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# Alder's Razor.

 Posts: 546 Add as FriendChallenge to a DebateSend a Message 11/9/2015 8:51:19 PMPosted: 2 years agoAlder's Razor: "Any matter that cannot be settled through observation is not worth debating."It's also known as "Newton's Flaming Laser Sword"; just as Occam's Razor cuts out redundancy, NFLS cuts out abstract, wishy-washy arguments with no basis in fact.https://en.wikipedia.org...https://philosophynow.org...
 Posts: 2,319 Add as FriendChallenge to a DebateSend a Message 11/9/2015 9:00:08 PMPosted: 2 years agoAt 11/9/2015 8:51:19 PM, SM2 wrote:Alder's Razor: "Any matter that cannot be settled through observation is not worth debating."It's also known as "Newton's Flaming Laser Sword"; just as Occam's Razor cuts out redundancy, NFLS cuts out abstract, wishy-washy arguments with no basis in fact.https://en.wikipedia.org...https://philosophynow.org...Logic and mathematics are tools for analysing information. They are part of the method of observation.That is to say, observation has to presuppose them. Thus, to settle disputes of logic or mathematics you cannot use observation. Yet both are worth debating. Thus the razor ought to be rejected.QEDPlease specify what observation consists in.
 Posts: 546 Add as FriendChallenge to a DebateSend a Message 11/9/2015 9:14:13 PMPosted: 2 years agoAt 11/9/2015 9:00:08 PM, Fkkize wrote:At 11/9/2015 8:51:19 PM, SM2 wrote:Alder's Razor: "Any matter that cannot be settled through observation is not worth debating."It's also known as "Newton's Flaming Laser Sword"; just as Occam's Razor cuts out redundancy, NFLS cuts out abstract, wishy-washy arguments with no basis in fact.https://en.wikipedia.org...https://philosophynow.org...Logic and mathematics are tools for analysing information. They are part of the method of observation.That is to say, observation has to presuppose them. Thus, to settle disputes of logic or mathematics you cannot use observation. Yet both are worth debating. Thus the razor ought to be rejected.QEDPlease specify what observation consists in.Read the Philosophy Now article in the OP link. It addresses your query far better than I can. Don't worry, it's easy to read.
 Posts: 13,775 Add as FriendChallenge to a DebateSend a Message 11/9/2015 9:19:32 PMPosted: 2 years agoHow exactly is one supposed to "observe" that only observation is capable of arriving at truth? Obviously some truth falls within the scope of science, but does all of it? How is science going to tell you, when the limitation of its scope is precisely the question at issue. So you're actually putting forth an axiom, which if we accept as valid, refutes your argument, since clearly a true axiom would show that not all truth has to be "observed", as your argument assumes.
 Posts: 2,319 Add as FriendChallenge to a DebateSend a Message 11/9/2015 9:19:49 PMPosted: 2 years agoAt 11/9/2015 9:14:13 PM, SM2 wrote:At 11/9/2015 9:00:08 PM, Fkkize wrote:At 11/9/2015 8:51:19 PM, SM2 wrote:Alder's Razor: "Any matter that cannot be settled through observation is not worth debating."It's also known as "Newton's Flaming Laser Sword"; just as Occam's Razor cuts out redundancy, NFLS cuts out abstract, wishy-washy arguments with no basis in fact.https://en.wikipedia.org...https://philosophynow.org...Logic and mathematics are tools for analysing information. They are part of the method of observation.That is to say, observation has to presuppose them. Thus, to settle disputes of logic or mathematics you cannot use observation. Yet both are worth debating. Thus the razor ought to be rejected.QEDPlease specify what observation consists in.Read the Philosophy Now article in the OP link. It addresses your query far better than I can. Don't worry, it's easy to read.You referr me to some lenghty article to dig for your response myself and then suggest deficiencies in my reading comprehension?Sorry, not gonna happen. Humans of the 21st century are gifted with Copy+Paste. Everything else is indeed a waste of time.
