There are many other areas of science where things are very much more uncertain.
Is this a snapshot of the matter as it stands now, or the ultimate state of the matter? Has the scientific process been halted permanently by insurmountable odds?
Science is a massive thing so this is really hard to answer, it isn't uniform and the same.
In many areas of biological science it is hard to be sure about anything and there is considerable uncertainty. I'm not sure progess has been halted but it is increasingly difficult to tell what is real/important from what isn't.
I was talking to a biologist the other day who was saying that there are labs that are pushing to have AI generate papers for results scientists don't have time to write up into papers. This just adds to the problem.
I can't answer questions I don't understand, @Martin54. Either be coherent or don't address me.
Was this unclear? Your not answering led to what followed from me.
Where is the handwaving in biology? And/or climate science?
Things that aren't primarily physics and mathematics.
I'm not sure what you want me to say or what point you think you are making.
What point are you making about handwaving? Can you point to it in geology and chemistry and biology? And combined sciences? I'm not making any point, apart from making the point that you haven't substantiated your point of handwaving in these sciences.
Privileging the hard sciences over other forms of inquiry when the hard sciences are far from stable is an epistemological move I don’t make, but I can see why people do so.
@KoF, as hand-waving is widely seen as a pejorative term, I wonder if a more specific and less metaphorical description of what you have in mind might help the discussion move forward rather than get into a tangle over a particular usage.
It would also be helpful to have one or two specific examples of the phenomenon, otherwise the discussion is liable to turn into a ‘they do’ ‘no they don’t’ argument which won’t get us anywhere.
@ Martin54: I don't see why any magical entity couldn't be supremely transcendent
True and that is the point don’t you think? It is about perception.
To get it you have to ken Thomas Aquinas.
However, to the broader issue..
In your schema you demand physical evidence for the non physical perception. When you don’t see it you go..
“There, told you so..bunch of cretins!”
A more social approach might be: “Well that may be but I don’t understand it.”
I actually hadn’t seen that limerick @mousethief quoted before but it brought a smile.
And I also find CS Lewis very insightful remembering the lived experience at the back of his faith.
In the end, if Jesus is not God he is neither a great teacher or even a good man. He is deluded.
Privileging the hard sciences over other forms of inquiry when the hard sciences are far from stable is an epistemological move I don’t make, but I can see why people do so.
For me it's because people can provide evidence for their claims. And demonstrate that the stuff they make based on the theory works. Other fields of enquiry seem to lack that.
I'd make a very good atheist. I often wonder why I'm not one, if I'm honest.
Privileging the hard sciences over other forms of inquiry when the hard sciences are far from stable is an epistemological move I don’t make, but I can see why people do so.
For me it's because people can provide evidence for their claims. And demonstrate that the stuff they make based on the theory works. Other fields of enquiry seem to lack that.
I'd make a very good atheist. I often wonder why I'm not one, if I'm honest.
Mathematics is interesting but I don't think it says much about other kinds of thinking.
I'm not a mathematician, but quite a lot of it feels like one has to suspend knowledge of the real world in order to accept a perfect one for it to work. It is certainly fascinating that it is possible to prove mathematical theorem and that the answers are so consistent. Quite a contrast to everything else, in my opinion.
The thing about maths is that you start with a set of axioms that everybody just agrees to, but never tries to prove. The whole thing pivots on a fulcrum of wax. As long as you leave those axioms in place, you can go on to create amazing patterns that are both beautiful and in many instances able to give structure to the physical sciences. (For instance the complex plane provides a mathematical framework for describing electromagnetic waves.)
But in philosophical terms, it's all if/then. IF you accept the axioms, THEN these mathematical statements unfold.
Theology's like that too, except for the messy interference of lived experience. Which gets interesting. (There's nothing like having one's carefully constructed doctrine blown up in your face by the one you're theorizing about sticking his oar in!)
The thing about maths is that you start with a set of axioms that everybody just agrees to, but never tries to prove. The whole thing pivots on a fulcrum of wax. As long as you leave those axioms in place, you can go on to create amazing patterns that are both beautiful and in many instances able to give structure to the physical sciences. (For instance the complex plane provides a mathematical framework for describing electromagnetic waves.)
But in philosophical terms, it's all if/then. IF you accept the axioms, THEN these mathematical statements unfold.
