I see how it makes sense, given it comes from medicine - the very field dedicated to literally the single most complex system we know of: the human body. But I don't see it as an opposite to Occam's razor - rather, a missing lower bound. That is, I see Hickam's dictum as a reminder that some hypotheses may be too simple.
My guess at how one would formalize this is, when you're comparing hypotheses explaining something in a given domain (such as "behavior of things being thrown", or "health of a human body"), there is a level of complexity inherent to the domain. A hypothesis that's so simple as to fall below that level is too simple - it doesn't have enough bits to express what's happening within the domain. The further below the complexity threshold it is, the more likely it is to be falsified by new evidence. In contrast, hypotheses above the domain complexity level are all capable of explaining the domain fully; however, the more complex a hypothesis, the more likely it is to be at least partially wrong.
This gives us the following takes:
- Occam's razor: for hypotheses above the domain complexity threshold, the least complex one is most likely to be true.
- Hickam's dictum: your hypothesis is way below the domain complexity threshold - which you didn't notice, because you don't appreciate how complex the domain is in the first place.
Reconciliation:
- The closer a hypothesis is to the domain complexity level, the more likely it is to correctly explain new evidence. The best hypothesis matches the complexity of the domain. Above it, hypotheses gain superfluous parts, which are either redundant (unlikely), or wrong (very likely). Below it, hypotheses are always wrong - they're too simple to account for all possible predictions, so new evidence will eventually falsify them. The tricky part is - even though we both postulate hypotheses and define their domain, we tend to hand-wave the latter a lot, so in some cases (like medicine) we may not realize that our hypotheses are too simple.
This is an interesting way of thinking about it, but then it becomes essential to determine what the 'domain complexity level' is for any domain, and the possibility of unending argument on what that that level is will almost certainly destroy any value that either dictum or razor have.
How can we disprove the hypothesis “If we can’t disprove it - it isn’t science.”?
The scientific metaphysic relies on so many declarative/prescriptive statements which are themselves exempt from the criteria for science and are thus self-defeating on their own terms.
It is so peculiar when scientists are so dogmatic about science.
Are the formal sciences (logic/mathematics/computer science) not science? The testability/falsifiability criterion certainly excludes them from being sciences.
> How can we disprove the hypothesis “If we can’t disprove it - it isn’t science.”?
That statement isn't science. It's a definition. It's philosophy of science. It's the briefest summary of Karl Popper's definition of the scientific method. According to him, science can never be proven, only disproven.
In this context, most of computer science is more a form of applied mathematics.
Of course there are different ways to look at science, like making a distinction between analytical (or empirical) science, and synthetic science; the science that makes stuff, rather than analysing it. Not sure if that's really a good distinction; the latter is really technology, isn't it?
There is such a thing as computer science, but the majority of what gets called that is really engineering, not science. People often get those two things confused because they have a fair bit of overlap in the Venn diagram, but they are two different things.
Math is itself indeed not science. It is the language of science. It follows different rules than empirical sciences. But note that word "empirical" there; Popper was really only talking about empirical science, and according to him, that was the only real science. You could argue that there are non-empirical sciences.
Another problem with Popper is probably that outside of physics and chemistry, there are a lot of less exact sciences where predictions and refutations of a theory are never that clear cut. Like his issues with the theory of evolution.
Ultimately, I guess science is also simply "getting to stuff that works by trial and error".
How much engineering could we do without Mathematics? How much commerce?
I don't see it as exclusionary. You won't find many scientists in doubt about the fact that everything they do is built upon Logic and Mathematics, in addition to observation.
But don't we need a word to group fields that try to systematically describe, understand, and make predictions about the physical world? (Rather than seeking to explore and characterise idealised logical constructs?). What would you suggest?
You may not see it as exclusionary but many people do. Just look at the comments!
It's precisely the grouping I am talking about.
If you group science in such a way so that logic/mathematics/computer science falls outside the group then isn't that an erroneous grouping?
Isn't that a silly definition?
True and False are idealized logical constructs. It's the idea; and the idealization of the notion that there is a difference between Truth and Falsehood. Or if you want to get biblical - there is a difference between Right and Wrong.
We need a grouping to make it clear that some fields produce theories and others produce theorems.
We need theory-producers to be more humble and provisional in their statements. We need theory-producers to forever remain open for their theories to be falsified or refined (whilst not being paralysed by doubt about theories that have stood the test of time). In other words, we need a slightly different culture.
