BP:

*Usually what skeptics are asking for is "signs and wonders". Some, like Loftus, have quite specifically demanded to see stars arrange themselves to spell out Bible verses, or some such nonsense like that.*

It's quite amusing, actually. They are perfectly willing to accept all sorts of stuff "from authority", such as the Big Bang, or Dark Matter, or the existence of subatomic particles, or even (especially!) historical events like the execution of Socrates or the Battle of Salamis, for which we have but single sources of information... but when it comes to the New Testament, nothing short of they themselves being eyewitnesses will satisfy them.

It's quite amusing, actually. They are perfectly willing to accept all sorts of stuff "from authority", such as the Big Bang, or Dark Matter, or the existence of subatomic particles, or even (especially!) historical events like the execution of Socrates or the Battle of Salamis, for which we have but single sources of information... but when it comes to the New Testament, nothing short of they themselves being eyewitnesses will satisfy them.

## 80 comments:

Bayes fail.

Maybe Victor is right that the comment deserves its own thread, but I suggest that people first read it in context (in the thread below this one).

I don't agree with Loftus on needing eye-witness testimony but we all have different prior probabilities for different events.

In courts today we (mistakenly) often rely on eye-witness testimony but even there no reasonable juror would treat all eye-witness testimony equally conclusive, nor should they.

Given we have very good evidence people are sentenced to death but we possess no evidence outside of testimony that anyone has ever walked on water, it really shouldn't be surprising these claims are treated differently even if they both only have one source supporting them.

Given we have very good evidence people are sentenced to death but we possess no evidence outside of testimony that anyone has ever walked on waterUnless you've directly witnessed someone being sentenced to death, it seems that all the evidence for the fact that people are sentenced to death comes through testimony as well. Saying we need something "outside of testimony" to believe things would shrivel our knowledge base.

Jayman,

You've caught be being too vague semantically. When I said we have "no evidence outside of testimony" for people walking on water I didn't literally mean only things we see first hand counts as good evidence. I meant instead more that there is no corroborating evidence for the reports.

To make it explicit: We can reproduce corpses, images, videos, court transcripts, history books, first-hand accounts, living witnesses, first-person accounts, etc. which all indicate that people are in fact sentenced to death (not to mention anthropological and legal reasons why this happens) and though the technology wanes as you go back in history there is still a significant amount of evidence people were in fact sentenced to death in ancient times. So someone's probability that Socrates was sentenced to death is placed against this backdrop in which death sentences are very well supported.

Conversely, for claims of walking on water we have reports, which do count as evidence, but no other evidence indicates such a feat is possible. Indeed quite the contrary, everything I know about physics says the probability of someone walking on water is vanishingly improbable so I must weigh the credibility of these reports against what I know about physics. Of course, what I think I know about physics could be wrong but surely that doesn't mean all claims should have the same prior probability.

"They are perfectly willing to accept all sorts of stuff "from authority", such as the Big Bang, or Dark Matter, or the existence of subatomic particles, or even (especially!) historical events like the execution of Socrates or the Battle of Salamis, for which we have but single sources of information... but when it comes to the New Testament, nothing short of they themselves being eyewitnesses will satisfy them."And that is exactly how it should be. Nothing short of personally witnessing the myths in the NT will suffice, from an evidentiary perspective. Period.

In drawing on Marcus's courtroom analogy, science provides a mountain, not a figurative but a literal mountain, of supporting documentation quite apart from from speculative hearsay; we can reproduce results, repeat experiments, studies, images, videos, laboratory and in-field transcripts, history books, living witnesses conducting the experiments and confirming the results, first-person accounts, etc etc. by which the 'stuff of authority' about such things as the Big Bang, or Dark Matter, or the existence of sub-atomic particles, or the inability for anyone able to walk on water, all of which can be verified or checked against, independently of those that claim 'this stuff'. No miracle needs to be invoked as a means to short-circuit the universally accepted requirement to produce evidence and proof to back up claims at the minimum of thresholds.

And why shouldn't we expect or demand a higher level of proof of the NT's veridicality? It is after all, claimed to be the greatest moment, the greatest occasion in human affairs that has changed the course of human history. And that we should all believe it, affirm it, hallelujah it, because ............. [fill in your subjective personal experience/revelation/prophecy].

Judaism never for one moment bought the 'greatest story ever sold' [Acharya S], even from the very get-go two thousand years ago, right at the very time Jesus was supposed to be a massively popular and famous preacher/teacher. [The best apologetics can muster now is that he was a nondescript, itinerant apocalyptic reactionary dissident]. And the muslims never for one moment bought into the fable even though christianity had 600 unrivaled years to establish its veracity. And despite all that time the Islamists simply couldn't stomach the claptrap of the christian mythos, kicked it aside [indeed literally kicked christianity right out of its birthplace, all over the Middle East, right across North Africa and into Eastern Europe] and invented their own version of the Abrahamic spectral numen.

I say, rocks in the head.

In many ways, this could be perhaps the most important and significant discussion ever held on this website - what exactly constitutes "evidence" and how does one evaluate its efficacy.

A common skeptical trope is "Where's your evidence?" Christians (I am not here concerned with other religions) dutifully respond with a smorgasbord of reasons for their belief, from historical to textual to revelatory to personal... to philosophical arguments such the one from reason, the Kalam argument, the Five Ways, and on and on and on.

So there is absolutely no grounds whatsoever for a skeptic to claim there is

evidence. He can only (legitimately) say that he is not satisfied with what is there. On the other hand, the Christian is faced with the undeniable fact that what is convincing and sufficient to him appears to not impress the skeptic.noThe answer to this dichotomy may lie in what Shakespeare wrote in

Julius Caesar, "The fault, dear Brutus, is not in our stars, but in ourselves." No amount of evidence will suffice for a mind unwilling to accept it. All the philosophical arguments and all the physical and historical facts in the world will not work against a deliberately hostile will.I am well aware that what I am saying will ruffle a few feathers. So be it. I am perfectly willing to take on whatever label you wish to pin on me. But I here and now propose a counter to Loftus's self-styled "Outsider Test for Faith". Let's call it the "Insider Test for Motivation" (Note to Self: needs a catchier name).

I started out years ago naively thinking that we were all debating on a level playing field. I have since (sadly) come to accept the fact that atheists are by and large impervious to logic, reason, and argument. they are what they are because that is what they wish to be, and not because of any argument. Therefore, for an atheist to change his mind, he must first change his heart.

I will continue to proclaim Truth and refute error, but I will leave the convincing of others to Someone far above my pay grade.

So there is absolutely no grounds whatsoever for a skeptic to claim there is no evidence. He can only (legitimately) say that he is not satisfied with what is there.Correct. As a believer in God but an unbeliever in Christian theism I can state that I am unsatisfied by the available evidence in favor of orthodox Christianity.

Prokop:

No amount of evidence will suffice for a mind unwilling to accept it. All the philosophical arguments and all the physical and historical facts in the world will not work against a deliberately hostile will.That sword cuts both ways. Obstinance in the face of defeaters against a cherished belief is a human problem that affects every one of us, atheist and theist alike.

Prokop:

Therefore, for an atheist to change his mind, he must first change his heart.What does that mean exactly? Are you implying that unbelief in your particular brand of religion is due to a moral failing on the part of the unbeliever?

