Philosophy is the mathematics of language
...
Philosophy is Greek and means the love of wisdom. Originally, it was a broad term encompassing most intellectual efforts that weren't religious (and some that were too). Before the natural sciences, psychology, economics and other specific disciplines were invented, more or less all theoretical things someone had to say were called philosophy. So by then, philosophy meant thinking, more or less.
Today, philosophy is the thinking that was left when the data-based sciences were formed. The residues that couldn't be organized into a science, came to be called philosophy.
Of what do those residues consist? My suggestion is that philosophy is the art of clarifying concepts. People doing philosophy find links between different concepts. Occasionally they invent new, clearer concepts.
Doing the maths
The sciences deal with data. Philosophy deals with concepts. That makes it most of all similar to mathematics. Just like philosophy clarifies the relationship between concepts in general, mathematics clarifies the relationship between a very small subset of concepts: Those representing what can be counted.
Mathematics is the exploration of relations between numbers. From very simple equations like 2+2=4 to a table full of mathematical proofs. They are all about relations between numbers.
What mathematics is to numbers, philosophy is to our conceptual world as a whole. Philosophy seeks the 2+2 of language. A typical philosophical statement has the form of “a actually is x”. “The world is all that is the case”, Ludwig Wittgenstein said. "Liberty consists in doing what one desires", John Stuart Mill said. "Happiness is the highest good", Aristotle said. "Whatever is reasonable is true, and whatever is true is reasonable", G. W. F. Hegel said.
All those statements can easily be transformed into the form of equations: The world = all that is the case. Liberty = what one desires. Happiness = The highest good. What is reasonable = what is true.
It started with Socrates
Philosophy seeks relations between concepts the way mathematics seeks relations between numbers. Socrates made this into a sport, through examining the consistency between concepts and explanations. Plato wrote 35 dialogues where someone, most often Socrates, takes down someone who believes themselves to have great knowledge of something. Through reasoning, Socrates can show that the person's claims are inconsistent with each other.
Was it the real, historical Socrates that annoyed his fellow Athenians this way? Plato wrote his Socrates dialogues early in life and it is widely believed that Plato's early texts give a more accurate description of the historical Socrates than Plato's later work. Then it could be reasonable to give Socrates credit for what is today known as philosophy: The method of comparing concepts against each other.
Then came Wittgenstein, 2400 years later
The closest I get to my idea that philosophy is the search for relationships between concepts is in the texts of Ludwig Wittgenstein. In Tractatus Logico-Philosophicus (1921), Wittgenstein writes:
“Most of the propositions and questions of philosophers arise from our failure to understand the logic of our language.”
Since Wittgenstein thought that humans owned only one, fixed set of concepts, he believed that one book was enough to tell everything that could be told about the most fundamental relationships between those concepts. (And what couldn't be told just couldn't be told, as Wittgenstein wrote in his famous last sentence of that book: “Whereof one cannot speak, thereof one must be silent.”)
Wittgenstein left philosophy for eight years, working as an elementary school teacher and a gardener. When he came back to philosophy, he started to recognize language as something imperfect and ever-changing that just tries to approximate reality. If language was never finished, philosophy could also never be finished.
A game of definitions
Essentially, philosophy is the art of making speech clearer. Philosophy is asking “What do we actually mean when we say x?” When we ask, for example, about the nature of truth, in practice we ask for the best use of the word “truth”.
“Wait”, someone will say. “If I ask about the nature of truth, I do not only want to know how to use the word truth. I want to know what truth is for real”.
Yes. But good luck with that. Empiricism is our window to the world. Whenever we want to know something about a phenomenon, we simply go where it is and study it. If we want to know about elks, we go out in the forest and study elks. If we want to study jealousy, we search for testimonies of jealous people and people around them. If we instead just ask ourselves “what is an elk?” or “what is jealousy?”, we only get to know what we mean by the words.
“Philosophical questions” are centered around concepts that can't be studied empirically. Time, truth, free will and God do not exist in any specific place. There is no way to get closer to them and study them. For that reason, philosophy is the only way to explore them at all. And the only thing philosophy can do is to ask what do we mean by…?
Whenever we want to know anything about anything, going there and looking at it is the key. Philosophical reasoning only has one use: To clarify what we mean when we talk. In areas where empiricism is impossible, nothing more can be done.
The words they are a-changin’
Philosophy has something of a bad reputation. Of being useless, outdated, empty and pretentious. It all has a simple explanation: Philosophy is imprecise because our conceptual world, its area of study, is imprecise and constantly changing. Philosophy gets outdated because concepts get outdated.
Concepts change in meaning, and above all they change in importance. For example, “God” was an enormously important concept in the 17th century - everyone who has read Spinoza knows that for sure. As the social environment changed, new concepts were invented, new concepts became important to people, and the meaning and use of concepts changed. However ingenious the philosophy of Baruch Spinoza was, it is outdated. Spinoza found links between the important concepts of his time. And the time has changed.
The changing nature of our conceptual world means that philosophers can't build much on each other's knowledge. Philosophers of the past found links between concepts. But only between concepts of the past. It is not uninteresting, but also not much to build on.
That is a reason why professional philosophers fail to impress. They try to be experts in an area where it is not really possible to be an expert. Knowing the links between concepts of the past is of little help when searching for links between the concepts of today. The endeavors of past philosophers can be inspiring. But that's it. As soon as we understand our own concepts better, we develop them and invent new ones.
