Guide to Thinking - 4 fundamental patterns + 1 limit

Realised in debate today just how little people know about thinking.

• Material Facts & Science
  Much debate revolves around facts. But facts are not thinking. Suppose someone says "I fly unicorns." Common debate will revolve around belief in unicorns and the debate will be pointless. Those that believe versus those that do not believe. All that can be decided is some method to resolve this issue. Perhaps people will agree on the results of an internet search, or they will agree on an expert to decide, or perhaps collaborate on designing a scientific experiment to decide. We could call this type of thinking Science. Designing good experiments requires good thinking. The great advances in science often revolve around excellent experiments like the ingenious Michelson-Morely experiment to test the prevailing belief in aether. In addition it established the Constant Speed of Light which is what triggered Einstein's to think about relativity. If speed of light is constant then everything else must adjust and exist in a frame of reference. But all this ground breaking thinking came from the simple established fact of constant speed of light. Right now the prevailing theory of Big Bang is coming under new testing as the JWST discovers new facts. Critical to experimental design is Falsifiability Essentially that experimental hypotheses are chosen that can be practically disproved. So we adopt the hypothesis "there are no unicorns" which is disproved when we observe a unicorn. This is actually quite complex, but note that all the thinking about this cannot be itself falsifiable! Not all thinking is about facts. 
• Immanent Critique & Socratic Method & Logic
  Now this is pure thinking. It involves examining the logic of given statements and axioms without concern for any material truth. Some one says "I fly unicorns." That sounds interesting, but we thought that Pegasus was the only flying horse. We ask them this. If they agree that Pegasus is the only flying horse we have a potential problem. If it turns out that Pegasus is not a Unicorn then we can argue they cannot then fly unicorns. We do not need to worry about material existence here, its enough to examine the internal structure of a belief. This opens up the whole world of psychology, literature and comparative culture. When the Sioux say that the great spirit Wakan Tanka was present at the start of the world why argue and stop the discussion? Keep listening and find out about Wakan Tanka it will tell you a lot about the Sioux. Likewise in the film "Back to the Future" we can discover that Marty McFly went back in time to 4 December 1985. Obviously this did not really happen, but that doesn't stop the story. If however he had gone to 4 December 3017 we can argue that he went forward in time and so could never have met his parents. It doesn't need to be "true" in any "material" sense for us to think about its consistency. The later Socrates never presented anything himself he only got people to speak inconsistent beliefs. 23 centuries later Gödel showed that all systems with self reference are either inconsistent or incomplete. Socrates was exploiting a loop hole in knowledge that it can never be complete and consistent. The establishment killed Socrates for that, Gödel survived.
• Allegory & Isomorphism (& Irony)
  Another critical thinking style is seeing similar patterns in different things. When Star Wars starts by saying "In a galaxy far, far away" it could be literal, but we wonder why say that? Perhaps Star Wars is saying there is a relationship between that far away galaxy and our own galaxy but don't worry for now, enjoy the story. But making the galaxies completely different there is the possibility that they map onto one another. I don't know if it was intentional or "true" in any material way (it doesn't need to be) but the Empire looks a lot like the Nazis, and the Jedi look a lot like Jews seeking to gain freedom from an Evil Dictatorship. The Force becomes the Power of God. And we can start mapping one world onto another. We can look at the history of the West for material to find in Star Wars, or we can look in Star Wars for material to find in the West. This is a very creative and synthetic process. It tells us a lot about Star Wars and also our world. This is common place in art, especially fine art, where painted figures often represent more general ideas and so the painting represent thoughts. In maths mapping problems from one solution space or discipline to another is an incredibly powerful method for gaining new insights. And we meet Gödel again who mapped logical sentences operating on numbers to numbers themselves so that they could speak about themselves. For instance if we can list something then its place in the list is a mapping of  the object to a number. With our "I fly unicorns" statement the options are huge now, what is the person really saying? Are they using Unicorns as an allegory/metaphor for something. The speaker does not need to see the allegory themselves, they can create the structures of their world in unicorns without issue, and the listener can map that onto another world quite independently. Perhaps a child is speaking of flying unicorns to express the joy and freedom they feel. Such an incredibly powerful ways to think, and again nothing to do with material reality or facts. Note if the mapping is to a subset then there will be a fixed point that is the same in both versions.
• Dialectics & Irony
  Have spoken at length in this blog about this one. Dialectics is like Negative Allegory. The most famous dialectic is Yin-Yang. In Allegory the mapping is just overlaying one thing over another and seeing they match. In Dialectic we see that what something is overlaps what it is not. I realised recently it depends upon context to bind the halves of together, or what binds the halves together is context. When we look at the Yin-Yang the obvious context is colour: the Black and the White depend upon each other: no black then no white, and vice versa: you need both to get the symbol and yet the parts are opposites. You also have geometry as the little circles map to the overall symbol shape and the halves are also half circles. The whole symbol is composed from opposing elements that must fit together for each to exist. A classic dialectic is male and female. I discussed this in a recent blog. But everywhere you look are dialectics: whenever you find a force you will find an equal opposite force. This is true in the world as much as in your mind or in a story. Consider something Large. You know immediately there must be Small things that it must be compared to in order to gain its Largeness. To be Large you need stand next to Small things, and so inside your Largeness is really Smallness. In a different world of bigger things, that exact same Large thing could be Small. This is why psychology is always ironic (to quote Adorno). Certain forces in any mind are always made from the opposite force. In the example of the person saying "I fly unicorns" we need look at the Yang of "not flying unicorns" and examine what force may lead the speaker to reject this and assert the opposite. Why would the speaker not just ride horses? which is much more straightforward. Again the material facts are not the point of this thinking at all.

So that concludes 4 fundamental patterns of thinking that no one can do without. I realise however that perhaps only 1 in 1000 have actually mastered these. And that rather worrying realisation underlines the apparent growth in ignorance in the West. 

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There is one important limit of thinking that is not formally recognised and is the topic of much of this blog. Called SRH here (Self-Reference Hypothesis) was a casual name to a disparate collection of problems revolving around systems referring to themselves. Perhaps a better name now that more is known about SRH is the Self-Refuting Condition (SRC)

•  Self-Refuting Condition (SRC)
  The most famous case of this is found in Descartes' Meditations. He begins a program of doubt to see whether anything cannot be doubted. He could have saved himself the whole exercise had he been aware of SRC. The system of doubting is limited by doubt itself. More generally any system is limited by itself. The argument roughly is that given a definition of something like doubt, we create limit to distinguish it from other things. The distinction is powerful to begin with, but it has an Achilles heel that when that distinction is applied to itself it breaks itself. It is obvious in a way that if we build steps to raise us up, we cannot then remove those steps.
  
  Douglas Hofstadter in Gödel, Esher, Bach notes that self-reference always seems to limit systems but he says nothing else about this.
  
  All thinking it seems is ultimately limited. The very act of taking up knowledge and thought commits us to the limits of knowledge and thought. Realising that thought is not infinite, and each system of thought is the condition for its own limits is exceptionally important in properly establishing any discussion or investigation.
  
  The fact that SRC exists suggests it may have a more formal definition, but since its about limits, the formulation must be very carefully done and include irony.