 Posts: 546 Add as FriendChallenge to a DebateSend a Message 11/9/2015 9:34:03 PMPosted: 2 years agoAnd I realise I didn't actually answer your question, so here:If you crunch the numbers, and they don't match observation, then your maths is wrong.
 Posts: 8,150 Add as FriendChallenge to a DebateSend a Message 11/10/2015 12:11:46 AMPosted: 2 years agoAt 11/9/2015 8:51:19 PM, SM2 wrote:Alder's Razor: "Any matter that cannot be settled through observation is not worth debating."It's also known as "Newton's Flaming Laser Sword"; just as Occam's Razor cuts out redundancy, NFLS cuts out abstract, wishy-washy arguments with no basis in fact.https://en.wikipedia.org...https://philosophynow.org...Ignoring all the other problems with this (and there are a lot) what do you do about undetermination? Where practical and useful theories can't be settled by observation alone?"At the heart of the underdetermination of scientific theory by evidence is the simple idea that the evidence available to us at a given time may be insufficient to determine what beliefs we should hold in response to it. In a textbook example, if all I know is that you spent \$10 on apples and oranges and that apples cost \$1 while oranges cost \$2, then I know that you did not buy six oranges, but I do not know whether you bought one orange and eight apples, two oranges and six apples, and so on. A simple scientific example can be found in the rationale behind the sensible methodological adage that "correlation does not imply causation". If watching lots of cartoons causes children to be more violent in their playground behavior, then we should (barring complications) expect to find a correlation between levels of cartoon viewing and violent playground behavior. But that is also what we would expect to find if children who are prone to violence tend to enjoy and seek out cartoons more than other children, or if propensities to violence and increased cartoon viewing are both caused by some third factor (like general parental neglect or excessive consumption of Twinkies). So a high correlation between cartoon viewing and violent playground behavior is evidence that (by itself) simply underdetermines what we should believe about the causal relationship between the two."http://plato.stanford.edu...At 10/3/2016 11:49:13 PM, thett3 wrote: BLACK LIVES MATTER!
 Posts: 546 Add as FriendChallenge to a DebateSend a Message 11/10/2015 1:26:35 AMPosted: 2 years agoAt 11/10/2015 12:11:46 AM, popculturepooka wrote:At 11/9/2015 8:51:19 PM, SM2 wrote:Alder's Razor: "Any matter that cannot be settled through observation is not worth debating."It's also known as "Newton's Flaming Laser Sword"; just as Occam's Razor cuts out redundancy, NFLS cuts out abstract, wishy-washy arguments with no basis in fact.https://en.wikipedia.org...https://philosophynow.org...Ignoring all the other problems with this (and there are a lot) what do you do about undetermination? Where practical and useful theories can't be settled by observation alone?"At the heart of the underdetermination of scientific theory by evidence is the simple idea that the evidence available to us at a given time may be insufficient to determine what beliefs we should hold in response to it. In a textbook example, if all I know is that you spent \$10 on apples and oranges and that apples cost \$1 while oranges cost \$2, then I know that you did not buy six oranges, but I do not know whether you bought one orange and eight apples, two oranges and six apples, and so on. A simple scientific example can be found in the rationale behind the sensible methodological adage that "correlation does not imply causation". If watching lots of cartoons causes children to be more violent in their playground behavior, then we should (barring complications) expect to find a correlation between levels of cartoon viewing and violent playground behavior. But that is also what we would expect to find if children who are prone to violence tend to enjoy and seek out cartoons more than other children, or if propensities to violence and increased cartoon viewing are both caused by some third factor (like general parental neglect or excessive consumption of Twinkies). So a high correlation between cartoon viewing and violent playground behavior is evidence that (by itself) simply underdetermines what we should believe about the causal relationship between the two."http://plato.stanford.edu...If I want to know how you divided the \$10 between apples and oranges, all I need to do is count the number of apples and oranges you purchased.If I want to know whether cartoons cause violence, I can set up an experiment with 4 groups: violent cartoon-watchers, non-violent cartoon watchers, violent non-cartoon watchers, and non-violent non-cartoon watchers. I can then expose half of the children in each group to cartoons, monitor their behaviour over the next 4 - 6 weeks, and compare them to the control groups.The problem with both your examples is a lack of observation, not a failure of observation as a method. If you don't make observations, you cannot draw conclusions. If you're not willing to make or accept observations, then that's as bad as being unable to, and thus the debate is not worth having. Alder's Razor is not just a tool for eliminating pointless debate topics; it also eliminates pointless debate opponents.