By this description philosophers are at least honest in their recognition that they are agreeing on something unproven, where mathematicians are not or don't care.
If the fulcrum is wax, then the axioms should at some times not work or lead to garbage, rather than a mathematical framework that describes real things. Wouldn't they?
@Kendel. My bloke on the bus understanding is that the fulcrum of wax is the fact that the meaning of the axioms, the self evident truths, is by agreement. The ultimate test, not proof, as there is no such thing, of axioms is in their mapping to nature. Mathematical proofs are a different thing; they are predicated on axioms.
How many axioms does it take to change a lightbulb? (1 dud + 1 working = 2). 379 pages worth.
My impression of science, from decades thinking and studying it, is this.
For scientific discoveries (at least in the biological sciences I'm most familiar with) to have stickability, the parameters have to be quite wide. So they have to be pretty obvious once we are looking in the right place. And they have to be robust enough to even out all the extremes.
By that I mean that there's a large amount of complexity including things that we haven't thought of when designing scientific experiments. Sometimes we have the ability to limit the factors that could skew or muddy results (working in a very clean lab to very tight practices with many replications) but a lot of the time we don't.
Engineering/tech has those massive steps forward as you've mentioned because of all the ways that the unexpected factors can be removed and then we can have the marvel of millions of phones being produced with their amazing abilities.
I'm sorry, I've lost the train of thought just thinking of how amazing it is that we've tamed nature to produce electronic components.
I guess what I was mostly thinking is that there are sciences where we can be very content and sure we have limited the known and unknown unknowns. In particular many areas of engineering, physics and chemistry. There are many other areas of science where things are very much more uncertain.
I'm afraid I'm still struggling to follow the thread of these posts, and the distinctions you're making.
I wouldn't categorise engineering and technology as science. STEM subjects or disciplines are often lumped together, but they're regarded as being distinct.
I suspect most of what I'd call the science in a smartphone is decades old - I'd guess the most recent scientific innovations are in the battery, display and maybe the screen. But there's a been an awful lot of technological / engineering refinement over the years.
Which is all by way of saying that I think the point you want to make is getting caught up in the way you're organising the various disciplines.
@ Martin54: I don't see why any magical entity couldn't be supremely transcendent
True and that is the point don’t you think? It is about perception.
To get it you have to ken Thomas Aquinas.
Or Aldous Huxley.
However, to the broader issue..
In your schema you demand physical evidence for the non physical perception.
What is non-physical perception? By what sense apparatus? Extrasensory?
When you don’t see
By which eyes?
it
See what?
you go..
“There, told you so..bunch of cretins!”
Whenever I have that ignorant, unkind, non-Rogerian impulse, I must add "we are" and dissolve it in unconditional positive regard including for myself. I am the worst of cretins.
A more social approach
More social in what sense? Obfuscating issues like my saying 'I know' to the point of disappearance of the meaning in layers of politesse?
might be: “Well that may be but I don’t understand it.”
What may be? That I might understand it?
I actually hadn’t seen that limerick @mousethief quoted before but it brought a smile.
It's having its hundredth birthday. It is amusingly specious isn't it?
And I also find CS Lewis very insightful remembering the lived experience at the back of his faith.
Like the lived experience of the characters in the Epistle to the Hebrews?
In the end, if Jesus is not God he is neither a great teacher or even a good man. He is deluded.
For you. For me he was a great teacher and a good man and deluded. I blame the parents.
@KoF, as hand-waving is widely seen as a pejorative term, I wonder if a more specific and less metaphorical description of what you have in mind might help the discussion move forward rather than get into a tangle over a particular usage.
It would also be helpful to have one or two specific examples of the phenomenon, otherwise the discussion is liable to turn into a ‘they do’ ‘no they don’t’ argument which won’t get us anywhere.
BroJames, Purgatory Host
These are a) fractal and b) widely known and discussed issues.
There’s a replication crisis in much of science, particularly biological science
And so on and so on. Many different scales: local, global, methodological, philosophical, practical.
Mix in the fact that biology is messy and the factors which influence others are or might be extremely complicated and possibly not even possible to model and be understood
The butterfly effect is really a thought experiment in the philosophy of science, bringing into question whether something as small as a butterfly could influence a tornado. Probably not, but how could we possibly know?
My impression of science, from decades thinking and studying it, is this.
