What are the reasons some thoughts cannot be simplified, reduced to a simpler set or phrases?

Question

What are the reasons some thoughts cannot be simplified, reduced to a simpler set or phrases? When reading Heidegger or Hegel, one wonders why those authors couldn't simplify their tangled web of phrases, is there any specific thing in language, philosophy that explains why certain things that can't prevent a person from simplifying an idea to a simpler set of phrases. I noticed even things in advanced mathematics and physics can be simplified to a certain extent, but certain ideas cannot really be, why?

Answer 1

Three (or so) thoughts:

1. Philosophers like Heidegger, Hegel or the French post-structuralists introduce a new vocabulary of technical termini. These new words, say "Zuhandenes" ("Ready-to-hand") in Heidegger, are implicitly defined by page-long explanations. At least some of these technical termini are usually irreducible.
2. The explanations which define these technical termini implicitly could most likely be given somewhat differently without changeing their meaning. Not all philosophers are the most talented teachers of their own philosophy.
3. That said, what is a difficult text to one reader may be fairly easy to another. Horkheimer and Adorno's "Dialectic of Enlightenment" is as impossible to understand for a beginner of philosophy as is Analysis III for beginner of mathematics. Both are easy reads to the advanced learner.

So, there are new irreducible words and there is necessarily text which defines these words as part of the theoretical web it builds. This text often could have been written better. But what is difficult or easy depends on ones state of knowledge.

The situation is not totally different in mathematics, for instance. What a set is, is implicitly (partly) defined by the axioms of ZFC. These axioms are (some of) the "text". And they are not that easy to understand, either.

Answer 2

I can provide an intuitive answer to how thoughts can be simplified. From a general language, we can create out "sub languages". That is, a smaller language which is capable of consistently dealing with the phenomena in a certain field.

So, for example, from the foundations of mathematics, one could come up with the "language" of differential forms. Once we understood that, then many of the multivariable theorems in arbitrary dimensions get unified into one single result.

For a simpler example, consider the sentence "three plus five is eight" and "eight is three plus five". Now, the information of these two statement is contained in the equality 3+5=8.

The reflexivity of the equality encodes the two statements and the symbols denote the objects inside the statement.

Now, in reverse, would it make sense to add any random words and define equality between sum of arbitary words? Maybe but it would beyond the scope of this sub language we created.

Answer 3

What do you mean by simplified and simplified to whom? Like for the respective author a text is simple if it gets the meaning across with as little text and explanation as possible.

That in turn can mean that a lot of the mental labor to decode the text comes down to the reader having to figure it out.

Like in general you could send an information in plain text or you can encode it, meaning the other end runs the code on their hardware and produces the message. So idk you maybe just nod to another person on a railway and that nod sets a series of events into motion that can produce idk the works of Shakespeare or whatnot. It's incredibly simple for the sender because the algorithmic work comes down to the receiver.

So often times the sender expects the receiver to be familiar with a subject matter or have general knowledge or experience so that they can simplify their task of writing by making use of these experiences and mental images. While if you want to send a complex piece of information without ANY prior knowledge on the end of the receiver you'd have to take much wider turns and write up a lot more information to the point where you might have to summarize the full human history and every science at which point you would agree that you'd touched upon something that is impossible. So at some point you need to simplify your ideas and/or take things for granted or leave it to the receiver to figure it out for themselves.

Answer 4

For easier thoughts:

Short version: Convenience

Long Version:

I think if you wanted to have a chance at being rigorous (without actually choosing to be rigorous) you could acknowledge that its possible to assign a complexity to thoughts not unlike the notion of "Kolomogorov complextiy" for arbitrary strings in computer science. Instead we treat the thought as a string (how much do you have to write or say to feel like you got the thought out (which is a subject experience)) and then take the kolomogorov complexity of this resultant string.

Some thoughts just have HIGHER complexity to the point that the amount of explanation you would need in terms of simple ideas is so high that it becomes pointless to explain that thought without assuming some baseline complexity in your ability to express. In the Kolomogorov world, you need a very expressive programming language for writing your programs down for expressing that string without having a bad time.

