↪jgill
There is a common confusion between intention and intentionality, just as there is between potential and potentiality. The former has content, the latter is indeterminate: better understood as a faculty rather than a capacity. — Possibility

OK. Thanks for the explanation. Makes sense. :smile:

Intentionality is a predictive distribution of effort and attention - it requires consciousness, but one need not be conscious of it — Possibility

SEP: "In philosophy, intentionality is the power of minds and mental states to be about, to represent, or to stand for, things, properties and states of affairs" . . . " ‘Intentionality’ is a philosopher’s word: ever since it was introduced into philosophy by Franz Brentano in the last quarter of the nineteenth century, it has been used to refer to the puzzles of representation, all of which lie at the interface between the philosophy of mind and the philosophy of language". . . "Consciousness and intentionality can seem to pervade much or all of mental life—perhaps they somehow account for what it is to have a mind; at any rate they seem to be important, broad aspects of it. But achieving a general understanding of either is an enormous challenge. Part of this lies in figuring out how they are related."

OK. This is technical jargon for philosophers. Not how I might have defined it.

Science has become more and more compartmentalized and specialized to a degree that the language of science is not easily accessible or comprehensible to the otherwise generally well educated. — magritte

How true. Up until the late 1800s, magazines like Nature and its predecessors had articles about discoveries in mathematics that were by and large intelligible to normal, well-educated readers. These days new ideas in the subject are usually too specialized for even mathematicians not working in those specific areas to understand.

An act is not recognised as ‘creative’ until an abstract thinker attributes intentionality - but the act still happens — Possibility

Not necessarily, if I am interpreting what you are saying correctly. My own experience in mathematics belies this statement. I have had ideas pop into my head without having primed myself by thinking about a subject; the ideas then have been recognized as creative - but without intentionality.

You seemed to have this misconception too. Probably you still do, considering your repeated snarky remarks, instead of actually putting forward arguments — leo

Sorry if I offended you, but all such arguments seem trivial, so why present them? Of course creativity is not always a good thing, nor destruction inherently bad. Was the creation of nerve gas or ISIS a good thing or a bad thing? Was the destruction of concentration camps or the Nazi Regime or a dangerous bridge good or bad? Notions of good or bad depend upon context and perspective.

Destruction being inseparable from creation is a more debatable issue IMO.

This isn't a diagram of how much emphasis any particular human society contingently puts on the different subjects, but of the inherent relationships between the different subjects — Pfhorrest

I can see a path from construction to geometry and back again in your diagram. But the image of the diagram infers (to me) philosophy is the bedrock of all activities. Is this your message? Or, if you mean to imply that philosophical conversations occur in all activities perhaps philosophy doesn't even belong in the illustration since it is pervasive. Communication, reflection, speculation - these bring people together from various disciplines rather than formal philosophy.

A social science is normally not considered a physical science. Oxford Dictionary on physical sciences: "the sciences concerned with the study of inanimate natural objects, including physics, chemistry, astronomy, and related subjects." If you didn't have ethical sciences I would say just "sciences".

So "coming before" simply refers to the existence of a certain piece of biological or mental machinery, which I would not consider creativity itself. Similarly, the ability to solve problems becomes "problem solving" before the act of problem solving.


"think in the abstract and form images of realities that are not present"

And "thinking in the abstract" doesn't necessarily lead to an act of creativity. I speculate that mostly it does not and is merely unproductive daydreaming. Am I thinking in the abstract when I contemplate mathematics? Does "abstract" mean non-physical? Am I thinking in the abstract when I imagine vanishing abruptly and re-appearing somewhere else? "images of realities" is pretty broad I guess.

What we create isn't always positive, and what we destroy isn't always negative. — leo

And this is your original thesis? I'm amazed someone hasn't thought of it before. :roll:

Does creativity come before the act? — Brett

Existing in some sort of abstract Platonic fashion? I would say, no. And you and others might say, yes. It's an argument devoid of substance IMO.

It’s an adaptation of the Quadrivium’s . . . — Pfhorrest

"A medieval university curriculum involving the “mathematical arts” of arithmetic, geometry, astronomy, and music." (Wiki)

Generally, social science is not considered a physical science. Look it up.

And your diagram accords philosophy an enviable position among virtually all human activities. At a time in the past that might have had merit, but I don't see it these days. Sorry, but it seems conceited and way out of proportion. And the mathematical world now is far too complicated to be encapsulated so trivially in your diagram.

But I am not a philosopher, and others hereabouts will have opinions supporting your views I suspect. That's OK.

Since when is social science a physical science? And your division of mathematics is naive.

Creativity itself has no purpose. But those who create usually do.

