Sir Michael Dummett, who has died aged 86, was one of the greatest British philosophers of the 20th century. He was also an international authority on tarot cards, a campaigner for racial justice and a devoted family man. His wife, Ann, was a co-worker in his fight against racism and collaborated with him on a number of publications on the subject.

Dummett was a staunch advocate of "analytic" philosophy, the fundamental tenet of which he took to be that "the philosophy of language is the foundation of all other philosophy". He also once characterised it as "post-Fregean philosophy", the 19th-century German philosopher Gottlob Frege having done as much as anyone to treat the philosophy of language in this way. Much of Dummett's own work was accordingly devoted to the interpretation and exposition of Frege's ideas, and he will be as well remembered for his exegesis of Frege as he will for his own seminal contributions to analytic philosophy.

Frege held that the way in which the words in a sentence combine reflects the structure of the thought that the sentence expresses. In the sentence "Michael smokes," a proper name combines with a verb so as to express the thought that a particular person, Michael, indulges in a particular activity, smoking. This thought is true if Michael does in fact smoke, and false otherwise.

On this apparently innocuous and simple basis, Frege erected an elaborate set of ideas that have had an immense influence. Nevertheless, Dummett believed that Frege made certain assumptions concerning truth and falsehood that could be called into question. Frege allowed for the possibility of a thought that was neither true nor false. An example would be the thought that Father Christmas smokes. Given that there is no such person as Father Christmas, then neither is there anything to make this thought true or false. But Frege was not in the least reluctant to admit that a thought could be true or false without our having any way of telling which. An example might be the thought that Plato would have enjoyed smoking. This is what caused Dummett to pause.

He did not see how we could understand a sentence without having some way of manifesting our understanding. And he did not see how we could manifest this without being able to tell whether the thought expressed was true or false. So the assumption that a given thought could be true or false even though we had no way of telling which – an assumption that Dummett called "realism" concerning the thought – was immediately problematical.

Not that Dummett flatly denied this assumption; his point was only that it needed justification. He was issuing a challenge. Although the challenge was something close to a lifelong crusade, he undoubtedly retained a sympathy for realism. It was as if he was engaged in a continual internal struggle with himself. Furthermore, it is hard to escape the feeling that this in turn had something to do with his deep religious convictions, many of which may well have had a realist cast which the philosopher in him found problematical.

It is certainly true that, although he rarely made explicit contributions to the philosophy of religion, what he did write was often motivated by religious concerns. One topic about which he wrote a great deal, for example, was the possibility of backward causation. Certainly, his interest in this derived from an interest in the efficacy of retrospective prayer.

No one who witnessed Dummett engage in debate could fail to be struck by the passion with which he upheld his philosophical views. Nor could anyone who came into professional contact with him fail to be struck by the passion with which he defended all that was precious to him in academia. In 1984, for example, he resigned from the British Academy, partly because of his belief that it had failed in its duty to defend universities against funding cuts.

Indeed, Dummett seemed to be constitutionally incapable of undertaking anything half-heartedly. Not only was similar commitment manifest in the way he lived out his Christianity (he converted to Catholicism when he was a young man) and in the tireless way in which he opposed racism in all its forms, there was even evidence of it in his recreational interest in the history of card games.

Dummett was uncompromising in his convictions. This often led to bruising encounters with opponents. But although his opposition to another person's views could occasionally spill over into opposition to that other person, his sole motivation was a desire to see truth prevail.

He also took great pleasure in the good things in life, and had a wonderfully infectious sense of humour. He was always a generous and inspirational teacher. He never lectured twice on exactly the same material, preferring to maintain as much freshness as possible in his delivery. It was impossible to hear him lecture and not to have a profound sense of thought in action. He would pace up and down, cigarette in hand, pausing periodically to formulate in his own mind how best to proceed, referring only occasionally, if at all, to his notes. The upshot would always be a beautifully structured and wonderfully conceived argument in which ideas about the most abstract topics were seamlessly woven together.

In supervisions with his graduate students, he was similarly intent on the issues, but with an additional determination to see what his students were getting at. He inspired not only great philosophy but great affection.

Born in London, Dummett was educated at Sandroyd school in Wiltshire; Winchester college; and Christ Church, Oxford, where he graduated with a first in philosophy, politics, and economics in 1950, having served in the Royal Artillery and Intelligence Corps in India and Malaya from 1943 to 1947. Upon graduating, he was elected to a fellowship at All Souls, Oxford. He remained there until 1979, when he was elected to the Wykeham professorship of logic and a fellowship at New College. He retired in 1992. He received the Lakatos award in the philosophy of science in 1994, was awarded the Rolf Schock prize for logic and philosophy in 1995, was knighted in 1999, and was awarded the Lauener prize for an outstanding oeuvre in analytical philosophy in 2010.

