Broad C(harlie) D(unbar) (1887–1971), English epistemologist, metaphysician, moral philosopher, and philosopher of science. He was educated at Trinity College, Cambridge, taught at several universities in Scotland, and then returned to Trinity, first as lecturer in moral science and eventually as Knightbridge Professor of Moral Philosophy. His philosophical views are in the broadly realist tradition of Moore and Russell, though with substantial influence also from his teachers at Cambridge, McTaggart and W. E. Johnson. Broad wrote voluminously and incisively on an extremely wide range of philosophical topics, including most prominently the nature of perception, a priori knowledge and concepts, the problem of induction, the mind– body problem, the free will problem, various topics in moral philosophy, the nature and philosophical significance of psychical research, the nature of philosophy itself, and various historical figures such as Leibniz, Kant, and McTaggart.
Broad’s work in the philosophy of perception centers on the nature of sense-data (or sensa, as he calls them) and their relation to physical objects. He defends a rather cautious, tentative version of the causal theory of perception. With regard to a priori knowledge, Broad rejects the empiricist view that all such knowledge is of analytic propositions, claiming instead that reason can intuit necessary and universal connections between properties or characteristics; his view of concept acquisition is that while most concepts are abstracted from experience, some are a priori, though not necessarily innate. Broad holds that the rationality of inductive inference depends on a further general premise about the world, a more complicated version of the thesis that nature is uniform, which is difficult to state precisely and even more difficult to justify.
Broad’s view of the mind–body problem is a version of dualism, though one that places primary emphasis on individual mental events, is much more uncertain about the existence and nature of the mind as a substance, and is quite sympathetic to epiphenomenalism. His main contribution to the free will problem consists in an elaborate analysis of the libertarian conception of freedom, which he holds to be both impossible to realize and at the same time quite possibly an essential precondition of the ordinary conception of obligation. Broad’s work in ethics is diverse and difficult to summarize, but much of it centers on the issue of whether ethical judgments are genuinely cognitive in character.
Broad was one of the few philosophers to take psychical research seriously. He served as president of the Society for Psychical Research and was an occasional observer of experiments in this area. His philosophical writings on this subject, while not uncritical, are in the main sympathetic and are largely concerned to defend concepts like precognition against charges of incoherence and also to draw out their implications for more familiar philosophical issues.
As regards the nature of philosophy, Broad distinguishes between ‘critical’ and ‘speculative’ philosophy. Critical philosophy is analysis of the basic concepts of ordinary life and of science, roughly in the tradition of Moore and Russell. A very high proportion of Broad’s own work consists of such analyses, often amazingly detailed and meticulous in character. But he is also sympathetic to the speculative attempt to arrive at an overall conception of the nature of the universe and the position of human beings therein, while at the same time expressing doubts that anything even remotely approaching demonstration is possible in such endeavors. The foregoing catalog of views reveals something of the range of Broad’s philosophical thought, but it fails to bring out what is most strikingly valuable about it. Broad’s positions on various issues do not form anything like a system (he himself is reported to have said that there is nothing that answers to the description ‘Broad’s philosophy’). While his views are invariably subtle, thoughtful, and critically penetrating, they rarely have the sort of one-sided novelty that has come to be so highly valued in philosophy. What they do have is exceptional clarity, dialectical insight, and even-handedness. Broad’s skill at uncovering and displaying the precise shape of a philosophical issue, clarifying the relevant arguments and objections, and cataloging in detail the merits and demerits of the opposing positions has rarely been equaled. One who seeks a clear-cut resolution of an issue is likely to be impatient and disappointed with Broad’s careful, measured discussions, in which unusual effort is made to accord all positions and arguments their due. But one who seeks a comprehensive and balanced understanding of the issue in question is unlikely to find a more trustworthy guide. See also PARAPSYCHOLOGY, PHILOSOPHY OF MIN. L.B Brouwer, Luitzgen Egbertus Jan (1881–1966), Dutch mathematician and philosopher and founder of the intuitionist school in the philosophy of mathematics. Educated at the Municipal University of Amsterdam, where he received his doctorate in 1907, he remained there for his entire professional career, as Privaat-Docent (1909–12) and then professor (1912–55). He was among the preeminent topologists of his time, proving several important results. Philosophically, he was also unique in his strongly held conviction that philosophical ideas and arguments concerning the nature of mathematics ought to affect and be reflected in its practice. His general orientation in the philosophy of mathematics was Kantian. This was manifested in his radical critique of the role accorded to logical reasoning by classical mathematics; a role that Brouwer, following Kant, believed to be incompatible with the role that intuition must properly play in mathematical reasoning. The bestknown, if not the most fundamental, part of his critique of the role accorded to logic by classical mathematics was his attack on the principle of the excluded middle and related principles of classical logic. He challenged their reliability, arguing that their unrestricted use leads to results that, intuitionistically speaking, are not true.
However, in its fundaments, Brouwer’s critique was not so much an attack on particular principles of classical logic as a criticism of the general role that classical mathematics grants to logical reasoning. He believed that logical structure (and hence logical inference) is a product of the linguistic representation of mathematical thought and not a feature of that thought itself. He stated this view in the so-called First Act of Intuitionism, which contains not only the chief critical idea of Brouwer’s position, but also its core positive element. This positive element says, with Kant, that mathematics is an essentially languageless activity of the mind. (Brouwer went on to say something with which Kant would only have partially agreed: that this activity has its origin in the perception of a move of time.) The critical element complements this by saying that mathematics is thus to be kept wholly distinct from mathematical language and the phenomena of language described by logic.
The so-called Second Act of Intuitionism then extends the positive part of the First Act by stating that the ‘self-unfolding’ of the primordial intuition of a move of time is the basis not only of the construction of the natural numbers but also of the (intuitionistic) continuum. Together, these two ideas form the basis of Brouwer’s philosophy of mathematics – a philosophy that is radically at odds with most of twentieth-century philosophy of mathematics.
See also PHILOSOPHY OF MATHEMATICS. M.D.