Change is both a creation and a destruction, creation of what comes to be and destruction of what ceases to be. So it would be misguided to use change as a synonym for destruction. — leo

I mentioned earlier that having an idea and writing it down can be an act of creation without destruction, and you replied that I destroyed a piece of paper in the process or destroyed a world in which the idea had not existed. All of which seems pedantic and is more than a little absurd. Perhaps you can demonstrate how your creation/destruction interplay applied uniformly to everything is of any value whatsoever.

You might also want to take a look at topology — TheMadFool

You mean a coffee cup being "destroyed" to become a doughnut? :chin:

This subject comes up among mathematicians when they are feeling a bit philosophical. A half century ago my late advisor simply stated there is nothing new in mathematics. I have found this to be debatable although many math people think it's not worth the effort. Most new and creative ideas in my profession arise, sometimes marginally, from previous notions, however they may be disguised in novel terms.

As an example, a functional integral is a concept that might have been difficult to explain to Eudoxus, who in 370BC devised a method of exhaustion to find volumes and areas. Archimedes then adopted this concept. But not until the 17th century did the foundations of modern calculus appear in works of Fermat and others. And Newton and Leibniz might have had trouble in understanding this abstraction of integration.

And then there are modern subjects that use normal language to describe what is being mathematically conjured, like category theory and schema. These areas of study arise from processes of abstraction and generalization.

From a personal perspective, I've recently defined and studied something I call a hybrid path line, which bears similarity to path lines from fluid dynamics or dynamical systems, but is different. It's of no consequence, a mere plaything, but illustrates how one concept leads to another. :cool:

Reflection or speculation, but with a bit of pomp and ceremony. :cool:

The point is that destruction isn’t inherently bad, contrary to popular belief. Maybe you need to overcome that belief too — leo

The word "destruction" has a negative connotation. Try using the word "change" instead. Just a thought.

I hope my participation in this thread doesn't inconvenience or distress you too much. — fishfry

Of course it doesn't. Your posts are uniformly excellent.

I don't see a point in continuing this conversation. — SophistiCat

That's all I meant.

As does yours. Mine moved us eight hours ahead! Now look where we are. :worry:

When did science relinquish logic from its tool box — Metaphysician Undercover

When it became apparent that lightening strikes were not Zeus hurling thunderbolts from Olympus.

There is no halting problem concerning this thread.

You say you created something because you focus on what comes to be, the field of mathematics that includes this "form". If you focus on what ceased to be, the field of mathematics without that "form", you would say you destroyed something. But really you both created and destroyed something — leo

I see why I didn't pursue philosophy in school . . . :roll:

If I said that I would be content enough if nothing happened after physical death . . . — TiredThinker

Be content now. After you pass the word will have no meaning.

I read recently that Dark Energy might be the aether resurrected, or simply what we know as the Vacuum of space. Where science inches ahead, philosophers go boldly. :nerd:

Russell is clearly wrong. This paradox is now clearly fixed. Can we move on in a unified manner? — Philosopher19

Yes. Off the first page of TPF. :roll:

I am a scientist — Sir Philo Sophia

Having made that statement you are obliged to supply details. — jgill

???

Guess you may not be a professional scientist. No big deal. :roll:

Mathematics was the creation of the destruction of the earliest forms of "guestimated bargaining", which was made possible due to the destruction of a previously unstable, constantly-warring society by the creation of more permanent civilizations which some argue was only due to the destruction of supernatural folklore as laws that govern reality due to the creation of science resulting in the creation of powerful, history shaping innovation. — Outlander

Can you say all that without taking a breath? I maintain that at the present time my form is harmless and non-destructive. :razz:

There is no such thing as a creation without a destruction, and a destruction without a creation — leo

I disagree with the generality of this statement. As an example, I recently "created" a "form" in mathematics that simply extends a particular kind of function. Nothing is destroyed in this process. As to whether this creation is of any importance, I admit it is quite unimportant. :chin:

Famous Introverts

A very thoughtful thread, Corinne. As a mathematician I find the quality productive, but in balance with social aspects of the discipline. :cool:

Wouldn't your definition for "action" be a lot simpler, and say essentially the same thing if it was worded something like this: "anything which results in a change"? — Metaphysician Undercover

I agree.

I am a scientist — Sir Philo Sophia

Having made that statement you are obliged to supply details.

my definition does not require any thinking — Sir Philo Sophia

Another gem from this forum. :grin:

↪fishfry
I admire and appreciate the trouble you go to here and elsewhere to put some of us back on the right track - even as some of us go right back off the rails! — tim wood

Kudos to fishfry and fdrake, resident experts in set theory. Both demonstrate great patience in unraveling the queries on that subject that crop up on TPF. :up:

Who cares about top speed? How about bringing light speed down to my neighborhood limit! :cool:

Light travels at 38 MPH

X=X+1 can never be true — Book273

Of course it can. As a recursion statement in BASIC. I use stuff like this all the time.

