How to comment on the phrase all mathematicians are philosophers ?

Philosophy and mathematics have many origins in history, so many philosophers are also mathematicians, and many mathematicians are also philosophers. Before about the 19th century, there were many people who did both because of the lack of differentiation in the disciplines, and this became less common in the future. Thales, Plato, Aristotle, Descartes, Leibniz, Poincaré, Brouwer, and many others were both mathematicians and philosophers.

And philosophers such as Heraclitus, Hume, Kant, Hegel, Nietzsche, etc., although some of them knew the mathematics of the time very well, did not make outstanding contributions to mathematics. Archimedes, Newton, Euler, Gauss, Cauchy, Verstrass and others were pure mathematicians who had little to do with philosophy. If mathematical logic is also regarded as a part of mathematics, then many philosophers in the 20th century are also familiar with it, Frege, Russell, Quinn, Putnam, Kripke, etc., have made important contributions to mathematical logic and philosophy.

In the first half of the 20th century, there were many philosophers or mathematicians who made many discussions on the foundations of mathematics or the problems of mathematical philosophy, among which they contributed to mathematics and the philosophy of mathematics, such as Hilbert, Poincaré, Brouwer, Frege, Russell, Gödel, and so on. In today's differentiation of these two disciplines has been very obvious, it is difficult to imagine that someone can make important contributions to the two disciplines at the same time, so that they can be called "xx family", in addition to those who specialize in mathematical philosophy, the vast majority of philosophers are most interested in mathematical logic and have understanding, and even those who do mathematical philosophy are more concerned about mathematical logic, if this field is regarded as mathematics, then there is still the possibility of intersection of the two, it is difficult to imagine that philosophers have deep attainments in professional mathematical fields such as topology and differential geometry, Not to mention contributing. On the other hand, few mathematicians would be interested in philosophical questions, and they would not dare to imagine that they would contribute to metaphysics and epistemology.

I don't understand what the definition of philosophy is, but I often hear someone say that the end of science is philosophy, this sentence is very disgusting to me, and some people who don't know the truth also say that the end of philosophy is theology, this sentence is not soft except rhyme, if it is reversed, there is still some truth, from the time is that theology is earlier than philosophy and science, as for why some people say that science is all philosophy, philosophy is all God, I think it should be that early human beings are not clothed and hungry, in order to understand some things, such as why people die, Let's just say that there is a king of Yama, and if you do good deeds, you can go to heaven, so God was born, and later, human beings entered the agrarian society, and some rich people appeared, and they were very idle, bored, and they thought about where people came from and so on, this is early philosophy, and philosophy also contains things like worldview, of course, they will also think of some things, such as what the world is made of, why the sun rises in the east and sets in the west, these involve science, early philosophy and science are mixed together, That's why the definition of philosophy is vague, as if there is a shadow of philosophy everywhere in science.

The meaning of a teacher of the history of mathematics is probably that ancient mathematicians had a high level of philosophical literacy, or that their profession was to teach philosophy. For example, Zeno and Hypatia, in the course of their studies, they traditionally or according to the rules have to go through philosophical learning. However, modern mathematicians such as Ramanujan and Chen Jingrun are obviously not philosophers, mainly because it is too energy-consuming to make a breakthrough in the cutting-edge theory of a certain branch of mathematics.

If all mathematicians are philosophers, and not all philosophers are mathematicians, then all mathematical studies are philosophical studies, and then mathematics falls under the category of philosophy. The proof of the proposition that "mathematics is philosophy" is a problem that the logicist philosophers of the nineteenth and twentieth centuries spent their lives proving.

When I first entered college, I read a book on Western philosophy, and I was deeply impressed by Descartes' "I think, therefore I am", and I was also deeply curious about his identity as a philosopher-dermatologist and mathematician. In my opinion, the combination of these two identities is indeed a strange thing.

After work, I was chatting with a colleague who was studying Western philosophy, and I asked her why many philosophers were mathematicians at the same time. She told me that mathematics is the source of the parapitaxis of philosophy, and that early Western philosophers believed that the operation of the world could be calculated mathematically.

Is it? The first time I heard such an explanation, I was even more confused, philosophy and mathematics are still the same? Can mathematical formulas solve philosophical problems?

