Question: When was the author of Introduction to Mathematical Philosophy born?

full_context: Document 1: Context principle: The context principle is one of Gottlob Frege's ``three fundamental principles ''for philosophical analysis, first discussed in his Introduction to The Foundations of Arithmetic (Grundlagen der Arithmetik, 1884). Frege argued that many philosophical errors, especially those related to psychologism in the philosophy of logic and philosophy of mathematics, could be avoided by adhering carefully to the context principle. The view of meaning expressed by the context principle is sometimes called contextualism, but should not be confused with the common contemporary use of the term contextualism in epistemology or ethics. This view need not be contrasted with the view that the meanings of words or expressions can (or must) be determined prior to, and independently of, the meanings of the propositions in which they occur, which is often referred to as compositionalism.
Document 2: Philosophiæ Naturalis Principia Mathematica: The French mathematical physicist Alexis Clairaut assessed it in 1747: "The famous book of "Mathematical Principles of Natural Philosophy" marked the epoch of a great revolution in physics. The method followed by its illustrious author Sir Newton ... spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses."
Document 3: Idealism: and proliferation of hyphenated entities such as "thing-in-itself" (Immanuel Kant), "things-as-interacted-by-us" (Arthur Fine), "table-of-commonsense" and "table-of-physics" (Sir Arthur Eddington) which are "warning signs" for conceptual idealism according to Musgrave because they allegedly do not exist but only highlight the numerous ways in which people come to know the world. This argument does not take into account the issues pertaining to hermeneutics, especially at the backdrop of analytic philosophy. Musgrave criticized Richard Rorty and Postmodernist philosophy in general for confusion of use and mention.
Document 4: Empiricism: Around the beginning of the 20th century, William James (1842–1910) coined the term "radical empiricism" to describe an offshoot of his form of pragmatism, which he argued could be dealt with separately from his pragmatism – though in fact the two concepts are intertwined in James's published lectures. James maintained that the empirically observed "directly apprehended universe needs ... no extraneous trans-empirical connective support", by which he meant to rule out the perception that there can be any value added by seeking supernatural explanations for natural phenomena. James's "radical empiricism" is thus not radical in the context of the term "empiricism", but is instead fairly consistent with the modern use of the term "empirical". (His method of argument in arriving at this view, however, still readily encounters debate within philosophy even today.)
Document 5: Philosophiæ Naturalis Principia Mathematica: The French mathematical physicist Alexis Clairaut assessed it in 1747: "The famous book of Mathematical Principles of Natural Philosophy marked the epoch of a great revolution in physics. The method followed by its illustrious author Sir Newton ... spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses."A more recent assessment has been that while acceptance of Newton's theories was not immediate, by the end of a century after publication in 1687, "no one could deny that" (out of the Principia) "a science had emerged that, at least in certain respects, so far exceeded anything that had ever gone before that it stood alone as the ultimate exemplar of science generally."In formulating his physical theories, Newton developed and used mathematical methods now included in the field of calculus. But the language of calculus as we know it was largely absent from the Principia; Newton gave many of his proofs in a geometric form of infinitesimal calculus, based on limits of ratios of vanishing small geometric quantities. In a revised conclusion to the Principia (see General Scholium), Newton used his expression that became famous, Hypotheses non fingo ("I feign no hypotheses").
Document 6: Introduction to Mathematical Philosophy: Introduction to Mathematical Philosophy is a book by Bertrand Russell, published in 1919, written in part to exposit in a less technical way the main ideas of his and Whitehead's "Principia Mathematica" (1910–13), including the theory of descriptions.
Document 7: Empiricism: The phenomenalist phase of post-Humean empiricism ended by the 1940s, for by that time it had become obvious that statements about physical things could not be translated into statements about actual and possible sense data. If a physical object statement is to be translatable into a sense-data statement, the former must be at least deducible from the latter. But it came to be realized that there is no finite set of statements about actual and possible sense-data from which we can deduce even a single physical-object statement. Remember that the translating or paraphrasing statement must be couched in terms of normal observers in normal conditions of observation. There is, however, no finite set of statements that are couched in purely sensory terms and can express the satisfaction of the condition of the presence of a normal observer. According to phenomenalism, to say that a normal observer is present is to make the hypothetical statement that were a doctor to inspect the observer, the observer would appear to the doctor to be normal. But, of course, the doctor himself must be a normal observer. If we are to specify this doctor's normality in sensory terms, we must make reference to a second doctor who, when inspecting the sense organs of the first doctor, would himself have to have the sense data a normal observer has when inspecting the sense organs of a subject who is a normal observer. And if we are to specify in sensory terms that the second doctor is a normal observer, we must refer to a third doctor, and so on (also see the third man).
Document 8: Alfred North Whitehead: Whitehead and Russell had thought originally that Principia Mathematica would take a year to complete; it ended up taking them ten years. To add insult to injury, when it came time for publication, the three-volume work was so massive (more than 2,000 pages) and its audience so narrow (professional mathematicians) that it was initially published at a loss of 600 pounds, 300 of which was paid by Cambridge University Press, 200 by the Royal Society of London, and 50 apiece by Whitehead and Russell themselves. Despite the initial loss, today there is likely no major academic library in the world which does not hold a copy of Principia Mathematica.
