• Culture wars and Military Industrial Complex
    ↪Athena
    You make a good point about the humanities being pushed aside after Sputnik. I'm surprised this thread is languishing. :chin:
  • Infinite casual chains and the beginning of time?
    Yes it's the case, and yes, it's more complicated than that. It's not mysticism, it's confirmed physics. — Relativist

    OK. I take it you are a physicist.
  • Infinite casual chains and the beginning of time?
    When quantum objects are entangled, measuring the properties of one changes those of the other — Relativist

    Is this exactly the case? I thought it was a bit more complicated than that, but I am not a physicist and could be mistaken. Kenosha Kid? :chin:

    It's easy to drift into quantum mysticism with topics like this.
  • 0.999... = 1
    Yeah, the comments here (one sub-thread in particular) have run their course — jorndoe

    Oh no! And we are so close to half a millennium! Don't stop now. This may be a record for total nonsense. :scream:
  • Culture wars and Military Industrial Complex
    Right-wing students were encouraged to spy on the classes of progressive professors (Henry Giroux) — Athena

    I never heard of this in my many years as a prof. But it may have happened at more prestigious institutions. On the other hand there have been numerous publicized attempts by various student and faculty groups to keep conservative speakers from expressing their opinions on campus.

    My argument is the Military-Industrial Complex, through educations, and the 1958 National Defense Education Act have had huge social, economic, and political ramifications — Athena

    No argument there. The USAF even funded one of my minor research projects that had no military applications. The Cold War has had a profound effect on society.
  • Infinite casual chains and the beginning of time?
    Think of going back in time one year, then from there back 1/2 a year, then from there back 1/3 a year, etc. At each stage there is "causation" before that point in time. However, the sum 1+ 1/2 + 1/3 +.... tends very slowly to infinity (the first six million terms add up to less than 21, if I recall correctly). So, we have an infinite chain of causation that has no starting point, no beginning of time.

    Just idle chatter . . . pay no attention to that men behind the curtain. :nerd:

    The first has it, almost as a trick of our need to find patterns in the world, that a series of events would still occur even if one entity in the series was erased. — substantivalism

    This more or less coincides with Stanislaw Lem's Ergodic theory of history. Some movements in society are so powerful that changing bits here and there have no appreciable effect. On the other end of the spectrum is the Butterfly effect.
  • If the Universe is infinite, can there be a galaxy made of computers?
    If I were to say, yes,there may be such a galaxy, would I be indulging in metaphysics? :chin:
  • If the Universe is infinite, can there be a galaxy made of computers?
    Unless you can establish that it is impossible...of course it is possible — Frank Apisa

    https://www.logicallyfallacious.com/logicalfallacies/Proving-Non-Existence

    :cool:
  • New here- i need my brain to stop racing. Any thoughts on slowing down?
    The practice of Zen might help. It's possible to reach a point where the mind still races, but one is able to stand apart and observe.
  • If the Universe is infinite, can there be a galaxy made of computers?
    The old monkeys and Shakespeare thing. If the probability of something happening is 10^-20 does that mean it could happen? But who or what assigns even that probability?

    The universe is a jungle, folks. :gasp:
  • Metaphysics Defined
    Mathematics proofs are empirical, of course, but mathematical constructions to be proven, are not empirical at all. — Mww

    empirical: "based on, concerned with, or verifiable by observation or experience rather than theory or pure logic."

    A mathematical proof of a theorem is a chain of logic.
  • Evolution & Growing Awareness
    Many modern scientists embrace pan-psychism — turkeyMan

    How many?
  • 0.999... = 1
    It’s not that one is a product of zero, it’s that one is the empty product. — Pfhorrest

    "Multiplicative identity" is more appropriate. But whatever. It appears this thread will go to infinity without ever leaving the starting point. Paradox?
  • Is there a culture war in the US right now?
    Why the year 1958? — ssu

    The impact of Sputnik.

    We replaced our liberal education that was addressing political and social problems through education from the first day a child entered school, — Athena

    I graduated high school in 1954 and college in 1958, but I don't remember that kind of instruction. In the 1960s the civil rights movement affected school curricula in that way.
  • Metaphysics Defined
    No transcendental object is susceptible to phenomenal predicates — Mww

    Are you saying human consciousness is not dependent on the brain?

    I don't think one can categorize or pin down a succinct definition of metaphysics. I see metaphysics in parts of mathematics.
  • 0.999... = 1
    And I consider infinitesimals as poor metaphysics — Metaphysician Undercover

    And I consider it the best of metaphysics, existing solely in the mind but useful in developing the mathematics describing physical phenomena.

    Carson Chow (Scientific Clearing House, 2012):

    "While metaphysics as science is a dead-end for me, metaphysics as mathematics is ripe for very interesting insights. Instead of asking directly about “our” reality, we should be asking about hypothetical realities."

    But, then, I am not a philosopher and must bow to your competence in this area, as I have to your competence in mathematics. :cool:

    (Refer to Metaphysics Defined in this forum)
  • 0.999... = 1
    What is important to apprehend, is that in the general sense, understanding follows from acting — Metaphysician Undercover

    Once apprehended, it should be incarcerated and prosecuted to the fullest extent. Understanding abets acting and is equally guilty.