For scientific discoveries (at least in the biological sciences I'm most familiar with) to have stickability, the parameters have to be quite wide. So they have to be pretty obvious once we are looking in the right place. And they have to be robust enough to even out all the extremes.
By that I mean that there's a large amount of complexity including things that we haven't thought of when designing scientific experiments. Sometimes we have the ability to limit the factors that could skew or muddy results (working in a very clean lab to very tight practices with many replications) but a lot of the time we don't.
Engineering/tech has those massive steps forward as you've mentioned because of all the ways that the unexpected factors can be removed and then we can have the marvel of millions of phones being produced with their amazing abilities.
I'm sorry, I've lost the train of thought just thinking of how amazing it is that we've tamed nature to produce electronic components.
I guess what I was mostly thinking is that there are sciences where we can be very content and sure we have limited the known and unknown unknowns. In particular many areas of engineering, physics and chemistry. There are many other areas of science where things are very much more uncertain.
I'm afraid I'm still struggling to follow the thread of these posts, and the distinctions you're making.
I wouldn't categorise engineering and technology as science. STEM subjects or disciplines are often lumped together, but they're regarded as being distinct.
I suspect most of what I'd call the science in a smartphone is decades old - I'd guess the most recent scientific innovations are in the battery, display and maybe the screen. But there's a been an awful lot of technological / engineering refinement over the years.
Which is all by way of saying that I think the point you want to make is getting caught up in the way you're organising the various disciplines.
Because Engineering is a practical outpouring of physics in a way that no other science is.
In biology we know all kinds of things about the human body, from the smallest cell to the largest organ. But we can’t build a human from all those pieces of knowledge.
In engineering someone used ideas from mathematics which seemed entirely theoretical and weird and then in time that’s been manufactured and perfected into something you can hold in your hand. The most similar thing to that in biology is agriculture, and even that isn’t close to being what engineering has done to ideas from physics.
@ Martin54: I don't see why any magical entity couldn't be supremely transcendent
True and that is the point don’t you think? It is about perception.
To get it you have to ken Thomas Aquinas.
However, to the broader issue..
In your schema you demand physical evidence for the non physical perception. When you don’t see it you go..
“There, told you so..bunch of cretins!”
A more social approach might be: “Well that may be but I don’t understand it.”
I actually hadn’t seen that limerick @mousethief quoted before but it brought a smile.
And I also find CS Lewis very insightful remembering the lived experience at the back of his faith.
In the end, if Jesus is not God he is neither a great teacher or even a good man. He is deluded.
Or simply misunderstood and then misquoted by later religious zealots.
I don’t think one really needs the named person in this scenario to be deluded, just a bunch of other people to put into him their own ideas of what he was about.
Of course exactly the same thing could be said about almost all religious figures from antiquity.
@ Martin54: I don't see why any magical entity couldn't be supremely transcendent
True and that is the point don’t you think? It is about perception.
To get it you have to ken Thomas Aquinas.
However, to the broader issue..
In your schema you demand physical evidence for the non physical perception. When you don’t see it you go..
“There, told you so..bunch of cretins!”
A more social approach might be: “Well that may be but I don’t understand it.”
I actually hadn’t seen that limerick @mousethief quoted before but it brought a smile.
And I also find CS Lewis very insightful remembering the lived experience at the back of his faith.
In the end, if Jesus is not God he is neither a great teacher or even a good man. He is deluded.
Or simply misunderstood and then misquoted by later religious zealots.
I don’t think one really needs the named person in this scenario to be deluded, just a bunch of other people to put into him their own ideas of what he was about.
Of course exactly the same thing could be said about almost all religious figures from antiquity.
The Mad, Bad or God trilemma has always had the fatal flaw that it depends on the gospels accurately reporting Jesus' words.
Mathematics is interesting but I don't think it says much about other kinds of thinking.
I'm not a mathematician, but quite a lot of it feels like one has to suspend knowledge of the real world in order to accept a perfect one for it to work. It is certainly fascinating that it is possible to prove mathematical theorem and that the answers are so consistent. Quite a contrast to everything else, in my opinion.
The thing about maths is that you start with a set of axioms that everybody just agrees to, but never tries to prove. The whole thing pivots on a fulcrum of wax. As long as you leave those axioms in place, you can go on to create amazing patterns that are both beautiful and in many instances able to give structure to the physical sciences. (For instance the complex plane provides a mathematical framework for describing electromagnetic waves.)
