. They are:
(1) The postulate of 'quasi-permanence': given an event A, it is usually the case that an event similar to A is found near to it in time and space.
(2) The postulate of 'separable causal lines': it is often possible to form a series of events which enables us to infer something from a few of its members to the others.
(3) The postulate of 'spatio-temporal continuity': if there is a causal connection between events which are 'non-contiguous, intermediate links in the chain can be found.
(4) The 'structural' postulate: if a number of structurally similar complex events occur close to a centre, then it is usually the case that they all belong to causal lines originating in an event of similar structure at the centre.
(5) The postulate of 'analogy': if we have reason to suppose of two classes of observed events, A and B, that A causes B, then it is probable that if A occurs then B also does, though we have not observed it.
ETHICS
[4] Russell started out [for example, Philosophical Essays, ch. I] by accepting the 'objectivist' view that good and bad are 'qualities' which belong to objects independently of any individual's opinion, and (the 'non-naturalist' view) that they cannot be inferred from any other properties. He also rejected the view that to say x is good is to say something about one's feelings or desires [a]. People, he said, generally agree on what is intrinsically valuable. He later [An Outline of Philosophy] radically reversed his account of ethics to adopt a 'subjectivist' position. Disagreement about values is a disagreement of 'taste', that is, they are about our feelings, desires, attitudes. There are no ethical 'facts'; good and bad are not independent qualities of objects of objects — indeed they are not qualities at all. Moral judgement is an expression of desire [b]: but Russell distinguished between personal desires (for example, for food) and impersonal desires (for example, that the monarchy should be abolished). It is the latter which are appropriate to moral judgement in the strict sense. Moreover, people disagree not only about the means to achieve particular ends but about the ends themselves (which may of course affect discussion about the means). Nevertheless the 'rightness' of actions must still be assessed in terms of their consequences, however we differently we may judge these consequences [c].
Despite this fundamental change of standpoint, Russell consistently regarded as illegitimate any 'naturalistic' move from factual premisses (be they empirical or metaphysical) to conclusions which are statements of value [d]. These do not assert anything, he said, and therefore cannot be true or false.
PHILOSOPHY OF RELIGION
[5] Russell's attitude to religion and theology was on the whole negative and sceptical. God's existence, he said, is not provable and although we cannot be certain, it is highly improbable that there is such a being, not least because of the presence of evil in the world [a] — a world which Russell described as being fundamentally horrible. Similarly he asserted that there is no evidence to support the view that anything 'spiritual' survives the dissolution of the body after death [b]. Nevertheless he had some sympathy for rationalist philosophers, as against 'fideists' and those who appeal to feeling. Faith is subjective and cannot support objective claims [c]. At least the rationalists attempt to argue their case — though Russell rejected the arguments. He regarded all organized religion as having bad consequences for individuals and societies, particularly when grounded solely in faith and feeling — a stance which for him was inconsistent with open-mindedness. In general his own attitude to what he perceived as 'cosmic injustice' has much in common with that of the Stoics; he admired the courage they showed in the pursuit of truth [d].
CRITICAL SUMMARY
Much criticism of Russell's philosophy may well be regarded as inappropriate in so far as his ideas were constantly changing and evolving. Indeed he was his own severest critic — thus reflecting his scrupulous intellectual honesty and his single-minded quest for truth and certainty. Nevertheless there are some permanent features of his thought. He remained committed to a denotative theory of meaning and to a general empiricism in his epistemology and metaphysics; and these positions have stimulated legitimate debate.
(1) Some critics have objected to his Theory of Descriptions (which he formulated to deal with consequences of his theory of meaning). Following Frege, they argue that Russell failed to take account of the way that descriptive phrases are actually used in everyday discourse, namely, that use presupposes the existence of the objects to which the descriptions refer. They criticize further Russell's assumption that underlying the potentially misleading grammatical forms of sentences are logical forms (which Russell also identified with the logical forms of the 'facts' which would verify what the sentences express).