Document 9: Philosophiæ Naturalis Principia Mathematica: Philosophiæ Naturalis Principia Mathematica (Latin for "Mathematical Principles of Natural Philosophy"), often referred to as simply the Principia (), is a work in three books by Isaac Newton, in Latin, first published 5 July 1687. After annotating and correcting his personal copy of the first edition, Newton published two further editions, in 1713 and 1726. The "Principia" states Newton's laws of motion, forming the foundation of classical mechanics; Newton's law of universal gravitation; and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically).
Document 10: Alfred North Whitehead: Whitehead did not begin his career as a philosopher. In fact, he never had any formal training in philosophy beyond his undergraduate education. Early in his life he showed great interest in and respect for philosophy and metaphysics, but it is evident that he considered himself a rank amateur. In one letter to his friend and former student Bertrand Russell, after discussing whether science aimed to be explanatory or merely descriptive, he wrote: "This further question lands us in the ocean of metaphysic, onto which my profound ignorance of that science forbids me to enter." Ironically, in later life Whitehead would become one of the 20th century's foremost metaphysicians.
Document 11: Idealism: Bradley was the apparent target of G. E. Moore's radical rejection of idealism. Moore claimed that Bradley did not understand the statement that something is real. We know for certain, through common sense and prephilosophical beliefs, that some things are real, whether they are objects of thought or not, according to Moore. The 1903 article The Refutation of Idealism is one of the first demonstrations of Moore's commitment to analysis. He examines each of the three terms in the Berkeleian aphorism esse est percipi, "to be is to be perceived", finding that it must mean that the object and the subject are necessarily connected so that "yellow" and "the sensation of yellow" are identical - "to be yellow" is "to be experienced as yellow". But it also seems there is a difference between "yellow" and "the sensation of yellow" and "that esse is held to be percipi, solely because what is experienced is held to be identical with the experience of it". Though far from a complete refutation, this was the first strong statement by analytic philosophy against its idealist predecessors, or at any rate against the type of idealism represented by Berkeley. This argument did not show that the GEM (in post–Stove vernacular, see below) is logically invalid.
Document 12: The Problems of Philosophy: The Problems of Philosophy is a 1912 book by Bertrand Russell, in which the author attempts to create a brief and accessible guide to the problems of philosophy. Focusing on problems he believes will provoke positive and constructive discussion, Russell concentrates on knowledge rather than metaphysics: If it is uncertain that external objects exist, how can we then have knowledge of them but by probability. There is no reason to doubt the existence of external objects simply because of sense data.
Document 13: Alfred North Whitehead: This is not to say that Whitehead's thought was widely accepted or even well-understood. His philosophical work is generally considered to be among the most difficult to understand in all of the western canon. Even professional philosophers struggled to follow Whitehead's writings. One famous story illustrating the level of difficulty of Whitehead's philosophy centers around the delivery of Whitehead's Gifford lectures in 1927–28 – following Arthur Eddington's lectures of the year previous – which Whitehead would later publish as Process and Reality:
Document 14: Empiricism: The neopositivists subscribed to a notion of philosophy as the conceptual clarification of the methods, insights and discoveries of the sciences. They saw in the logical symbolism elaborated by Frege (1848–1925) and Bertrand Russell (1872–1970) a powerful instrument that could rationally reconstruct all scientific discourse into an ideal, logically perfect, language that would be free of the ambiguities and deformations of natural language. This gave rise to what they saw as metaphysical pseudoproblems and other conceptual confusions. By combining Frege's thesis that all mathematical truths are logical with the early Wittgenstein's idea that all logical truths are mere linguistic tautologies, they arrived at a twofold classification of all propositions: the analytic (a priori) and the synthetic (a posteriori). On this basis, they formulated a strong principle of demarcation between sentences that have sense and those that do not: the so-called verification principle. Any sentence that is not purely logical, or is unverifiable is devoid of meaning. As a result, most metaphysical, ethical, aesthetic and other traditional philosophical problems came to be considered pseudoproblems.
Document 15: Karl Popper: As early as 1934, Popper wrote of the search for truth as "one of the strongest motives for scientific discovery." Still, he describes in Objective Knowledge (1972) early concerns about the much-criticised notion of truth as correspondence. Then came the semantic theory of truth formulated by the logician Alfred Tarski and published in 1933. Popper writes of learning in 1935 of the consequences of Tarski's theory, to his intense joy. The theory met critical objections to truth as correspondence and thereby rehabilitated it. The theory also seemed, in Popper's eyes, to support metaphysical realism and the regulative idea of a search for truth.
ground_truth: 1872
sub_queries: Introduction to Mathematical Philosophy >> author Answer: Bertrand Russell
When was Bertrand Russell born? Answer: 1872