 Posts: 223 Add as FriendChallenge to a DebateSend a Message 11/10/2015 4:23:22 AMPosted: 2 years agoYou still haven't given a coherent account of logic if only observable things are worth discussing.
 Posts: 546 Add as FriendChallenge to a DebateSend a Message 11/10/2015 6:09:56 AMPosted: 2 years agoAt 11/10/2015 4:23:22 AM, BlueDreams wrote:You still haven't given a coherent account of logic if only observable things are worth discussing.Read my response to Fkkize. Logic and mathematics are tools for interpreting observations, and are derived from such.Take "1 + 1 = 2". This can be inferred by counting one apple, counting another apple, and then putting them together and counting both apples. Hence, the equation is an extension of a real-world observation regarding how apples add together. When dealing with more complex observations (e.g. anything in Quantum Physics), more complicated mathematics is required (such as imaginary numbers)."Logic" itself is analogous to a language, and languages are merely tools for conveying meaning to others.Soooo.... not really sure what your problem is here.
 Posts: 223 Add as FriendChallenge to a DebateSend a Message 11/10/2015 6:35:06 AMPosted: 2 years agoAt 11/10/2015 6:09:56 AM, SM2 wrote:At 11/10/2015 4:23:22 AM, BlueDreams wrote:You still haven't given a coherent account of logic if only observable things are worth discussing.Read my response to Fkkize. Logic and mathematics are tools for interpreting observations, and are derived from such.Take "1 + 1 = 2". This can be inferred by counting one apple, counting another apple, and then putting them together and counting both apples. Hence, the equation is an extension of a real-world observation regarding how apples add together. When dealing with more complex observations (e.g. anything in Quantum Physics), more complicated mathematics is required (such as imaginary numbers)."Logic" itself is analogous to a language, and languages are merely tools for conveying meaning to others.Soooo.... not really sure what your problem is here.Explain how it is possible for logic to be derived from observation. You can't derive logic from observation because this necessarily requires one to assume a logical framework, and if you're already assuming a logical framework, then there is no sense in which logic gets its justification from those observations
 Posts: 223 Add as FriendChallenge to a DebateSend a Message 11/10/2015 6:37:18 AMPosted: 2 years agoFurthermore, mathematics is not always a description of real world entities like apples. The average household cannot have 3.5 people in it.
 Posts: 223 Add as FriendChallenge to a DebateSend a Message 11/10/2015 6:43:07 AMPosted: 2 years agoAt 11/10/2015 6:09:56 AM, SM2 wrote:Take "1 + 1 = 2". This can be inferred by counting one apple, counting another apple, and then putting them together and counting both apples. Hence, the equation is an extension of a real-world observation regarding how apples add together.As a final note, this is completely backwards. You are not deriving 1+1 =2 by counting one apple, another apple, and then concluding that they equal two. Rather, you are assuming that 1+1 =2 in the first place. Counting two apples does not prove that 1+1=2. Rather, 1+1 =2 allows you to prove that you have two apples. 1+1 will continue to equal two whether or not there are apples, or whether or not there are any physical entities at all.