The complete solution to this problem came after I read A Minimalist History of Europe.

Knowledge is figured out, and the solution of philosophical problems is finally found in the history books.

To talk about philosophy, we must go back to ancient Greece, which is the source of modern civilization. One of the characteristics of the way the Greeks thought was the importance they attached to mathematics. "The Greeks believed that the world was simple and that the rules by which it operated could be expressed in mathematics. ”

The Greeks considered geometry to be a simple, elegant, logical system that was both pleasing and beautiful. "Well, for that, I admit, I was not up to the height of the Greeks, and when I went to school I did geometry as an exercise, and the most troublesome thing was solid geometry. By the way, the geometry we learn now is due to the Greeks, and no other civilization in the world has produced something similar, in the fourth century BC, Euclid wrote the "Geometry Original", and this knowledge was not introduced to China until the Ming Dynasty.

In the eyes of the Greeks, geometry was a way to lead human beings to understand the nature of the universe, and they believed that behind the pluralistic appearance of the world, there must be a simple, regular, and logical principle to support it, such as geometry. From this, they speculate boldly based on inspiration.

The Earth is the center of the universe, and other planets, including the Sun and the Moon, orbit the Earth in a circle. This is the Greeks' perception of the universe. Why do other planets circle the Earth?

Because the Greeks thought that the circle was a perfect shape. It was also part of the Greek geometry doctrine.

This cosmology prevailed for 2,000 years until it was overthrown in the 17th century. Science as we know it today began with this scientific revolution 400 years ago. But the reason why he was able to overturn Greek science was to follow the Greek inspiration of burning skin:

Answers should be simple, logical, and mathematically expressed.

We now know that the Earth and other planets orbit in an elliptical shape centered on the Sun. And this is also Newton's mathematical formula to calculate the law of universal gravitation.

Scientists in the 17th century overturned the Greek theory of the universe, but they did so using Greek mathematical methods.

By the way, the great philosopher Descartes, who also lived in the 17th century, was the one who founded analytic geometry.

Everyone is a philosopher" does not mean that everyone is a scholar who studies philosophy and has the knowledge of a philosopher. Rather, everyone has their own unique view of the world and others, which is the so-called worldview, values, and outlook on life. In a way, these ideas reflect man's understanding of the world, and this understanding is precisely what philosophers think about.

So, everybody is a philosopher.

I don't quite agree with you. Here's why:

The reason why a philosopher is a "home" and an expert in an industry must be to receive systematic philosophical training and treat it as his life's work. In a word, philosophers are people with strong professional skills.

I think everyone you are talking about here can be understood as "the masses, ordinary people", so as to distinguish them from philosophers. It can be said that the so-called "philosophy" of ordinary people is just an unsystematic and illogical fragment of thinking, and it is not very reliable to come up with things that come up with it simply by being in a daze, and the philosophy of ordinary people is just a speculative thought close to philosophy, and the depth and breadth of thinking are limited, and they often drill the tip of the horns, which cannot rise to the thought of a philosopher, if you continue to study, cultivate logical thinking, enhance your vision, and devote your life to the cause of philosophy, it is possible to become a philosopher.

Ordinary people and philosophers have different philosophical outcomes. The so-called philosophical ideas of ordinary people can only convince themselves, at most their friends, and are unlikely to be widely accepted by society. Although the research of philosophers also needs to be very speculative, their results are not groundless, their results are systematic and logical, can be widely circulated in society, have a wide range of influence, and some can even last for a long time, can be described as classics, such as religion, Marx, Nietzsche, Kant, these philosophers of the Enlightenment social progress.

But very few ordinary people who have not received training can reach this level, and at most they only use their own ideas to make themselves live better and see problems more deeply.

In a word, everyone has the seeds of philosophy in their hearts, and they can easily enter the door of philosophy, but philosophy is a science after all, and if you want it to sprout, you must water and fertilize it frequently.

When social reform is made! What is most needed is ideological reform! And what is most needed for ideological reform is the idea of sifting out from the ideas that have been deposited for thousands of years to satisfy the interests of the reformers! And the author of this idea became a philosopher!

One is secular evaluation, the other is evaluation in the philosophical circle, to put it bluntly, a bunch of people say that you are a philosopher, and quote your text in **, you are. Nothing standard.