Nothing is nothing of a paradox. :roll:

I'm pretty sure a logarithmic spiral is the same as the Fibonacci sequence, if not incredibly similar. — Justin Peterson

Close, but no cigar. :wink:

"The golden spiral is a logarithmic spiral that grows outward by a factor of the golden ratio for every 90 degrees of rotation (polar slope angle about 17.03239 degrees). It can be approximated by a "Fibonacci spiral", made of a sequence of quarter circles with radii proportional to Fibonacci numbers. " (Wikipedia)

Could be used to communicate with the future via technology — Enrique

Why bother? Just use cuneiform on clay tablets. It works.

. . . with enough precision by experiment to make the model useful for predicting retroactive causality amongst categories of wavicle ensemble, — Enrique

No comment.

Not having been a number theorist I had not thought about the Fibonacci sequence in a long while, recalling its definition, rabbit populations, and the relationship with the Golden Ratio, so I was surprised at the lengthy Wikipedia article about it.

If the Universe is like the Fibonacci sequence — Justin Peterson

I assume this is a metaphysical conjecture. Galaxy spirals, to my knowledge, aren't necessarily Fibonacci related. A logarithmic spiral might describe some of them. I don't know. A Golden Spiral is a special case of a log spiral, but I don't think there is evidence it predominates in galaxies. :cool:

I sometimes wonder if philosophy can really contribute anything about the quantum world. All the talk of waves and excitations and duality hasn't brought clarity to that tiny kingdom. It may be that Max Tegmark's mathematical universe ideas actually exist and the understanding of quantum phenomena is nothing more than understanding the mathematics that yields predictable results. And that mathematical edifice is, at present, not adequately described by existing mathematical applications.

What was it Feynman said about it? That it was kind of dippy. One should not have to regularize or renormalize in such bizarre ways to get predictive results. Once the true mathematical structure is found, then it may be the only way to "understand" quantum science.

Do you mean experimental physicists or perhaps engineers? — magritte

I don't mean anything. This is a Wikipedia article. Argue with them. :cool:

Since I piddle around with dynamics in the complex plane - force (vector) fields that predict the movements of particles, I suppose I am somewhat a "mathematical physicist". Like you, magritte, I will await my Nobel Prize in the mail! :victory:

There are theoretical physicists (hand waving) and mathematical physicists (mathematicians working in physics). — jgill


To be fair, I don't think that these disciplines are very distinct — SophistiCat

There are theoretical physicists (hand waving) and mathematical physicists (mathematicians working in physics). — jgill

Even speculative physics of other possible physical worlds is intended to be fully mathematical as soon as the needed maths are invented. Without mathematics what physics is there? — magritte

You guys . . . :roll:

Wikipedia:

Mathematical vs. theoretical physics

The term "mathematical physics" is sometimes used to denote research aimed at studying and solving problems in physics or thought experiments within a mathematically rigorous framework. In this sense, mathematical physics covers a very broad academic realm distinguished only by the blending of some mathematical aspect and physics theoretical aspect. Although related to theoretical physics,[3] mathematical physics in this sense emphasizes the mathematical rigour of the similar type as found in mathematics.

On the other hand, theoretical physics emphasizes the links to observations and experimental physics, which often requires theoretical physicists (and mathematical physicists in the more general sense) to use heuristic, intuitive, and approximate arguments.[4] Such arguments are not considered rigorous by mathematicians, but that is changing over time[citation needed] .

Such mathematical physicists primarily expand and elucidate physical theories. Because of the required level of mathematical rigour, these researchers often deal with questions that theoretical physicists have considered to be already solved. However, they can sometimes show that the previous solution was incomplete, incorrect, or simply too naïve. Issues about attempts to infer the second law of thermodynamics from statistical mechanics are examples. Other examples concern the subtleties involved with synchronisation procedures in special and general relativity (Sagnac effect and Einstein synchronisation).

The effort to put physical theories on a mathematically rigorous footing not only developed physics but also has influenced developments of some mathematical areas. For example, the development of quantum mechanics and some aspects of functional analysis parallel each other in many ways. The mathematical study of quantum mechanics, quantum field theory, and quantum statistical mechanics has motivated results in operator algebras. The attempt to construct a rigorous mathematical formulation of quantum field theory has also brought about some progress in fields such as representation theory.

You overlooked my "may not be the same"

There's no shortage of confidence on TPF. Amusing at time. :smile:

Theoretical mathematical physics is Pythagorean-Platonic — magritte

You are lumping two things together here that may not be the same: There are theoretical physicists (hand waving) and mathematical physicists (mathematicians working in physics).

More government benefits and support in metro areas, a greater degree of socialism. Seems obvious.