## A (simple) definition for philosophy

• 486
A statement about a fact is not philosophical. For example:

It is raining today.

A statement is philosophical, if it is a statement about another statement. For example:

It is irrelevant that it is raining today.

This explains in simple words what the true meaning is of Godel's incompleteness theorem.

A theory is incomplete if it can express statements about its own statements. In other words, a theory is incomplete if it is capable of philosophy.

Self-referential statements are just a special case of the general case, which is the philosophical statement. If a statement can talk about other statements, then it can also talk about itself.

Philosophical statement:

K(#S)

--> Statement S has property K.

Self-referential statement:

S <-> K(#S)

--> I have property K.

Hence, philosophy is a mathematical capability of the language at hand.

This language's greatest power is also its worst deficiency, because it necessarily makes the language inconsistent or incomplete or even both.
• 2.6k
if it is a statement about another statement

That is called metalanguage, not philosophy.

A theory is incomplete if it can express statements about its own statements.

If a statement can talk about other statements, then it can also talk about itself.

Hence, philosophy is a mathematical capability of the language at hand.

Huh
• 486
That is called metalanguage, not philosophy.

First-order arithmetic is its own metalanguage. It is capable of talking about its own statements.

A language is philosophical if it is its own metalanguage.
• 486

If a statement can talk about other statements, then it can also talk about itself.

The long form:

If it is possible to express a statement about other statements in the language at hand, then it is also possible to express statements about themselves in this language.

K(#S)

S <-> K(#S)

This language would only need support for the equivalence operator, i.e. the biconditional.

But then again, I doubt that a language that does not support this operator, or cannot implement it using a detour, is capable of expressing much logic at all. In the end, the equivalence operator is just a simple truth table.
• 2.6k
First-order arithmetic is its own metalanguage. It is capable of talking about its own statements.

So is English.

A language is philosophical if it is its own metalanguage.

That is not what the word 'philosophical' means, which goes back to my first post.
• 486
So is English.

Yes, English is a philosophical language because it is its own metalanguage.

That is not what the word 'philosophical' means, which goes back to my first post.

In this post, I am trying to point out what I believe, is the correct -- or actionable -- definition for the term philosophy.

The existing definition is known not to be usable. It is not predicable. My alternative is eminently predicable and therefore a viable alternative, unless you can point out that it would lead to glaring contradictions.
• 21.7k
Hence, philosophy is a mathematical capability of the language at hand.

Some feedback: I notice since you've joined that you have a strong tendency to devise your own definitions, interpretations and standards for what constitutes philosophy. All well and good, but consider the implications of the term 'idiosyncratic'. Idiosyncratic means 'pertaining to a particular individual' (It is the same word root as 'idiom' and 'idiot', which originally meant 'one who speaks a language nobody else can understand' - no pejorative intended, as there are also idiosyncratic talents.)

Just sayin'. ;-)
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• 486
I notice since you've joined that you have a strong tendency to devise your own definitions, interpretations and standards for what constitutes philosophy.

For a starters, the term philosophy does not have a single definition:

https://en.m.wikipedia.org/wiki/Philosophy

Attempts to provide more precise definitions of philosophy are controversial[17] and are studied in metaphilosophy.[18]

Precise definitions are often only accepted by theorists belonging to a certain philosophical movement and are revisionistic according to Søren Overgaard et al. in that many presumed parts of philosophy would not deserve the title "philosophy" if they were true.[20]

Some definitions characterize philosophy in relation to its method, like pure reasoning.

Many definitions of philosophy emphasize its intimate relation to science.[24] In this sense, philosophy is sometimes understood as a proper science in its own right.

Other definitions focus on the contrast between science and philosophy.

Another definition characterizes philosophy as thinking about thinking to emphasize its self-critical, reflective nature.[31]

The definition that I propose, is actually not particularly new. It is quite close to thinking about thinking:

Overgaard, Gilbert & Burwood 2013, pp. 36–37, 43, What Is Philosophy?
Nuttall 2013, p. 12, 1. The Nature of Philosophy

"Thinking about thinking" and "statements about other statements" are notions that are very close to each other.

The origin for what I write, is of course, the foundational crisis in mathematics. I believe that it sheds new light not just on metaphysics but also on metaphilosophy.

Again, Godel's seminal publication is now almost a century old.

Its implications have, however, not been absorbed outside the narrow field of mathematical logic. There are many reasons for that; one of which is the fact that the language of mathematical logic is considered to be impenetrable.