 Posts: 546 Add as FriendChallenge to a DebateSend a Message 11/10/2015 7:48:09 AMPosted: 2 years agoAt 11/10/2015 6:35:06 AM, BlueDreams wrote:Explain how it is possible for logic to be derived from observation. You can't derive logic from observation because this necessarily requires one to assume a logical framework, and if you're already assuming a logical framework, then there is no sense in which logic gets its justification from those observationsLogic and Mathematics are not "things". They are not objects. They are not external forces imposed upon the world. They are merely a way of representing a relationship between two or more variables. The rules of logic arise from observing patterns. If your logic is false, then you will not be able to continue the pattern.If you're struggling with this concept, then imagine the following scenario: You've been transported to another universe, where the rules of logic are different. How would you discover what these rules are?Furthermore, mathematics is not always a description of real world entities like apples. The average household cannot have 3.5 people in it.3.5 people is an average; it refers to a trend in the larger population, and not in a specific house. The math is descriptive, it just isn't describing what you claim.Take "1 + 1 = 2". This can be inferred by counting one apple, counting another apple, and then putting them together and counting both apples. Hence, the equation is an extension of a real-world observation regarding how apples add together.As a final note, this is completely backwards. You are not deriving 1+1 =2 by counting one apple, another apple, and then concluding that they equal two. Rather, you are assuming that 1+1 =2 in the first place. Counting two apples does not prove that 1+1=2. Rather, 1+1 =2 allows you to prove that you have two apples. 1+1 will continue to equal two whether or not there are apples, or whether or not there are any physical entities at all.Continue the "other universe" scenario. Suppose you counted one apple, counted another apple, and then put them together and counted three apples (assume that you counted correctly). Would that not invalidate the 1 + 1 = 2 rule?Suppose that, no matter how many apples you added, having more than one apple produced three apples? 1 + 1 = 3, but so does 1 + 1 + 1, and 1 + 1 + 1 + 1. Basically, any numbers other than 1 and 0 add to 3. Would that not invalidate the entirety of arithmetic and, by extension, all of mathematics?If you want proof that this is how stuff works, look at all the new types of numbers we have to work with nowadays (e.g. the ones where A x B = -B x A). We didn't pull those numbers out of thin air; they were created out of necessity to describe a concept that our existing mathematics couldn't.
 Posts: 904 Add as FriendChallenge to a DebateSend a Message 11/10/2015 8:46:06 AMPosted: 2 years agoAt 11/9/2015 8:51:19 PM, SM2 wrote:Alder's Razor: "Any matter that cannot be settled through observation is not worth debating."Whether it is worth debating is relative to the mindset of the debater.There are a lot of instances where reasonable inferences can be made through observation of indirect sources, without observation of the direct source, but that might also be covered under this law.
 Posts: 729 Add as FriendChallenge to a DebateSend a Message 11/10/2015 8:51:28 AMPosted: 2 years agoYou can have it both ways. You could say that 1+1=2 is a generalisation of our observations of gathering objects together or that 1+1=2 is a inviolable rule of abstract mathematics that can be applied usefully in the real world when gathering objects together.I don't think either model is more correct than the other. Rather it is good to have a 'split personality' and hold both models in your head so you can use the model that works best for whichever problem you are working on at the time. There's no over-riding necessity to dogmatically adopt one and abandon the other, rather like you don't have to decide if electrons are waves or particles.
 Posts: 546 Add as FriendChallenge to a DebateSend a Message 11/10/2015 9:47:47 AMPosted: 2 years agoAt 11/10/2015 8:51:28 AM, kp98 wrote:You can have it both ways. You could say that 1+1=2 is a generalisation of our observations of gathering objects together or that 1+1=2 is a inviolable rule of abstract mathematics that can be applied usefully in the real world when gathering objects together.My point is that the inviolable rule is derived from the observations. They are not separate; one exists because of the other. We only have the rule because some caveman (or -woman) put in the effort to make the observations and figure out how this addition thing worked. Or, more likely, Natural Selection wired addition into some primitive mammal's brain so they could tell how many more nuts to gather. Regardless, the rule only exists because we can observe it and it works.