    You might say that I believe in metaphysics, and modern math demonstrates a poverty of metaphysics — Metaphysician Undercover

    Perhaps. But there are instances where it arises, like non-standard analysis which incorporates Leibniz's infinitesimals - which I claim are metaphysical actualities. And from my perspective, modern transfinite set theory seems somewhat metaphysical (others will probably disagree). The higher one goes into the thin air of mathematical abstraction the more likely one will encounter metaphysics - in my opinion. For example, one new developing area is that of "magnitude" in abstract spaces. Although the groundwork has been laid, this concept seems to me metaphysical. :cool:
  • Random Equation
    Learn Mathjax in the tutorial on this forum. Or use MathType or some similar program. Few if any will try to unravel what you have posted.
  • 0.999... = 1
    Clearly you haven't got a clue what a number is, yet you keep insisting that such figures represent numbers. — Metaphysician Undercover

    Still attacking those windmills with your insightful lance, eh? I have to admit, you've got gumption! :nerd:
  • I would like to talk about abstraction
    If I understand it correctly, I can't jump on board with this third point — Tommy

    Feynman, not me. But he had a point about the set theory. I taught college algebra in the era of the New Math, and the first chapter in the book we used was axiomatic structure. No matter who taught the course, the students were not happy.
  • I would like to talk about abstraction
    How about abstract art, people? :chin:
  • I would like to talk about abstraction
    Here's a good description of abstraction in mathematics:

    https://en.wikipedia.org/wiki/Abstraction_(mathematics)

    It's an ongoing process, moving further and further away from specific, focused areas of math to "higher" levels of mathematical thought in which conceptual umbrellas are cast over seemingly different subjects, showing common features. Sometimes this results in solutions of long-standing problems, but being more distant from the nitty-gritty of specific areas of thought, like looking at Earth from the space station and not being able to distinguish details, problems, or even opportunities for exploration in those disciplines don't show up.

    Higher levels of abstraction are difficult for most students to comprehend. When I entered college in the 1950s I took a course in analytic geometry (AG), drawing figure after figure in the Cartesian plane. With this background, calculus was easier to understand, whereas AG was dropped from most curricula several years later and the subject was quickly and somewhat breezily covered in the first few weeks of calculus. Then, later I came across an introductory calculus text that began with elementary linear algebra in n-dimensional Euclidean space. This coincided roughly with the "New Math" movement.

    Richard Feynman (1965):

    "If we would like to, we can and do say, 'The answer is a whole number less than 9 and bigger than 6,' but we do not have to say, 'The answer is a member of the set which is the intersection of the set of those numbers which are larger than 6 and the set of numbers which are smaller than 9' ... In the 'new' mathematics, then, first there must be freedom of thought; second, we do not want to teach just words; and third, subjects should not be introduced without explaining the purpose or reason, or without giving any way in which the material could be really used to discover something interesting. I don't think it is worthwhile teaching such material."

    Abstraction and generalization in mathematics also have the effect of opening up potential areas of thought and research topics when the lower levels of mathematics have been pretty much "mined out". So, PhD programs are influential in pushing in these directions. :cool:
  • 0.999... = 1
    Maybe a professional will have better luck getting through. — Michael
    :rofl:
  • Math ability and intelligence
    I've been a mathematician for almost sixty years and have known good mathematicians with poor language skills and others with high language skills, colleagues who could write brilliantly and others who did poorly expressing themselves. Some had artistic talents, like sculpturing and carving lovely and exotic figures, and others lacked such talents. Some were accomplished musicians and others couldn't carry a tune. Some who were musicians could only play what others had created, while some could compose as well.

    There is certainly a talent for mathematics, as there is for music, and, more often than one might suspect, mathematicians can have both. I don't. :sad:

    Years ago I knew a professor who was recognized for his contributions in calculus of variations, but, to the amusement of his students, consistently made mistakes at the blackboard doing elementary fractions. The ability to mentally compute - what idiot savants excel at - is not essential for producing interesting mathematics. What is essential, beyond a native talent in the subject, is a desire and ability to explore and discover, to use one's imagination to create.

    I was a rock climber for over sixty years, and have had a number of climbing friends who were mathematicians. That may seem odd, but both activities are exploratory and creative. The Brits in the 1880s used the word "problem" to describe unclimbed but appealing sections of rock, like questions in a text that required "solutions". Mathematicians and climbers are problem solvers. :cool:
  • 0.999... = 1
    Great, now we're making some progress — Metaphysician Undercover

    Oh boy, made it to 400 posts!! That's progress! :nerd:
  • At the speed of light I lose my grasp on everything. The speed of absurdity.
    ↪Kenosha Kid
    Being an expert is something of a challenge in this forum. :roll:
  • At the speed of light I lose my grasp on everything. The speed of absurdity.
    ↪Kenosha Kid
    I appreciate your knowledgeable commentaries. Thanks. :cool:
  • 0.999... = 1
    Can you imagine how offended they would be if I addressed something of more importance? — Metaphysician Undercover

    I know, I know. You'd be driven from your castle in the dead of night by an angry mob of mathematicians waving their torches and holding their frothing mastiffs on chains. They are an uncivilized and ignorant bunch, so it serves them right you are withholding precious knowledge. :scream:
  • 0.999... = 1
    If there is such a thing, then it is part of "our world". And so the mathematical axioms must be "true to it", in order to be correct. — Metaphysician Undercover

    That's just the point. Perhaps we don't really understand "our world" that well. Odd looking axioms should not be cavalierly discarded simply because they are "not true" to our limited view of reality. You misuse the word "correct" IMO.