But in philosophical terms, it's all if/then. IF you accept the axioms, THEN these mathematical statements unfold.
Well yes, but no.
Mathematics is particularly weird because it has such depth. It’s deep and goes deeper and deeper and deeper.
And as others said, it maps onto the world as we experience it in so many different ways. Just look at how many different biological functions are related to Pi.
Would it really be possible to do all that useful stuff if the fundamentals were just axiomatic porridge?
Would it really be possible to do all that useful stuff if the fundamentals were just axiomatic porridge?
No. Nor have I said so. Nor have I hinted so. Nor have I given any indication I believe anything similar. Hopefully you get the point.
The axioms are very, very, very well chosen. But they are still axioms, unproven and accepted as an unproven starting point. Call that porridge if you will. I think the very results you are so triumphant about prove that is a foolish thing to call them.
Ok what’s a better word? The axioms have created a system of mathematics that works. Doesn’t that say something about the axiom?
Kurt Gödel's Incompleteness Theorems are widely regarded to have ended the search for a complete axiomatic system for mathematics. However he distinguished between truth and proof. Just because an axiomatic system has its limitations in providing mathematical proofs, this doesn't mean that mathematics doesn't contain necessary truths. Gödel remained a Platonist regarding mathematical entities until his death.
@ Martin54: I don't see why any magical entity couldn't be supremely transcendent
True and that is the point don’t you think? It is about perception.
To get it you have to ken Thomas Aquinas.
However, to the broader issue..
In your schema you demand physical evidence for the non physical perception. When you don’t see it you go..
“There, told you so..bunch of cretins!”
A more social approach might be: “Well that may be but I don’t understand it.”
I actually hadn’t seen that limerick @mousethief quoted before but it brought a smile.
And I also find CS Lewis very insightful remembering the lived experience at the back of his faith.
In the end, if Jesus is not God he is neither a great teacher or even a good man. He is deluded.
Or simply misunderstood and then misquoted by later religious zealots.
I don’t think one really needs the named person in this scenario to be deluded, just a bunch of other people to put into him their own ideas of what he was about.
Of course exactly the same thing could be said about almost all religious figures from antiquity.
The Mad, Bad or God trilemma has always had the fatal flaw that it depends on the gospels accurately reporting Jesus' words.
I have total good will toward Jesus and his words. That doesn't make him God. The flaw of the false trilemma is that Jesus was not mad and/or bad, or God. He was an exceptional but nonetheless historically deterministic son of an exceptional mother. I see no evidence of mental illness or ill intent in either of them.
Some sets of axioms generate systems of mathematics that work.
True. But no axiomatic system which is developed enough to allow basic arithmetic can be both complete and consistent. With axiomatic systems which work they will be consistent (or they wouldn't work) but incomplete (i.e. there will be axioms whose truth are assumed but not proved).
In geometry at least you can replace at least some axioms with theorems deduced from the axiom you replaced and you get all the same theorems from a different set of axioms. For example, Euclid's fifth axiom - if two lines each cross a third line and on one side the angles sum to less than two right angles then the lines cross over on that side - can be replaced with various theorems, for example: for any given line and point not on that line there is exactly one parallel line that passes through that point, or even the interior angles of a triangle sum to two right angles. More importantly you can replace Euclid's fifth axiom and get a different geometry (geometry on a curved surface basically).
From a mathematical point of view, axioms aren't so much intuited as chosen because they lead to interesting results.
Some sets of axioms generate systems of mathematics that work.
True. But no axiomatic system which is developed enough to allow basic arithmetic can be both complete and consistent. With axiomatic systems which work they will be consistent (or they wouldn't work) but incomplete (i.e. there will be axioms whose truth are assumed but not proved).
Incompleteness means that there are theorems that are true but cannot be proven. As I understand it, it also means that you can't prove that your set of axioms is consistent.
If you can use notation in algebra which can then formally prove concepts, how can it then not be consistent. Surely the one thing we can say about mathematical axioms is that they produce amazingly consistent results.
@KoF, as hand-waving is widely seen as a pejorative term, I wonder if a more specific and less metaphorical description of what you have in mind might help the discussion move forward rather than get into a tangle over a particular usage.
