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Logic and First Principles, 7: The problem of fallacies vs credible warrant

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When we deal with deeply polarised topics such as ID, we face the problem of well-grounded reasoning vs fallacies. A fallacy being a significantly persuasive but fundamentally misleading argument, often as an error of reasoning. (Cf. a classic collection here.) However, too often, fallacies are deliberately used by clever rhetors to mislead the unwary. Likewise we face the challenge of how much warrant is needed for an argument to be credible.

All of these are logical challenges.

Let us note IEP, as just linked:

A fallacy is a kind of error in reasoning. The list of fallacies below contains 224 names of the most common fallacies, and it provides brief explanations and examples of each of them. Fallacies should not be persuasive, but they often are. Fallacies may be created unintentionally, or they may be created intentionally in order to deceive other people. The vast majority of the commonly identified fallacies involve arguments, although some involve explanations, or definitions, or other products of reasoning. Sometimes the term “fallacy” is used even more broadly to indicate any false belief or cause of a false belief. The list below includes some fallacies of these sorts, but most are fallacies that involve kinds of errors made while arguing informally in natural language.
An informal fallacy is fallacious because of both its form and its content. The formal fallacies are fallacious only because of their logical form. For example, the Slippery Slope Fallacy has the following form: Step 1 often leads to step 2. Step 2 often leads to step 3. Step 3 often leads to … until we reach an obviously unacceptable step, so step 1 is not acceptable. That form occurs in both good arguments and fallacious arguments. The quality of an argument of this form depends crucially on the probabilities. Notice that the probabilities involve the argument’s content, not merely its form.

This focus on probabilistic aspects of informal fallacies brings out several aspects of the problem, for we often deal with empirical evidence and inductive reasoning rather than direct chained deductions. For deductive arguments, a chain is no stronger than the weak link, and if that link cannot be fixed, the whole argument fails to support the conclusion.

However, inductive arguments work on a different principle. Probability estimates, in a controversial context, will always be hotly contested. So, we must apply the rope principle: short, relatively weak individual fibres can be twisted together and then counter twisted as strands of a rope, giving a whole that is both long and strong.

Of chains, ropes and cumulative cases

For example, suppose that a given point has a 1% chance of being an error. Now, bring together ten mutually supportive points that sufficiently independently sustain the same conclusion. Odds that all ten are wrong in the same way are a lot lower. A simple calculation would be ([1 – 0.99]^10) ~10^-20. This is the basis of the classic observation that in the mouth of two or three independent witnesses, a word is established.

However, many will be inclined to set up a double-standard of warrant, an arbitrarily high one for conclusions they wish to reject vs a much softer one for those they are inclined to accept. Nowadays, this is often presented as “extraordinary claims require extraordinary evidence.”

In fact, any claim simply requires adequate evidence.

Any demand for more than this cometh of evil.

This is of course the fallacy of selective hyperskepticism, a bane of discussions on ID topics. (The strength of will to reject can reach the level of dismissing logical-mathematical demonstration, often by finding some excuse to studiously ignore and side step as if it were not on the table.)

Of course, an objection will be: you are overly credulous. That is a claim, one that requires adequate warrant. Where, in fact, if one disbelieves what one should (per adequate warrant), that is as a rule because one also believes what one should not (per, lack of adequate warrant), which serves as a controlling belief. Where, if falsity is made the standard for accepting or rejecting claims, then the truth cannot ever be accepted, as it will run counter to the false.

All of this is seriously compounded by the tendency in a relativistic age to reduce truth to opinion, thence to personalise and polarise, often by implying fairly serious ad hominems. This can then be compounded by the “he hit back first” tactic.

This also raises the issue of the so-called concern troll. That is one who claims to support side A, but will always be found undermining it without adequate warrant, often using the tactics just noted. Such a persona in fact is enabling B by undermining A. This is a notorious agit prop tactic that works because it exploits passive aggressive behaviour patterns.

The answer to all of this is to understand how arguments work and how they fail to work, recognising the possibility of error and of participants who are in error (or are in worse than error) then focussing the merits of the case.