 Posts: 729 Add as FriendChallenge to a DebateSend a Message 11/10/2015 11:12:39 AMPosted: 2 years agoWhat about i*i=-1?
 Posts: 546 Add as FriendChallenge to a DebateSend a Message 11/10/2015 11:33:58 AMPosted: 2 years agoAt 11/10/2015 11:12:39 AM, kp98 wrote:What about i*i=-1?Complex numbers are used in Physics.
 Posts: 729 Add as FriendChallenge to a DebateSend a Message 11/10/2015 12:58:30 PMPosted: 2 years agoThey are indeed. But you said "We only have the rule because some caveman (or -woman) put in the effort to make the observations and figure out how this addition thing worked."Cavemen didn't have imaginary numbers! Imaginary numbers arose our of efforts to solve algebraic equations - a problem of pure mathematics. Imaginary (or complex) numbers are certainly used in physics (e.g. for working out the parameters of resonant LCR networks - but complex numbers pre-date electronic circuit design.Non-euclidean geomety is another example where mathematics came first and was applied later when it was realised the universe was not flat after all.I am not arguing that mathematics does not have its roots in observation and practical problems - my position is that its not an either/or thing.
 Posts: 2,319 Add as FriendChallenge to a DebateSend a Message 11/10/2015 1:47:31 PMPosted: 2 years agoAt 11/9/2015 9:30:40 PM, SM2 wrote:First you said:Logic and mathematics are tools for analysing information. They are part of the method of observation.Now you say:The rules of logic arise from observingEither they are built into the method of observation (1) or they arise from it (2).You cannot have both. That would be circular reasoning.Please specify what observation consists in.I'll repeat the question. Observation, the gathering of data, is, for all means scientific, distinct from analysing data.Alder's response is that mathematics is merely an extension of real-world stuff. For example, Euclidean geometry (geometry on a flat surface) is abstracted from the Egyptian method of using pegs and ropes to mark out fields. Since field markers deal with flat surfaces, Euclidean geometry cannot be used in situations where the surface is not flat. Or, to put it another way, Euclidean geometry tests whether the surface you're working on is flat. If you construct a peg-and-rope triangle, and the angles add to more than 180 degrees, then your surface is probably spherical (a version involving mountains and telescopes was used to determine the curvature of the Earth).Ok, this is his and presumably your view on the nature of numbers. Which is a philosophical topic that seemed worth debating at least for him and presumably you, too. What it is not is a response to my objection.My objection was about solving problems is mathematics. The Goldbach conjecture quite possibly is a theorem. So fart we have no prove for or against that.But obviously it either is or it is not. Tell me, how is an observation supposed to bring a solution here? We cannot observe an infinite amount of numbers and any finite amount we could observe is no solution.This is why we use fancy mathematics such as imaginary numbers: they are abstracted from real-world phenomena that obeys those rules.Lol. Now you show me what complex numbers are abstracted from. Your pyramid example at best gives you rational numbers. Not real numbers, not irrational numbers and most certainly not complex numbers.No human can even imagine the complex plane (no pun intended) without falling back to imagining a regular coordinate system.And yes, I am aware they have various applications in the natural sciences, but no, we do not use them because we observed them somehow. They have been introduced to solve until then unsolvable polynomials like x^2=-1.
 Posts: 2,319 Add as FriendChallenge to a DebateSend a Message 11/10/2015 1:56:20 PMPosted: 2 years agoSince we are talking about complex numbers, I think this is hilarious :Dhttp://xkcd.com...
 Posts: 2,319 Add as FriendChallenge to a DebateSend a Message 11/10/2015 3:48:36 PMPosted: 2 years agoCorrections:My objection was about solving problems in mathematics. The Goldbach conjecture quite possibly is a theorem. So far we have no prove for or against that.No human can even imagine the complex plane without falling back to imagining a regular coordinate system.Brackets removed. Originally I wrote "imaginary part".
