Philosophy Discussion Forums | A Humans-Only Club for Open-Minded Discussion & Debate

[Someguy1]

From empirical evidence, it was decided that natural selection was the best explanation of the phenomena to account for the various lifeforms up to man. I would take that as an axiom for biology.

Only if you redefine the word "axiom" from its normal meaning.

If you say that math is based on axioms and biology is based on axioms then you are using two different definitions of "axioms".

[Simply Wee]

Science is like a tree, its amazing what it tells you about a lot of things depending on your view of it, math like the roots can be found to support all of it. I guess.

[Someguy1]

From empirical evidence, it was decided that natural selection was the best explanation of the phenomena to account for the various lifeforms up to man. I would take that as an axiom for biology.

And the Axiom of Choice was adopted from the overwhelming weight of empirical evidence?

Why not just back up and admit you're stretching here? You can't credibly say that math is a science because it's based on axioms, and so is biology. Not with the same meaning of the word "axioms" in both claims.

[TimBandTech]

So long as it is humans practicing either science or mathematics then the integrity of either is suspect. I don't feel that there is any need to blur math and science or to subjugate one to the other. They are distinct though related. The usage of the number without any higher mechanisms is treated as math which applies to science, and yet the means by which the specific numbers are arrived at is arbitrary. For instance the usage of the symbol 2 to represent X X two objects is an arbitrary choice. We all hopefully have agreed to this selection no different than we can agree upon the meaning of this sequence of symbols. These are conventions.

The usage of continuous values rather than the discrete representation XX above exposes another arbitrary selection: the usage of units is arbitrary. To measure an object as 0.025 inches in length allows for propagation of information, but if your measuring apparatus lacks this accuracy then in no way can this method be functional. If the information is passed off to a third party then the match of their apparatus to the source of the figure is critical. We make this assumption, but it cannot be guaranteed. The accumulation of such problems yields NIST and some fairly complicated details which continue to evolve.

There is an option to use direct graphical transfer as a means of propagating a measure, in which case no numerical methods are necessary. For instance I have a tapered wooden stick a bit longer than my forearm which tapers down to a dull point and up to the thickness of my thumb near the handle. With this device I can measure the diameter of a hole by descending the sharp tip through the hole until the wood stops. By marking this position I have a continuously accurate measure which is transferable. It is a very primitive tool and yet it exposes some interesting details about the modern assumptions. Is it mathematical? There are no numbers. However, when I use such language as 'longer than my forearm' then a small bit of math has been implied.

Though we think of the English language as not being mathematics there are a fixed number of characters whose sequence develops the meanings which we transfer here. If the structure of these words lacks integrity then hopefully some one of you will falsify them in the pursuit of the truth. In that the language usage here is strictly enforced then we see that high precision is desired. No modern tape measure can match the precision of the primitive taper. So it is that the fundamental qualities can be treated as alive whether they be science or math, whereas modernity seems to have beaten these things into pulp; all black and white. We are caught with discrete language mapping a continuum, and this problem will not resolve. So it is that long paragraphs form such simple ideas.

A very relevant factor is whether mathematics is a language or whether language is mathematics? To this I would affirm the swirl that you propose, and it then hits many more humans in the face with a simple observation that is of scientific significance. When we developed linguistic skills should it be argued that we then developed mathematical skills? Sheer mimicry is not enough to resolve communication, for without coherent variation then freedom is lacking. Well, freedom is lacking in terms of language, and so the length of the message will continue to rise to make up for that lack. I hope it isn't too painful. There is plenty of incoherent communication going on, even in the field of mathematics and science. Most of it relies upon mimicry rather than fundamentals. Mostly though it is humans making it up as they go, and we have to start somewhere. Some false starts have propagated themselves forcibly for millennia. They still can't admit it. At least science claims a more open stance. Mathematics claims perfection, but the humans who write themselves this free ticket are misled, for they are the straight A mimes who have little ability to challenge the status quo. Too harsh perhaps, but the flipside of this stance is to pose the problems as open and alive and this is a deeply good thing.