It would also be helpful to have one or two specific examples of the phenomenon, otherwise the discussion is liable to turn into a ‘they do’ ‘no they don’t’ argument which won’t get us anywhere.
BroJames, Purgatory Host
These are a) fractal and b) widely known and discussed issues.
There’s a replication crisis in much of science, particularly biological science
How does this concern relate to handwaving? And is it of most concern in the actual biological sciences?
And so on and so on. Many different scales: local, global, methodological, philosophical, practical.
Mix in the fact that biology is messy and the factors which influence others are or might be extremely complicated and possibly not even possible to model and be understood
The butterfly effect is really a thought experiment in the philosophy of science, bringing into question whether something as small as a butterfly could influence a tornado. Probably not, but how could we possibly know?
Sorry I’m on holiday and I’m not being obtuse but I’m not getting into any kind of debate with you about clarity, @Martin54. I don’t understand two-thirds of what you write and yet somehow I’m the one lacking clarity on things I know about.
Last time I looked, medicine was a biological science. And it absolutely is a problem in other biological fields.
I’m not answering any more questions from you. Either accept that it is what it is, or don’t. I don’t care.
Sorry I’m on holiday and I’m not being obtuse but I’m not getting into any kind of debate with you about clarity, @Martin54. I don’t understand two-thirds of what you write and yet somehow I’m the one lacking clarity on things I know about.
Last time I looked, medicine was a biological science.
Find medicine here. Or psychology. Where did you look? That's rhetorical of course.
And it absolutely is a problem in other biological fields.
I’m not answering any more questions from you. Either accept that it is what it is, or don’t. I don’t care.
Accept what is what it is to do with handwaving? Rhetorically.
There's a name for your fallacy. At least one. False. Oooh, and Straw Man. As for formal (non sequitur), I don't have the degree for that. Feels like an argument from fallacy fallacy.
Excuse me? How am I manipulating you into questioning your version of reality? You can't answer I know.
Generously I'd say that you were handwaving any attempt to get you to identify handwaving in biology in the context of existentialism and essentialism in particular.
If you can use notation in algebra which can then formally prove concepts, how can it then not be consistent. Surely the one thing we can say about mathematical axioms is that they produce amazingly consistent results.
For example, if you have, say, five axioms, you may be able to use axioms one to four to prove that axiom five is untrue. As long as your set of axioms gives you enough complexity to model basic arithmetic using the system, it's impossible to prove it will never happen. That this is impossible has been proven.
(The proofs roughly work on the principle that if you could do that, you could create aa additional valid axiom that went this axiom is consistent with the others if and only if it isn't consistent with the others.)
As an analogy, a sudoku grid might either be x) soluble, y) insoluble because there's not enough information, or z) insoluble because one set of numbers in the starting grid leads to a different answer from another set.
In this analogy, any system of axioms complex enough to do arithmetic with cannot be x) fully soluble and you can never be sure you've got case y) - all you can be sure of is that you haven't yet found you've got case z).
If you can use notation in algebra which can then formally prove concepts, how can it then not be consistent. Surely the one thing we can say about mathematical axioms is that they produce amazingly consistent results.
For example, if you have, say, five axioms, you may be able to use axioms one to four to prove that axiom five is untrue. As long as your set of axioms gives you enough complexity to model basic arithmetic using the system, it's impossible to prove it will never happen. That this is impossible has been proven.
(The proofs roughly work on the principle that if you could do that, you could create aa additional valid axiom that went this axiom is consistent with the others if and only if it isn't consistent with the others.)
As an analogy, a sudoku grid might either be x) soluble, y) insoluble because there's not enough information, or z) insoluble because one set of numbers in the starting grid leads to a different answer from another set.
In this analogy, any system of axioms complex enough to do arithmetic with cannot be x) fully soluble and you can never be sure you've got case y) - all you can be sure of is that you haven't yet found you've got case z).
But that doesn’t appear to be how mathematical proofs work. Take this example of students who are offering a new proof of Pythagoras. To be accepted and not fall into a fallacy, the proof has to use unrelated mathematical reasoning. In that case the law of Sines and trigonometry.
But that doesn’t appear to be how mathematical proofs work. Take this example of students who are offering a new proof of Pythagoras. To be accepted and not fall into a fallacy, the proof has to use unrelated mathematical reasoning. In that case the law of Sines and trigonometry.
I do not see why you think that contradicts what I was trying to explain?