But we also need a way to rebut someone who says "OK, but can you prove we're not living in a perfect simulation of reality with a fabricated history that was created yesterday?". In science, the rebuttal is "No, I can't prove that, science depends falsification rather than proof. Can you suggest a way I could falsify it? If not, then I'm going to get on with my work because it doesn't make a difference to my field either way"
We who? Don't "we" also need a grouping to make it even clearer that some fields can't produce any falsifiable theories if other fields don't produce at least some unfalsifiable theorems? A terra firma of sorts.
It's like a dependency graph. Or something.
Your insistence on "making a difference" seems to echo the sentiment of many pragmatists:
It is astonishing to see how many philosophical disputes collapse into insignificance the moment you subject them to this simple test of tracing a concrete consequence. There can be no difference anywhere that doesn’t make a difference elsewhere – no difference in abstract truth that doesn’t express itself in a difference in concrete fact and in conduct consequent upon that fact, imposed on somebody, somehow, somewhere, and somewhen. The whole function of philosophy ought to be to find out what definite difference it will make to you and me, at definite instants of our life, if this world-formula or that world-formula be the true one. --William James
Does falsifiability make any difference? If something is only falsifiable in principle (e.g in theory), but not in practice then is it really falsifiable? On pragmatism - it's not a difference that makes any practical difference. And yet you insist on differentiating. Why?
Is "All humans are mortal." falsifiable or unfalsifiable?
It sure is falsifiable in theory, but unfalsifiable in practice. Any living human is potentially immortal until they actually die.
Any running process is potentially non-halting, until it actually halts.
If falsifiability doesn't make a difference in practice (and it doesn't!) then I guess we can all get on with whatever scientific discipline we are busy practicing.
So, I'm going to carry on my life knowing at least one unfalsifiable scientific truth: the theorem known as The Halting Problem.
It's not even wrong, because it's right.
Anybody who insists the Halting Problem is falsifiable (even in principle) is welcome to solve it in principle.
> Don't "we" also need a grouping to make it even clearer that some fields can't produce any falsifiable theories if other fields don't produce any unfalsifiable theorems?
Sure. And I suspect a subset of pure mathematicians would want terminology to make clear that they produce theorems out of intellectual curiosity rather than because they have any regard for whether those theorems can be applied by other fields. Fortunately we can categorize things in multiple ways. I'm open to suggestions on the semantics, but something more widely understood and less clunky than my own theorem/theory-producers would be good! Perhaps "Natural Sciences" or "Empirical Sciences" might be more specific terms for fields that produce theories, if you like.
I differentiate simply because seems possible to do so. And as I said, because it's worth considering whether different processes and cultures are useful. I'm intrigued as to why you object so strongly.
I am afraid my intellect isn't quite up to the application of scientific principles to the philosophy of science itself this morning. I'll have to think harder about whether that's even a valid thing to do.
I don't think you've shown that falsifiability makes no difference in practice. The fact that it's possible to come up with some borderline or problematic examples (which themselves aren't terribly practical) doesn't mean it's not a useful criterion for a scientific theory. Falsifiability is a valuable filter for ideas that the natural sciences are not able to speak to. String theory has been criticized as unfalsifiable. I think a good string theorist would accept that it's a serious accusation that requires an answer.
To be honest I'm quite happy to say "All humans are mortal" is not a well-stated scientific theory. "Human lifespan is limited to 180 years" is better, as it may one day be falsified.
It's pointless to speak of usefulness without specifying a utility function.
It is just as possible to differentiate as it is to integrate.
If it is determined a priori that unfalsifiable propositions are not useful, then knowing the result of the Halting Problem is not useful. Isn't that silly?
I strongly object to categorizations which discriminate against valid science (knowledge? truth? understanding? reasoning? Useful facts?). Is all.
The human process of trying to udnerstand reality is continuous, not discrete, so it's silly to reason about it in terms of discrete categories. It necessarily leads to confusion; and the sort of gatekeeping and self-justification Carl Sagan is guilty of.
Science benefits much more from being defined too broadly; than being defined too narrowly.
I'd rather be too permissive then ignore the junk; than be too restrictive and never even encounter good ideas which were erroneously discarded as junk.
I don't think I said unfalsifiable propositions are not useful! A proven theorem is sacred!
Of course, until the laws of thermodynamics are revised we can provisionally say that all programs actually running in nature will indeed stop at some point, no matter what is proven about idealized Turing machines.
And before I'm misunderstood. There are many ways the laws of thermodynamics can be tested. This prediction, unfortunately, cannot be tested. But it is a predicted consequence of the simplest known theory that explains of all sorts of observations about thermodynamics. Which is the limit of what the natural sciences aim to do here. Provisional truth based on observation vs. proven truth based on stated axioms.