"

Are you implying that unbelief in your particular brand of religion is due to a moral failing on the part of the unbeliever?"No.

A wise man once wrote:

"Of course, one can still believe that unbelievers disbelieve because of 'sin' or 'suppressing the truth,' or what have you. But given the legitimate differences that can exist concerning the antecedent probability of the miraculous, I don't see how such charges can be defended."

Reasonable people disagree about tough topics all the time. Politics, economics, ethics, law, religion. No wonder: the evidence is often ambiguous and allows for different rational interpretations. But the ideologue or the fundamentalist cannot accept this. He has to believe the infidel is "without excuse." Orwell said it best: "The Catholic and the Communist are alike in assuming that an opponent cannot be both honest and intelligent."

Bob, can you clarify what you mean by stating that a person must first have a change of heart before they can or will believe. Many of us on the skeptic side reject Christian miracles because they run afoul of our plausibility structures. If you are part of a community that affirms a particular set of religious miracles, then the plausibility of those claims rises considerably because you have a kind of mutual reinforcement going on. If you exist outside of this community of like-minded individuals, you are far less likely to consider certain miraculous claims to be plausible.

Too long have people allowed the likes of Loftus, et.al., to get away with the idea that, while it takes an act of will to believe, it does not take one to disbelieve. What I am declaring war on is this notion that skepticism or disbelief is some sort of neutral position that the atheist does not choose.

Is disbelief a "moral failing"? I did not say so -

but neither will I say that it is not. I am silent on this issue, and will remain so. But although I cannot read into others' hearts, I can still discern when said hearts are engaged.And they most certainly are in this case.Which is why I maintain that ultimately it is not a matter of evidence or lack of it, but rather a case of one's inner alignments.

Might I recommend

The honour of Israel Gowby G.K. Chesterton, one of his "Father Brown" mystery stories? It concerns how one can approach evidence form varying angles and arrive at radically different conclusions, dependent upon one's going-in agenda."The Catholic and the Communist are alike in assuming that an opponent cannot be both honest and intelligent."Chris,

I have accused the "opponent" of being neither dishonest nor unintelligent. On the contrary, I have merely asserted that his honesty and intelligence are actively engaged in his decision (and it is a decision) to be an atheist.

Yes, you can quote me saying "atheists are by and large impervious to logic, reason, and argument." I stand by that statement, and see no impugning of anyone's honesty or intelligence in doing so. Indeed, it takes a remarkable degree of intelligence to navigate the tortured (il)logical path one must travel by to arrive at the conclusion that the universe is without meaning or purpose, and yet insist that objective truth is nevertheless knowable.

That I have hit upon a nerve (and a sensitive one at that) is demonstrated by the rapidity with which some people feel their morality has been questioned, or their intelligence impugned. Seems it's OK as long as we engage in a bloodless aetherial debate over high-sounding topics, but Heaven forbid that anyone try to bring the conversation down to where it might actually matter, to where words and ideas have consequences!

I think Bob is just making the (quite obvious) observation that atheists are just as vulnerable to irrational and dogmatic thinking as anyone else when it comes to religion. I don't think any intelligent person will attempt to dispute this point. As to whether such atheists are guilty of moral failure I think the answer is clearly yes.

They are hypocrites because they ask people to base their beliefs upon evidence yet they themselves will never base their beliefs about God on evidence. They are liars because they claim to be open minded and happy to believe if only the religious would show them evidence (when in fact they know that no amount of evidence will convince them). They are ignorant in the morally culpable sense that they claim that no evidence for God exists when it is usually clear that they have not studied the evidence and do not intend to study the evidence even though they could. They claim that if God existed he would make evidence of his existence more plain but they hold arguments for God to a standard unheard of in any area of discourse. Observe PZ Myers' declaration that should he wake up in the afterlife he still would not believe because it possible that he could be hallucinating, Jack Smart's admission that if he and the rest of the world saw that the stars spelt out the Apostle's Creed he still would not believe because it's possible that the world had gone mad, Graham Oppy's claim that if it were demonstrated that Moses had split the red sea this would not be enough to prove the Biblical God, Richard Dawkins' claim that a universe popping uncaused out of nothing by magic is a better explanation then it's being brought about by causal agent, Peter Atkins' proclamation that God could not have created the universe because the universe does not actually exist etc etc.

These people will believe anything if they think it helps them avoid theism and their irrationality is morally culpable. They are worse than any religious fundamentalists because fundamentalists are happy to admit that their beliefs are based on faith without evidence. These people are liars who claim to be rational and to care about the truth. In fact they are murderers of the truth and they have no respect for reason so long as it serves their purposes. They abuse words like 'science', 'evidence' and 'reason' in truly repulsive manner and twist them beyond all recognition. That some of them genuinely believe their attitude exemplifies reason demonstrates how truly corrupt they are. I am not saying that all or even most atheists are like this. I am saying that the idea that atheists cannot be fundamentalists is a delusion. I am saying that atheist fundamentalists are morally deficient and in many ways worse than religious fundamentalists. Just look at someone like Paps. Assume for a moment that he is not mentally ill, that he is not intellectually challenged and his brain functions normally and that he is not a troll but a generally intelligent and honest person. Do you actually mean to tell me that the level of stupidity he displays is not morally culpable? If we make those assumptions it should be clear that it's not that Paps can't understand what people say to him it's that he does not want to understand. That desire to not understand is in my view an immoral betrayal of the human intellect of our capacity for honest reflection.

"

[Atheists] know that no amount of evidence will convince them."An extremely interesting statement, and worthy of much thought. It ties in to my assertion that the real issue is not evidence or the lack of it. It even goes beyond one's willingness to consider what evidence we do have objectively. The rock bottom fact is that belief or non-belief are both full-body activities. As Someone once said, "You shall love the Lord your God with all your heart, with all your soul, and with all your mind." (Matthew 22:37) What so often happens in these debates is the mind gets all the attention, while the real action is going on in the heart and soul.

It's now time to bring out the Toolbox Analogy. The most vocal atheists have laid claim to "reason". I will not dispute that for the moment (despite actually have grave objections to their claim), but for the sake of argument will allow them that. Fine. "Logic" is like a single tool in one's toolbox - say, a hammer. It's good for driving in nails, but lousy at turning screws or tightening a bolt. For those tasks, you have to pull out your screwdriver or your wrench. But the stubborn atheist insists as seeing everything as a nail, and flails away with his one-and-only tool, regardless of whether it is even remotely appropriate to do so. There's a word for such a mindset - it's called insanity.

Meanwhile, the person of Faith recognizes when it's time to pull out the wrench of literature (note that my reference to Dostoevsky in another thread was ridiculed by one prominent hammer-wielder on this site), the screwdriver of art, the needle-nosed pliers of music, or the tape measure of personal experience.

I know, I know... the skeptic is already scorning my equating of such different means of acquiring wisdom (or even knowledge), having predetermined that what he calls "reason" (although it is actually far from it) is the only thing that counts. The inevitable result is what sadly just what one can expect from repeated blows of a hammer to anything - i.e., a mess.

Apologies for the extra "what" in the final sentence.