One goal of metaphilosophy is to finally discover a usable definition for philosophy. I think that Godel's theorem can help with that.
• 24.1k
One goal of metaphilosophy is to finally discover a usable definition for philosophy.
No sooner would that be done than philosophy will then be about undermining that very definition.
A statement is philosophical, if it is a statement about another statement.

Anyway, the definition you offer is trivially too broad. "John said it is raining" is about a statement, but not philosophy.
• 486
Anyway, the definition you offer is trivially too broad. "John said it is raining" is about a statement, but not philosophy.

If SaidByJohn(#S) is a legitimate predicate, then your example sentence would indeed satisfy the definition proposed.

If this is a problem, then how can we exclude it from the definition?

There are precedents for excluding predicates from Godel's language. For example, true(#S) is not definable.

In fact, it would also be interesting to elaborate why exactly your example sentence is not philosophical.

Another angle would be to find a statement that is philosophical but that does not satisfy the definition.
• 1.9k
Interesting. Didn't know that
• 24.1k
If this is a problem, then how can we exclude it from the definition?
You missed the point of my post. Any definition will be contradicted by some philosophy.

...find a statement that is philosophical but that does not satisfy the definition
"Know thyself".

"Here is a hand".

"I think, therefore I am".

"The world is all that is the case".
• 21.7k
Didn't know that

I picked it up in a podcast about Trump's use of language.

The origin for what I write, is of course, the foundational crisis in mathematics.

Of course. Should be obvious to everyone.
• 486
"Know thyself" is not a logic sentence. It is not true or false.

"Here is a hand" is a statement about a physical fact.

"I think, therefore I am". S => Q does not mention any predicate about a statement. Furthermore, P and Q are arguably physical facts. Unless "I am" is written by using a predicate as: exists(me). However, "me" is not a sentence. The sentence may be considered philosophical even though it is not recognized by the definition as such. Interesting potential counterexample!

"The world is all that is the case". It is a statement about the world, which is a physical fact.
• 24.1k
So are you claiming that these sentences, each famously part of important philosophical discussions, are actually not philosophical?

You sure you want to do that?
• 9k
"The world is all that is the case". It is a statement about the world, which is a physical fact.

Or is it a statement about the meaning of words? Like a definition is about the meaning of words.
Oh dear - it looks like your topic is not philosophical according to your own definition. Does that trouble you at all?
• 486
So are you claiming that these sentences, each famously part of important philosophical discussions, are actually not philosophical?

You sure you want to do that?

"I think therefore I am" is problematic. Not sure what to do with that. It would fit fine with "thinking about thinking" but not with necessarily with "statements about statements". The problem with philosophy of the mind is that it necessarily always rests on introspection, which badly damages the potential to have an objective, shared understanding on the matter.
• 486
Or is it a statement about the meaning of words? Like a definition is about the meaning of words.
Oh dear - it looks like your topic is not philosophical according to your own definition. Does that trouble you at all?

I think that the definition of a word is an abstraction about an abstraction, a statement about a statement. It is clearly a language expression about another language expression. So, I think that the definition of the term philosophy is a philosophical question. The literature even terms it a "metaphilosophical" question.
• 24.1k
So you agree it is philosophical, but it is not a statement about another statement, and so doesn't meet your definition.

Your definition of "philosophy" seems to include things unnecessary and insufficient to philosophy.
• 486
So you agree it is philosophical, but it is not a statement about another statement, and so doesn't meet your definition.

The definition for philosophy is a predicate:

isPhilosophical(#S)

which is true if S is philosophical.

So, the definition of philosophy is the source code for a particular predicate.

isPhilosophical(#S) is a statement about any other statement S.

Your definition of "philosophy" seems to include things unnecessary and insufficient to philosophy.

Possibly. That requires an investigation of possible counterexamples. I think that these counterexamples should be quite interesting. Why exactly are they legitimate counterexamples? That will probably shine some more light on the issue.
• 24.1k

And you proposed

isPhilosophical(#S) IFF S is about another statement.

And I gave examples of statements that were about other statements, but not philosophical, and statements that are philosophical, but not about other statements.

• 486
And you proposed

isPhilosophical(#S) IFF S is about another statement.

And I gave examples of statements that were about other statements, but not philosophical, and statements that are philosophical, but not about other statements.