    Instead of writing virtual tomes about the drivel on this thread you should apply your critical thinking skills to actual controversial items like the Axiom of Choice.
  • 0.999... = 1
    So it's completely acceptable to criticize the principles of mathematics when they are not "true of the world", because mathematics is used for purposes which require them to be true of the world. But the game of chess is not used in this way — Metaphysician Undercover

    However, modern, abstract mathematics may be more like the game of chess and less likely to describe our world. For a number of years it's been fashionable to move away from the kinds of mathematics that we normally associate with physical reality and into "higher" levels that are increasingly abstract and generalize concepts and processes to the extent that ideas and technicalities peculiar to classical math don't even appear on the radar.

    But then I wonder, perhaps what seem like total abstractions really do point to some underlying aspects of reality that we have not reached the point of comprehending. One might think this possibly true with regard to QM, although most of the math used there is fairly traditional. Even oddities like virtual particles are really just mathematical terms in the series solution of difficult integrals. Or so I am told.

    Maybe there is a mathematical universe, and somewhere, through all the "chess game rules" mathematicians study, a path to understanding it can be found.
  • The Self
    ↪SophistiCat
    You are certainly reaching far back in history - Ship of Theseus - for your argument.

    All the philosophical banter about self has little if any impact and probably pales beside the dramatic shift of perspective Zen provides.
  • The principles of commensurablism
    That there is such a thing as a correct opinion, in a sense beyond mere subjective agreement. (A position I call "objectivism", and its negation "nihilism".) — Pfhorrest

    Sorry to intrude. I am not a philosopher, but I am not sure what you mean, here. For example, in the philosophy of morals or ethics, what is the "correct" opinion regarding Sophie's Choice?
  • 0.999... = 1
    What I believe is that it's about time for a good dose of healthy skepticism to be directed at mathematical axioms. — Metaphysician Undercover

    It must be brutal that few in the mathematical community seem concerned. But I do agree that the axiom of choice is an unhealthy pathology. :cool:
  • Transition from Philosophy to Math.
    I'm a retired mathematician. There seems to be a considerable overlap with analytic philosophy in the foundations of mathematics and set theory, very abstract topics that occasionally generate what are called pathological examples. However, these areas of mathematics are not extraordinarily popular in my profession. More traditional paths of mathematical thought align with the physical sciences better. Other than that, my opinion is there is very little common ground in the two disciplines.
  • The Self
    Thought my post would inspire comments. :cool:

    I repeated verbatim what a friend who has practiced Zen for over twenty years said in another forum. I would argue with him that "empty awareness" wasn't possible, for in that state he would have been aware of that state.

    Ironic, you deny the individual while presupposing it. Who’s this “one” who learns or has experiences, if not the individual person or subject? — aRealidealist

    In fact, I'm denying the sense of self, not the one who experiences.

    I would place more faith in neuroscience than Zen or philosophy. :smile:
  • Immaterial substances
    "Material" here is in the contemporary sense that if it is affected by and/or affects material things — Kenosha Kid

    Self-referential definition? Try, ". . . and/or affects physical objects"
  • 0.999... = 1
    ↪TheMadFool — Michael

    "What I'm particularly concerned about is the ratio between consecutive elements in the set N"

    n/(n+1) = 1/(1+1/n) -> 1/(1+0) = 1

    Rest easy, mate. Time for a toddy.
  • The Self
    This is more a subject for Zen meditation. There one learns, or experiences one's "I" as a fabrication. Instead of "I am aware" there is only awareness. An instant of realization is worth more than a lifetime of philosophical dialogue. :cool:
  • 0.999... = 1
    I wonder how efforts to attract a professional philosopher to this forum are progressing? :roll:
  • What use is philosophy?
    Philosophy is about figuring out how to do sciences. It uses the tools of mathematics and the arts, logic and rhetoric, to do the job of creating the tools of the physical and ethical sciences — Pfhorrest

    I think it is unnecessary to even use the word "philosophy" in this regard. It appears you are trying to find a niche, a recognition for something that pervades creative efforts and can be more commonly thought of as combinations of imagination and technical knowledge. You seem to want philosophy on some sort of pedestal rather than admitting it is so ubiquitous, so ethereal that it touches everything but adheres to nothing . . . one needn't even use the term, particularly in scientific research.

    I admit, however, that philosophy of mathematics (a truly dreadful discipline IMO) displays the characteristics of both subjects as realized in academic departments.
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