But that doesn’t appear to be how mathematical proofs work. Take this example of students who are offering a new proof of Pythagoras. To be accepted and not fall into a fallacy, the proof has to use unrelated mathematical reasoning. In that case the law of Sines and trigonometry.
I do not see why you think that contradicts what I was trying to explain?
Well again, I’m not a mathematician, but it seems to me that the branches of mathematics (in that case trigonometry and algebra) have developed essentially independently and follow rules which are independent of each other. Presumably mathematicians think this, otherwise they wouldn’t accept that a proof using trig and sines for algebra.
What mathematical axioms are there that link algebra and trig?
Why would we expect trig and algebra to elegantly prove each other other than that they’re correct? And this is just a fairly simple idea based on thousands of year old mathematics. There are loads and loads of different links between different branches that have no good reason to be that closely linked and yet are.
It’s not just notation, it’s not just something about axioms, it’s that it is a complex puzzle that seems to fit together in a million different complex ways that have no business being connected.
Pythagoras's theorem and standard trigonometry are both theorems in Euclidean geometry. (Neither holds true in geometries that don't accept Euclid's fifth axiom.)
The whole reason this is a new proof is that it was previously believed that in order to derive any theorem in trigonometry you had to pass through Pythagoras's theorem. This new proof if valid shows that some trigonometric identities can be derived from the axioms of Euclidean geometry by another route.
(Geometry is dependent on the axioms of arithmetic and algebra is just generalised arithmetic with convenient notations.)
I too am a mathematical Platonist - the proof that no axiomatic system can be complete is phrased in terms that presuppose that mathematical truths exist - but I think mathematical entities are a lot more complicated than just collections of true propositions.
@MPaul:Well that may be but I don’t understand it.” @Martin 54:What may be? That I might understand it?.
Well Mr Sealion ..I am not tempted to engage further.
@KOF: I don’t think one really needs the named person in this scenario to be deluded, just a bunch of other people to put into him their own ideas of what he was about.
Yep, the assumption I make is that Jesus did and said what the gospels state he did and on that basis, CS Lewis is on the money for mine.
@MPaul:Well that may be but I don’t understand it.” @Martin 54:What may be? That I might understand it?.
Well Mr Sealion ..I am not tempted to engage further.
@KOF: I don’t think one really needs the named person in this scenario to be deluded, just a bunch of other people to put into him their own ideas of what he was about.
Yep, the assumption I make is that Jesus did and said what the gospels state he did and on that basis, CS Lewis is on the money for mine.
If small changes have big consequences then it adds a huge amount of uncertainty into all science. Because nobody is factoring in the impact of a butterfly into the weather models.
The butterfly effect is really a thought experiment in the philosophy of science, bringing into question whether something as small as a butterfly could influence a tornado. Probably not, but how could we possibly know?
The butterfly effect isn't really a thought experiment - as the wikipedia page explains, it's a poetic description of a chaotic system, in which a small perturbation can have big consequences. The butterfly effect is demonstrable, in the movement of a double pendulum in the example shown in the wikipedia page.
Lorenz originally used a metaphorical sea gull, but was persuaded to change it to a butterfly.
Comments
Things that aren't primarily physics and mathematics.
I'm not sure what you want me to say or what point you think you are making.
Science is a massive thing so this is really hard to answer, it isn't uniform and the same.
In many areas of biological science it is hard to be sure about anything and there is considerable uncertainty. I'm not sure progess has been halted but it is increasingly difficult to tell what is real/important from what isn't.
I was talking to a biologist the other day who was saying that there are labs that are pushing to have AI generate papers for results scientists don't have time to write up into papers. This just adds to the problem.
What point are you making about handwaving? Can you point to it in geology and chemistry and biology? And combined sciences? I'm not making any point, apart from making the point that you haven't substantiated your point of handwaving in these sciences.
It would also be helpful to have one or two specific examples of the phenomenon, otherwise the discussion is liable to turn into a ‘they do’ ‘no they don’t’ argument which won’t get us anywhere.
BroJames, Purgatory Host
To get it you have to ken Thomas Aquinas.
However, to the broader issue..
In your schema you demand physical evidence for the non physical perception. When you don’t see it you go..
“There, told you so..bunch of cretins!”
A more social approach might be: “Well that may be but I don’t understand it.”
