Throughout history, there have been many great thinkers. They have sprawled among many disciplines, from philosophy to physics. Nevertheless, some of these have made important contributions to many fields at the same time. One of these cases is that of Blaise Pascal, who was deeply influential in mathematics, philosophy and theology.
In a sense, one could say that these three disciplines were intertwined in his work. By studying the loftier aspects of the human experience, Pascal was able to bring together probability theory and his worries about the existence of God. As such, his notorious wager was a turning point in philosophy, as it enmeshed infinity, probability, utility and God, so as to provide a rational perspective and justification for the belief in God.
Therefore, it is important to study Pascal’s thinking integrally, bringing together his contributions to different fields. The present text will begin by exploring the thinker’s life, providing a brief biography to understand the context of the important contributions that he made.
Then, his mathematical contributions will be explored, especially his famous triangle and other contributions to probability theory. After, his philosophy of mathematics will be briefly explored. Both of these will lead to his more theological ideas, including his notorious wager for the existence of God.
Biography
Blaise Pascal was born on June 19, 1623 in Clermont-Ferrand, France. He was considered a child prodigy, and, with aid from his father developed to be one of the greatest thinkers of his era. In order to more fully comprehend the genius’ oeuvre, it is important to consider the context in which he grew up, where religion, rationality and war were all in the mixture.
Blaise’s father, Etienne Pascal “was not only an excellent lawyer and Latinist, but a considerable mathematician, and also greatly interested in the physical sciences” (Coleman 28). As one can see, there are many parallels in the interest of Blaise’s father that then transferred onto him. This was also true of religion, as Etienne also experienced a late conversion into Catholicism, even though he had been a social believer throughout his life before.
He was in charge of raising the kids and upholding the house, as Blaise’s mother died when he was only three years old. Etienne educated the children, and much of what Blaise learnt was from his own father. “What Blaise deduced, or imagined, or prayed for was the natural result of the son’s own genius” (Coleman 29), and he was not sent off to learn, as many other bright children are.
One of the main historical events happening at the time of Pascal’s birth was the Crusades, in which the Catholic Church was fighting the Muslims in order to recover the Holy Land. Nevertheless, according to Coleman, Pascal interpreted these wars as being “against the atheist, the skeptic, the materialist, the pyrrhonist, the unconverted, and finally against anyone who believed that science was or would ever be capable of giving the answer to the meaning of man’s existence” (27). This will be a recurring theme in his works, as one will be able to see later the relationship between his mathematics, philosophy and theology through rationality.
“Gilberte even implies that her brother Blaise had discovered the first principles of geometry by the age of twelve” (Coleman 25). This is exceptional because, at the time, it was not common for thinkers to have biographies unless they were noblemen or saints. “Pascal’s life obviously falls into none of these categories: lives of philosophers and scientists, or savants, were not deemed important enough to be written about” (Coleman 26). Therefore, as one can see, not only was his life groundbreaking, but what they did with it as well.
As will be discussed later, one of the most important moments in Pascal’s life was his vision of the holy, which marked a turning point in his works. Before this, he had been making major contributions in both mathematics and physics. Nevertheless, afterwards, his interests turned towards theology and Christianity. Would it be possible that these were all connected?
Mathematics
Blaise Pascal made many contributions to mathematics. This included many fields of study, including the first steps in some of them. At an early age, he wrote a text on projective geometry, including the theorem that still bears his name. This states that the three pairs of opposite sides’ intersection points for hexagon inscribed in a conic section, including a circle, are collinear. In addition, he also had many other developments with regards to conic sections, deeply influenced by his teacher Desargues. He was also an inventor, developing a working calculator that sadly was too cumbersome and complicated to catch on in the market.
One of the developments that is most known and associated with him is the triangle that bears his name. This is an ordering of the binomial coefficients in the form of a triangle, and which is useful for showing the recursion construction method that supports it. Pascal’s triangle is made by having the numbers be the sum of the two numbers that are directly above it. It also has many other properties, and is commonly taught in primary school to this day. For example, the first non-trivial diagonal has the natural numbers in order; the second one has the triangular numbers; the third, the pyramidal numbers, and so on. It also includes many series and patterns, such as Fibonacci numbers and fractal pattern.
Perhaps his greatest contribution to mathematics was in probability, as he was one of the pioneers of the modern conception of this theory, which included making the association of probability with his famous triangle. This included the calculation of combinations: the number of possible cases of a certain amount of objects being taken another certain amount at a time. Furthermore, the triangle also allowed him to solve the Problem of Points.
Although he did not develop probability very far, he was fundamental in establishing its first steps, which would lead to important studies in economics. Along with Pierre de Fermat, he concocted the concept of expected value, considering the probability that each player had of winning a game. This would also prove to be influential in developing differential calculus. As a whole, this great thinker was very influential in establishing relationships between different fields of study in order to examine probability, games and odds, including Pascal’s triangle, the Problem of Points, ratios and number theory.
His work in these fields made him brush with the concept of infinity, which would amaze him as it had many others before and has also done to many after. He believed in the existence of a mathematical infinity, and this allowed him to make the transference of this concept to his philosophy and theology as well. As he could believe that something mathematical could be infinite, such as his triangle, and still exist, this meant that God’s infiniteness was not grounds on which to dispel His existence. Therefore, God could be infinite and still exist, much like many mathematical constructs.
