A very brief introduction to Frege’s philosophy of mathematics. — Empirism and Rationalism — The Two Most Important Points of View in the Philosophy of Mathematics These are the two most basic distinctions in the philosophy of mathematics. So we can roughly say that any philosopher of mathematics has to take a stand on these two currents of thought, and Gottlob Frege (1848–1925) did so. He discussed Mill’s empiricist ideas and Kant’s rationalist ideas about the…

This is a difficult problem. If you can solve it, then you should be considered a genius. — The Meaning of “Something to Do With” Can you prove something on the other side of the planet has absolutely “nothing to do with” you? But in the sense that, let us say, a rock on the other side of the planet doesn’t involve you in any sort of manner? So far, we can’t prove it’s not…

So why is Cantor’s Set Theory still considered flawed? — Set Theory is the greatest mathematical-logical invention since Leibniz's functions Leibniz dreamed of a Characteristica Universalis (a universal formal language that would be used on logical analysis of concepts or on structures of scientific systems) to become a reality, and that’s exactly what Cantor’s Set Theory helps us achieve. From numbers to functions, syllogisms, or subway train cars in Japan…

Is it a science or an art? — It’s science and it works You can say a car work when you drive it without trouble, and the same thing applies to a bike or any other sort of vehicle. We can also say a theory in physics works when it helps you describe or even predict some sort of phenomenon. But can we…

Who is responsible for mediocrity and anti-progress in contemporary thought? — There is a crisis in contemporary science According to Nature’s famous article Scientists behaving badly (by Brian C. Martinson, Melissa S. Anderson, and Raymond de Vries), there are many unethical practices that became common in modern scientific research. Here I selected four among the sixteen practices listed in the article:

From Malba Tahan’s most famous book: The Man Who Counted. — Malba Tahan is the pen name of Júlio César de Mello e Souza (1895–1974), a Brazilian mathematician who is the author of a famous adventure book called The Man Who Counted, in which the protagonist, Beremiz Samir, uses his mathematical skills to settle disputes, give wise advice, overcome dangerous enemies…

Do pure logical-philosophical questions still exist? — Where Does This Word Come From? At least one hundred years after Aristotle’s death, an editor of his works, Andronicus of Rhodes (as far as historians can assume) titled fourteen of his books “Ta meta ta phusika” — “the after the physicals” or “the ones after the physical ones” — the “physical ones” being the books…

A 3-minute lecture on Leibniz’s optimistic analysis of the world — I usually present Leibniz’s arguments in two ways: in a more religious way (which is the original way), or in a way I consider less religious. But let’s begin with the most religious and original way. The original way We may say Leibniz’s explanation begins with “there is a God and he is…

There are many explanations for what it means to be human. — The “Human Nature” Debate Understanding human nature is one of the main aims of scientific areas like psychology, sociology, anthropology, and philosophy, while the consequences of their ideas is felt in politics, laws, government actions, and even in medicine. These are the kind of questions the ideas around “human nature” may help answer:

The top-4 famous philosophers that hated philosophy. — I’m a philosophy teacher, and from time to time, I have to deal with students that despise most of what they see in and study about philosophy. I reach out to these students by showing them there is a way they can hate philosophy more professionally. I introduce them to…

Is there something indivisible in the world? Is everything discontinuous, or continuous? — The continuum problem could be described in different ways (either in arithmetics, geometry, physics, or philosophically). Here, we will see it appearing in one of Euclid’s fundamental propositions, and then in one of Zeno’s paradoxes of movement. …

Natural numbers were created by God, everything else is the work of men — Kronecker (1823–1891). —

I.e., who is responsible for post-modernity? —

The three main contemporary ways to understand the fundamentals of mathematics. — Introduction: If you are looking for the answer to the question “which one is best suited to fundament the entire mathematics?” I’m afraid this article can’t give it to you. But I do encourage you to work on it. In fact, to develop a good answer to the question “what the…

Yes, it is. — What the philosophy of mathematics is useful for? Max Black, the author of The Nature of Mathematics (1933), thought the main task of the foundation of mathematics (and, consequently the main task of any philosophy of mathematics) would be to elucidate “and analyze the notion of integer or natural number” [1]. Is the task described by Black really…

Was his philosophy of mathematics underrated? — Who was Henri Poincaré? Henri Poincaré was a very distinguished astronomer, mathematician, physicist, and philosopher. And, because of this variety of areas to which he contributed he is known as the “last universalist”, and treated as a “polymath”. Some take him as the father of relativity theory. According to Adlam, before Einstein, Poincaré “had…

Anyone can easily note that most people don’t give much importance to solve philosophical problems (problems that books and scholars defend as very important ones). So, to figure out why, I began to attend philosophy classes. Soon enough it seemed to me that no one was capable to solve those…

(and he was right) — In 1956 a few writings of Wittgenstein that he didn't publish in his lifetime were revealed to the public. These writings were gathered in the book Remarks on the Foundations of Mathematics (1956). …