So, as we proceed, let us bear in mind the significance of adequate warrant, and the problem of selective hyperskepticism. END

PS: As it is relevant to the discussion that emerged, let me lay out the path to intellectual decay of our civilisation, adapting Schaeffer:

Extending (and correcting) Schaeffer’s vision of the course of western thought, worldviews and culture, C1 – 21

H’mm: Geostrategic picture:

As Scuzzaman highlights the slippery slope ratchet, let me put up the Overton Window (in the context of a ratchet that is steadily cranking it leftward on the usual political spectrum) — where, fallacies are used to create a Plato’s cave shadow-show world in which decision-making becomes ever more irrational, out of contact with reality:

Likewise, here is a model of malinvestment-led, self-induced economic disaster due to foolishly tickling a dragon’s tail and pushing an economy into unsustainable territory, building on Hayek:

Let me add, a view of the alternative political dynamics and spectrum:

U/d b for clarity, nb Nil

PPS: Mobius strip cut 1/2 way vs 1/3 way across vid:

Comments
hazel:
You are paranoid, and attaching vastly more significance to the discussions here then they deserve
Wow. Why are you even here, hazel? Clearly you must think the discussion is important as you and Ed have both put your time into it- no effort but timeET
January 11, 2019
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hazel, I will ask again- What is the evidence that demonstrates humans invented mathematics (as opposed to discovering it)?ET
January 11, 2019
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No, kf, I am not "ignoring" anything. You are paranoid, and attaching vastly more significance to the discussions here then they deserve. There is no excuse for your unkind remark to Ed, whoever he may be. 'Nuf said.hazel
January 11, 2019
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H, you have again chosen to ignore highly relevant context; here, of actual hoaxing and of a linked long-term penumbra of abusive objector sites . I must note, that in such a context, we must take due note of patterns of behaviour and where they may well point. Not what we desire, what we must face in a world where, decades ago now many major objectors to design theory chose not to primarily engage on substance but on agit prop operations, administrative lockout, expulsion, tainting and lawfare. KFkairosfocus
January 11, 2019
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kf writes, "Folks, this is not a verandah coffee break." Kf, this is a verandah coffee break. It's just a little internet forum populated by a couple dozen regular or semi irregular participants.hazel
January 11, 2019
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kf writes, you are again failing to acknowledge the force of the distinction between the world-embedded substance of structure and quantity and the culturally influenced study of it." No kf, I specifically addressed this distinction in post 26.hazel
January 11, 2019
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ET, You are quite right to highlight Ramanujan as an example of discoveries of world-embedded intelligible rational principles of structure and quantity. I here clip Wikipedia as a testimony against known ideological agenda:
Srinivasa Ramanujan From Wikipedia, the free encyclopedia Jump to navigation Jump to search "Ramanujan" redirects here. For other uses, see Ramanujan (disambiguation). In this Indian name, the name Srinivasa is a patronymic, not a family name, and the person should be referred to by the given name, Ramanujan. Srinivasa Ramanujan FRS Srinivasa Ramanujan - OPC - 1.jpg Born 22 December 1887 Erode, Madras Presidency, British India (present-day Tamil Nadu, India) Died 26 April 1920 (aged 32) Kumbakonam, Madras Presidency, British India (present-day Tamil Nadu, India) Residence Kumbakonam, Madras Presidency, British India (present-day Tamil Nadu, India) Madras, Madras Presidency, British India (present-day Chennai, Tamil Nadu, India) London, England, United Kingdom of Great Britain and Ireland (present-day United Kingdom) Nationality Indian Education Government Arts College (no degree) Pachaiyappa's College (no degree) Trinity College, Cambridge (BSc, 1916) Known for Landau–Ramanujan constant Mock theta functions Ramanujan conjecture Ramanujan prime Ramanujan–Soldner constant Ramanujan theta function Ramanujan's sum Rogers–Ramanujan identities Ramanujan's master theorem Ramanujan–Sato series Awards Fellow of the Royal Society Scientific career Fields Mathematics Institutions Trinity College, Cambridge Thesis Highly Composite Numbers (1916) Academic advisors G. H. Hardy J. E. Littlewood Influences G. S. Carr Influenced G. H. Hardy Signature Srinivasa Ramanujan signature Srinivasa Ramanujan FRS (/??ri?ni?v??s? r???m??n?d??n/;[1] About this soundlisten (help·info); 22 December 1887 – 26 April 1920)[2] was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable. Ramanujan initially developed his own mathematical research in isolation: "He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered".[3] Seeking mathematicians who could better understand his work, in 1913 he began a postal partnership with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognizing the extraordinary work sent to him as samples, Hardy arranged travel for Ramanujan to Cambridge. In his notes, Ramanujan had produced groundbreaking new theorems, including some that Hardy stated had "defeated [him and his colleagues] completely", in addition to rediscovering recently proven but highly advanced results. During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations).[4] Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research.[5] Nearly all his claims have now been proven correct.[6] The Ramanujan Journal, a peer-reviewed scientific journal, was established to publish work in all areas of mathematics influenced by Ramanujan,[7] and his notebooks—containing summaries of his published and unpublished results—have been analyzed and studied for decades since his death as a source of new mathematical ideas. As late as 2011 and again in 2012, researchers continued to discover that mere comments in his writings about "simple properties" and "similar outputs" for certain findings were themselves profound and subtle number theory results that remained unsuspected until nearly a century after his death . . .
It often takes genius to discover many things and here we have a case of isolation leading to independent witness. Where, many of the results in question are in theory of numbers. Numbers being demonstrably embedded in the structure of any world, as they emerge from the import of distinct identity. This is indeed an empirical case in point. KFkairosfocus
January 11, 2019
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H, we know the history of invention of i in the context of cubic polynomials. We also know the history of recognising rotation operators and vector numbers. You were part of an exchange in recent weeks here on precisely that topic. Going further, you are again failing to acknowledge the force of the distinction between the world-embedded substance of structure and quantity and the culturally influenced study of it. I have already pointed out how physical length obtains in a spatially extended world (as opposed to how in any world we may see a mathematical space), which is antecedent to our culturally influenced creation of a standard unit for length such as the metre or the yard (or the fathom, ell or cubit, etc). Likewise, I have pointed out the difference between numbers in themselves and culturally influenced numerals and representations. Pi can be expressed in many ways, the decimal place value notation being only one. The fact that in a planar space corresponding to Euclid's framework circles and diameters are such that circumference length to diameter will stand in a specific numerical ratio is a case of world-embedded structure and quantity which we discover rather than invent. Then, we find that pi is very relevant in a world of approximately round objects, e.g. ponder how round gearing attains to evenly spaced, uniform, properly meshing teeth. (Nice slideshow: http://ocw.uc3m.es/ingenieria-mecanica/machine-theory/lectures-1/gears Also notice for example the significance of pi in various tabulated formulae: https://www.engineersedge.com/gear_formula.htm ) That applies to the power train of cars and other vehicles, it applies to the watches and clocks we use to tell time, it applies even to fishing reels. The balance I am pointing to is critical, and the consistent refusal to address both aspects in a balanced way as was just evident again, is a tell relevant to the focus of this thread. And as we see also the tendency to seize upon any pretext to trumpet taking offence (and to thereby suggest that the offended party is therefore in the right) I will not name names on fallacies involved. But, they clearly are there. KFkairosfocus
January 11, 2019
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Folks, this is not a verandah coffee break. I noted the possibility of what intel agencies term legends in order to underscore the realities of the sort of polarisation we have to routinely deal with, especially when anonymous and often adverse commenters are involved. Indeed, several years ago we faced an elaborate hoax by someone who was given a guest post and had put up a false front (changing his sex, using a handle that properly belongs to a college professor of Mathematics, and much more), in a case that was quite close to the classic definition of concern trolling. I add, that case was in part broken when the persona failed to recognise a mathematical property that was pivotal to a heuristic model developed to quantify a threshold metric for functionally specific complex organisation and/or associated information. He also used part of the penumbra of attack sites to boast of his hoax. That context must not be forgotten. The issue is not paranoia, but whether we are sufficiently aware of what sort of agit prop operations may be going on and the dangers involved. KF PS: The case also highlights the question of degree of warrant required for acknowledging credible truth. That is, it brings to bear selective hyperskepticism and Clifford-Sagan evidentialism. PPS: Definition, FYI: Legend A spy's claimed background or biography, usually supported by documents and memorized detailskairosfocus
January 11, 2019
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KF “PS: On the assumption of truth regarding declared personal circumstances, I wish you well on that front.“ I have to agree with Hazel. Your comment is insensetive and beyond the pale. An apology might be in order. Just a suggestion.Brother Brian
