The English version is: What is asserted without evidence can be dismissed without evidence and is attributed to the famous atheist late Christopher Eric Hitchens (13 April 1949 – 15 December 2011). — TheMadFool

In that case, axioms are not legitimate. If axioms are not legitimate, then mathematics is not legitimate, because mathematics is exclusively axiomatic. If mathematics is not legitimate, we must remove the entire bureaucracy of formalisms that maintains consistency in science and engineering. In that case, science and engineering will mostly go out of the window.

In the meanwhile, we are already back in the stone age.

Informal mathematics means any informal mathematical practices, as used in everyday life, or by aboriginal or ancient peoples, without historical or geographical limitation. Modern mathematics, exceptionally from that point of view, emphasizes formal and strict proofs of all statements from given axioms. This can usefully be called therefore formal mathematics. Informal practices are usually understood intuitively and justified with examples—there are no axioms. This is of direct interest in anthropology and psychology: it casts light on the perceptions and agreements of other cultures. It is also of interest in developmental psychology as it reflects a naïve understanding of the relationships between numbers and things.

In other words, Hitchen's razor is something suitable for aboriginal tribes in the one or the other virgin rainforest only.

In that case, axioms are not legitimate. If axioms are not legitimate, — alcontali

Have you perhaps slipped on the distinction between evidence of and proof of? Axioms are at the least rules for which there is all evidence, but not a standard proof.

(A non-standard proof of the truth/validity of the axiom, or rule, of non-contradiction, is that it had better be true! (The Hermeneutics of Original Argument, P.C. Smith, p. 7)

And Hitchen's razor is no axiom, rather it is a tool in rhetoric for dealing with matters themselves the proper subject of rhetoric. (I shall assume you have a reasonably clear idea of what constitutes proper subjects of rhetoric - saves me time and effort.)

Have you perhaps slipped on the distinction between evidence of and proof of? — tim wood

Axioms are by definition asserted without evidence.

I think you’re conflating “can be dismissed” with “is false or insignificant”. All the razor is doing is saying: sure you can start with this axiom, or this one, or that one, as long as there’s no evidence for them they’re all equally worthless. In math you can “dismiss” any axiom you want, you’ll just get wacky useless math most of the time.

A conjecture in science is the same way. It can be dismissed without evidence, that doesn’t mean it is automatically false or insignificant. Notice the quote says CAN be dismissed without evidence not MUST be dismissed due to lack of evidence

Axioms are by definition asserted without evidence. — alcontali

Have you perhaps slipped on the distinction between what or how things are, and how they're presented, or asserted?

Here's a definition: "Axiom definition, a self-evident truth that requires no proof."

And what @khaled said.

Here's a definition: "Axiom definition, a self-evident truth that requires no proof." — tim wood

That is a wrong definition outdated now for almost a century. The following is the long story of the role of axioms in mathematics and what they mean:

A philosophical defeat in the quest for "truth" in the choice of axioms

Hilbert's axiomatic system – his formalism – is different. At the outset it declares its axioms.[15] But he doesn't require the selection of these axioms to be based upon either "common sense", a priori knowledge (intuitively derived understanding or awareness, innate knowledge seen as "truth without requiring any proof from experience"[16] ), or observational experience (empirical data). Rather, the mathematician in the same manner as the theoretical physicist[17][18] is free to adopt any (arbitrary, abstract) collection of axioms that they so choose. Indeed, Weyl asserts that Hilbert had "formaliz[ed] it [classical mathematics], thus transforming it in principle from a system of intuitive results into a game with formulas that proceeds according to fixed rules".[19] So, Weyl asks, what might guide the choice of these rules? "What impels us to take as a basis precisely the particular axiom system developed by Hilbert?".[19] Weyl offers up "consistency is indeed a necessary but not sufficient condition" but he cannot answer more completely except to note that Hilbert's "construction" is "arbitrary and bold".[19] Finally he notes, in italics, that the philosophical result of Hilbert's "construction" will be the following: "If Hilbert's view prevails over intuitionism, as appears to be the case, then I see in this a decisive defeat of the philosophical attitude of pure phenomenology, which thus proves to be insufficient for the understanding of creative science even in the area of cognition that is most primal and most readily open to evidence – mathematics."[19] In other words: the role of innate feelings and tendencies (intuition) and observational experience (empiricism) in the choice of axioms will be removed except in the global sense – the "construction" had better work when put to the test: "only the theoretical system as a whole ... can be confronted with experience".

In other words, axioms have fundamentally been arbitrary rules since the first half of the 20th century. They are certainly not correspondence-theory "true" in any way.