Mathematics, on the other hand, builds on a very narrow range of concepts that are extremely stable: Numbers. All human languages do not have words for numbers. But when languages develop numbers, they tend to stick. Once invented, they are perfect as they are. Even the words for numbers tend to be remarkably stable: Linguists who have reconstructed the proto-Indoeuropean words for numbers arrive at words remarkably similar to those of modern languages.
For that reason, mathematicians can build on each other's knowledge. A mathematician hundreds of years ago found links between the same numbers as a mathematician today. One mathematician continues where another finished, generation after generation. And that makes mathematicians as a professional category much more meaningful than philosophers as a professional category. The mathematics of the 17th century is as valid now as it was then, while the bulk of philosophy is since long passé.
In the wild
When I was young, I thought it was dreadful that people stopped engaging in philosophy when they got older. I thought people stopped doing explicit philosophy because they got old, tired and disillusioned.
Now I know better: When people get older, they have more data. Then they switch to more data-heavy endeavors. Young people have sharp minds but little data. For them, it makes a lot of sense seeking links within the data they have and the concepts they know.
And, in fact, people don't cease doing philosophy just because they leave pure philosophy for more data-driven areas of study. Everyone who tries to understand anything needs to use concepts. And those concepts need reflection and clarification.
Since numbers are not changing, mathematics have become increasingly advanced and increasingly dependent on special knowledge and skills. Philosophy, on the other hand, is deemed to be rudimentary. For that reason, specialists do not have much of an advantage. Instead, there are good reasons to believe that the people who are using concepts while dealing with science and politics are the best suited to study those very concepts. People who are collecting and analyzing data on the scientific level now and then stop and think of what they really mean. People who are trying to build a better society now and then stop for a moment and ask themselves what they actually mean by a better society. There are good reasons to believe that concepts are best studied in the wild, where they live and thrive.
That way, the best philosophers are not specialists policing other people's use of concepts. The best philosophers are people out there doing things, who once in a while stop for a moment and reflect over what they are talking about.
I like the question of why mathematics builds on itself better than philosophy, and I agree with the gist of what you are saying. However, I would quibble that mathematics is not just numbers, but extreme abstraction.
When we model something with math, we have to ignore a lot of details. Ignore the right details and you can get something very useful.
One problem I have with some philosophy is that it isn’t always honest about the implications of the abstractions/simplifications they make. Utilitarianism is a good example. To add up agent-independent utility you have to create some new concept that isn’t exactly like ‘good’ in all of its complexity. Then you do math-like reasoning and end up with something that seems really not good. But of course you do, because utility is an extreme simplification.
I like your model where the task of philosophy is to grapple with concepts that emerge as life/society/information environment evolve. But philosophy isn’t twitter (or even journalism). It operates on the concepts that emerge from new fact patterns.
I have been thinking a lot lately about the role of philosophy as a destructive force--it sees through the things society treats as sacred right down to the weakness and corruption of prevailing social norms. This of course undermines those norms and destabilizes society.
So I ask myself what is the relationship between philosophy as developing new conceptual connections/heuristics and philosophy destroying old norms.
Reflecting on Tove's post and considering my own journey with philosophy, I find the exploration of truth across mathematics, physics, and philosophy deeply resonant. As an 81-year-old retired ChE, my initial encounter with philosophy during my college years, especially with a challenging German professor, left me somewhat disconnected from the subject. However, my interest was rekindled through engaging with modern platforms like YouTube and podcasts, particularly those by John Vervaeke and Sean Carroll.
This personal journey mirrors the collaborative and interdisciplinary nature of truth-finding in these fields. In mathematics, the formalism of symbols and processes leads to undecidable statements within certain axiomatic systems. In physics, fields like quantum mechanics present fundamental limits to empirical knowledge. Philosophy, with its focus on language and conceptual analysis, navigates its own undecidables, delving into areas beyond empirical reach.
The collaborative nature of truth-finding in these disciplines underscores the importance of diverse perspectives. It's a multi-person, multi-disciplinary endeavor that allows for a more robust and nuanced understanding, acknowledging the limitations of individual disciplines while leveraging their collective strengths.
In essence, the pursuit of truth, whether in life or in mathematics, physics, or philosophy, is about the ongoing process of inquiry, collaboration, and the evolution of understanding. This dynamic and collective journey is at the heart of our intellectual endeavors. My experience, from initial skepticism to renewed interest and understanding through modern mediums, reflects the ever-evolving nature of our pursuit of knowledge.
As I conclude my thoughts, I'd like to extend a special acknowledgment to GPT-4 for its assistance in articulating these ideas. The strength of GPT-4 lies not just in its ability to generate text, but in its capacity to serve as a thinking assistant, enhancing the clarity and depth of my expressions. This tool has been instrumental in bridging the gap between my thoughts and their articulation, a skill I honed later in life. While I didn't learn to write effectively until I was 30 and still don't write nearly as well or as quickly as GPT-4, this technology has been a valuable ally in translating my complex ideas into coherent and articulate written form.
P.S.: I’ve also learned that I must proofread every response, as GPT-4, like any tool, is not infallible. For instance, it confused me with an alternate spelling of 'acknowledgment' in this very text, reminding me of the importance of a vigilant and discerning eye in the writing process.