Descartes' "Cogito ergo sum" is a problem. It is covered by "thinking about thinking" but not by "statements about statements". We cannot expect Godel's work to cover philosophy of the mind by using arithmetic. So, it leads to two definitions: "philosophy not of the mind" and "philosophy of the mind".

The statements about statements that are not philosophical was about predicates such as PeterSaidThat(#S). So, predicates that merely indicate the origin of a sentence may also be excluded from the definition. It just means that not all predicates are allowed. So, it may mean that there is a list of permissible predicates (or a list of excluded ones).
• 9k
I think that the definition of the term philosophy is a philosophical question. The literature even terms it a "metaphilosophical" question.

I agree with you here, and one of my favourite philosophy books is an exhaustive and exhausting treatment of the varied definitions of the word "meaning" which is obviously crucial to an understanding of 'definition'.

But I see a further difficulty in your definition of philosophy, which is hinted at by my comment on your treatment of Wittgenstein's statement below.

"The world is all that is the case". It is a statement about the world, which is a physical fact.

One can take this as definitive, in which case it is philosophical, and likewise Moore's "This is a hand".

But at the same time, one can hardly deny that they are statements about the world. And this means that the separation between statements about the world and statements about statements cannot be so sharply made as to answer the question what is and is not philosophy. And We should be glad of that, because if philosophy was merely talk about talk, and had no connection with the world, it would be an entirely trivial pursuit.

But Wittgenstein also said, "Meaning is use." and one does not have to establish exact boundaries to the meaning of a a word, but rather the boundaries are established by the ways in which the word is used in the community. "Ways" plural, because a word can be used with different meaning and scope in different contexts. Thus language is part of the world, and has real causal function in the world, and philosophy 'matters'.
• 40

Often, the aim of people who try to redefine established concepts is to try and create a more consistent definition, not a new definition that immediately bakes in the known inconsistencies of some other theory so they can say "Here's my new definition of P which is purposefully inconsistent and therefore implies that the inconsistencies of theory M are ALSO inherent inconsistencies of theory P!".

Maybe I'm missing something, but unless you're something like a Used Paradigm Salesman who's trying to make up some suddenly catastrophic problems in the existing paradigm so you can sell a new one... I don't see any value in this proposition.
• 486

Google Translate is not 100% accurate but it is quite good nonetheless. It could be interesting to have the starting point for something that can detect philosophical sentences. Most existing definitions are not suitable for that purpose just like most language textbooks would never be a good starting point for building Google Translate. I think that Gödel's theorem suggests a more interesting starting point. Some predicates must be excluded and philosophy of the mind requires a different approach. Besides that, I think that things are still nicely on target.
• 40
I personally think that this is a terrible motivation. But I have to admit that it seems like a good approach for your stated objective, and it does indeed sound like an interesting exercise either way. Carry on.
• 1.3k

My understanding of a definition is that it explains the use of a word or term. As it happens, that roughly corresponds to what the dictionaries say, but obviously we can't necessarily rely on them. Nevertheless, I think that approach is helpful here. Let's call it a working definition.
We need to remember that not all definitions are linguistic. Ostensive definitions need not employ any words at all, although they do presuppose a basic understanding of language - except when we are training animals.
I suggest two basic varieties of definition which need to be taken into consideration here. One is the attempt to capture (perhaps codify) the use of an existing word or term. One might call these empirical definitions, paradoxical as it may seem. The other lays down a rule; this is commonest when a new term is being created (or a new use of an existing term, perhaps in a specific context, as in technical terms). One might call these stipulative definitions.

Cutting to the chase, I suggest that you need to clarify in your own mind whether you wish to capture the existing use of the term "philosophy" or stipulate a definition to be used in a specific context.

The origin for what I write, is of course, the foundational crisis in mathematics. I believe that it sheds new light not just on metaphysics but also on metaphilosophy.
This suggests that your definition is formulated in a specific context, but that you think it has consequences for philosophy more widely. I'm not clear whether you consider the possibility of that extension to be a philosophical thesis or not.

BTW, is meta-philosophy philosophy or not? - is that a philosophical question? It seems to be an extension of a concept that is used (and therefore defined) within a specific context, which may or may not be considered to be philosophical.