All the razor is doing is saying: sure you can start with this axiom, or this one, or that one, as long as there’s no evidence for them they’re all equally worthless. — khaled

Mathematics does not make any claim as to usefulness or meaningfulness. That is so by design.

In other words, axioms have fundamentally been arbitrary rules since the first half of the 20th century. They are certainly not correspondence-theory "true" in any way. — alcontali

This is Procrustean - and a variety of category error. Your "axiom" is clearly a term of art, properly restricted to its limited area. Which "area" has nothing whatever to do with Hitchens's razor or its applicability. Perhaps you've slipped on the various distinctions to be made in the meaning and usage of the word "axiom." And is my assumption about your understanding of rhetoric reasonable? It appears not to be.

This is Procrustean - and a variety of category error. Your "axiom" is clearly a term of art, properly restricted to its limited area. Which "area" has nothing whatever to do with Hitchens's razor or its applicability. Perhaps you've slipped on the various distinctions to be made in the meaning and usage of the word "axiom." And is my assumption about your understanding of rhetoric reasonable? It appears not to be. — tim wood

Hitchens' razor just expresses that he does not understand mathematics, science, engineering, nor the link between these domains. By design, it all starts from arbitrary rules with zero justification. Hitchens simply had no clue about the true nature of modern knowledge.

You see, the flagship of mathematics is, beyond any doubt, general abstract nonsense, i.e. category theory. It has absolutely arbitrary starting points (axioms), and, to the non-mathematician, leading to pretty much absurd conclusions.

These things are not something for people like Hitchens. That is why he produced that kind of low-knowledge "razor".

Fair enough, then. You know nothing whatever about rhetoric or its subjects. Your subjects are all apodeictic; they are as they are, and cannot be otherwise. But for all that, nor they nor you can, nor ever will, be able to tell me what colour tie it would be best to wear to my next interview, or whether to attack at dawn, or whether to build ships or a wall. Because these are are all topics allowing of contradictory answers, thus topics for consideration and weighing, on the basis of best argument best presented by the best person with the best understanding, judgment, and intentions, to the end of making a decision with respect to some action to be taken.

Agreed, Hitchens's razor is a pig in the parlor of mathematics, but in rhetoric a fine and useful tool. And in rhetoric, your "axioms" (quotes because yours is a term of art) non-sequiturs.

This isn't argument or debate, it's about the distinctions to be made, that ought to be made, in the usage of a word.

Fair enough, then. You know nothing whatever about rhetoric or its subjects. Your subjects are all apodeictic — tim wood

Well, yeah, probably. So?

Agreed, Hitchens's razor is a pig in the parlor of mathematics, but in rhetoric a fine and useful tool. And in rhetoric, your "axioms" (quotes because yours is a term of art) non-sequiturs. — tim wood

Well, a good part of the body of modern knowledge is actually quite counter-intuitive, when you think of it. That is undoubtedly why Hitchens, who is completely ignorant of its caveats, sounds so ignorant. Hitchens was someone who took great pleasure in depicting other people as idiots, but his own views were clearly even worse.

So? — alcontali

So you're off your reservation with the wrong opinions on the wrong topics on and about which you don't have adequate information, knowledge, or understanding. And predictably, you're thereby dismissive and defensive - very weak stances from the standpoint of rhetoric. Of course from your area, it's simpler: you're just plain wrong.

And Hitchens was making a living dueling with ignorant people. He was not inclined, usually, to be gentle - bad theater. And no one looks good against ignorant and stupid opponents.

Well, a good part of the body of modern knowledge is actually quite counter-intuitive, — alcontali

And this just continues the mistake - mistake in this context. "A good part of the body of knowledge" is itself not the body of knowledge, however "good" a part it might be. Parts and wholes. Categories. Genus and species. I yield yours to you. Now how about you get back to your own corral on your own ranch? .

The English version is: What is asserted without evidence can be dismissed without evidence and is attributed to the famous atheist late Christopher Eric Hitchens (13 April 1949 – 15 December 2011).

I would like an analysis of this purportedly rational stance on, possibly, all matters under the sun.

Personally, I think it has a flaw because it doesn't allow, in fact stifles, rational inquiry. — TheMadFool

I believe this saying was used specifically to argue that assertions of the existence of God do not have to be taken seriously, although it certainly could be applied to other situations. I think he was talking about phenomena claimed to exist in the "real" world, i.e. outside our minds. I don't think it applies to logical or mathematical entities. If I'm wrong, please somebody set me straight.

On today's episode of Adventures of Creative Misreading . . .