I actually hadn’t seen that limerick @mousethief quoted before but it brought a smile.
And I also find CS Lewis very insightful remembering the lived experience at the back of his faith.
In the end, if Jesus is not God he is neither a great teacher or even a good man. He is deluded.
For me it's because people can provide evidence for their claims. And demonstrate that the stuff they make based on the theory works. Other fields of enquiry seem to lack that.
I'd make a very good atheist. I often wonder why I'm not one, if I'm honest.
Come on in, the water's fine.
The thing about maths is that you start with a set of axioms that everybody just agrees to, but never tries to prove. The whole thing pivots on a fulcrum of wax. As long as you leave those axioms in place, you can go on to create amazing patterns that are both beautiful and in many instances able to give structure to the physical sciences. (For instance the complex plane provides a mathematical framework for describing electromagnetic waves.)
But in philosophical terms, it's all if/then. IF you accept the axioms, THEN these mathematical statements unfold.
By this description philosophers are at least honest in their recognition that they are agreeing on something unproven, where mathematicians are not or don't care.
If the fulcrum is wax, then the axioms should at some times not work or lead to garbage, rather than a mathematical framework that describes real things. Wouldn't they?
How many axioms does it take to change a lightbulb? (1 dud + 1 working = 2). 379 pages worth.
Got ten thousand hours?
I wouldn't categorise engineering and technology as science. STEM subjects or disciplines are often lumped together, but they're regarded as being distinct.
I suspect most of what I'd call the science in a smartphone is decades old - I'd guess the most recent scientific innovations are in the battery, display and maybe the screen. But there's a been an awful lot of technological / engineering refinement over the years.
Which is all by way of saying that I think the point you want to make is getting caught up in the way you're organising the various disciplines.
For you. For me he was a great teacher and a good man and deluded. I blame the parents.
These are a) fractal and b) widely known and discussed issues.
There’s a replication crisis in much of science, particularly biological science
https://en.m.wikipedia.org/wiki/Replication_crisis
There is wide concern about the misuse of statistics
https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2016.00006/full
There is concern about too many papers being published
https://www.pnas.org/post/journal-club/scientific-progress-waning-too-many-new-papers-may-mean-novel-ideas-rarely-rack-up-citations
And so on and so on. Many different scales: local, global, methodological, philosophical, practical.
Mix in the fact that biology is messy and the factors which influence others are or might be extremely complicated and possibly not even possible to model and be understood
https://en.m.wikipedia.org/wiki/Butterfly_effect
The butterfly effect is really a thought experiment in the philosophy of science, bringing into question whether something as small as a butterfly could influence a tornado. Probably not, but how could we possibly know?
Because Engineering is a practical outpouring of physics in a way that no other science is.
In biology we know all kinds of things about the human body, from the smallest cell to the largest organ. But we can’t build a human from all those pieces of knowledge.
In engineering someone used ideas from mathematics which seemed entirely theoretical and weird and then in time that’s been manufactured and perfected into something you can hold in your hand. The most similar thing to that in biology is agriculture, and even that isn’t close to being what engineering has done to ideas from physics.
Or simply misunderstood and then misquoted by later religious zealots.
I don’t think one really needs the named person in this scenario to be deluded, just a bunch of other people to put into him their own ideas of what he was about.
Of course exactly the same thing could be said about almost all religious figures from antiquity.
The Mad, Bad or God trilemma has always had the fatal flaw that it depends on the gospels accurately reporting Jesus' words.
Well yes, but no.
Mathematics is particularly weird because it has such depth. It’s deep and goes deeper and deeper and deeper.
And as others said, it maps onto the world as we experience it in so many different ways. Just look at how many different biological functions are related to Pi.
Would it really be possible to do all that useful stuff if the fundamentals were just axiomatic porridge?
No. Nor have I said so. Nor have I hinted so. Nor have I given any indication I believe anything similar. Hopefully you get the point.
The axioms are very, very, very well chosen. But they are still axioms, unproven and accepted as an unproven starting point. Call that porridge if you will. I think the very results you are so triumphant about prove that is a foolish thing to call them.
Kurt Gödel's Incompleteness Theorems are widely regarded to have ended the search for a complete axiomatic system for mathematics. However he distinguished between truth and proof. Just because an axiomatic system has its limitations in providing mathematical proofs, this doesn't mean that mathematics doesn't contain necessary truths. Gödel remained a Platonist regarding mathematical entities until his death.