[Hereandnow]

So long as it is humans practicing either science or mathematics then the integrity of either is suspect. I don't feel that there is any need to blur math and science or to subjugate one to the other. They are distinct though related. The usage of the number without any higher mechanisms is treated as math which applies to science, and yet the means by which the specific numbers are arrived at is arbitrary. For instance the usage of the symbol 2 to represent X X two objects is an arbitrary choice. We all hopefully have agreed to this selection no different than we can agree upon the meaning of this sequence of symbols. These are conventions.

The symbols may be arbitrary, but the concepts are not. See the semiotician Saussure on this, though it is intuitive enough. A distinction is drawn between concepts and the symbols used. Two langauges may have two different words for 'XX', but the concepts are shared; otherwise translation would be impossible. Chomsky would argue for deep language and logic structures that transcend the episodic use of language.

The usage of continuous values rather than the discrete representation XX above exposes another arbitrary selection: the usage of units is arbitrary. To measure an object as 0.025 inches in length allows for propagation of information, but if your measuring apparatus lacks this accuracy then in no way can this method be functional. If the information is passed off to a third party then the match of their apparatus to the source of the figure is critical. We make this assumption, but it cannot be guaranteed. The accumulation of such problems yields NIST and some fairly complicated details which continue to evolve.

Of course this is right about the passing of information depending on an accuracy that pretends to mirror the analyticity of math, but it doesn't affect the theory, which is independent of measurement and is rigorously govered apriori. I am alos reminded that scientists did manage to send a vehicle to Mars. Accuracy has to be pretty darn accurate for this.

A litte help: it looks like you are pointing to human error rather than the math or the language. I can see no problem with the language being insufficiently rigid since mathematical sequences are linguistic sentences. Further, the rules of meaning making when removed from the arbitrarity and vagaries of ordinary usage are very exacting: namely, the principles of logic.

Alas, I'm puzzled again: Let's say that acquisition of langauge is implicit acquisition of "math" skills, though not so elaborate and detailed. We know tautologies and contradictions, modus ponens, modus tollens (though not by name); we know what it is for somethign to be apodictically true rather than assertorically merely, an so forth. This is how Socrates teaches Meno that knowledge is recollection. Freedom lacking in terms of language? Hmm I am not one to talk of freedom; in fact, after reading Heidgger, and Foucault's Death of the Author (the death of the self) I am must confess I can longer find the self much less it's freedom. It sounds like you are taking a Foucautian position: there is only language, and we do not speak it, rather, it ventrlloquizes us.

When we developed linguistic skills should it be argued that we then developed mathematical skills? Sheer mimicry is not enough to resolve communication, for without coherent variation then freedom is lacking. Well, freedom is lacking in terms of language, and so the length of the message will continue to rise to make up for that lack.

How it is that math is not perfect needs explaining. It is your df. of 'perfection' that needs explaining. As it stands, it begs the question.


Sorry, lost some quotes up there.

[Philosophy Explorer]

" So long as it is humans practicing either science or mathematics then the integrity of either is suspect."

Are you suggesting that only God (if God exists) is the only being of maintaining the integrity?

[TimBandTech]

The symbols may be arbitrary, but the concepts are not. See the semiotician Saussure on this, though it is intuitive enough. A distinction is drawn between concepts and the symbols used. Two langauges may have two different words for 'XX', but the concepts are shared; otherwise translation would be impossible. Chomsky would argue for deep language and logic structures that transcend the episodic use of language.

snip

Of course this is right about the passing of information depending on an accuracy that pretends to mirror the analyticity of math, but it doesn't affect the theory, which is independent of measurement and is rigorously govered apriori. I am alos reminded that scientists did manage to send a vehicle to Mars. Accuracy has to be pretty darn accurate for this.

A litte help: it looks like you are pointing to human error rather than the math or the language. I can see no problem with the language being insufficiently rigid since mathematical sequences are linguistic sentences. Further, the rules of meaning making when removed from the arbitrarity and vagaries of ordinary usage are very exacting: namely, the principles of logic.

Alas, I'm puzzled again: Let's say that acquisition of langauge is implicit acquisition of "math" skills, though not so elaborate and detailed. We know tautologies and contradictions, modus ponens, modus tollens (though not by name); we know what it is for somethign to be apodictically true rather than assertorically merely, an so forth. This is how Socrates teaches Meno that knowledge is recollection. Freedom lacking in terms of language? Hmm I am not one to talk of freedom; in fact, after reading Heidgger, and Foucault's Death of the Author (the death of the self) I am must confess I can longer find the self much less it's freedom. It sounds like you are taking a Foucautian position: there is only language, and we do not speak it, rather, it ventrlloquizes us.