January 10, 2019
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Hazel@26, I think we are saying the same thing, although you are saying it far more eloquently than I have. I think the difference of opinion I have with KF, WJM and maybe ET, is simply how we look at reality. They see an organized system and think that the system was designed to obey specific mathematical constructs. I see the system as something that we, because of the abilities we have been given, can describe in terms we have defined mathematically. It is really the chicken and egg problem. But, again, thank you for your best wishes. I have just been forwarded a picture of my new grandson. I think he is the most beautiful baby ever born. But, I might be a little biased. :)Ed George
January 10, 2019
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KF
PS: On the assumption of truth regarding declared personal circumstances, I wish you well on that front.
On the assumption of truth???? You are a really sad little man. I think this is my last attempt at a discussion with you.Ed George
January 10, 2019
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Could the person who first used i used a different word and symbol, like maybe "pretend" number and p?hazel
January 10, 2019
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I claim that all information, mathematics included, comes from The Source. That is from where Srinivasa Ramanujan discovered his many formulae. What is your evidence that humans invented mathematics?ET
January 10, 2019
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kf writes, "PS: On the assumption of truth regarding declared personal circumstances." Why in the world would you start that sentence "on the presumption of truth ..."? Did you seriously think there is a chance that Ed would have made up a story about becoming a new grandfather?hazel
January 10, 2019
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OK, ET: where did the term imaginary number and the symbol i to represent it come from? I claim a human being (or set of human beings) created it. What do you think?hazel
January 10, 2019
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H, you would be well advised to start from the principle of distinct identity and its consequences which give us a large core of structure and quantity. FYI, too, vector quantities and fields are indeed embedded in the world in many relevant ways. Where, field implies infinitesimal components, so yes, calculus is embedded in the world as rates, flows, gradients and thus also vectors. As just one example a magnetic field is a vector field. There is much more. KFkairosfocus
January 10, 2019
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EG, the evidence of your attempt to dismiss mathematical-logical demonstration as imposition of opinion is there. That, you cannot wave away rhetorically. KF PS: On the assumption of truth regarding declared personal circumstances, I wish you well on that front.kairosfocus
January 10, 2019
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hazel:
First, I think that there is general agreement that the particular words and symbols in which we express our mathematics are human creations.
I strongly disagree. I will emphasize that this is not a philosophical question. It is a question that can be scientifically explored.ET
January 10, 2019
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Ed, you ask, “Do you think that they (for instance, laws describing orbital mechanics) are inherent in the universe, or do you think we invented the math required to describe it?” This sentence gets to the heart of the issue, and there are several components. Let me break this into two parts. First, I think that there is general agreement that the particular words and symbols in which we express our mathematics are human creations. However, once certain ideas are formulated, logical deductive trains lead us to discoveries of mathematical facts, including some/many that are not at all obvious. So within a mathematical system, there is a feedback loop, so to speak, of invention and discovery, with insightful inventions leading to large sets of discovered facts, and the further invention of new symbols and concepts leading to further discoveries. (I used to spend a class period at the start of second semester of my pre-calculus class giving a lecture on the development of the number system from counting numbers up to complex numbers: It’s a fascinating subject.) The second part of your question is the philosophical one about math being able to describe the physical world - as you say, using math to model the world - as opposed to just developing logical mathematical systems. Things in the physical world behave in orderly ways which can be accurately modeled by mathematics. This is an empirically true fact. In my opinion, this doesn’t mean that somehow the components of our mathematics themselves are out there in the real world. Let me illustrate with a somewhat lengthy example. I used to start a chapter on differentials in calculus by asking, Why doesn’t the moon fall down?” I then showed that if we consider the moon as a point on a circle with the earth, we can represent two forces on the moon by vectors: one pointing down to represent the force of gravity and one tangent to the circle representing the moon’s movement. By looking at the hypotenuse created by the the