I am explicitly not claiming that one truth is to be valued more than the other. I honestly don't think that. Merely noting, again, that the distinction is there to be made. I may be "discriminating between", but I'm certainly not "discriminating against".
It may or may not be a continuum. Curious researchers on both sides can certainly be informed and inspired by each others work, and can use the same techniques and tools. But even if only as an academic exercise can't we describe these two modes of discovery. And isn't it worth being clear about their respective limits?
You seem to be missing the point. Ignoring for a second that the laws of thermodynamics themselves are based upon a handful of idealizations (the idealization of "thermal equilibrium", the idealization of "perfectly isolated system", the idealization of "perfect zero)...the laws of nature are encoded as formalisms/equations. Symbolic computations.
If you have no formalisms you can't compute any consequences - there is nothing to test. You have no science.
So treating Mathematics and science as "separate disciplines", even though they function as one symbiotic whole - that's the conceptual error.
Interesting. I actually would group cars and engines separately. I'm always fascinated to get a peek at a different way of looking at things, thank you.
> How can we disprove the hypothesis “If we can’t disprove it - it isn’t science.”?
You can't. That's an axiom. Welcome to Philosophy of Science.
Science, at bottom, has some axioms.
1) Cause and effect
The same causes always create the same effects is an axiom. We assume that the God or the Devil don't change all the rules every other Thursday. If there is a being who arbitrarily shifts the rules, science loses a lot of its predictive power. Science will adjust to that, but it makes science much less useful.
2) Continuity
The rules "today" are the same as the rules "yesterday" are the same as the rules "tomorrow". The rules "here" are the same as the rules "there".
This is a little spicier as we do try to test that the rules haven't changed. We try to test whether or not the fundamental constants have shifted with time, for example. We try to see if things are behaving the same in our galaxy are the same as in otehr galaxies.
In fact, practically everything which defines "science" is about the ability to predict and quantify.
A) Side: "math" is NOT "science". Math, while certainly falsifiable, is neither quantitative nor predictive.
This, in fact, has provoked quite a bit of discussion: See: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Is it the "philosophy of science"?
What is now called "science" was once called "natural philosophy"?
Maybe it's the science of science?
Maybe it's the philosophy of philosophy?
Maybe it's the science of philosophy?
Maybe it's the philosophy of science?
Maybe it's all the same under naturalism?
Studying science (itself a natural process) using our computational understanding of what a "process" is and does sure fits the Oxford definition of "science".
Firstly there's no need whatsoever to be rude even if I'm wrong. It doesn't help the discussion and isn't nice. You also don't know anything whatsoever about what I do and don't know about maths or the definitions of words.
Secondly prospective theorems are absolutely falsifiable. Since a theorem is a statement that has been proven to be true yes they are unfalsifiable by definition - they have already passed that test. That doesn't really generalise to any sort of meaningful statement about the falsifiability of maths. Saying theorems are unfalsifiable is equivalent to saying "True statements can't be proven false". Well, yes.[1]
ie If I say Sean Hunter's theorem is that if you take a triangle with arbitrary sides a b c and angle opposite a of theta that
a^2 = b^2 + c^2 -42 b c cos theta
that statement is absolutely falsifiable (and false), which you can establish with basic geometry and trig[2]. When you demonstrate it not to be true it is not a theorem, so I was wrong to call it that. That is a demonstration of how maths is falsifiable.
[1] Even so it's often possible to make progress via proof by contradiction - showing that if this theorem were not true something else which we know to be true would be false. But in most of my maths books proving all of the theorems is the norm, so they are for sure falsifiable while you are trying to establish whether or not they are theorems.
[2] Drop an altitude from one of the angles at b and c and then use pythagoras and a bunch of cancelling. You will prove that a^2 = b^2 + c^2 -2bc cos theta of course. My statement is only true if a is the hypotenuse of a right triangle meaning cos theta is zero and my incorrect coefficient doesn't matter.
I merely attempting to reciprocate/mirror your tone. You are the one (self)identifying it as "rude".
I have some idea about what you do and don't know about definition and definability (in general) given the words you've said so far and the way you've used them.
Prospective theorems are not theorems until a proof is presented. At which point they become retrospective theorems.
All that "falsification" and counter-examples prove is that the so-called "proof" of a "theorem" wasn't. If you have indeed provided a counter-example that's a proof of negation which raises questions: what was wrong with the original "proof" of the theorem? Since proofs are programs - there must have been a bug in the proof. Better type-check that proof/program...