(2) Objections have also been made against Russell's account of knowledge (and the 'metaphysics' associated with it). His distinction between knowledge by acquaintance and knowledge by description involved the postulation of basic entities — 'logical atoms', subsequently identified with percepts, images, 'sensa', as immediate objects of acquaintance. Physical objects and the self are therefore regarded variously as constructions or inferences. Recent critics have argued against such inferential realism and postulation of 'sensa', not least because of their alleged status as 'private' entities, that is, private to the perceiver.
One's attitude to such criticisms of both Russell's Theory of Descriptions (and his account of meaning) and his theory of perception will of course depend on what view one holds of the nature and functioning of language. This continues to be a disputed issue. In the recent climate of 'linguistic' or 'ordinary language' philosophy it is arguable that the later philosophy of Russell has probably been underrated.
(3) Many commentators (and not only professional philosophers) have balked at Russell's 'subjectivist' ethics and his agnostic, sceptical pessimism about matters of religion. And they have suggested that it is difficult to reconcile this with Russell's public advocacy of the rightness or wrongness of statements and actions of political or religious leaders. In answer to this it might be said that while he certainly held that morality is in some sense a matter of personal 'taste', one's preferences can be justified on rational grounds (say, with reference to ends and means) supported by discussion, and they may come to be shared by others in the community. This of course underpins Russell's commitment to the open society, freedom of thought, and his concerns about excesses of state power.
READING
Russell: [of many writings] The Problems of Philosophy (1912); Our Knowledge of the External World (1914); The Analysis of Mind (1921); An Inquiry into Meaning and Truth (1940); Human Knowledge: Its Scope and Limits (1948); My Philosophical Development (1959). See also 'On Denoting' (1905) and 'Lectures on the Philosophy of Logical Atomism' (1918-19) — both in R. C. Marsh (ed.), Logic and Knowledge. More works are listed in the Bibliography.
Studies:
Introductions
A. J. Ayer, Russell.
A. C. Grayling, Russell.
More advanced
C. W. Kilmister, Russell.
D. F. Pears, Bertrand Russell and the British Tradition in Philosophy.
R. M. Sainsbury, Russell.
J. Watling, Bertrand Russell.
Collections of Essays
N. Griffin (ed.), The Cambridge Companion to Bertrand Russell.
D. F. Pears (ed.), Bertrand Russell.
P. A. Schilpp (ed.), The Philosophy of Bertrand Russell.
CONNECTIONS
Russell
[1a] Rejection of empiricist and intuitionist accounts of mathematics; mathematical propositions necessarily true (tautologies); maths reducible to formal logic (tautologies); 'constructionism' Hume→
Kant→
Mill→
→Ayer
[1g]
[1b]
[1d]
[1a c]
[1a]
[1d 1e 2f]
[2b 4a]
[1a]
[1b; cf. 1d h] Theory of types — different syntactical functions of sentences; classes not real [1b]
[1b]
[1c] Word meaning: names (as 'logically proper names') denote; denoting phrases do not denote entities; sense in terms of definite descriptions (grammatical but not logical subjects); meaning by virtue of role in logical structure of sentences Mill→
→Moore→
→Ryle
[1b]
[1c]
[2c e j]
[1a c 2a 2e]
[2a]
[1h i 2c]
[1b c 1d]
[1d]
[1a c]
[1d] Logical analysis to uncover logical structures; grammatical forms misleading; restructuring →Ryle
→Ayer
[1e]
[2c]
[2a b]
[1d]
[2a e]
[3a 3c d]
[1a]
[1e]
[1a]
[1e; cf. 2f] Truth and falsity attributes of propositions (objects of intentional acts of belief or of thought) →Ayer