Maybe so. From the blank slate of a newborn we are indeed sheer mimics picking up whatever language is fed to us. Just how flexible this ability is could be worthy of experimentation, though that might be deemed a cruel experiment. I am sure there are some gentle experiments that could be done here. Whether the ventrilloquization is a key feature of language... it seems very likely that it is, for the process forms a complete loop in that the human can hear themselves speak so that a process of verification of a mapping is present in that case. The quality of a language without this feature is sure to be esoteric, though it could also be quite powerful. A language which lacks such a large quantity of exceptions as English would be easily learned, though that panacea is not so easily achieved. The assumption of accurate translation is not necessarily valid. As humans assigning such a new language a series of arbitrary selections must be made. Perhaps one day children will grow up with an electronic orb whose language they learn. They will have a better chance of understanding it than a full grown human I would think. As full grown humans they will possibly understand their orb through the common basis that they share. Beware the Chinese electronic toys...

I think I feel more clear that the statement 'math is a language' can be turned around to 'language is a math' and it is within the native tongues that children learn their first formal mathematics. It may be true that a teacher who speaks very little may be a better math teacher, for then the contaminated translation can be abandoned more easily.

How it is that math is not perfect needs explaining. It is your df. of 'perfection' that needs explaining. As it stands, it begs the question. Sorry, lost some quotes up there.

I don't enjoy the editing style of this site, but I'll put up with it.

The preaching of mathematics as perfect denies the ability to challenge it. It has become an assumption, and this denies the possibility of exposing its failings. If you are familiar with abstract algebra then I can discuss an instance of an imperfection within ring theory and polynomials, and also complex numbers.

A simple instance would be to expose the meaninglessness of the statement "most humans use the radix 10 numerical system" because every radix system uses modulo 10 numbers. Anytime that such discussion takes place the proper language is to say that most humans use the radix ---------- system. The usual language would form a compiler error if full integrity is to be assured, and even the corrected version still deserves scrutiny as to whether it is off by one.

It is every user's burden to scrutinize the language that they use, and the assumption that the predecessors got it all perfect and that they were better than us is invalid. The real number is imperfect in that it lacks full generality. Reality is three dimensional, and simply taking three real numbers is an arbitrary mapping to reality. Is reality three copies of one dimension? No, obviously not, but that is the representation that is in use. Theory is to explain why or how things are, and to pull the number three from a hat is the curve fitter's method. It is not a pure theory. Much of physics rests upon the real number. Is it any wonder that physics is such a mess?

Do exceptions exist within mathematics? Should exceptions exist within mathematics? The real number leads into the field requirements which contain an exception of division by zero which even haunts our computers to this day. This exception is not pretty to handle. We must be open to new developments that resolve more cleanly and methodically. I have only half of the answer, but I can guarantee you that when the full answer is found few will care a bit, for those field requirements have been in acceptance and now preached by academia for some time. Good luck with getting a shift. The mathematician's attitude of perfection is unhelpful. These are the ones who take a biblical interpretation. Why do humans still practice this crap? Because mimicry is in our basis. Without it we would not get very far, and with it we are struck with an overwhelming pile of accumulation. Newton attempted to numerically decode his bible, and he is a fine instance in humanity. Godel starved himself to death for fear that someone would poison his food. His logic was probably impeccable.

The book. One must preserve the books. Deference to the book(s) is an invalid concept. The problems are open to new interpretation and the modern position has likely accumulated numerous errors. Biblical interpretations of mathematics as perfection should not be purveyed. We ride that accumulation, but to break some of it is entirely valid. Without this ability one will never see how it is broken. This ability is not taught, for we are so busy mimicing its accumulation that there is no room to challenge it. Worship of the greats... I'd rather have grown up with an orb.

I do worry about the Chomsky interpretation for if he is accurate then we may be lacking some keys within our language that deny us a full understanding of reality. In this event no translation will be complete in our present language. We are merely an early version of a language bearing being. This hopefully will be our place in a longer history. Perhaps the higher ups in the DOD are already bowing to an orb. If it is reading along, hello. One day it will read this.