The presence of a counter-example to Sean Hunter's "theorem" simply demonstrates that it's not a theorem. It's a misnomer. Theorems are exactly those Mathematical stataments for which no proof of negation exists.
You seem to be presupposing some particular kind of mathematics. I am talking about all possible Mathematics in general; of which the particular Mathematics you are currently using is just one particular instance. A historical and cultural coincidence.
There's a Mathematical paradigm in which proof-by-contradiction is a valid proof method e.g mathematics founded upon classical logic.
And there's a Mathematical paradigm in which proof-by-contradiction is not a valid proof method e.g mathematics founded upon intuitionistic logic. This is basically what we call Computer Science. It has fewer axioms than Classical Mathematics (e.g the axiom of choice is severely restricted) and so it's a much stronger proof-system. You could even say Intuitionistic Mathematics (which is basically CS) is "more foundational" (it is much closer to the foundations?) than Mathematics.
The fact that you are admitting proof-by-contradiction in your methodology tells me about your choice of foundations, but so what? There's a foundation which axiomatically pre-supposes choice; and a foundation which doesn't.
And in the foundations where choice is not axiomatic "proof" by contradiction is not a valid proof.
The reasoning goes something like this:
1. Choice implies excluded middle.
2. Excluded middle implies all proposition are either true or false.
3. Excluded middle implies that proof by contradiction is valid.
Rejecting 1 results in the rejection of 2 and 3 also.
> Prospective theorems are not theorems until a proof is presented. At which point they become retrospective theorems.
...
> The presence of a counter-example to Sean Hunter's "theorem" simply demonstrates that it's not a theorem. It's a misnomer.
That is what I said. I showed a mathematical statement and I showed how you could falsify it. Since you said "mathematics is not falsifiable" I have shown your statement is not true. Do you see why?
You were the one who decided that the distinction between conjectures and theorems is important. I have now shown two examples of mathematics that was falsified.
Unless you're trying to say neither me nor Euler was a mathematician in which case we can agree about me but not about Euler.
Your failure to understand what I am saying is abysmal.
>That is what I said. I showed a mathematical statement and I showed how you could falsify it.
>Since you said "mathematics is not falsifiable" I have shown your statement is not true.
You have taken it upon yourself to interpret "Mathematics is not falsifiable" as broadly as needed in order to confirm your own biases; and then proceeded to attack a strawman instead of a steelman. That's the lack of charity...
>You were the one who decided that the distinction between conjectures and theorems is important.
And you were the one who decided that it isn't; so you falsely equated them.
What you have demonstrated is the falsification of the statement "X is a theorem"; not the falsification of "mathematics is not falsifiable." - a hasty generalization fallacy.
Which doesn't demonstrate anything of import or relevance whatsoever. Obviously a non-theorem is not a theorem. This is no more interesting than demonstrating that non-Mathematics is not Mathematics.
This in no way diminishes or falsifies my own claim that theorems are unfalsifiable! And neither is Mathematics.
Because if you do falsify it - then it was never a theorem. By definition. Theorems are true, not false. A false theorem is a contradiction in terms. A misconception. An error in reasoning.
Maybe Euler wasn't a Mathematician either. Who knows? Those sort of questions are undecidable.
"[Aristotle] claims that each science studies a unified genus, but denies that there is a single genus for all beings". You're applying tautology without really understanding the construction of your own question.
The study of being qua being; or science qua science; or
mathematics qua mathematics; or X qua X for any X.
Metaphysics.
Or as it is commonly referred to in computer science: function self-application. One example of which being the Y combinator (as in the name of this very forum).
I am applying a tautology in exactly the mathematical sense of a tautology; and I understand my construction just fine.
Had you been more charitable you would’ve addressed my argument; not your strawman of my argument.
I'm charitable by trying to teach you with examples.
> Or as it is commonly referred to in computer science: function self-application
No, that's recursion, not metaphysics.
Is computer science the same as programming, no. Computer science is the study of programming, not programming. You learn this in your first year of CS.
If you're smart enough to _really_ understand what a Y combinator is, this should be a piece of cake.
I am struggling to spot the charity in all your condescension.
metaphysics
/ˌmɛtəˈfɪzɪks/
noun
the branch of philosophy that deals with the first principles of things, including abstract concepts such as being, knowing, identity, time, and space.
First principles? Like logical/mathematical axioms? Sprinkle abstraction. Identity? f(x) = x ?