@B. Prokop:

(HTH to Holopupenko)

1. Atheists sin against the First commandment.

2. Sin dehumanizes the sinner.

3. If sin de-humanizes, the human capacities suffer in result of such de-humanization.

4. Reason is a human capacity.

5. Insofar as the atheist sins against the first and greatest commandment, it is to be expected that his capacity for reason itself suffers in result ofg such de-humanization.

6. If the atheist's capacity for reason is damaged, it is to be expected that he will be unable to rationally evaluate the rational arguments for God's existence.

7. Insofar as the atheist is rationally incapable of rationally evaluating the evidence for God's existence, he will sin against the first and greatest of all commandments.

Assuming the above contains a semblance of truth, how do you untie this gordian knot? You said it best. But to quote T. S. Eliot from the Four Quartets "For us, there is only the trying. / The rest is not our business."

See: http://www.firstthings.com/article/2007/11/003-can-atheists-be-good-citizens-5

grodrigues,

How dare you quote T.S. Eliot - and a poem at that?

Don't you know that that is... illogical???

I'd like to wade into this conversation, but I'm having a hard time figuring out how I'll swim against all your preconceived notions, from grodrigeus' assertion that I'm less than human to hyperentity's assertion that I'm a hypocrite. I guess that explains the quality of atheist contributors here.

I'm mean, really, do you want people to speak for themselves, or do you just want to paint atheists with broad brushstrokes?

Paintbrush! Now there's one tool I forgot!

By the way, my comments weren't referring to Bob, whose comments on this matter I found to be eminently reasonable.

@Dan Gilson:

"from grodrigeus' assertion that I'm less than human"

That is not what I asserted.

"

I mean, really, do you want people to speak for themselves?"Yes, we do. But speak

from the heart.I am personally inclined to throw irrationality charges around like manhole covers. There are atheists out there who think in lockstep and have no idea that that's exactly what they are doing, the intellectual fault that they accuse Christians of committing.

The exception is when it seems to me that people are padlocking their own most cherished beliefs from reconsideration.

Bob

"A common skeptical trope is "Where's your evidence?" Christians (I am not here concerned with other religions) dutifully respond with a smorgasbord of reasons for their belief, from historical to textual to revelatory to personal... to philosophical arguments such the one from reason, the Kalam argument, the Five Ways, and on and on and on.

So there is absolutely no grounds whatsoever for a skeptic to claim there is no evidence."

A couple of things:

1. "

I am not here concerned with other religions."A euphemism for: 'Based on exclusively christian tradition, all other religions are false'.

2. It is clever how

"a smorgasbord of reasons ... from historical to textual to revelatory to personal, ....to philosophical arguments, the Kalam arguments, the Five Ways, and on and on and on"[unspecified], segues into "evidence". Well no. Philosophical arguments, Kalam, Five Ways, history, textual interpretation, etc etc are reasoned propositions, not evidence. To generate a reasoned proposition can equally apply in substantiating the Book of Mormon, and millions of Mormons will tell you that. But as you and I know, the Book of mormon is highly unlikely to be regarded as evidence for its claims. And like the Book of Mormon, philosophical arguments, Five Ways etc are untested propositions, none [that I am aware of] have ever been tested to validate them. They are not proofs in themselves. Any construal of their constituting some form of evidence would be 'circumstantial' at best. To substantively meet a minimum standard, circumstantial evidence must be contextually corroborated by ancillary other, and independent evidence to justify a claim.And therefore the trope "Where's your evidence?" remains unchallenged.

The evidence that seems to be mounting is that religion is a social/cultural phenomenon and as history is telling us many social phenomena remain or disappear according to their usefulness in that culture or community. As the Mesopotamian, Egyptian, Greek and Roman etc religions became redundant, they were put out to pasture by new and different forms. So too is christianity undergoing gradual change as the community realizes that it is no longer capable of serving as a useful model for explaining the existential issues going forward. In essence, religion, particularly institutional religion as we know and understand it now, is reaching its use-by date.

Pope Benedict clearly understands that there will inevitably be a much smaller role for the church going forward, as the community explores more meaningful explanatory models. He notes:

"“The church will become small and will have to start afresh more or less from the beginning.She will no longer be able to inhabit many of the edifices she built in prosperity. As the number of her adherents diminishes . . . she will lose many of her social privileges. . . As a small society, [the Church] will make much bigger demands on the initiative of her individual members…. "

The rest can be read HERE

So, all this evidence you speak of Bob seems moot.

Dan: ''human to hyperentity's assertion that I'm a hypocrite.''

I didn't assert that you were a hypocrite. Nor did I assert that most atheists are hypocrites. I simply observed that some atheists are fundamentalists and that I consider fundamentalism to be morally objectionable. Do you disagree that atheist fundamentalists exist? And can you at least understand why someone would regard fundamentalism as morally objectionable?

Philosophical arguments, Kalam, Five Ways, history, textual interpretation, etc etc are reasoned propositions, not evidence. To generate a reasoned proposition can equally apply in substantiating the Book of Mormon, and millions of Mormons will tell you that. But as you and I know, the Book of mormon is highly unlikely to be regarded as evidence for its claims. And like the Book of Mormon, philosophical arguments, Five Ways etc are untested propositions, none [that I am aware of] have ever been tested to validate them. They are not proofs in themselves. Any construal of their constituting some form of evidence would be 'circumstantial' at best. To substantively meet a minimum standard, circumstantial evidence must be contextually corroborated by ancillary other, and independent evidence to justify a claim.And therefore the trope "Where's your evidence?" remains unchallenged.

WOW. Are you SERIOUSLY trying to say that reasoned argument is invalid because it can't be corroborated by the scientific method? Holy shit. Never underestimate the power of stupidity, I guess.

I guess we should disbelieve in the Pythagorean theorem because it can't be supported by independent evidence and can only be proven by "reasoned argument". Because science is TOTALLY the only way to gain ANY knowledge about ANYTHING. Logical reasoning is SO pre-scientific.

I guess it fits since your reductive materialist worldview can't accommodate logical reasoning anyway (since it entails that people can't literally think about anything).

ingX24

>

"WOW. Are you SERIOUSLY trying to say that reasoned argument is invalid because it can't be corroborated by the scientific method? "Yes I am, if reasoned arguments cannot be substantiated by evidence. The scientific method is simply a process to help us discern reality and to help us understand how nature operates. Its methodology simply dwarfs any other explanatory method conceived by man into abject insignificance, and can be applied in almost any, if not every, area of scholarship, and human activity, be it historical, sociological, anthropological and even theological. In fact such a method would assist in clearing away much accreted flotsam and jetsam accrued over millennia of acquired knowledge. Reasoned argument alone is not evidence or proof. It must be substantiated. Philosophy is reasoned argument, not substantive proof. That is why philosophy works equally well for supporting atheism as it does for theism and why there are two camps in the theo-philosophical arena. Let's line them up HERE and HERE

I'd say a smorgasbord of talkfest.

As I have iterated here on a number of occasions, there are two forms of philosophy, scientifically-informed philosophy or scientifically-uninformed philosophy. Scientifically-uniformed philosophy is just .... well, theology. [Or in keeping with the christian mythos, theology is just scientifically-uniformed philosophy with wings.]

