Could abstract thinking become a subject in early and secondary education? Osmosis via myth/religion/fiction is the usual way, attempts to make it explicit are typically horrendous, conflating idiom with metaphor and so on. The tyranny of literal thought. My nephew brought home a worksheet that asked him to create similes, remove "like" and call them metaphors! As for grown ups, it's either lumped into "creativity" or, with Wikipedia's definition of inductive reasoning as one example, confined to...- Generalization and syllogism
- Analogy
- Simple induction
- Causal inference
- Guessing
...paying no attention to when or how metaphor is useful, unique, and essential. As Will Durant notes, Aristotle mis-characterized the human psyche as deductive rather than inductive. Yet, secular discourse keeps itself to the Logic=Reason fallacy. Even as machines perform logic, the least of our reasoning faculties, more reliably and efficiently than humans can, we continue to undervalue every quality other than quantity.
In education, the ability to apply something learning in one context to a new and unfamiliar context is termed "bridging". That an important idea, but I'm talking about the deep roots of bridging, the ability to forge an insight, not "creativity" as scrap-booking Aristotelian "nothing's new, only recombined" sense but in the Entelechy, Hegelian negativity, sense. The difference is huge. Shakespeare and Chaucer weren't coming up with catchy ad phrases and they're metaphors became idioms only after they were absorbed and subsumed by the usefulness of their function in communication and expression.
How would we go about teaching Induction, Abstraction, and Metaphorical Reasoning?
In addition to clear acknowledgment limits (namely, the ease of its abuse and the enormity of its persuasive power as evident in fundamentalism), teaching inductive, abstract, metaphorical reasoning would require two things:
- Defining the power of induction as a result of its being unbound from the usual (western) goals of consensus-building or objectivity. Weak forces.
- Identifying contexts where only abstraction will do (i.e. broad theoretical concepts, edges of understanding, the places where art thrives and most science throws up its hands)
As one example:
Parallel universes are like integers, each having its own particular infinite range of fractions. But in physics, the fractions would be temporal (Whatever time may be. Flux.)
Abstractly conceiving of space as an integer enables us to reverse the idea. If entanglement is a property of split spatiotemporal dimensions we can think of fractions as dimensional entanglements as well. Pi, prime numbers, etc.
So, parallel universes would not be the same idea as Bohr's or Schroedingers who seem (not having read either) to contemplate change of state (potential to kinetic) rather than a blossoming of temporal (maybe not even spatial!) dimensions.
In either the case of integers or photons, running fwd and back along a causal spatial temporal line would be the direction/mode that's most precisely un-entangled, interdimensional, and most interesting. That was always my hunch as a kid: that 2+2 just equals more 2. Prigogene's indeterminacy when I learned about it, felt like "ha, I knew it."
I've had some thoughts about global education curriculum too. Standards grounded/organized around principles that tip from one disciplinary domain into others. They'll read like platitudes but "getting" cliches is what a lot of novice learning is actually about. Laying traps, so they're proud when they catch their own ankles. Good training indeed for a life of "grab yer ankles"
Let's try to jot down some spastic truisms or hell, have a kid and they'll probly start to pour out. The notion is to articulate some milestone concepts for a global curriculum that needs to cross boundaries such as faith/reason but also form/content, subjective/objective, and space/time (aka here/now). That's where abstraction outperforms literal thinking.
Abstractly conceiving of space as an integer enables us to reverse the idea. If entanglement is a property of split spatiotemporal dimensions we can think of fractions as dimensional entanglements as well. Pi, prime numbers, etc.
So, parallel universes would not be the same idea as Bohr's or Schroedingers who seem (not having read either) to contemplate change of state (potential to kinetic) rather than a blossoming of temporal (maybe not even spatial!) dimensions.
In either the case of integers or photons, running fwd and back along a causal spatial temporal line would be the direction/mode that's most precisely un-entangled, interdimensional, and most interesting. That was always my hunch as a kid: that 2+2 just equals more 2. Prigogene's indeterminacy when I learned about it, felt like "ha, I knew it."
I've had some thoughts about global education curriculum too. Standards grounded/organized around principles that tip from one disciplinary domain into others. They'll read like platitudes but "getting" cliches is what a lot of novice learning is actually about. Laying traps, so they're proud when they catch their own ankles. Good training indeed for a life of "grab yer ankles"
Let's try to jot down some spastic truisms or hell, have a kid and they'll probly start to pour out. The notion is to articulate some milestone concepts for a global curriculum that needs to cross boundaries such as faith/reason but also form/content, subjective/objective, and space/time (aka here/now). That's where abstraction outperforms literal thinking.
"To live alone one must be a beast or a god, says Aristotle. Leaving out the third case: one must be both‹a philosopher."
-Friedrich Nietzsche
What was religion to the Greek philosophers?
- Aristotle- born of wonder, it finds xpression in myth
- Epicureans- born of fear and ignorance, it seeks protection
- Euhemerists- born of heroism, it is cultural memory
- Stoics- born of some universal, transcultural spermatikos logos
..external link..
Except that it focuses exclusively on money motives and business management, Edward de Bono's "thinking hats" is an interesting example of a curriculum for modes of reasoning..
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