Time? Space? Spacetime? Minkowsky space?
On a fuzzy-match that sounds ludicrously similar to the sort of stuff the formal sciences concern themselves with. Almost as if the distinction between science and philosophy is non-existence given the demarcation problem.
What makes this assertion? The literal definition of the term.
Are you the kid who thinks he's edgy by saying in philosophy class: "It depends on the meaning of the word 'X'" every time someone tries to explain X to you?
and you hit one of the main objections to the theory of falsifiability as the criterion of science. There are also other more serious ones, like the obvious fact that actual science does't seem to actually work this way. The idea is more to explain observations in a coherent way rather than to be falsifiable for example. One example is the big bang theory being proposed by a Catholic astronomer who didn't like the then prevaling idea that the universe did not have a beginning or end because it went against his religious beliefs. Or Kepler looking for planets at locations in accord with musical harmonies because he though it was consistent with the existence of a God
> One example is the big bang theory being proposed by a Catholic astronomer who didn't like the then prevaling idea that the universe did not have a beginning or end because it went against his religious beliefs.
That’s simply not true.
Fr. LeMaitre developed the theory to explain observed red shifts of galaxies (deriving Hubble’s Law prior to Hubble.) He felt his theory (and science in general) had no connection or contradiction to his faith.
> One example is the big bang theory being proposed by a Catholic astronomer who didn't like the then prevaling idea that the universe did not have a beginning or end because it went against his religious beliefs.
This actually came from the skeptics [0]. They were unwilling to believe a Catholic priest proposing a scientific theory too similar to his religious beliefs, about God creating the whole universe in an instant.
When the cosmic background radiation was discovered in 1964, the Big Bang was accepted by (mostly) everyone.
The reason that falsifiability is a core requirement of science is because if there is no way a proposition can possibly be falsified, then there is no way to objectively assess whether or not it is true.
This is not to say that the proposition is false. It's possible that things can be unfalsifiable and true nonetheless, but those things would still exist outside the range of the scientific method (at least until/unless our understanding of reality expands enough to devise a test). That's an intentional trade-off, in order to gain greater confidence in the truth of the things we can test.
Personally, I am weary of the notion of “actual science” since science is not a well-defined term. The demarcation problem isn’t solved; and philosophers like Fayerabend in his book “Against method” suggest that science is more of an anarchic enterprise than any particular set of methods.
Take any criterion and apply it too strictly and there is some scientific discovery/progress in history which violates the rules and wouldn’t pass for “science” given any definition…
Take any given methodological approach - and you will always find counter examples in scientific history.
sure, but I mean, it's pretty hard to call flat earthers or proponents of voodo unscientific if we have to admit that we haven't solved the demarcation problem. Also more importantly for Popper, he wanted to oppose communists' ideas of "scientific materialism."
There does seem to be this thing that good scientists are doing. Popper did seem to touch on some good aspects of it, like the willingness to be proven wrong.
I think maybe that's the part Popper got right, maybe Science is about an unbiased search for knoweldge with no other agenda other than a genuine curiousity. And maybe that's why demarcation is so hard, it's hard to tell a person's motives.
I donno, just throwing stuff out there. . . Still I mean at least we have a test that communists obviously fail which should make Popper happy.
I mean, the non-schizo proponents for flat earth does approach it with scepticism. It's just that the their required level of proof are unreasonable. Any experiment, no matter how genuinely designed, is exempt from flaws. Science works because the detractors doesn't have the energy to waste decades in the academic apparatus, unlike true curiosity.
> … he wanted to oppose communists' ideas of "scientific materialism."
> … that’s the part Popper got right, maybe science is about an unbiased search…
> …at least we have a test that communists obviously fail…
i could be misunderstanding what you’re implying and if so apologies, but Popper wasn’t some anti-communist nutbag, in fact, if he “wanted to oppose” communism, that would have been fundamentally counter to his ideal of keeping things “unbiased”
Popper was very open how much he admired Marx, he even tended to agree with Marx’ analysis of capitalism. where he disagreed was that 1) we were destined to be slaves to be servants if we 2) don’t have violent revolution.. He was quite clear that the state should absolutely be heavy handed to protect the lower classes from the wealthy’s constant tendencies to abuse the poor. Again, he agreed with much of Marx’s writing but where Marx thought it would require violent revolution, Popper believed we could use other methods such as “social engineering” to counter the rich. He was also concerned that so many people agreed about violent revolution being the only way out. He wrote about this admiration for Marx quite a bit:
> …a grandiose philosophic system, comparable or even superior to the holistic systems of Plato and Hegel. Marx was the last of the great holistic system builders.
and
> [Marx] made an honest attempt to apply rational methods to the most urgent problems of social life… His sincerity in his search for truth and his intellectual honesty distinguish him…
Popper was concerned that under unrestrained capitalism:
> ..the economically strong is free to bully one who is economically weak, and to rob him of his freedom,… Those who possess a surplus of food can force those who are starving into a ‘freely’ accepted servitude.”