>

"I guess we should disbelieve in the Pythagorean theorem because it can't be supported by independent evidence."But can be supported by independent evidence. Every day regardless of where they may live around the world, mathematicians, engineers, builders, designers, normal average people, etc etc prove it by application every single day. The square of the hypotenuse of a triangle is exactly equal to the sum of the squares of the other two sides. Even logarithmic [sine, cosine, tangent] tables substantiate it.

Anyone who does not believe in the efficacy of the scientific method is a doubting Thomas, a science denier.

But can be supported by independent evidence. Every day regardless of where they may live around the world, mathematicians, engineers, builders, designers, normal average people, etc etc prove it by application every single day. The square of the hypotenuse of a triangle is exactly equal to the sum of the squares of the other two sides. Even logarithmic [sine, cosine, tangent] tables substantiate it.You must not have any idea what math is. The reason the Pythagorean theorem is justified is not because we have empirical evidence that it works. The reason it's justified because the mathematcal reasoning behind it is valid. Let me repeat: THE SCIENTIFIC METHOD DOES NOT HAVE ANYTHING TO DO WITH MATHEMATICAL PROOFS. If you cannot understand this, you are a fucking idiot. Period.

Anyone who does not believe in the efficacy of the scientific method is a doubting Thomas, a science denier.So anyone who doesn't think science can be applied to LITERALLY EVERYTHING is a "science denier". Right. It couldn't POSSIBLY be that maybe science doesn't have a monopoly on rational inquiry, noooo...

Also:

Even logarithmic [sine, cosine, tangent] tables substantiate it.Sine, cosine, and tangent are not logarithmic. They are trigonometric.

ingX24

'Sine, cosine, and tangent are not logarithmic. They are trigonometric."Yes they are. Sine cosine and tangent are trigonometric

functionsbut they also happen to be logarithmic.Plerase note:

"Briggs and Vlacq also published original tables of the logarithms of the trigonometric functions. Briggs completed a table of logarithmic sines and logarithmic tangents for the hundredth part of every degree to fourteen decimal places, with a table of natural sines to fifteen places, and the tangents and secants for the same to ten places; all of which were printed at Gouda in 1631 and published in 1633 under the title of Trigonometria Britannica. Tables logarithms of trigonometric functions simplify hand calculations where a function of an angle must be multiplied by another number, as is often the case."Wiki@Papalinton:

"Sine cosine and tangent are trigonometric functions but they also happen to be logarithmic."

No they are not. It is right there in the first sentence of your quote: "Briggs and Vlacq also published original tables of the logarithms of the trigonometric functions." Notice the phrasing? Logarithms *of* trigonometric functions, that is, log(sin(x)), log(cos(x)), etc.

Pap:

The functions (sine, cosine, tangent) are trigonometric.

The tables used in the 17th century for engineering or navigation often were tables of the logarithms of the trigonometric function values, ie

A table of Log10(tangent(x)) x from 0 to 90 degrees

...this was because in the 16th century it was easier to add logs and do a table look-up of the logarithmic result than to do a large multi-digit multiplication.

Yes, they had no calculators then :)

ingx,

You made a statement about how the Pythagorean theorem had no independent support, not about why we believe it to be true. The fact of the matter is that there is empirical evidence that does support its truth and that can be demonstrated to anyone who can see: http://www.youtube.com/watch?v=CAkMUdeB06o

If you think bringing mathematical proofs into the discussion is relevant, then you have misunderstood what Papalinton was saying about syllogisms. He is not saying that valid arguments don't bring forth true conclusions, he is commenting on why we think the premises are true. The comparison to mathematics is why we think the axioms are true (as in, do they relate to reality), and that requires empirical evidence.

ingX24

>

"So anyone who doesn't think science can be applied to LITERALLY EVERYTHING is a "science denier".Yep, pretty much. There is much work now being undertaken in the the various neurosciences [neurological and a neurophysiological studies etc ] that is providing a solid foundation on the neuro-cognitive systems involved in the development of morality/moral behaviour.

Theism will largely become redundant and will be obligated to relinquish its claim to any exclusive prerogative it imagines it has as the purveyors of all things moral. The evidence of this transition is clearly evident in the community. Theism was incapable of resolving the issue of a woman's right to control her own body, theism was incapable of resolving the issue of homophobia and extending fairness and justice towards gays, to name but a few. Indeed theism was relegated to the margins of the debate when these heavily-weighted moral issues were decided within the community.

A new moral landscape [hat tip to Dr Sam Harris] is emerging that will advance our understanding of what it is to be moral, how morality works and why morality is an integral element of the evolution of humans and human behaviour.

Any philosopher who does not take account and incorporate this perspective in their deliberations is not contributing to productive philosophy.

William

>

'..this was because in the 16th century it was easier to add logs and do a table look-up of the logarithmic result than to do a large multi-digit multiplication."Spot on. Fast forward 300 years, I only have to go back to my highschool days in the 1960s to appreciate the use of the ubiquitous log tables. There were no personal or readily accessible calculators in those days. We would not have been able to do math without them.

@cautiouslycurious:

"The comparison to mathematics is why we think the axioms are true (as in, do they relate to reality), and that requires empirical evidence."

No it does not. Only an ignorant of modern mathematics can make such a statement.

ingX24: "

So anyone who doesn't think science can be applied to LITERALLY EVERYTHING is a "science denier."Linton: "

Yep, pretty much."There you have it, in one short exchange.

Like I said - a hammer-wielder. Only one tool in the toolbox.

grodrigues,

"No it does not. Only an ignorant of modern mathematics can make such a statement."

There's not much to say because you've simply responded with a "Nuh uh" and ridicule; no content what so ever. Perhaps you can think of an application of mathematics where the relevant axioms don't apply, I'd like to see a counerexample since I can't think of any at the moment.

Recent HuffPost blog - this is my chance to put it up, while the discussion is at least slightly about the value of philosophy:

For a Better Society, Teach Philosophy in High Schools

http://www.huffingtonpost.com/mike-shammas/for-a-better-society-teac_b_2356718.html

Just guessing here (since I'm not Grodrigues), but perhaps he's alluding to the axioms underlying non-Euclidian (hyperbolic or elliptic) geometries?

"Recent HuffPost blog - this is my chance to put it up, while the discussion is at least slightly about the value of philosophy:

For a Better Society, Teach Philosophy in High Schools"

I've always felt that a Philosophy of Science course would benefit me greatly, as a BioTech major. I regret not registering for one, and it seems like a daunting undertaking to study be myself. Are there any good books people recommend? Instead of just teaching what to think, they should also teach how to think.

@cautiouslycurious:

"There's not much to say because you've simply responded with a "Nuh uh" and ridicule; no content what so ever."

There was no ridicule, but a simple statement of fact: you do not know what you are talking about, period. I do not know how more explicit do you want me to be. You said and I quote:

"The comparison to mathematics is why we think the axioms are true (as in, do they relate to reality), and that requires empirical evidence."

There are two distinct claims here:

(A) we believe axioms are true because of a "comparison to reality".

(B) "comparison to reality" requires empirical evidence.