Throughout his career he held numerous additional academic posts, including a readership in the philosophy of mathematics at Oxford and various visiting positions at universities around the world. He gave several of the most prestigious lecture series in philosophy, including the William James lectures at Harvard University in 1976 and the Dewey lectures at Columbia University in 2002. He was elected a fellow of the British Academy in 1968, later settling his differences and being re-elected in 1995. In 1966 he chaired the Oxford Committee for Racial Integration, of which he had been a founder member the previous year. In 1966–67 he was a member of the executive committee of the Campaign Against Racial Discrimination, and in 1970–71 chairman of the Joint Council for the Welfare of Immigrants.

His first major publication, Frege: Philosophy of Language (1973), appeared when he was at the comparatively ripe age of 48. One reason why it had not appeared earlier was that he had made a conscious decision to pursue what he conceived as his duty to oppose the racism that had become manifest in Britain. He completed the book when he reluctantly concluded that he no longer had any significant contribution to make to the fight and felt justified in returning to "more abstract matters of much less importance to anyone's happiness or future". He commented in the book's preface on the deep shock of having discovered, some years previously, that Frege himself, whom he had always revered "as an absolutely rational man", was a virulent racist. "From [this discovery]," he wrote, "I learned something about human beings which I should be sorry not to know; perhaps something about Europe, also."

Several other books on Frege followed: The Interpretation of Frege's Philosophy (1981), a defence of the main ideas of the earlier book; Frege and Other Philosophers (1991), a collection of essays; and Frege: Philosophy of Mathematics (1993), the long-awaited sequel to the first book, which Dummett had originally intended to publish along with it as a single volume.

He also wrote Elements of Intuitionism (1977), on the intuitionist school in logic and mathematics; The Logical Basis of Metaphysics (1991), a systematic statement of his own most basic ideas; The Origins of Analytic Philosophy (1993), in which he emphasised the significance of Frege to the analytic movement; Truth and the Past (2004), in which he applied some of his basic ideas to claims that we make about the past; Thought and Reality (2006), in which he set out his views about anti-realism; and The Nature and Future of Philosophy (2010), in which he gave a succinct account of his conception of his discipline.

Many of his numerous articles were anthologised in Truth and Other Enigmas (1978) and The Seas of Language (1993). The reverence with which he approached Frege's ideas, and the irritation and puzzlement with which he often approached the ideas of other philosophers, prompted one reviewer of the collection Frege and Other Philosophers to remark that Dummett seemed to regard the parallel between the title of that collection and the earlier collection Truth and Other Enigmas "as more than just a parallel".

Dummett's many non-philosophical publications included books on immigration, Catholicism, tarot cards, and voting procedures (he devised the Quota Borda system of voting), as well as Grammar and Style for Examination Candidates and Others (1993), the culmination of his relentless fight against low standards of literacy.

That fight occasionally found amusing expression in his other work. His last book on Frege included a delicious footnote in which, having forestalled a possible misunderstanding of one of the sentences in the main text, he went on to lament the fact that the only reason for the note was that few writers or publishers nowadays "evince a grasp of the distinction between a gerund and a participle". He continued, with characteristic tetchiness: "People frequently remark that they see no point in observing grammatical rules, so long as they convey their meaning. This is like saying that there is nothing wrong with using a razor blade to cut string, so long as the string is cut. By violating the rules, they make it difficult for others to express their meaning without ambiguity."

Some readers of Dummett would say that it was ironic that he was so preoccupied with style, since his own prose left much to be desired. It is true that his sentences often displayed a rather unwieldy complexity. But they also displayed an acute sensitivity to the structure of the thoughts that they were intended to convey; and that fact, combined with the precision with which Dummett chose his words, meant that there was a real clarity about his writing, however lacking it might have been in facility. The writing was in some respects like the man – marked by honesty and integrity, though it could at times be difficult.

Dummett is survived by Ann, whom he married in 1951, and by three sons and two daughters. A son and daughter predeceased him.

• Michael Anthony Eardley Dummett, philosopher, born 27 June 1925; died 27 December 2011

• Michael Dummett discussing Gottlob Frege at Philosophy Bites

• Frege in the Stanford Encyclopedia of Philosophy

• Realism in the Stanford Encyclopedia of Philosophy

• Dummett in the Internet Encyclopedia of Philosophy