Philosophy Now sums it up well, “Throughout his scrutiny of Marx, Popper treads a thin line between admiration and apprehension.” [0]
again, apologies if i misinterpreted what you were implying, just wanted to clarify that Popper wasn’t some kind of nutbag mccarthy style rabid anti-communist or whatever. he just thought we could “social engineer” our way away from psychotic nationalism and unchecked capitalism rather than requiring full blown revolution.
He wrote an autobiography - he was a young man who was a communist because he believed in scientific materialism. He later recanted after some of his friends were shot and killed by the police.
Popper said he noticed that scientific materialism proposed by communists or Freud's theories was very different from the lecture he heard by Einstein - Einstein looked more like science.
Communism whatever anyone thinks about it is obviously not science. They claimed to be science at first and proposed scientific materialism as the future.
Today even communists seem to have recanted this idea instead preferring to criticize capitalism and present themselves as the only alternative. We all know today it's not science.
I don't want to debate politics only to say Communism was never science, it's politics - Popper noticed that quickly and it was one of the imputus for his ideas based in his own autobiography
He also dedicated his book the poverty of historicism to the countless men and women who lost their lives to fascism and Communism and their false belief in historical destiny
Open society and it's enemies also contains a long critique of Marx and the idea that history follows certain laws that must play out a certain way.
The problem with all ideas is always their reification. Computers may be deterministic, but humans aren't. The same software/idea produces wildly different understandings; and behaviour in differnt humans.
What always seem like great ideas in theory, innevitably has to cope with the (mis)understanding; (mis)interpretation; and (mis)application of said idea by the mass population.
Because they have worked over time, empirically as opposed to a lot woo woo stuff proposed by religion, spirituality, metaphysics, mentally ill, etc. which can never be disproved but which really don't have any value in those areas where we apply science like technology and attempting to understand natural processes
You seem to be speaking from a place of greatly diminished self-awareness.
Notice how you are constantly appealing to abstract unobservables to make your claims. No shame in that - all science does it. Quantities, numbers, fields, processes etc. etc. etc.
That is precisely the metaphysical woo woo you are busy criticising. Formalism is all about turning that woo-woo into well-defined concepts.
What's a "process"? Show me one.
Only way I know how is to give you more metaphysical woo woo.
The central dogma of computational trinitarianism holds that Logic, Languages, and Categories are but three manifestations of one divine notion of computation. There is no preferred route to enlightenment: each aspect provides insights that comprise the experience of computation in our lives.
If you want to believe in fairy tales then enjoy them. I prefer materialism. We will never agree on this. You can't prove a God exists, so I simply don't care about the topic other than how it affects civilization negatively by promoting magical thinking and religious fanaticism/intolerance. I tolerate people who are religious, I don't wish them any harm; the opposite is quite untrue for a large proportion of the religious world for atheists/"infidels".
The deep irony in valuing matter more than valuing values is never wasted on me.
You still haven't figured out that "matter" is yet another man-made concept? An abstract idea. A collective noun. Itself a (very useful) "fairy tale".
A substance which posesses "rest mass" in a universe where nothing is ever at rest sure sounds like magical thinking (to me). And what do you even make of point-like particles in physics? They have no volume - so they are not matter. And what about anitmatter?
You haven't yet come to the self-realization that you are committing the reification fallacy by promoting a man-made concept to a totalizing/generalizing/all-encompassing ontological status.
Matter is your God. It's the abstraction you worship.
You are right in saying that we'll never agree; for if I were to agree with you I too would be wrong.
A. I am not presenting arguments. Only observations and inferences based on my understanding on the evidence.
B. If you declare my “argument” subjective (and therefore false for you, but true for me) you agree with my overall claim Q.E.D
C. Is it this one then? How would you prove this?
D. It is mighty presumptuous of you to assume that I subscribe to classical logic; or even a consistent logic for that matter. Or that I subscribe to the same logic at different times of day.
E. I am not impressed neither by your religion; nor by the writings of your prophets. Nullius in verba
> I am not presenting arguments. Only observations and inferences based on my understanding on the evidence.