 Posts: 546 Add as FriendChallenge to a DebateSend a Message 11/10/2015 7:46:16 PMPosted: 2 years agoAt 11/10/2015 12:58:30 PM, kp98 wrote:They are indeed. But you said "We only have the rule because some caveman (or -woman) put in the effort to make the observations and figure out how this addition thing worked."Cavemen didn't have imaginary numbers!I didn't say they did. Literacy standards really are falling around here.Imaginary numbers arose our of efforts to solve algebraic equations - a problem of pure mathematics. Imaginary (or complex) numbers are certainly used in physics (e.g. for working out the parameters of resonant LCR networks - but complex numbers pre-date electronic circuit design.I won't deny that mathematicians, like all people, sometimes go off on a wild goose chase for the sheer hell of it. And sometimes, they catch a goose.Non-euclidean geomety is another example where mathematics came first and was applied later when it was realised the universe was not flat after all.I am not arguing that mathematics does not have its roots in observation and practical problems - my position is that its not an either/or thing.I think we're actually in agreement here. My only issue is when people act as though numbers are somehow divorced from reality. No matter how abstract and impractical your number manipulations are, you're still working with an observational tool.
 Posts: 546 Add as FriendChallenge to a DebateSend a Message 11/10/2015 7:57:50 PMPosted: 2 years agoAt 11/10/2015 1:47:31 PM, Fkkize wrote:At 11/9/2015 9:30:40 PM, SM2 wrote:First you said:Logic and mathematics are tools for analysing information. They are part of the method of observation.Now you say:The rules of logic arise from observingEither they are built into the method of observation (1) or they arise from it (2).You cannot have both. That would be circular reasoning.It would be, if logic was a single unit. It's not; it's layered and composed of many parts. The logic we put in is not the same as the logic we get out.Please specify what observation consists in.I'll repeat the question. Observation, the gathering of data, is, for all means scientific, distinct from analysing data.Alder's response is that mathematics is merely an extension of real-world stuff. For example, Euclidean geometry (geometry on a flat surface) is abstracted from the Egyptian method of using pegs and ropes to mark out fields. Since field markers deal with flat surfaces, Euclidean geometry cannot be used in situations where the surface is not flat. Or, to put it another way, Euclidean geometry tests whether the surface you're working on is flat. If you construct a peg-and-rope triangle, and the angles add to more than 180 degrees, then your surface is probably spherical (a version involving mountains and telescopes was used to determine the curvature of the Earth).Ok, this is his and presumably your view on the nature of numbers. Which is a philosophical topic that seemed worth debating at least for him and presumably you, too. What it is not is a response to my objection.My objection was about solving problems is mathematics. The Goldbach conjecture quite possibly is a theorem. So fart we have no prove for or against that.But obviously it either is or it is not. Tell me, how is an observation supposed to bring a solution here? We cannot observe an infinite amount of numbers and any finite amount we could observe is no solution.Conjectures, by definition, are unproved. So... your question is kinda dumb.This is why we use fancy mathematics such as imaginary numbers: they are abstracted from real-world phenomena that obeys those rules.Lol. Now you show me what complex numbers are abstracted from. Your pyramid example at best gives you rational numbers. Not real numbers, not irrational numbers and most certainly not complex numbers.No human can even imagine the complex plane (no pun intended) without falling back to imagining a regular coordinate system.And yes, I am aware they have various applications in the natural sciences, but no, we do not use them because we observed them somehow. They have been introduced to solve until then unsolvable polynomials like x^2=-1.Read the posts by and to kp98. This issue has already been discussed there.