[2a]
[1a]
[1b]
[4f]
[1b 2a]
[1a]
[1c 3e]
[1f] Material and formal implication — same meaning but latter as class of former; inference between propositions not psychological — logic not a form of enquiry [1d]
[1f 1f]
[1a 2a]
[1a]
[1a]
[1c]
[1a]
[1g; cf. 1e i j 2e] Propositions complex mental images — true by correspondence to facts (resemblance) (problem of false propositions) →Moore→
[7f]
[1c]
[1b]
[6a 2a]
[2a 2b]
[1a]
[1e]
[1h; cf. 1b 2d] Object word language and second-order language hierarchy of languages; form describable through meta-language [1b]
[2a]
[1i] Word meaning in terms of utterances; propositions as common feature of sentences making same assertions and as 'significance' — understood as implicit behaviour →Ayer
[2g h i]
[1a]
[3a 3c]
[1d]
[1b]
[1j; cf. 1g] Meaning and truth in terms of verifiability; non-empirical propositions (analytic) true by virtue of form of sentences; rejection of warranted assertibility and coherence theories →Ayer
[6a]
[2b]
[2d]
[1a 3a]
[1b d]
[1b]
[2a; see also 2g] Rejection of internal relations; initial realism as regards universals, points, numbers, etc; pluralism Hume→
[1b d]
[1d f]
[1d]
[4f]
[1a b]
[2b; cf. 2f 3b] Logical constructions of events — physical objects in terms of actual/ possible sense-data (physical entities in nervous system) — phenomenalism Hume→
Mill→
→Moore→
→Ryle
→Ayer
[1c]
[2b]
[1b]
[2d 2g]
[1b]
[4a b]
[3d]
[2a]
[2a]
[2c; cf. 2f] Self as collection of 'mental states', apprehended as act of awareness, but no direct acquaintance Hume→
Mill→
→Ryle
→Ayer
[2d]
[2c]
[2c]
[4a]
[3d]
[2d; cf. 1h] Ordinary and 'scientific' languages →Ayer
[2b]
[2b]
[2a]
[1b]
[2c 3c]
[2e; cf. 1g 3b] 'Ideal'/ basic language — isomorphism with real world; plurality of 'logical atoms' (sense-data, universals) →Ayer
[1e 2a]
[1b]
[1a 2b]
[2b]
[2f; cf. 2b c 3b c] Neutral monism: mind and matter neutral constructions of complexes of particulars (sense-data as physical or psychical, but notions of sense-data and intentional mental acts soon abandoned) →Ayer
[2b]
[2b]
[2c]
[2d 3b 3c 3e]
[2g; cf. 2a e] Universals real but as qualities common to particular things Hume→ [1f]
[3a] Knowledge of truths (logic, maths, principles); know of things: (i) sense-data, universals, mental states ('acquaintance'); (ii) physical objects, other minds (by 'description' + truths) Hume→
→Moore→
→Ryle
→Ayer
[1c 1g 2a]
[1e 1j]
[3a]
[2e]
[3d 4a c]
[2b d]
[3b; cf. 1g 2a b e f] Objects of knowledge (physcal objects, mental states) as constructions from immediate experience, and become constituents of atomic facts (sense-data, universals) Hume→
→Ryle
→Ayer
[1c]
[1b]
[1c]
[1a]
[4a b]
[3d 4a c]
[2d 3b]
[3c; cf. 2f 3a] [Later] inference as basis for justified knowledge (after rejection of sense-data) [2f]
[2c 3c]
[3d] Principles/ postulates for framework in which our propensity to draw inferences operates; successful in that whole system of science 'works' Ayer [4e f]
[4a] 'Good', 'bad' are objective qualities — cannot be inferred; not about feelings/ desires [3a]
[5a-c]
[4b] [Later subjectivism] — values about feelings, taste; no ethical facts; good and bad not qualities [5a]
[3a]
[3a]
[5c]
[hence general rejection of all dogmatic
ethical systems, such as religion based
ethics and idealism]
[4c] 'Rightness' of actions in terms of consequences (however judged) Mill→
[3a]
[3b]
[3a]
[4d] Fact to value inferences not legitimate Hume→
[3j]
[1i]
[5a] God's existence improbable (not least because of evil in world) and not provable Hume→
Mill→
[5a]
[5c]
[5b] No evidence for immortality Hume→ [2d]
[5c] Faith subjective and cannot support objective claims [Representative:]
[1a]
[5d] Stoical attitude [Representative:]
[1f g]