If you were employing AT jargon there is indeed a sense, a qualified sense, in which both (A) and (B) are true. Since you are not, they are not. It can range from demonstrably false to plainly incoherent depending on how exactly you spell out "comparison to reality" and "empirical evidence". And I stick by what I said: such statements are made by people ignorant of mathematics, of its relation to the empirical sciences and of empirical sciences themselves.

"Perhaps you can think of an application of mathematics where the relevant axioms don't apply, I'd like to see a counerexample since I can't think of any at the moment."

I do not understand what you are asking exactly.

ozero91,

Not explicitly books on the philosophy of science, but two that delve deeply into the subject in quite different ways are:

1.

The Geographies of Marsby K. Maria D. Lane, which explores at length the relationship between scientific consensus and cultural environment. Extremely fascinating and quite readable.2.

Voyagerby Stephen J. Pyne, a wide-ranging book which relates the story of the Voyager space probes in their historical, cultural, anthropological, political, and philosophical contexts. One of the best "Meaning of Science" books I have ever read - and a lot of fun.Highest recommendations to both! Either one covers an area far larger and more significant than either their titles or putative subject matters might suggest.

Grodrigues,

My statement is fairly trivial, which is why I’m shocked that you are putting up so much resistance against it. If the axiom is that you need a right triangle, I’m asking how do you know that axiom applies to the triangle in front of you, not whether Pythagoras’s theorem is valid or not. Basically, we can think of mathematics as conditional claims; if X, then Y. If you have a right triangle, then the square of the hypotenuse is equal to the sum of square of the legs. However, does that antecedent apply to the triangle in front of me? I don’t know; I need to measure the angles of the triangle in front of me. In other words, I need to gather empirical data. If I find that the triangle in front of me does not contain a right angle, I can’t apply Pythagoras’s Theorem because the assumptions don’t apply to the given example. To argue from thereon would be to use an argument with a false premise (i.e. a premise that doesn’t relate to reality). Basically, the conditional statements are being used as a premise in an argument, but the assumptions, axioms, etc. themselves are also being used as a premise and they need to be supported by empirical evidence in order to make the argument sound.

Tldr: There is nothing wrong with trying to find out what follows from a set of assumptions. However, I merely said that the assumptions need to apply to reality in order for them to be considered true and the only way I know how to determine that is by empirical evidence. Perhaps you can suggest a counterexample.

cautiouslycurious,

Repeating myself here, but perhaps the axioms underlying non-euclidian geometries could be the counterexample you are looking for. Try verifying Lobachevskian Geometry by empirical evidence!

@cautiouslycurious:

"However, I merely said that the assumptions need to apply to reality in order for them to be considered true and the only way I know how to determine that is by empirical evidence. Perhaps you can suggest a counterexample."

Thanks for the clarification.

If I am reading you right, and since "axioms are true" is shorthand for "they relate to reality", what you are saying boils down to "in order to know if some set of axioms applies to reality we need to know if they apply to reality".

I do not wish to quibble with such profound insights, but since there is some wiggle room to maneuver between "applies to reality" to "need empirical evidence", I must ask you for your argument that mathematical Platonism is false.

Bob

'Like I said - a hammer-wielder. Only one tool in the toolbox."A misconstrual at best. Under the rubric of science is a panoply of scholastic and investigatory disciplines, ranging from the 'soft' to the 'hard' sciences.

Theism, particularly christian theism, is not one of those disciplines. Theism resides in the same category of humanity's knowledge base alongside mythology, new-age spiritualism etc.

Bob,

“Repeating myself here, but perhaps the axioms underlying non-euclidian geometries could be the counterexample you are looking for. Try verifying Lobachevskian Geometry by empirical evidence!”

What are the applications of that area of geometry?

Grodrigues,

“If I am reading you right, and since "axioms are true" is shorthand for "they relate to reality", what you are saying boils down to "in order to know if some set of axioms applies to reality we need to know if they apply to reality".”

Basically. It’s like forming an argument that says:

1. If you have a right triangle, then the square of the hypotenuse is equal to the sum of square of the legs.

2. The triangle in question is a right triangle.

3. Therefore, the square of the hypotenuse of the triangle in question is equal to the sum of square of the legs of said triangle.

For the purposes of mathematics, premise two is simply assumed in order to find the implications of such a statement. However, in the argument, application, real world example, etc., if you want the conclusion to be sound, you need to support it (dare I say, by empirical evidence).

“I do not wish to quibble with such profound insights, but since there is some wiggle room to maneuver between "applies to reality" to "need empirical evidence", I must ask you for your argument that mathematical Platonism is false.”

But quibble you did. I wasn’t seeking to be profound; I was merely correcting an analogy, but nonetheless you’ve made a mountain out of a molehill. Sure, there is some wiggle room, which is why I asked you for a counterexample. It is not something that is entailed, but it is supported inductively. I don’t see how whether mathematical Platonism being true or false is relevant here so I’m disinclined to jump down that rabbit hole at this time. Regardless, shifting the burden of proof is not the correct way to go about things.

I've always felt that a Philosophy of Science course would benefit me greatly, as a BioTech major. I regret not registering for one, and it seems like a daunting undertaking to study be myself. Are there any good books people recommend? Instead of just teaching what to think, they should also teach how to think.A great starting place is

The Routledge Companion to Philosophy of Science. If you look it up on Amazon, you can find the TOC and see that it includes historical analysis, more contemporary issues ('naturalism'), and a great deal of analysis to specific concepts such as 'evidence', 'confirmation', etc. It's a bit pricy - but with the amount of (quality) reading it's worth it.Another, less expensive choice is

Introductory Readings in the Philosophy of Scienceedited by Hollinger, Kline, and Rudge. It is not as exhaustive as the Routledge companion, but it will provide a sufficient introduction to philosophy of science.Can't you support the pythagorean theorem with a mathematical proof/deduction, and show that no matter the case, the theorem is necessarily true for right triangles? I don't see how something like the water demonstration in the video makes us any more or less confident about the theorem's validity.

Can't you support the pythagorean theorem with a mathematical proof/deduction, and show that no matter the case, the theorem is necessarily true for right triangles? I don't see how something like the water demonstration in the video makes us any more or less confident about the theorem's validity.This is the point I was trying to make. Finding examples of the Pythagorean theorem working isn't the reason we believe it - we believe it because the logic (mathematics) supporting it is sound.

Mathematical truth is a matter of internal consistency within the schema. It's like the truth of a word's definition, only harder to see than the dictionary.

Common usage for "truth" often means external validity, not just internal consistency.

Commonly we mean by truth a correct correspondence of our model (mathematical or otherwise) to the facts of our shared external world, and hopefully the ability to predict future new data in a way a bad model cannot.

This might help frame the discussion. Credit to Sam Nelson.

"Theorems are what mathematics is all about. A theorem is a statement which has been proved true by a special kind of logical argument called a rigorous proof. A rigorous proof is simply a sound deductive argument, meaning that it starts with statements which we know to be true and then makes small steps, each step following from the previous steps, until we reach our conclusion. One statement follows from another if it's impossible for the first statement to be false while the second is true. For example, the statement "Socrates is mortal" follows from the statement "All Greeks are mortal, and Socrates is a Greek" -- it is impossible for "All Greeks are mortal, and Socrates is a Greek" to be true without "Socrates is mortal" also being true. Hence, if we start with statements which we know to be true, then any statement which follows must just as certainly be true.