I have total good will toward Jesus and his words. That doesn't make him God. The flaw of the false trilemma is that Jesus was not mad and/or bad, or God. He was an exceptional but nonetheless historically deterministic son of an exceptional mother. I see no evidence of mental illness or ill intent in either of them.
True. But no axiomatic system which is developed enough to allow basic arithmetic can be both complete and consistent. With axiomatic systems which work they will be consistent (or they wouldn't work) but incomplete (i.e. there will be axioms whose truth are assumed but not proved).
From a mathematical point of view, axioms aren't so much intuited as chosen because they lead to interesting results.
So in which actual branches of actual biological science is this an actual problem? So there should be. In which branches of science by prevalence? How does this concern relate to handwaving? And is it of most concern in the actual biological sciences?
Handwaving must have a much bigger effect.
And why should we be concerned?
Last time I looked, medicine was a biological science. And it absolutely is a problem in other biological fields.
I’m not answering any more questions from you. Either accept that it is what it is, or don’t. I don’t care.
See also this in Nature: https://www.nature.com/articles/533452a
Accept what is what it is to do with handwaving? Rhetorically.
There's a name for your fallacy. At least one. False. Oooh, and Straw Man. As for formal (non sequitur), I don't have the degree for that. Feels like an argument from fallacy fallacy.
Generously I'd say that you were handwaving any attempt to get you to identify handwaving in biology in the context of existentialism and essentialism in particular.
(The proofs roughly work on the principle that if you could do that, you could create aa additional valid axiom that went this axiom is consistent with the others if and only if it isn't consistent with the others.)
As an analogy, a sudoku grid might either be x) soluble, y) insoluble because there's not enough information, or z) insoluble because one set of numbers in the starting grid leads to a different answer from another set.
In this analogy, any system of axioms complex enough to do arithmetic with cannot be x) fully soluble and you can never be sure you've got case y) - all you can be sure of is that you haven't yet found you've got case z).
But that doesn’t appear to be how mathematical proofs work. Take this example of students who are offering a new proof of Pythagoras. To be accepted and not fall into a fallacy, the proof has to use unrelated mathematical reasoning. In that case the law of Sines and trigonometry.
https://www.theguardian.com/us-news/2023/mar/24/new-orleans-pythagoras-theorem-trigonometry-prove
If you have a bit more specialized knowledge or feel slogging through more technical stuff, the Stanford Encylopedia of Philosophy is quite good. https://plato.stanford.edu/entries/goedel-incompleteness/
Well again, I’m not a mathematician, but it seems to me that the branches of mathematics (in that case trigonometry and algebra) have developed essentially independently and follow rules which are independent of each other. Presumably mathematicians think this, otherwise they wouldn’t accept that a proof using trig and sines for algebra.
What mathematical axioms are there that link algebra and trig?
Why would we expect trig and algebra to elegantly prove each other other than that they’re correct? And this is just a fairly simple idea based on thousands of year old mathematics. There are loads and loads of different links between different branches that have no good reason to be that closely linked and yet are.
It’s not just notation, it’s not just something about axioms, it’s that it is a complex puzzle that seems to fit together in a million different complex ways that have no business being connected.
Who’d have thought.
The whole reason this is a new proof is that it was previously believed that in order to derive any theorem in trigonometry you had to pass through Pythagoras's theorem. This new proof if valid shows that some trigonometric identities can be derived from the axioms of Euclidean geometry by another route.
(Geometry is dependent on the axioms of arithmetic and algebra is just generalised arithmetic with convenient notations.)
I too am a mathematical Platonist - the proof that no axiomatic system can be complete is phrased in terms that presuppose that mathematical truths exist - but I think mathematical entities are a lot more complicated than just collections of true propositions.
Yep, the assumption I make is that Jesus did and said what the gospels state he did and on that basis, CS Lewis is on the money for mine.
What do you base that assumption on?
The butterfly effect isn't really a thought experiment - as the wikipedia page explains, it's a poetic description of a chaotic system, in which a small perturbation can have big consequences. The butterfly effect is demonstrable, in the movement of a double pendulum in the example shown in the wikipedia page.
Lorenz originally used a metaphorical sea gull, but was persuaded to change it to a butterfly.
But similar to the wings of a gull.