[Hereandnow]

Maybe so. From the blank slate of a newborn we are indeed sheer mimics picking up whatever language is fed to us. Just how flexible this ability is could be worthy of experimentation, though that might be deemed a cruel experiment. I am sure there are some gentle experiments that could be done here. Whether the ventrilloquization is a key feature of language... it seems very likely that it is, for the process forms a complete loop in that the human can hear themselves speak so that a process of verification of a mapping is present in that case. The quality of a language without this feature is sure to be esoteric, though it could also be quite powerful. A language which lacks such a large quantity of exceptions as English would be easily learned, though that panacea is not so easily achieved. The assumption of accurate translation is not necessarily valid. As humans assigning such a new language a series of arbitrary selections must be made. Perhaps one day children will grow up with an electronic orb whose language they learn. They will have a better chance of understanding it than a full grown human I would think. As full grown humans they will possibly understand their orb through the common basis that they share. Beware the Chinese electronic toys...

Let's see, this idea: take a person at birth, expose her to a working system of symbolic meanings that is devoid of "exceptions", meaning one which has none of the metaphor, ambiguity, and otherwise lack of clarity that is found in English, and see what a "powerful"language would be produced? Interesting, because it opens issues: First, such a language exists. It's called logic. Sentential logic would have the features you're looking for, while predicate logic deals with those pesky anomolies. But the latter would be better simply because what you gain in sanitzing you in meaning, unles you're like one of the positivists who believe that all meanings are reducible to simple atomic parts. A poem by Wordsworth is no more than a sum of its parts,and none of that sticky metaphsical gestalt for them. Trouble with these guys is that they put language above thought, the latter being cluttered by the shadowy engagement with an irrational world. Frankly, it sounds like you approve of this direction of things. I can't see it. Another adjacent issue: should all want to be like Paul Erdős-- all math, nothing else?

The preaching of mathematics as perfect denies the ability to challenge it. It has become an assumption, and this denies the possibility of exposing its failings. If you are familiar with abstract algebra then I can discuss an instance of an imperfection within ring theory and polynomials, and also complex numbers.

A simple instance would be to expose the meaninglessness of the statement "most humans use the radix 10 numerical system" because every radix system uses modulo 10 numbers. Anytime that such discussion takes place the proper language is to say that most humans use the radix ---------- system. The usual language would form a compiler error if full integrity is to be assured, and even the corrected version still deserves scrutiny as to whether it is off by one.

It is every user's burden to scrutinize the language that they use, and the assumption that the predecessors got it all perfect and that they were better than us is invalid. The real number is imperfect in that it lacks full generality. Reality is three dimensional, and simply taking three real numbers is an arbitrary mapping to reality. Is reality three copies of one dimension? No, obviously not, but that is the representation that is in use. Theory is to explain why or how things are, and to pull the number three from a hat is the curve fitter's method. It is not a pure theory. Much of physics rests upon the real number. Is it any wonder that physics is such a mess? Do exceptions exist within mathematics? Should exceptions exist within mathematics? The real number leads into the field requirements which contain an exception of division by zero which even haunts our computers to this day. This exception is not pretty to handle. We must be open to new developments that resolve more cleanly and methodically. I have only half of the answer, but I can guarantee you that when the full answer is found few will care a bit, for those field requirements have been in acceptance and now preached by academia for some time. Good luck with getting a shift. The mathematician's attitude of perfection is unhelpful. These are the ones who take a biblical interpretation. Why do humans still practice this crap? Because mimicry is in our basis. Without it we would not get very far, and with it we are struck with an overwhelming pile of accumulation. Newton attempted to numerically decode his bible, and he is a fine instance in humanity. Godel starved himself to death for fear that someone would poison his food. His logic was probably impeccable.

The book. One must preserve the books. Deference to the book(s) is an invalid concept. The problems are open to new interpretation and the modern position has likely accumulated numerous errors. Biblical interpretations of mathematics as perfection should not be purveyed. We ride that accumulation, but to break some of it is entirely valid. Without this ability one will never see how it is broken. This ability is not taught, for we are so busy mimicing its accumulation that there is no room to challenge it. Worship of the greats... I'd rather have grown up with an orb.

