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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
Each of us have a unique set of concepts in our mind, and they vary widely in how similar they are to other people’s.
Everyone has different experiences and sense impressions about this or that triangle, but everyone's concept of a right triangle is the same if they know what it is.StephenB
January 16, 2019
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H, it seems that on the contrary, the core point has been sufficiently warranted that there is no effective counter. Going beyond, I took up the nominalism, addressing first its role in evolutionary materialism, which cannot be ignored. Onwards, I addressed the challenge that abstracta are so inextricably entangled in our thinking that nominalism falls apart. Further, once we see mind beyond claimed emanations of computational substrates, one deals with the abstract domain. All of this is before one gets to actual claims about mathematical platonism as such. I would suggest that the only viable views will be those that allow key facts of structure and quantity as shown, to materially affect reality by being part of the fabric of what give a world its distinct identity. KFkairosfocus
January 16, 2019
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WJM, H is by her admission, a mathematician, so she understands the logic at work. That she clearly has no logical counter is significant. We can take the basic point as made: there is in any world that is possible, a substantial core of mathematical facts that will necessarily be present, starting with N and progressing therefrom. Given that historically, imaginary numbers were proposed to solve polynomials, it would seem plausible that they are an arbitrary invention -- which gave rise to much resistance. However, it was later realised that we are dealing with an algebraic expression of vectors, with rotations. Consequently, they actually have a natural sense and should not be regarded as in effect an artifact of human ingenuity. All of this suffices to ground that certain key abstract entities exhibiting structure and quantity are mathematical facts that constrain what is possible of being and constrain certain relational possibilities. In a simple case, self evidently || + ||| --> ||||| . Beyond such, it is clear enough that nominalism fails, as abstract entities are inextricably entangled in reasoned thought. KFkairosfocus
January 16, 2019
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Hazel said:
I don’t think those are the only two.
I didn't say there are only two; I said that there have been two presented and that rejecting those is not the same as offering a third alternative.
My mind, a non-material part of me with cognitive, rational abilities, generates abstractions, embodied in symbolic language but existing within me as broader, non-verbal, holistic thoughts, based on my experience of the world, including what other teach me.
What you are doing here for the most part is describing your experience, which is not an explanation of that experience. The single explanatory term you use is "non-material", which explains that you are not talking about a material phenomenon (or, at least, a phenomena generated by material causation). Both the physicalist and Platonic Realism explanations for that experience have been given; you've rejected both. Part of what Platonic Realism attempts to explain is the universality of certain aspect of mind - certain values, forms, principles, etc. That was really the meat of those first threads - how does anyone explain that any mind can discover the universality of 2+3+5? Or A=A? Or circles, pi, the equations of mass and velocity? Your description of your personal mental experience is not an explanatory model for the universal consensuality (and, indeed, necessity & absolute nature) of certain mental, non-material abstractions, as is Platonic Realism. Until you have an alternative model that explains these things, we are left with physicalism vs Platonic Realism.
My theory of mind, with I discussed quite a bit with Gpuccio, is that it is something (I don’t know what, and I don’t think anyone does) that we experience “internally” through the medium of consciousness. Somehow (I don’t know how and neither does anyone else) it has a two-way interface with the external world, though my body. It is capable of, among other things, logical rational thought and the embodiment of abstractions in symbolic form which it can then manipulate to reach new conclusions. I think that is sufficient for me. It isn’t sufficient for you. I think we will have to leave it at that.