 Posts: 2,319 Add as FriendChallenge to a DebateSend a Message 11/10/2015 8:29:11 PMPosted: 2 years agoAt 11/10/2015 7:57:50 PM, SM2 wrote:At 11/10/2015 1:47:31 PM, Fkkize wrote:At 11/9/2015 9:30:40 PM, SM2 wrote:First you said:Logic and mathematics are tools for analysing information. They are part of the method of observation.Now you say:The rules of logic arise from observingEither they are built into the method of observation (1) or they arise from it (2).You cannot have both. That would be circular reasoning.It would be, if logic was a single unit. It's not; it's layered and composed of many parts. The logic we put in is not the same as the logic we get out.That is irrelevant. The question is whether there is something worth discussing that cannot be decided by observation.Say logic is comprised of two "parts". You cannot assume part one in you method to "observe"part one (whatever "observe" means to you, you have yet to specify what constitutes your unscientific understanding of the term).The same applies to part two.Now, of course you could assume part one to "observe" part two, if you already have established part one. But how are you going to do that without either assuming part two or part one for you observation of part one.It is circular reasoning either way.My objection was about solving problems is mathematics. The Goldbach conjecture quite possibly is a theorem. So fart we have no prove for or against that.But obviously it either is or it is not. Tell me, how is an observation supposed to bring a solution here? We cannot observe an infinite amount of numbers and any finite amount we could observe is no solution.Conjectures, by definition, are unproved. So... your question is kinda dumb.....that is not the point...at all. The question is whether it actually can be proven, we just don't have that proof yet, or whether it cannot and most importantly, how "observation" is going to give the answer.This is why we use fancy mathematics such as imaginary numbers: they are abstracted from real-world phenomena that obeys those rules.Lol. Now you show me what complex numbers are abstracted from. Your pyramid example at best gives you rational numbers. Not real numbers, not irrational numbers and most certainly not complex numbers.No human can even imagine the complex plane (no pun intended) without falling back to imagining a regular coordinate system.And yes, I am aware they have various applications in the natural sciences, but no, we do not use them because we observed them somehow. They have been introduced to solve until then unsolvable polynomials like x^2=-1.Read the posts by and to kp98. This issue has already been discussed there.How does anything you said to him constitute a response to my contention?Fact is, we did not "observe" complex numbers. We cannot even properly comprehend them in the complex plane, as we do with real numbers in a coordinate system "abstracted" from a plane of the real world.Mathematicians have not gone "wild goose" and randomly stumbled upon complex numbers. Read kp's and my responses. They have been proposed specifically to solve until then unsolvable polynomials.The important point is we did not "observe" them whatsoever. Even if we humans could in principle abstract them from something we have encountered in this world (which I do not concede for a second), they have not been originally "observed" that way.Proving my point.
 Posts: 2,319 Add as FriendChallenge to a DebateSend a Message 11/10/2015 8:39:08 PMPosted: 2 years agoAt 11/10/2015 7:57:50 PM, SM2 wrote:Further, you have yet to justify your razor. And I do not think you can do that without begging the question.
 Posts: 729 Add as FriendChallenge to a DebateSend a Message 11/10/2015 9:09:01 PMPosted: 2 years agoHey - I'm trying to be neutral here, sm2!I think that maths certainly started out as little more than a way of organising our experience of dealing with small collections and quanties, expanding only a little when we began to trade (non trading hunter gatherer societies often had no words for quantities larger than two or three). It is relatively recently - and gradually - that maths has became divorced from the mundane and became truly abstract. I confess that if I hear mathematicians discussing their trade with each other it is like a different world. n-ploid toroidally tesselated z-manifolds aren't something I have ever experenced....A classic paper on this topic is this one. Everyone should read this before posting on mathematics!http://citeseerx.ist.psu.edu...
 Posts: 729 Add as FriendChallenge to a DebateSend a Message 11/10/2015 9:11:36 PMPosted: 2 years agoI'll just quote from the wigner paper I linked:Furthermore, whereas it is unquestionably true that the concepts of elementary mathematics and particularly elementary geometry were formulated to describeentities which are directly suggested by the actual world, the same does not seem to be true of the more advanced concepts, in particular the concepts which play such an important role in physics.