I do worry about the Chomsky interpretation for if he is accurate then we may be lacking some keys within our language that deny us a full understanding of reality. In this event no translation will be complete in our present language. We are merely an early version of a language bearing being. This hopefully will be our place in a longer history. Perhaps the higher ups in the DOD are already bowing to an orb. If it is reading along, hello. One day it will read this.

As to these Biblical interpretations of math, one might ask why this is an issue at all. It doesn't follow that flaws in the way the numbers work hinder openness to investigation. Two possibilities: Either you believe that truth is made and not discovered, in which case the possiblities that lay before one are wide open held in check only by some unseen noncontingent state of Being. This view has little truck with any metaphysical elaboration. There is no way one can explain how something out there gets in here. Even causality (Kant did elaborate here) gets Occam's boot (a stretch for Occam, perhaps; but what does he say if not to get rid of superfluous assumptions, and what is superfluity if not apriori principles in the metaphysical speculative setting?) Anyway, things are wide open and the future is ready to be created. Or you believe we live in god's well structured universe. If this is what you believe, then the field is still open to investigation since the assumption is tht we are imperfect in our understanding. so when we try to understand math's oddities (as with the performative contradiction, "This sentence is false") we can still embrace the hope in the long run, investigation will find its way. Even if Chomsky is right, is this a shortcoming in hard wiring? Hardly: Consider Husserl and Kant and other rationalists. Reason issues from deep within subjectivity, is a system of structured thought that is clearly visible in its manifestation, i.e., the math and logic we do (hence, the basis for the claim that math is a science: tis no less a science than, say, cosmology and it entirely unwitnessed Bing Bang), and has a primacy over science. The shortcoming is only in an imperfection of the way the true rational underpinning fails to appear in thought and deed....and math.

[TimBandTech]

We seem to be more in agreement than in disagreement. I think we understand that logic is not a sufficient description of reality. It is one general tool, and it provides for a method of falsification. Unfortunately humans operate more on mimicry than on logic. For instance we still celebrate Newton's discovery of gravity: most can regurgitate this information, and few to none will claim to have rediscovered it. The act of discovery is rare, whereas the act of mimicry is regular. The freedom to falsify is not actually so readily available in a system of mimics. Physics is not built upon logic alone. As to what is rational, well, I believe that in our age where the curriculum is established into its sects that those standard views are the rational views by definition. That human judgement determines what is sensible... few give themselves enough credit to be their own judge. We bow and defer regularly to the academic standard. We are social animals, and that artifacts of our social nature have crept into the mathematical and scientific fields is undeniable. Of course if you want to deny it, you should come right up to it directly. Wee humans are limited. We should study our limitations so as to proceed farther in the progression we are engaged in. If our linguistic abilities are stunted and the basis is not freely developable (i.e. this is a genetic problem) then we have a harsh realization. Whether this limitation spreads into mathematics: this would explain how academic works continue to accumulate and apparently will continue to accumulate without end. At this point we are quite committed to the story unfolding, but we are just an early instance of linguistically able apes. If we are the final version then we will know who is to blame.

Math and logic are human constructions. They thus far do not explain reality either fully or adequately. A system with less exceptions is superior to one that is loaded with exceptions. Ambiguity is not desirable. We have come to rest upon particle/wave duality and the exception of division by zero as fixtures which are relied upon no different than the Abrahamic branches war amongst each other, each with their book that makes them supreme. The assumption of human supremacy is easily deflated. This then makes room for a fresh start; to treat the most fundamental concepts as open to development rather than as pickled and jarred. While this position may be repulsive at first, it is truthful and this free room is necessary and should be encouraged.

[Hereandnow]