Once a theorem has been proved, we know with 100% certainty that it is true. To disbelieve a theorem is simply to misunderstand what the theorem says."

http://www.esotericka.org/cmc/tth.html

Ozero,

“Can't you support the pythagorean theorem with a mathematical proof/deduction, and show that no matter the case, the theorem is necessarily true for right triangles?”

Sure, but that alone has no real world application. It would be like formulating syllogisms without having any means of knowing whether the premises are true. This would be satisfactory for someone looking only for validity, but not for someone who is looking for soundness. The only way for those syllogisms to be relevant for someone looking for soundness is if we have some information about whether or not the premises are true. Since we are able to verify the axioms of Pythagoras’s theorem in real world examples by using a protractor and straight edge, the math becomes relevant.

“I don't see how something like the water demonstration in the video makes us any more or less confident about the theorem's validity.”

Let’s put it this way, if you draw out (http://www.mathsisfun.com/geometry/images/pythagoras-abc.gif) and you tell someone that the area of C is equal to the area of B+A, and they doubt you, the water illustration is demonstrable evidence for that claim. I’m quite positive that it would raise their confidence in the theorem’s validity.

@William:

"Mathematical truth is a matter of internal consistency within the schema."

This is not quite correct; if mathematical truth was just a "matter of internal consistency" then there would be no difference between PA + Con(PA) and PA + not-Con(PA). But no one gives a hoot about PA + not-Con(PA), not even those like E. Nelson that suspect that not-Con(PA) is true.

@cautiouslycurious:

My previous response seems to have been eaten by blogger; no problem, as my first suspicions were confirmed by your response to ozero91. I cannot help however to repeat this little tidbit:

To B. Prokop's question (about non-Euclidean geometry) you answer:

"What are the applications of that area of geometry?"

You *have* got to be joking, right?

"Sure, but that alone has no real world application."

And?

"It would be like formulating syllogisms without having any means of knowing whether the premises are true."

No, it is not. Mathematicians have ways of arguing for the correctness of axiomatic systems -- just witness the vast body of work on large cardinal axioms, inner models, Woodin's Ultimate Set Theory, the reverse mathematics programme, etc. A lot of work, both on the mathematical and the philosophical front has been done, and to put it shortly, you simply do not know what you are talking about.

"This would be satisfactory for someone looking only for validity, but not for someone who is looking for soundness."

Do not misabuse technical jargon. What you mean by soundness is whether it applies to modeling the physical, real world or not. The fact that a piece of mathematics does not have such an application does not make it "unsound".

"The only way for those syllogisms to be relevant for someone looking for soundness is if we have some information about whether or not the premises are true."

They are relevant to mathematicians and to mathematics as the autonomous theoretical discipline that it is. And for the second time you are conflating two things: "whether or not the premises are true" and whether some piece of mathematics can be used to model the world.

"Since we are able to verify the axioms of Pythagoras’s theorem in real world examples by using a protractor and straight edge, the math becomes relevant."

No we are not able to "verify the axioms of Pythagoras’s theorem". You are talking foolishness.

Grod: Even if we found that PA was inconsistent when dealing with problems related to infinities, wouldn't that leave a very large swath of PA (the practically calculable part) that was yet consistent? I haven't seen it, but I got the impression that Nelson's maybe proof has to do with inconsistencies related to the infinities not supported in PA?

Grodrigues,

“You *have* got to be joking, right?”

You’re aware of the Socratic Method, right?

“No, it is not. Mathematicians have ways of arguing for the correctness of axiomatic systems -- just witness the vast body of work on large cardinal axioms, inner models, Woodin's Ultimate Set Theory, the reverse mathematics programme, etc.”

Look up the definition of axiom. And before you retort that it is not the primary definition of the dictionary, my usage of it should be clear from context, as in, using it interchangeable with the term assumption, but you apparently missed that part. For your convenience:

Logic, Mathematics . a proposition that is assumed without proof for the sake of studying the consequences that follow from it.

“Do not misabuse technical jargon. What you mean by soundness is whether it applies to modeling the physical, real world or not. The fact that a piece of mathematics does not have such an application does not make it "unsound".”

When I am talking about soundness, I am talking about the topic and argument that is being discussed, but maybe you missed that part of the discussion. If the premise is false (2. The triangle in question is a right triangle.), then yes, the argument is not sound. It is inconsequential whether the first premise is true and I never doubted that, and this point seems to have gone over your head. If you don’t have a right triangle, then the conclusion that follows from that will not be sound. You keep harping on the first premise and that is not the scope of this discussion. You need both premises for a sound argument so your objection is bizarre to say the least.

“They are relevant to mathematicians and to mathematics as the autonomous theoretical discipline that it is. And for the second time you are conflating two things: "whether or not the premises are true" and whether some piece of mathematics can be used to model the world.”

Again, you’re missing the point. The argument includes more than simply the theoretical framework. So, yes, whether or not the premises are true impacts whether or not that piece of mathematics can be used to model the world. I also explained why they are relevant to mathematicians, but you apparently missed that part as well.

“No we are not able to "verify the axioms of Pythagoras’s theorem". You are talking foolishness.”

Can you determine whether a shape is composed of three straight lines and has a right angle? Congratulations, you can verify that the preconditions for Pythagora’s theorem apply to your real world example. I don’t understand why you insistently argue against simple statements with such conviction yet don’t put any effort into understanding what is said. If you don’t spend more time listening, then this is not a dialogue, this is simply an endless stream of me correcting your misinterpretation of what I’ve said and it’s getting quite tiresome.

Bob Prokop does make a convincing case that when 2 Peter mentions a talking donkey, then a talking donkey could really exist.

But why do sceptics want evidence before accepting the veracity of a book which has talking animals in it?

It is like them asking for evidence that Muhammad really did ascend to Heaven on a horse.

Look, Muslims say it happened.

Isn't that enough for sceptics?

If the New Testament says Jesus flew into Heaven after being resurrected, why do sceptics point out that this is the product of a culture that believed that Heaven was somewhere above the sky?

Steven,

You obviously have never read C.S. Lewis's explanation of the Ascension in chapter 16 of his book

Miracles(this is a website about Lewis, after all), and why it appeared to the Apostles as a vertical movement into the sky. Either that (which is, by the way, the charitable explanation) or you have either:A. demonstrated a complete inability to comprehend the written word, or

B. shown yourself to be even more "mule-headed" than Balaam's ass, of which you make so much fun.

I'll play nice (for now) and give you a chance to fill the gap in your education by reading said chapter. But that's it. You only get one chance. After that, I will have no choice but to lump you into the same category as Linton, i.e., a person impervious to any thought outside his self-made mental prison.

You obviously have never read C.S. Lewis's explanation of the Ascension in chapter 16 of his book Miracles (this is a website about Lewis, after all), and why it appeared to the Apostles as a vertical movement into the sky.Why not enlighten us on Lewis's explanation? I don't have Lewis's book, nor am I that interested in buying it. I have stated before on this blog that I find the ascension to be even more unbelievable than any of the resurrections mentioned in the bible. One Christian commenter suggested that Jesus staged a dramatic exit into the sky in an attempt to stave off the heresy of docetism. Other commenters suggest that if you accept one miracle you might as well accept all of them.