Precise definitions are often only accepted by theorists belonging to a certain philosophical movement and are revisionistic according to Søren Overgaard et al. in that many presumed parts of philosophy would not deserve the title "philosophy" if they were true. — Wikipedia
Wikipedia is not wrong, especially in this observation. I would question "often" unless someone can come up with a definition of philosophy that is universally accepted by philosophers. Your definition is no exception - it has a philosophical agenda and is constructed in the pursuit of that agenda. That's fair enough, until you claim that it is a definition of philosophy.

Dogmatically, I would start by saying that philosophy is a practice (or a family of inter-related practices), the scope of which is effectively defined by what its practitioners do when they are philosophizing. One may compare music or the visual or performance arts, or even science itself.
• 14.9k
That's merely a metastatement (@Lionino)

IMO, a "philosophical statement" is a non-propositional expression (i.e. proposal) of a presupposition or an implication derived from a proposed answer to a philosophical question or from a philosophical question itself. A philosophical question, OTOH, is a counterfactual supposition (or thought-experiment) that cannot be definitively answered by either empirical or formal means (i.e. propositions).

Example:
Is the world (i e. a concept of "the world") deterministic or indeterministic?

If the world is deterministic, meaning that every event is caused by a prior event (i.e. non-random), then every person's choosing is epiphenomenal (or an illusion).

However, if the world is indeterministic, meaning that every event is uncaused (i.e. random), then, yet again, every person's choosing is epiphenomenal (or an illusion).

Suppose the world has both deterministic properties and indeterministic properties, meaning that any chain, or sequence, of events consists in alternating causal and noncausal relations, which therefore implies that every person's choosing is unconstrained-within-constraints, or compatible with the world conceived of having both deterministic and indetetministic properties.
I'm not satisfied with this simplistic example but I think it works well enough. My point is that philosophy's sine qua non is her questions (even meta-questions) – the how what when & why of them – rather than any answers, or "statements". In Socratic manner, I think, philosophizing strives to reason to more probative questions (or more clear, precise formulations of a question) and not just the academic penchant for masturbating each other with cleverer and cleverer logical puzzles.
• 486
Cutting to the chase, I suggest that you need to clarify in your own mind whether you wish to capture the existing use of the term "philosophy" or stipulate a definition to be used in a specific context.

I am interested in a computable predicate, i.e. a computer program or a function, that will be able to distinguish between statements that are philosophical and statements that are not. Therefore, the most important requirement is that it can be implemented as source code.

However, the output does not need to be correct all the time.

We do not require that from Google Translate either. It just needs to be correct "most of the time" or "substantially more often than not".

BTW, is meta-philosophy philosophy or not? - is that a philosophical question? It seems to be an extension of a concept that is used (and therefore defined) within a specific context, which may or may not be considered to be philosophical.

Is philosophical(#S) is a statement about statement S. So, in this definition, the metaphilosophy is a subdivision of philosophy.

Dogmatically, I would start by saying that philosophy is a practice (or a family of inter-related practices), the scope of which is effectively defined by what its practitioners do when they are philosophizing.

That would be compatible with the ChatGPT approach.

Let the algorithm read a large sample of philosophy, summarize it into an appropriate numerical data structure, and then get it to discriminate inputs between philosophy and not philosophy.

This approach will undoubtedly still require an underlying notion of what exactly to extract and summarize from the sample ("machine learning"), and therefore, what exactly matters when trying to distinguish philosophy from the alternative.

For example, object recognition in computer vision ultimately rests on relatively simple underlying notions such as haar-like features, without which the discrimination algorithm would not even work properly.

Therefore, without some basic notion of at least what to look for in a sentence, the philosophy-detection algorithm's ability to discriminate can be expected to be disappointingly poor.

One may compare music or the visual or performance arts, or even science itself.

It is actually possible to detect if any particular sound is music or not, with a tool such as Spleeter from Deezer research:

https://research.deezer.com/projects/spleeter.html

There are, of course, more research budgets available for music than for philosophy. So, the fact that a discrimination algorithm exists for music and not one for philosophy, should not come as a surprise.

Not all sound is music. Thus, there are algorithms available that can quite precisely discriminate between music and other sounds.

The discrimination problem is not necessarily easier for music than for philosophy. It is just that there are people who have worked on a solution for music but not on one for philosophy.
• 13.4k

Some more philosophical statements that don't meet your standard.

• The Tao that can be spoken is not the eternal Tao - Lao Tzu
• God will not have his work made manifest by cowards - Emerson
• All our knowledge begins with the senses, proceeds then to the understanding, and ends with reason. There is nothing higher than reason - Kant
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