We can look at a particular thought to see how this kind of thing manifests:

An example which comes to mind for example is Einstein's theory of general relativity. In its most DIRECT sense this is just a system of partial differential equations (I think 16 in all) which any one with basic knowledge of multivariable calculus should be able to understand (meaning look at and say "yea in principle I know what that is").

But writing down that formula is extremely tedious and requires a lot of explanation on how to write it down that you'll never find an author talk about the theory this way.

Instead they will talk about concepts like curvature (and the curvature tensor and christoffel symbols) and set up a whole bunch of theory and language and make you process a textbook or two's worth of knowledge BEFORE you can even make sense of the modern formulation

$$ R_{\mu \nu} - \frac{1}{2} R g_{\mu \nu} + \Lambda g_{\mu nu} = \frac{8\pi G}{c^4} T_{\mu nu} $$

That equation is just ONE line, as opposed to 16 and it requires quite a bit of understanding in order to actually make sense of. The way you critique some philosophers with overcomplicated the matter I too feel about this equation sometimes but... I guess the onus is on us to write out in the verbose but "simple" way if no one else has bothered to do it first.

For Harder thoughts:

If we try to ask ourselves what is a "set" and go to the dictionary you would find it defined to be a "collection" and if we ask what a collection is you would find "grouping" and if you look for a grouping it would be a "set" etc...

Some ideas / thoughts are just ALL or nothing. If you try to break them down you are missing the point. We learn these by conditioning and habit, and its entirely possible for some advanced philosopher to discover a new such ALL or nothingism and then when trying to explain it frantically beat around with complex words because there simply isn't a way to break this idea down that isn't ALL or nothing. Learning the idea cannot be done abstractly by reading and thinking it but by living it.

Answer 5

I'm not sure if I really agree with this statement. Who says those statements can not be simplified further? I think if enough effort is put into it most statements can be simplified, possibly at the cost of requiring more time/space to describe. Many things that are taught now in schools/universities were once considered out of reach for the general public but after many decades of rehashing and simplifying it is now part of some curriculum.

Yet I do think that there is some kind of "minimal complexity" to concepts, like mentioned by Sidharth. But the complexity of a single statement can be traded for time/space. For example consider adding the two numbers 952+462 in decimal. If you write those above each other you can perform the addition using 3 rounds of adding the appropriate digits. If you convert to binary the addition looks like 1110111000 + 111001110. The benefit of working in binary is that each operation is the absolute simplest possible, there are only 3 possible ways to add digits: 0+0=0, 1+0=1 and 1+1=10. But the downside is that instead of 3 rounds of "hard" operations you now need 10 rounds of simple operations. Likewise, you could convert the split the contents of a hard-to-read book into a large number of simpler books until the content is readable by anyone with basic mental capacity. The amount of space you need to write a statement in dumb-dumb language could a measure of the actual complexity of that statement. This is similar to how Shannon Entropy measures the "true" information content of something.

Answer 6

The purpose of a language is to encode concepts or cognitive structures in a form that conveys those concepts or structures to others adequately. That last word — adequately — places a lower limit on how simple an expression can be. With physical objects and emotional states — sphere, chair, love, envy, etc — others have strong internal references of their own for those concepts, so using a single word or phrase will often be adequate to convey the sense. For abstract concepts — Dasein, capital, qualia, angst — others may lack both internal references to the idea and internal references to other concepts and structures are necessary to properly represent the idea. So philosophers often find themselves building not just an idea, but the entire worldview in which that idea can be adequately expressed.

To put it in context, this is what I think of as the 'cricket' problem. The first time Americans see a UK cricket match, they find it utterly incomprehensible, looking like some weird perversion of baseball. They have to be taught all of the things that Brits know from a young age — to enter into the British sports worldview, with all the practical and experiential cognitive structures Brits share — and only then can they understand cricket properly. Complex concepts cannot stand alone outside of the worldviews that encompass them; that's just not cricket.

Incidentally, maths are exactly the same. A phrase like 1+1=2 seems very simple, because we can relate it easily to everyday objects: one apple and another apple gives me two apples. But in the abstract, well... Bertrand Russell's "Principe Mathematica" doesn't work its way up to the concept "2" until (if I remember correctly) page 365. Appearances can be deceiving…