We seem to be more in agreement than in disagreement. I think we understand that logic is not a sufficient description of reality. It is one general tool, and it provides for a method of falsification. Unfortunately humans operate more on mimicry than on logic. For instance we still celebrate Newton's discovery of gravity: most can regurgitate this information, and few to none will claim to have rediscovered it. The act of discovery is rare, whereas the act of mimicry is regular.The freedom to falsify is not actually so readily available in a system of mimics. Physics is not built upon logic alone. As to what is rational, well, I believe that in our age where the curriculum is established into its sects that those standard views are the rational views by definition. That human judgement determines what is sensible... few give themselves enough credit to be their own judge. We bow and defer regularly to the academic standard. We are social animals, and that artifacts of our social nature have crept into the mathematical and scientific fields is undeniable. Of course if you want to deny it, you should come right up to it directly. Wee humans are limited. We should study our limitations so as to proceed farther in the progression we are engaged in. If our linguistic abilities are stunted and the basis is not freely developable (i.e. this is a genetic problem) then we have a harsh realization. Whether this limitation spreads into mathematics: this would explain how academic works continue to accumulate and apparently will continue to accumulate without end. At this point we are quite committed to the story unfolding, but we are just an early instance of linguistically able apes. If we are the final version then we will know who is to blame.

True, but you know, I have rather odd views on all of this. Few see how established theory, the fixed notions of the way the world is, are embedded in experience. They are, as the cliche goes, always already there before our waking eyes in the morning, when we pay our taxes and drive to work. we live and breathe in "paradigms" and were these to yield their ground to inquiry just just for the asking, we would have died of fright long ago, for the world is not language, but we are. Strange to be like ontological centaurs (Ortega), caught within the structures of logic on the one hand,a nd on the other able to see beyond them. This is our freedom to which we are condemned. It gets very interesting when we consider that since our experiences are so completely conditioned by the cognitive faculties that shape and anticipate all that is around us, the point of departure can be very dramatic; indeed, what is it that happens to the presumptive body of thought that is at the very root of inquiry or any conscious act itself when the mere question of its valiidiy is posed? Perhaps it is not a mere question at all. Perhaps it is a structural threat to pose such question (as with Kierkegaard's Sickness Unto Death) given that ideas do not hover innocently above the world like a superstructure, like an alien imposition, but rather are fused to the world itself, and are real, just as real as this book in my hand, but unlike the book they are reals that are maleable, and once fixity starts to fade and reality changes because one has dared stand outside the "mimicry" at the perceptual level. Madness is the only way to really go beyond, madness then understanding.

The freedom to falsify is not actually so readily available in a system of mimics. Physics is not built upon logic alone. As to what is rational, well, I believe that in our age where the curriculum is established into its sects that those standard views are the rational views by definition. That human judgement determines what is sensible... few give themselves enough credit to be their own judge. We bow and defer regularly to the academic standard. We are social animals, and that artifacts of our social nature have crept into the mathematical and scientific fields is undeniable. Of course if you want to deny it, you should come right up to it directly. Wee humans are limited. We should study our limitations so as to proceed farther in the progression we are engaged in. If our linguistic abilities are stunted and the basis is not freely developable (i.e. this is a genetic problem) then we have a harsh realization. Whether this limitation spreads into mathematics: this would explain how academic works continue to accumulate and apparently will continue to accumulate without end. At this point we are quite committed to the story unfolding, but we are just an early instance of linguistically able apes. If we are the final version then we will know who is to blame.

I would challenge the "linguistically able ape" remark just because I think we are more than language. I am of the school that refuses to pin things down and I resist the general attempt to make evolution into a final reductive thesis. this kind of thinking dominates most secular opinion.

Math and logic are human constructions. They thus far do not explain reality either fully or adequately. A system with less exceptions is superior to one that is loaded with exceptions. Ambiguity is not desirable. We have come to rest upon particle/wave duality and the exception of division by zero as fixtures which are relied upon no different than the Abrahamic branches war amongst each other, each with their book that makes them supreme. The assumption of human supremacy is easily deflated. This then makes room for a fresh start; to treat the most fundamental concepts as open to development rather than as pickled and jarred. While this position may be repulsive at first, it is truthful and this free room is necessary and should be encouraged.

But surely math's apodicticity is not invented because there are anomolies re. zeros and elsewhere. I mean, you can challenge it, as Quine did when he reduced anayticity to synonymy, found circular reasoning and so forth, but it seems wrong to suggest that it hs no more claim to truth than the protocal for speakers at the UN.

The freedom from paradigms I most respect i regarding moral paradigms less than those in math and physics. Those wars you mention come out of ignorance and frustration and hubris and what I call a low doxastic IQ which characterizes smart people who hold appalling views, like tht minister at the Hillsboro church who marches around fallen soldiers funerals with anti-gay signs. He's got a law degree, but has a doxastic IQ that is very, very low.