So you're off your reservation with the wrong opinions on the wrong topics on and about which you don't have adequate information, knowledge, or understanding. And predictably, you're thereby dismissive and defensive - very weak stances from the standpoint of rhetoric. Of course from your area, it's simpler: you're just plain wrong. — tim wood

--------------------------------------------------
Exsurge Domine
Condemning the Errors of Al Contali
--------------------------------------------------
We can scarcely express, from distress and grief of mind, what has reached our ears for some time by the report of reliable men and general rumor; alas, we have even seen with our eyes and read the many diverse errors. Al Contali's errors are either heretical, false, scandalous, or offensive to pious ears, as seductive of simple minds, originating with false exponents of the faith who in their proud curiosity yearn for the world’s glory. We can under no circumstances tolerate or overlook any longer the pernicious poison of the above errors without disgrace. No one of sound mind is ignorant how destructive, pernicious, scandalous, and seductive to pious and simple minds these various errors are. Therefore we, in this above enumeration, important as it is, wish to proceed with great care as is proper, and to cut off the advance of this plague and cancerous disease so it will not spread any further. With mature deliberation on each and every one of Al Contali's theses, we condemn, reprobate, and reject completely each of these theses or errors as either heretical, scandalous, false, offensive to pious ears or seductive of simple minds!
--------------------------------------------------

Here's a definition: "Axiom definition, a self-evident truth that requires no proof." — tim wood

One person's self-evident truth is to another person an assumption without evidence. Axioms are assumed to be true for sake of argument, for example. And you have axioms in geometry that are assumed, and interestingly some axioms in Euclidian geometry, if accepted as correct, might have stopped non-euclidean geometry, which has practical applications in physics.

All the razor is doing is saying: sure you can start with this axiom, or this one, or that one, as long as there’s no evidence for them they’re all equally worthless. — khaled

That would be a very bad conclusion or rule. The evidence of the usefulness or accuracy of the axiom might come much later on, after the axiom is assumed for the sake of argument/investigation. Sure, having a hypothesis, in science say, that seems to have some evidence for it is a good starting point. But there is no reason oan a Tuesday, to decide that Tuesday, well that axiom or that assumption has no evidence, so let's throw it out.

It gets used broadly now in philosophical discussions. So even if the original was aimed at one issue, it is used in general.

It gets used broadly now in philosophical discussions. So even if the original was aimed at one issue, it is used in general. — Coben

Well, ever since the annexation and reappropriation of logic by mathematics, the remaining flagship sailing for the colours of philosophy is epistemology.

If knowledge is defined as a justified (true) belief, then knowledge has the shape of an arrow. Therefore, we do not reject a knowledge claim because we do not like its starting point. We also do not reject a knowledge claim because we do not like its conclusion. We only reject it because the conclusion does not necessarily follow from the starting point.

Therefore, Hitchens' approach in which he arbitrarily rejects starting points, is just a cheap slogan that he could use and abuse to reject pretty much any knowledge claim. The late, dead Hitchens was a rhetorical attack dog, with a strong emphasis on the word "dog". May his carcass rot in hell.

Mathematics does not make any claim as to usefulness or meaningfulness — alcontali

Which is why this razor wouldn’t affect it

Which is why this razor wouldn’t affect it — khaled

Yes, of course. People like Hitchens are obviously no credible threat to the field of mathematics, if only, because they wouldn't survive for thirty seconds if they had to steer their own ship through uncharted waters on the high seas. It is just that I do not like people like Hitchens, whose only goal in life is to discredit and otherwise viciously attack other people. Hitchens was a cherished accomplice of Satan. Richard Stallman said about Steve Jobs: "I am not glad that he is dead but I am glad that he is gone." About Hitchens, I rather abbreviate all of that to "dead and gone", and we wouldn't want it any other way.

Generally I agree. Of course one need not accept someone else's axiom, but there's not reason to reject it. It's simply a bad heuristic.

I do not have a dog in this fight, but it seems like Quod grātīs asseritur, grātīs negātur is valid. I can claim there is intelligent life on 23 planets, but I make this claim without evidence. There are quite a few planets that MIGHT POSSIBLY host life of some sort, and there is evidence for that claim. But there is no evidence at all for the claim that 23 planets host intelligent life. So you can say, "No there are not." with as much confidence as I said it with. "Donald Trump is a moron." can be asserted and dismissed with equal confidence. There does not seem to be any evidence for his being a moron. There is no evidence that he is a distinguished statesman, either. He provides daily evidence that he lurches from topic to topic in his Twitter pronouncements.