Even though some may state that he desisted on his mathematical inclinations after his religious conversion, which will be discussed below, one could think of them as the continuation of his work in mathematics. The prime example of this would be his wager, in which he introduces probability and decision theories to justify the belief of God’s existence. His whole philosophy of mathematics also belies trust in the Lord. Therefore, one could see these different disciplines as weaving into one another, his rationality being the common denominator for all of them.
Philosophy of Mathematics
As many other philosophers, one of Pascal’s main worries when it came to mathematics was establishing how one would know if a proposition were true or not. As such, he took the view that one should attempt to found all of one’s sentences on pre-established truths. Nevertheless, he reasons that this is problematic, as it requires first principles that would, themselves, be supported by other principles, and so on into infinity. Therefore, he argued that one must assume the truth of certain principles that would be the first ones, in order to allow the other ones to follow from then, much as Euclid did in his geometry.
Therefore, one can see that in his exploration of the philosophy of mathematics, he is both approaching mathematics itself, and theology, in the sense that he is attempting to establish a parameter for the ultimate truth. For him, first principles could be taken as axiomatic in nature inasmuch their truth value was accepted through intuition. This would imply a submission to God, as opposed to the strict rationality that one may traditionally attribute to mathematics. As a consequence, one can see that mathematics and theology are deeply intertwined in Pascal’s philosophy.
Theology
Blaise Pascal’s theology is remarkable, if only for the wild intensity that it often had. At first, he seems to not have been particularly devout. Nevertheless, he seems to have had a very vivid religious vision, which led to his conversion. He wrote a note of this occasion down on a piece of paper, beginning as such: "Fire. God of Abraham, God of Isaac, God of Jacob, not of the philosophers and of the learned” (Pascal). He would carry this around everywhere, as a memorial of this very fateful day.
As an important side note, it is significant to mention the distinction that Pascal makes with regards to the two Gods. Before this intense vision, one could find him believing in the God of mathematical infiniteness and wisdom, much as the scholars would. Nevertheless, he finds that he had been visited by the same God as Abraham, Isaac and Jacob had. As such, this was not the result of reflection and reason, but of a vivid experience. Therefore, his work on apologetics could be seen as the attempt to understand and diffuse this encounter that he had had.
One of the most famous parts of the Pensées is what is now known as Pascal’s wager. In it, he attempts to prove that it would be foolish for a thinking person to position himself against the existence of God. Pascal’s argument is that “decision-theoretic reasoning shows that one must (resolve to) believe in God, if one is rational” (Hájek 27).
Instead of looking outwards for empirical evidence towards the existence of God, or inwards to find Him in a spiritual manner, Pascal decides to take mathematics as the prime instrument towards the search for the Deity. “Pascal deliberately ‘ties his hands’ and refuses to look at any observations or experimental data bearing on the existence of a Christian God” (Hacking 186).
He is not interested in what his worldly experience shows him, but what rationality could bring to the table. “Pascal’s wager illustrates that this newly conceived rationality was not only a cognitive revolution, but a new form of morality as well” (Gigerenzer & Selten 2). Therefore, one can see that this was truly revolutionary, as he was taking rationality to its limits, leading people to act as if God existed, if only because it would bring them something so infinitely good that it would be comparatively foolish to spend one’s life on more trivial goods.
He sees the way that one leads one’s life as the consequences of a bet: either one acts as if God exists, or as if He does not. Obviously, then one would have to compare this to whether He actually exists or not, something that most people believe cannot actually be demonstrated empirically; He is infinitely incomprehensible for Pascal. According to the French thinker, one should lead one’s life seeking God because, if he actually does exist, the benefits would be infinite. As such, he believed that “even if the probability that God exists were small, the expectation is infinite: infinite bliss for the saved and infinite misery for the damned” (Gigerenzer & Selten 2). By seeking God rationally, he was one of the pioneers of probability and decision theory, as well as working with infinites.
Conclusion
As one can see, Blaise Pascal’s thinking was not limited to just one subject, often combining mathematics, philosophy and theology. He was a child prodigy, being largely taught by his father, after his mother died at a very young age. Pascal made significant contributions in mathematics, especially the triangle that bears his name and towards probability.
In his philosophy of mathematics, one can see that he believed that one should submit one’s self to God due to the impossibility of grounding all principles on pre-existing true ones. His theology is a very rational one, even though he had a very intense vision, which was what finally converted him into Christianity.
Perhaps his most representative and influential passage is his wager, in which he argues that the infinite utility that one may find through God renders irrelevant any other possible forms of enjoyment on the Earth. Therefore, he argued that the rational course of action would be to believe in Him, taking very important steps in theology and decision theory. It is astonishing to see how such great minds can relate such different aspects of the human experience.
Works Cited
Coleman, Francis X. J. Neither Angel nor Beast: The Life and Work of Blaise Pascal. New York: Routledge, 2013. Print
Gigerenzer, Gerd & Reinhard Selten. Bounded Rationality: The Adaptative Toolbox. Massachusetts: Massachusetts Institute of Technology, 2002. Print.
Hacking, I. (1972). The Logic of Pascal's Wager.American Philosophical Quarterly, 9(2), 186-192. Retrieved from http://www.jstor.org/stable/20009437
Hájek, A. (2003). Waging War on Pascal's Wager. The Philosophical Review, 112(1), 27-56. Retrieved from http://www.jstor.org/stable/3595561
Pascal, Blaise. “Pascal’s Memorial: Le Memorial de Pascal.” College of Saint Benedict & Saint John’s University. Web. 27 Jul. 2016. <http://www.users.csbsju.edu/~eknuth/pascal.html>.