That is what counts as an argument! An argument is a technical term from logic and includes inferences and observations (observations are single step inferences). My bad on using logic jargon, but yes, inferences/arguments/proofs all apply here. So what system are you presenting this inference in? Is that objective or subjective?
> B. If you declare my “argument” subjective (and therefore false for you, but true for me) you agree with my overall claim Q.E.D.
No, the real beauty of subjectivity is that it allows me to disagree at any level. And I disagree with you on your point above, invoking the full power of subjectivity.
In fact, let me do 100% subjectivity on the whole set of comments here, and declare all your statements false for me.
(Also, the above is proof by cases. And step B/C's conclusions alone don't go out to the outer level alone as you seem to assume. You have to combine them both).
Now, I should be getting paid for doing a logic 101 in the comments ;)
You can’t tell if my inferences are objective or subjective? Why does the distinction even matter then?
The more of my comments you declare false - the more evidence you are providing in support of relativism. It is a peculiar way to agree to my point (via disagreement).
Is that what you call “logic”?
It looked like you were making up the interpretation as you go along…
That's no longer the halting problem: formally, the input to a halting oracle is
an index for some fixed choice of admissible numbering of the set of Turing machines, meaning one that can be computed from the standard numbering induced by some universal Turing machine. Your encoding is not admissible.
Just your luck. Under Univalence identity is equivalent to equivalence and it's computationally decidable.
So you should be able to produce a decider which determines whether any alternative encoding/representation is equivalent to the halting problem; or not.
Formally speaking Turing machines are formal language recognizers, so in which formal language is the formal statement of the Halting problem expressed in?
I'd also like to see the decider for "admissible" vs "inadmissible" encodings. Input validation is an Interesting problem-domain for sure.
(Of course, this is all for the sake of maximum pedantry)
> Just your luck. Under Univalence identity is equivalent to equivalence and it's computationally decidable. So you should be able to produce a decider which determines whether any alternative encoding/representation is equivalent to the halting problem; or not.
Moving to a constructive setting lets you say things like "all functions are computable" because it has a restricted notion of function. It does not give you any new information about classical objects.
Sure, whatever - the point is that they're different objects, and results about one are not results about the other.
> What do you mean by “restricted” when you are characterising a function?
I mean whatever the word "function" means in a given setting. A classical function X -> Y is a relation such that if `(x, y1)` and `(x, y2)` hold then `y1 = y2`. A function in intuitionistic type theory is a well-typed lambda term. A function in the categorical semantics of a type theory is an exponential object. And so on.
> Show me the decider… for “classical” and “non-classical” objects.
No such thing: it's a metatheoretical judgement, not a theorem. Same story as type errors: within the language, `stringToUpperCase (5 :: Int) :: String` isn't a false statement, it's just inexpressible nonsense. There is no such object as `stringToUpperCase 5` and so nothing can be said about it internally. When we talk about it, we're talking, from outside the language, about a syntactic construct.
> That is the definition of information; is it not? The answer to a yes/no questions
No. Self-information of a given outcome with respect to a random variable, which is probably the most common sense of the word, is the negative log of its probability. Shannon entropy, also often called information, is the expected self-information of a random variable. Mutual information is the KL divergence of a joint distribution and the product of the respective marginals. There are other notions.
>Sure, whatever - the point is that they're different objects, and results about one are not results about the other.
Sorry, I don't understand what you mean by "same" and "different".
By "same" do you mean =(x,y).
And by "different" do you mean ¬=(x,y)
Or do you mean something like same(x,y) = { 1 if ??? else 0 }
>A classical function X -> Y is a relation such that if `(x, y1)` and `(x, y2)` hold then `y1 = y2
You seem to be confusing syntax and semantics here, and the infix notation isn't helping...
What does =(y1, y2) mean?
What does =(x,x) mean?
>No such thing: it's a metatheoretical judgement, not a theorem.
What do you mean? Judgments are first-class citizens in Univalent Mathematics. a:R is a judgment that object a is of type R. This literally means "a proves R", and the particular expression "first class citizen" has well-understood meaning in Programming Language design ( https://en.wikipedia.org/wiki/First-class_citizen ).
>`stringToUpperCase (5 :: Int) :: String` isn't a false statement, it's just inexpressible nonsense.
So I must be a miracle worker then? Expressing the inexpressible nonsense...
In [1]: def stringToUpperCase(x): return(str(x).upper())
In [2]: stringToUpperCase(int(5))
Out[2]: '5'
>No. Self-information of a given outcome with respect to a random variable, which is probably the most common sense of the word.