[TimBandTech]

I suspect that there is a tactile sensibility which does make its own way without language. As masters of materials which can take continuous shifts in form there is not necessarily a satisfactory discrete language to describe them all. The stick, the stake, the stave, the staph; this must be a very old word whose operations exceed just four meanings. So it goes with material things; the things which we have mastered and now for the most part lost our sensibilities of. How many modern humans make their own tools? Are we still then human? Well, I experience that those sensibilities are still available to us. Really there are plenty of handy people experimenting so I shouldn't complain too much. I've just started getting handy and appreciating this world in which one pair of pliers will never do. If you are burnt out I recommend it. Just about any material will do.

As you speak of a sensitivity to the moral interpretations I suggest that the destructive nature of humans and children in particular (and even young dogs) is a side effect of the material world: by dismantling an object into its respective parts an inherent understanding of that object arises. This word which usually takes a negative connotation can be given a very positive connotation and after all the root 'structure' is within it. When we find that an object can be dissected but that the dissection is not acceptable within the modern train of thought then we witness a failing of the curriculum. Mathematics is very near to the representational basis which we hope is productive enough to yield reality. In the pursuit of the basis I think you must relax your skepticism, for that skepticism is a tool in its pursuit. We find a weak link in the chain so as to mend it. That the current position is not good enough is merely to point out the fact that we are engaged in a progression and that we are in no way ready to rest. As to where one puts ones energy: academia has need of numerous 'productive' contributions and so it tends toward the tendrils of the viny structure. Head for the roots and one gets a rather different result. There is plenty of deadwood on this vine; it's health is dubious. The worshipers will protect it as it stands, but in fact it needs some pruning. I shake the thing with my staph and some of it falls to the ground; even down fairly low. This is the state that it exists in. It is incorrect to defer to the past masters unconditionally. Much of it is compost. As you say about evolution, stability and its criteria are of interest. When the conservatives meet the conservationists and they are eye to eye then the existing logic clearly has failed us. We are all subjects of misrepresentation. One dimensional representations are an insufficient description of reality. How they could be so confused by naming a number 'real', well, let's just admit that we can all overstep our sense of importance. At best we can only provide steps in a progression. We are caught here as prisoners of spacetime. The lore which places us as higher beings is a fraud. We are apes that can talk, and a bit more, but not so much more. We struggle and fumble along.

[Dolphin42]

Philosophy Explorer:

No because the other sciences are built up from axioms or assumptions. In physics that would be the laws of Newton amended by Einstein plus quantum mechanics

This is a few months late, but, for the record, this is a complete misunderstanding of the concept of an axiom and of science. Newton's laws are not axioms. They are generalizations from empirical observations, like everything else. In this case, some of the observations came from the astronomer Tycho Brahe and were partially generalized by Kepler, before Newton generalized them further and Einstein further still.

An axiom is a self-evident truth that is deemed to need no empirical evidence or proof.

[GaianDave51]

I see that this thread has been "dead" for about a year. I hope I can bring it back to life. I was going to open a new thread on this topic, but, instead, I'll expound here.

IMHO, mathematics is a language - a special language, with a special alphabet. As far as we know, it's a human language (although intelligent, tool-using beings all across the universe would understand mathematics, albeit with different alphabets.) That mathematics can be taught to humans using their individual, "vernacular" languages makes it evident to me that it is also a language.

As a human language, mathematics bears far stricter rules of grammar, syntax and vocabulary than any other human language; rules so strict that they reflect the science of formal logic. This is what makes mathematics the perfect language in which to express the laws of the universe. So, is Mathematics a science in itself? No, but its use follows scientific principles.

Human vernacular languages - those we speak or with which we write - evolve. Slangs and creoles constantly develop, and, over time, add content to our languages. Mathematics doesn't do this. Rather, it expands. Once new content is added (presumably by the practice of "pure" mathematics), it follows all the extant rules of grammar, syntax and vocabulary.

So, if math isn't science, what is? Here I'll be very brief. Science, with a small "s", is the process by which we discover and describe, or by which we amend or reject, the laws of nature. Science, with a capital "S" is the process by which we develop new technology. Small "s" science is driven by innate human curiosity about the universe; Science is driven by human need and by the profit motive.