@William:

"Even if we found that PA was inconsistent when dealing with problems related to infinities, wouldn't that leave a very large swath of PA (the practically calculable part) that was yet consistent?"

What would be "left" depends on where the inconsistency is located exactly. But *something* like what you say is probably true. For one, because consistency of PA is equivalent to certain infinitary statements about sequences. For another, because at least in the case of Nelson, and if my meager knowledge and even thinner memory is not betraying me, much of his discussion is centered around the totality of the exponential function.

"I haven't seen it, but I got the impression that Nelson's maybe proof has to do with inconsistencies related to the infinities not supported in PA?"

Me neither, but you can knock yourself out by reading his "Predicative arithmetic" to get a taste for his views as it is available online. His alleged proof of the inconsistency of PA in 2011 was retracted because an error was found. Nelson is a hard-core formalist and a finitist, but he views commonly accepted *finitary* reasoning as unjustifiable. His critique is not so much about effective computability (this would be the most plausible interpretation of the ultrafinitist stance -- an insistence on having effective, polynomial say, bounds on the constructions and algorithms) but on impredicative uses of the induction axiom schema. He neither regards all primitive recursive functions as predicatively defined (so he would reject even PRA, which is commonly viewed as the formalization of finitary reasoning) neither he accepts Sigma_1-induction.

Two more comments.

1. In the original post I objected on the reduction of mathematical truth to a "matter of internal consistency" on grounds that there is a real asymmetry between formal systems. But there are other arguments. For one, such a reduction takes as implicit that mathematical truth is reducible to provability, but if there is one thing that Goedel taught us is that truth is not exhausted, and therefore not reducible, to provability.

2. You say that "a very large swath of PA" would survive an inconsistency proof. I cannot measure how large it would be, I will say this however. If a consistency were found in ZFC, even in ZF, it would be a most stunning and spectacular achievement no doubt, and a clear sign that the mathematical community at large had taken a wrong turn somewhere. Really wrong turn. Even so, it would survive. We would pare down ZF(C) to some acceptable subsystem and business would go on as usual. After all, outside of logicians and set-theory experts what mathematician sticks his nose beyond the first few stages of the Von-Neumann hierarchy? V_{w}? Hardly ever. V_{w_1}? What is *that*?. So ZF(C) is way way overkill for most practical purposes. But PA? C'mon. If PA were found inconsistent, there would be something *fundamentally wrong* with our mathematical intuitions, and if that happened we should probably all go home and stop doing mathematics.

@cautiouslycurious:

"You’re aware of the Socratic Method, right?"

Are you not aware that in general relativity space-time is a four-dimensional manifold with a Lorentzian metric - oh look, a non-euclidean geometry! That in classical mechanics, the phase space of a classical system is a symplectic manifold (usually the cotangent bundle of the configuration space) - oh look, another non-euclidean geometry!

I will skip your "correcting [my] misinterpretation" right to the last paragraph.

"Can you determine whether a shape is composed of three straight lines and has a right angle? Congratulations, you can verify that the preconditions for Pythagora’s theorem apply to your real world example."

You are wrong on all counts: on the nature of mathematics, on its relation with the empirical sciences and on philosophical grounds. Just to give you a hint of how confused and muddle-headed you are, let us take your words at face value: lines as existing in the real world, being enmattered, *cannot* be perfectly straight lines. Triangles as existing in the real world, being enmattered, *cannot* have right triangles. Euclidean geometry, in any of its mathematical formalizations, is an abstraction of our common sense experience; lines, right triangles, etc. being abstract objects, if they have any extra-mental reality, do not exist in the physical world, but rather as universals they are *imperfectly* instantiated by the particulars of our common sense experience. Or more prosaically, no physical, real world triangle is really a triangle, much less a right-angled triangle. Does this answer your question about verifying "the preconditions for Pythagora’s theorem"?

"I don’t understand why you insistently argue against simple statements with such conviction yet don’t put any effort into understanding what is said. If you don’t spend more time listening, then this is not a dialogue, this is simply an endless stream of me correcting your misinterpretation of what I’ve said and it’s getting quite tiresome."

Above you say that I "keep harping on the first premise" and that my "objection is bizarre to say the least". Then in the quoted paragraph that I am "insistently" arguing "against simple statements", that I am not putting any effort into understanding and whatnot. Ok. According to quantum mechanics the state space of a quantum system is a complex Hilbert space, in most realistic cases infinite-dimensional, and an observable is an operator (closed but alas, usually unbounded) on this Hilbert space. Now tell me, how do you "verify" this?

"

I don't have Lewis's book, nor am I that interested in buying it."Walter, you can get a used copy for just $2.64 plus shipping on amazon.com. Surely you can spring for that. The chapter is just too long to adequately summarize in a pithy blog posting. Wouldn't do it justice.

Besides, I really do think that reading

Miraclesought to be a prerequisite for anyone getting on this particular website.Walter, you can get a used copy for just $2.64 plus shipping on amazon.comActually, I just found the chapter online. I agree that some arguments simply cannot be effectively reduced to sound bites, but I do find it a little annoying that you yourself will not follow links or read anything that is not posted in Victor's combox, while at the same time berating others for not doing what you won't do. Sauce for the goose...

But I didn't ask you to go to a link... :)

Anyways, this very website is

based, for Heaven's sake, on Lewis's Argument From Reason. AndMiraclesis where Lewis put forth that argument. It seems incumbent on anyone who wants to explore the subject to at the very leastreadit.I am at this site because I have read Victor's version of the AFR, and I have also read Beversluis' book critiquing Lewis.

But we are not exploring the argument from reason in this discussion, we are currently discussing the Ascension, so I don't feel that I need to be familiar with every single thing Lewis ever wrote before I am qualified to inquire about this particular issue. Having said that I have now read the relevant chapter where Lewis defends a vertical ascension and I find his explanation to be rather unsatisfying.

"

I find his explanation to be rather unsatisfying"Interesting. A perfect example of how the identical information can strike two persons so differently. I found the chapter to be profound and downright

wise. All sorts of implications there, concerning how a supernatural concept needs to be communicated to beings like ourselves through the senses, which means employing what amounts to sensory metaphor. (e.g., an upward movement during the Ascension is 1. literal, in that it is what the Apostles saw, and 2. metaphorical, in that it conveys a far more important reality, of which the literal upward movement is only a means of expression.)Grodrigues,

“Just to give you a hint of how confused and muddle-headed you are, let us take your words at face value: lines as existing in the real world, being enmattered, *cannot* be perfectly straight lines. Triangles as existing in the real world, being enmattered, *cannot* have right triangles.”

So let me get this straight, if someone comes to you and says that they want to form a right triangle. That they have cut out a piece that is 3 feet long and a piece that is 4 feet long and they have set them at ninety degree from each other so that the edges are touching. He comes to ask you how much he should cut for the third leg, what do you say? Do you say that if we assume perfectly straight lines, we can use Pythagorean Theorem and determine that you would need 5, but since you don’t have perfectly straight lines (and you can’t be accurate enough with the protractor), we are unable to determine how much you need for the third piece? With such a view, the Pythagorean Theorem becomes irrelevant to the real world because as you say, the assumptions are always false. If you think that it can be used in this example to tell the person to cut out a piece 5 feet long, I’d really like to see the argument you use to support your conclusion because you definitely can’t use the one I posted earlier because you think that one is unsound.