vectors, we can see that the moon will move at an angle. Now since the moment the moon moves, the directions of the two vectors change, any one vector diagram is only an approximation of what the moon will do at any moment. However, if we shrink the vectors down to infinitesimal size, then the resulting triangle represents the instantaneous direction of motion. And then, if you learn how to do the calculus, I would point out, mathematicians can show that movement describes not a circle, but an ellipse. This process, elaborated extensively, is how the mathematical models of celestial orbits were created, and one of the main vehicles for Newton’s development of calculus. Pardon the long story, but here is now the big question. Are there really little infinitesimal vectors in the world? No, there are not. Gravity is acting, the moon is moving with inertia: those are true facts, but the vectors are a model, not something “inherent” in the world. Let me emphasize: it is absolutely true, and a mystery which arouses philosophical questions, that the world is such that mathematical models such as those using vectors work. Various people have different beliefs about the philosophy about why this is true. In my opinion there is no sure-fire way to determine which philosophical views are correct. We all, to use kf’s metaphor (which I like), wind various strands of thought into a rope of belief, but the ropes are not the same as logical deductive chains. Furthermore, people have different attachments to their beliefs (here the rope analogy breaks down) - but that’s a different topic.hazel
January 10, 2019
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Ed:
Do you think that they are inherent in the universe, or do you think we invented the math required to describe it?
It will be interesting to see if whatever hazel responds with is supported by something other than what hazel says.ET
January 10, 2019
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Ed George:
Do you think that there will ever be an intelligent ET?
When compared to you, Ed, there are, have been and will continue to be, many. :razz:ET
January 10, 2019
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Hazel@21, thank you for the good wishes. I appreciate it. I would love to say that I am ready for this, but ....Ed George
January 10, 2019
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ET
And that when we do encounter intelligent ET’s...
Do you think that there will ever be an intelligent ET?Ed George
January 10, 2019
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That is wonderful, Ed. Your life is changed. You will enjoy, and be inspired about the wonders of life, by your grandchild in ways that will be different, and bigger, than when you had you own children. Congratulations! But I'm still going to respond somewhat extensively to your question at 15. :-)hazel
January 10, 2019
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Ed:
So, all I can say is that all of the petty bickering I have seen over the short time I have been here means absolutely nothing.
The petty bickering has you as the common denominator and instigator, Ed.ET
January 10, 2019
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Well, I just got a phone call letting me know that I am a first time grandfather. So, all I can say is that all of the petty bickering I have seen over the short time I have been here means absolutely nothing.Ed George
January 10, 2019
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"If you accept the idea that both space itself, and all the stuff in space, have no properties at all except mathematical properties," then the idea that everything is mathematical "starts to sound a little bit less insane," Tegmark said in a talk given Jan. 15 here at The Bell House. The talk was based on his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality" (Knopf, 2014)
ET
January 10, 2019
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In response to E.G. @ 11 who writes "And to propose that mathematics was used by the designer to create the universe is beyond preposterous." I give you quotes by Galileo and Kepler, respectively "The book of nature is written in the language of mathematics." and "Geometry, which before the origin of things was coeternal with the divine mind and is God himself (for what could there be in God which would not be God himself?), supplied God with patterns for the creation of the world, and passed over to Man along with the image of God; and was not in fact taken in through the eyes. " Now I will conclude with a quote attributed to Lincoln, Twain, and several others "Better to remain silent and be thought a fool than to speak out and remove all doubt."math guy
January 10, 2019
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hazel:
I don’t think it is preposterous to believe that an intelligent designer of some cosmic kind conceived first of math and then used math when creating the universe. That’s a philosophical position with a long history.
Except it isn't a philosophical position. See? I can just dismiss what you say because you just say it. Your say-so isn't evidence. I don't see anything that prevents us from determining that mathematics permeates the universe. And that when we do encounter intelligent ET's their mathematics will be ours, with advancements (perhaps).ET
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