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Why do some claim that philosophical writing should be clear?

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Why do some claim that philosophical writing should be clear?
In mathematics a proof is judged to be correct according to the axioms of the mathematical systmes which it pressuposes. i.e. Mathematical systems tell the user what operations and what sequences of operations are correct or true so a sequence of claims and arguments and operatiosn can be judged to be true or false without doubt after a proper analysis.

But in many philosophical arguments and writings the goal is often to make the reader think of a completely new idea or even a new mode of thinking.
Lets say that in the future we will have a new mode of thinking and new concepts.
How do we get from not having them to having them? It starts with intuitions which try to convey something, a thought, a concept a way of thinking, that is not available yet. that readers do not know about and cannot fathom.
In philosophical writings new modes of thinking and percieving reality can be conveyed through means that can only be understood as appropriate once you try to understand them intuitivly. You start reading omething and it seems unclear, ill defined aligorical, obfuscating but, if you read on, finish reading and try to make sense of it, through this process you suddenly become aware of a new mode of thinking and after that, in retrospect you see how what you read was not dumb or obfuscating but nesseecary to make you understand this new mode of thinking.
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>>1362236
>Bearded Greek heads
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>>1362236
So strange sentences, strange word uses, strange grammer, strange combinations of arguments can still be enlightning.
Perhaps to make us understand certain new ideas and ways of thought the use of never before seen sentence structures and combinations of arguments is required.

Perhaps things we take for granted, even the most basic things like "fallacies" can be challanged but to make a person think about challnaging them a text has to do it so that when a person reads it and gives it the benefit of the doubt he is then able to challange some basic understanding he has and suddenly become aware of how it can be thought about differently.
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Did you ever achieve like to be if it was seriously and over with?
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>>1362265
You see, you can ask to a certain extent wether all posts on 4chan can be considered valueable information that should be analyzed.
Your commic statment is also indicatie of certain things and can be interesting to think about.

This is where authority and persuasion come into play.
How does an author make sure his good ideas are explored?
For a philosopher it means getting a proper philosophical education with credentials so he is taken seriously by other philosophers and so they even look at what he writes.
Then there is also the way in which he writes that can either be engaging or not.
Here comes the question of what makes a text have a potential for interesting and fruitful interpretations?
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>>1362236
The axioms of philosophy are that existence exists, consciousness exists, and the law of identity.
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