A lot of discussion that goes on here is based on assertions without evidence. This is an entirely normal state of affairs, because we understand that we all have opinions about all manner of things that are not supported with evidence. If we had to present evidence for all our opinions, we would become terminally constipated and would eventually explode.

I do not have a dog in this fight, but it seems like Quod grātīs asseritur, grātīs negātur is valid. I can claim there is intelligent life on 23 planets, but I make this claim without evidence. There are quite a few planets that MIGHT POSSIBLY host life of some sort, and there is evidence for that claim. But there is no evidence at all for the claim that 23 planets host intelligent life. So you can say, "No there are not." — Bitter Crank

A knowledge claim is an arrow between a starting point and a conclusion. In the empirical realm -- life on other planets is clearly a claim about the physical world -- it is an arrow between observations and a conclusion that follows from these observations.

In an axiomatic domain, a knowledge claim is an arrow between a starting-point rule and a consequential rule. The starting point simply does not consist of observations but of a rule. For example, if there is a countable infinite number of natural numbers, ∞, then the number of real numbers is 2^∞.

Hitchens was using his so-called razor, not to argue that the consequential rule does not necessarily follow from the starting-point rule, but to attack the starting-point rule itself. In the example above: There is absolutely no reason to believe that there is an infinite number of natural numbers, i.e. ∞. This is obviously true, but that is not what it is about.

Attacking the knowledge claim "if cardinalityOf(N) is ∞ then cardinalityOf(R) is 2^∞" cannot be achieved merely by rejecting "cardinalityOf(N) is ∞", and also not by rejecting "cardinalityOf(R) is 2^∞". You have to conclusively show that "cardinalityOf(R) is 2^∞" does not follow from "cardinalityOf(N) is ∞".

So, if Hitchens' so-called razor makes sense, you can use it to successfully attack the axiom of infinity, or any axiom in ZFC, because none of ZFC's axioms, i.e. the foundations of axiomatic set theory, can be justified with any evidence.

Of course, Hitchens did not dare to attack mathematics on those grounds. He pointed his arrows to a seemingly easier target: religion, but it is obviously the same attack. Hitchens' views are epistemically unsound, and clearly invalid, but obviously still popular with other atheists, who will defend them, because they like his conclusions. As I already pointed out, Hitchens was a cherished accomplice of Satan.

Look up “assertion” in regards to logic. It makes perfect sense then.

A conjecture in science is the same way. It can be dismissed without evidence, that doesn’t mean it is automatically false or insignificant. Notice the quote says CAN be dismissed without evidence not MUST be dismissed due to lack of evidence — khaled

:up:

These things are not something for people like Hitchens. That is why he produced that kind of low-knowledge "razor". — alcontali

In partial agreement with you but there's one area of philosophical argumentation that Hitchen's Razor is extremely useful viz. the issue with burden of proof. I'm familiar with it from the God debate (theism/atheism). In some cases a debate ends in theists demanding proof that god doesn't exist. As you will notice this task is the contrary of but equally difficult to proving that god exists. I don't know if @tim wood agrees but this is probably a rhetorical device, shifting the burden of proof. As you may have already noticed Hitchen's Razor can be very effective in countering such a move because you can simply dismiss a motion on the basis that it has no evidence to back it up.

Thanks. Read above.

If we had to present evidence for all our opinions, we would become terminally constipated and would eventually explode. — Bitter Crank

:rofl: :rofl: :up:

I do not have a dog in this fight, but it seems like Quod grātīs asseritur, grātīs negātur is valid. I can claim there is intelligent life on 23 planets, but I make this claim without evidence. — Bitter Crank

There is at least one missing assumption here.
First, just to be anally clear. I think you mean I should not make this claim without evidence. Since one clearly can. Further I think it is implicit that you also mean, one should not make this claim and expect that anyone has a good reason to take you seriously or believe you.

Here's why I think you are wrong. The processes through which we come to knowledge include all sorts of thought experiments. The specificity of the claim you are using as an example is problematic, but let's say you assert, as part of some research team:

There is intelligent life on many planets in the galaxy.

You want the group to take this on as a workign assumption. This can be useful. You assume this, then ask questions, for example. Why don't we see their tv shows or other things that indicate they are there. Then we can come up with proposed solutions that still fit the assumption.

Scientists and other experts and regular people make assumptions all the time, because it can lead to fruitful lines of thinking. Einstein did this and it was decades before some of his conclusions were confirmed empirically.

There is no reason to dismiss claims that do not have evidence.

However it would be silly for people to assume you should believe their claims if there is no evidence.

That I get. Someone tells you they know God exists or they know that there is life on other planets, well, they can't expect you to be convinced. There is no need to dismiss them however.