@cautiouslycurious:

Answer my last question, please, and then I will have a clearer idea of how to address your other questions.

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Grodrigues,

“According to quantum mechanics the state space of a quantum system is a complex Hilbert space, in most realistic cases infinite-dimensional, and an observable is an operator (closed but alas, usually unbounded) on this Hilbert space. Now tell me, how do you "verify" this?”

Well, I usually don’t touch quantum mechanics even with a ten foot pole, so forgive me that this is not on my radar. Because of that, I can't respond with specifics, but I hope this will suffice. When you say “according to quantum mechanics” is this part of a given interpretation or is this part of the hypothesis that was used to make predictions? Basically, how do you know that “the state space of a quantum system is a complex Hilbert space”? If the former, does that interpretation make predictions that differentiate it from other interpretations? If so, then we can test those. If the latter, then it already has to a certain extent. It is not conclusive proof, but it does raise our confidence in it, and if it does so to a certain degree, it’s considered verified.

@cautiouslycurious:

"Basically, how do you know that “the state space of a quantum system is a complex Hilbert space”?"

Nothing to do with any interpretations, just basic textbook QM.

I repeat my question. You said and I quote:

"Can you determine whether a shape is composed of three straight lines and has a right angle? Congratulations, you can verify that the preconditions for Pythagora’s theorem apply to your real world example."

So to "verify" the preconditions to apply Pythagora’s theorem, it is necessary to determine "whether a shape is composed of three straight lines and has a right angle". So I am perfectly entitled to ask a parallel question: you have a quantum system. According to QM its state space is (the projective space of) a complex Hilbert space. How do you verify it or what are the preconditions -- pre-conditions, the assumptions -- needed to be verified. Your vague gesturing answers nothing.

note: repost; blogger does not like me and keeps eating my responses.

Grodrigues,

“How do you verify it or what are the preconditions -- pre-conditions, the assumptions -- needed to be verified. Your vague gesturing answers nothing.”

It’s vague because I don’t know QM, but nonetheless, I answered your original question. The accurate predictions made by QM validate the background assumptions. It would be like me giving you a loaded die and asking you to check whether it’s loaded. You can roll it a trillion times and see if the probability space is probably consistent with a fair die. If it’s not, then that is evidence that the die is loaded is true. So you verify the assumption behind the hypothesis by making predictions and seeing if they hold true.

note: copy your post before you submit it, if it eats it, it's a simple paste and you'r good to go

@cautiouslycurious:

"It’s vague because I don’t know QM, but nonetheless, I answered your original question. The accurate predictions made by QM validate the background assumptions."

Let us go back to one earlier response:

"My statement is fairly trivial, which is why I’m shocked that you are putting up so much resistance against it. If the axiom is that you need a right triangle, I’m asking how do you know that axiom applies to the triangle in front of you, not whether Pythagoras’s theorem is valid or not. Basically, we can think of mathematics as conditional claims; if X, then Y. If you have a right triangle, then the square of the hypotenuse is equal to the sum of square of the legs. However, does that antecedent apply to the triangle in front of me?"

The problem is simply: you consistently use using sloppy and confusing language. For example: "However, I merely said that the assumptions need to apply to reality in order for them to be considered true and the only way I know how to determine that is by empirical evidence." You equivocate between two *different* claims: "the assumptions need to apply to reality" and the truthfulness of the assumptions. To repeat, what you interested is: does the piece of mathematics we know as Euclidean geometry apply to the real world? Now, this is not a mathematical question. Whatever answer it has (in one reading of the question, the answer is *no*), it says nothing about mathematics itself in general, or Euclidean geometry in particular. From the validity of QM, nothing follows about the theory of Hilbert spaces except the fact that Hilbert spaces are useful in formulating a specific theory about the physical, extra-mental reality, namely QM. Nothing more. To go back to your response to ingx that motivated this back-and-forth, the scientific method has absolutely nothing to say about the validity or not of mathematical reasoning. Suppose for example tomorrow we found that QM was false. QM would be ditched but the theory of Hilbert spaces would carry on as a theory about a certain specific family of mathematical objects (and as a tangential point, the way mathematicians understand axioms is not exactly as you described, that is "as unproven assumptions"). In the same way we found that the geometry of space is not Euclidean, but Euclidean geometry continues being a relevant portion of mathematics. Or as I said earlier, you are stating a tautology:

"If I am reading you right, and since "axioms are true" is shorthand for "they relate to reality", what you are saying boils down to "in order to know if some set of axioms applies to reality we need to know if they apply to reality"."

You could retort that I am being overly pedantic and raising a storm in a glass of water. Perhaps; but your implied assertion that ingx was somehow wrong is also wrong. That you confuse "mathematical truth" with "applies to reality" is *your* problem, not ingx's, and certainly not mine.

Grodrigues,

“You equivocate between two *different* claims: "the assumptions need to apply to reality" and the truthfulness of the assumptions”

They mean the same to me. If you think otherwise, define the terms and show how they are different.

“To repeat, what you interested is: does the piece of mathematics we know as Euclidean geometry apply to the real world? Now, this is not a mathematical question.”

I agree, I suggested it was an empirical one.

“To go back to your response to ingx that motivated this back-and-forth, the scientific method has absolutely nothing to say about the validity or not of mathematical reasoning.”

I don’t think that it’s the case that the scientific method has *absolutely* no say about the validity of mathematical reasoning. If you have an assumption that is true, a conclusion that is false, and mathematical reasoning that suggests the opposite, then that mathematical reasoning is false, because otherwise you would have an argument with true premises leading to a false conclusion. It’s an example of empirical evidence suggesting that a piece of mathematical reasoning is incorrect. Sure, you can double check the reasoning and find a mathematical flaw in it, but it’s the empirical evidence that told you to do that.

“and as a tangential point, the way mathematicians understand axioms is not exactly as you described, that is "as unproven assumptions"”

Well, this is not a mathematics blog, nor do I presume to be talking to mathematicians. I’ve used a term in its everyday use, and I’ve specified the meaning I’m using it in. Also, since the original point involved an argument with premises with questionable truth values, I think that the definition I used is more relevant.

“In the same way we found that the geometry of space is not Euclidean, but Euclidean geometry continues being a relevant portion of mathematics.”

I agree, but this has no relevance to the discussion at hand.

“Or as I said earlier, you are stating a tautology…you could retort that I am being overly pedantic and raising a storm in a glass of water.”

You are being overly pedantic. When someone puts something in parentheses after an idea, it can be used as a restatement of that idea so as to illustrate the point better. It means the same and is merely there because the author was not satisfied in the original wording of the idea. It is overly pedantic to point out that a restatement of the same idea is a tautology.

“You Perhaps; but your implied assertion that ingx was somehow wrong is also wrong.”

I’m saying that his analogy was incorrect, not that this example was incorrect. Do you understand the difference?

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