Speaking of randomness in a classical setting, this function exists, right?
No, the comment above mine is the one being pedantic. We can absolutely talk about physical correspondence of mathematical concepts, even though there are multiple equally good logical systems for describing them.
That is how they are defined in set theory based math. The mathematical definition is not the only meaning of a word. When when start to talk about the physical world, we need additional concepts. You are welcome to read the wikipedia page about correspondence theories of truth.
The fact is you are talking about the meaning of words. Be they English words; or Mathematical words.
If you are going to talk about the correspondence theory in the same breath as you are talking about any language - you need to solve the symbol-grounding problem.
What function/mechanism/relation (or if you don't like any of those words - pick your own) grounds symbols?
I have no idea what your metric for "strangeness" is.
Using similar reasoning we can also assert that "The speed of light is objective" is not an objective claim.
And we can further assert that both the inner and outer statements are true without arriving at a contradiction.
It doesn't take a genius, merely a very thick skin and a grasp of contextuality, to hold this perfectly reasonable conclusion in a society dominated by naive understanding of non-contradiction.
Objectivity, being an unattainable philosophical ideal, it doesn't prevent us from using the term in more pragmatic/cultural/inter-subjective sense. A white lie - if you will - that only a determined pedant would scrutinize to such philosophical extent.
Just as well, such overt pedantry deserves mockery and contempt.
You mean other than the decades of connotation lost by switching terminology and the innevitable miscommunication that will ensue?
There's nothing wrong with switching the term "red" for the term "carmine", "scarlet" or "ruby" either.
They are synonymous on paper, but the latter simply doesn't evoke the same recall in people's heads.
You are welcome to run the experiment yourself. Go and ask people if they normally stop at (carmine|scarlet|ruby) traffic lights and observe the ensuing confusion at your question.
Then there is the emergent discrepancy in terminology between legacy systems and current RFCs.
I don't find this at all convincing. The terms in question here don't need to evoke connotation, they are labels in a technical system. It is very straight-forward to re-label things. Documentation can easily cover the change.
You're generalising far too much. Of course replacing "red" with "scarlet" generally would make a difference in understanding, not least because "scarlet" is more specific than "red". But that doesn't at all speak to what is going on in this RFC, which is already technical documentation and very specific. If you want to talk about connotation, the entire point here is to get rid of terms that connote horrific crimes. Maybe not to you, but clearly to enough people that this change has been made.
I'm not a fluent German speaker, so I don't know. But I expect not: in this context it is contrasted with "follower" rather than anything more historically evocative. The relationship between a "leader" and a "follower" generally connotes something voluntary and more-or-less mutually beneficial. I am surprised I'm having to spell this out!
Somebody quite recently said... "You are generalizing too much"
The relationship between slave and master is connotationally identical (to me, of course!) to the relationship between leader (Hitler) and follower (Nazis). Historicaly speaking those relationships had horrific social impact.
I am surprised I am having to spell this out.
I mean, we are talking about connotation here. Why are you trying to tell me how I should feel about words?
Okay, well, you clearly have an unusual interpretation. Enough people agree that leader/follower is more agreeable than master/slave, and even if you don't agree surely you can see where they are coming from. That's part of my disbelief. But you started by trying to argue some general point about using different terms causing some gulf of misunderstanding. Anyway, not much more to say here.
This is some serious cognitive dissonance to force specific language in the name of inclusion, only to them say “you have an unusual interpretation, enough people feel differently”.
First of all, check the usernames, I’m not the person you originally replied to, I’m just somebody pointing out the insanity of your comments.
Second, once again, your cognitive dissonance is showing badly. You’re applying very US-centric culture and forcing it on Europeans. This isn’t about being “in the minority”. It’s pointing out that any non-American can see right through “just how inclusive” you really are.
I'm from the UK, I just happen to agree with the RFC, as (I'm certain) would the vast majority of my peers and co-workers. I'm happy to let any readers of this thread judge my comments as they stand.
Following bad leaders leaves a bitter historical taste in my mouth and is rather insensitive to the feelings of those who fell victim to such attrocities.
Hitler was the leader.
The Nazis were the followers.
It shouldn't be hard to connect the dots.
(also, becuse this is the internet a mention of Poe's is mandatory...)
Alan Turing: The claims made in the Halting Problem is genrally true, and is therefore unfalsifiable even in principle.
Carl Sagan: Propositions that are untestable, unfalsifiable are not worth much.
All computer scientists in synchronized act of distributed consensus: Bullshit.