I'm certainly not here to try and force it to not be sufficient for you. I'm primarily here just to develop and challenge my own thoughts and views. I do hope you will take into account, though, in future discussions with others, when they appear to lose their patience, become frustrated and start utilizing appeals to motive, character, etc., that it can be quite challenging to engage with someone who rejects explanatory models for no logical or evidential reason, offers no alternative and then ends further discussion by saying, essentially, that they are comfortable not pursuing the matter further and accepting their own internal ambiguity on these issues. I'm not saying there's anything wrong with such a personally held position - IMO, there isn't. IMO, such accepted internal ambiguity offers a certain experiential value. My point is rather that from the perspective of many that take these things very seriously, that internal acceptance of conceptual ambiguity while also rejecting other ideas that certainly do not violate any principle within that ambiguity looks like something else entirely. Something to keep in mind going forward.William J Murray
January 16, 2019
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KF, I think Hazel is putting forth a good faith contribution to the discussion inasmuch as she can. While many of us understand the first principles arguments and the necessity of their validity in all matters both esoteric and practical, it takes a high degree of commitment to discovery and self-analysis to navigate that terrain. For some it also takes a willingness to break down what is a very comfortable (and operationally successful) ambiguity when it comes to these things. They don't see (IMO) how the mental discipline and commitment can ever pay off. For me, these are essential question that go to the root of who and what I am, where I am, what I'm doing, what existence means, how it works and what it is ultimately about. For most people, these things don't even rise to the level of conscious consideration, much less considering them worth the kind of commitment required to dive in and learn to swim. I appreciate that you at least attempt to point out the danger of such superficial and vague mindsets (when it comes to these issues), but it's sort of a chicken and egg problem - it's difficult to understand how not understanding these things is dangerous if you don't understand them and their importance. I know you try to explain that as well, but without that commitment to understanding them in the first place, the danger part falls on deaf ears, unfortunately.William J Murray
January 16, 2019
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I am not interested in continuing this conversation with kf, as it continues to cover the same ground, and he doesn’t seem to really engage what I am saying. I don’t dismiss abstractions. I think they reside in my mind. Kf thinks, “The real issue going forward is, how do we account for a world in which abstracta are inextricably in the roots of reality. This of course makes mind antecedent to matter.” This is not the “real issue” to me, nor a conclusion I agree with, but I understand this is the heart of kf’s philosophy. I think it’s time to leave it at that also. But I’m going to succumb to a temptation: In the Wigner article, Wigner writes, “mathematics is the science of skillful operations with concepts and rules invented just for this purpose. The principal emphasis is on the invention of concepts. As kp would say, oops! Wasn’t arguing against the idea that mathematics is invented one of the stimuli behind this whole series of threads. :-)hazel
January 16, 2019
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wjm writes that there are two categories,
(1) physicalism/materialism (such thoughts are generated by material forces) and (2) Platonic Realism
I don't think those are the only two. My mind, a non-material part of me with cognitive, rational abilities, generates abstractions, embodied in symbolic language but existing within me as broader, non-verbal, holistic thoughts, based on my experience of the world, including what other teach me. You then say
it might be interesting to explore what it is that you do believe (via your own personal introspection) about what is going on when you think and imagine, about the nature the existence of universal mental forms and values and how it is they occur.
But I don’t see my thoughts as being about “universal mental forms and values”. I see them as being about the world I experience, a combination of my own rational ability and the heritage of symbolic understandings, including math, that have been developed and handed to me. I don’t see any of that as existing, as a mental concept, outside of me (other than in shared symbolic language, which is the means by which I create a commonality of understanding with other human beings.) And you write,
If I remember correctly from other threads, you have rejected both. Furthermore, you don’t object to Platonic Realism based on an evidential or logical basis (in fact, I think you agreed to at least some of the evidence and logic), but rather because the enormity of what would reside in such a realm if true is something you cannot accept (if I remember correctly), which I’m sure you understand is not a logical objection.
I appreciate it that you do remember correctly. The issue is not whether I can develop a logical objection to Platonic Realism. The issue is whether I can think of logical and evidentiary reasons that seem sufficient to believe in such, and I can’t. My theory of mind, with I discussed quite a bit with Gpuccio, is that it is something (I don’t know what, and I don’t think anyone does) that we experience “internally” through the medium of consciousness. Somehow (I don’t know how and neither does anyone else) it has a two-way interface with the external world, though my body. It is capable of, among other things, logical rational thought and the embodiment of abstractions in symbolic form which it can then manipulate to reach new conclusions. I think that is sufficient for me. It isn’t sufficient for you. I think we will have to leave it at that.hazel
January 16, 2019
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WJM, one may argue p => q, ~q so ~p. This means we are back at competing premises, in factual adequacy, coherence and explanatory balance of power. Nominalism is in a problem of inextricably entangled abstracta, across its various forms. It wants to dismiss abstracta and cannot escape them. It is dead. The real issue going forward is, how do we account for a world in which abstracta are inextricably in the roots of reality. This of course makes mind antecedent to matter. KFkairosfocus
January 16, 2019
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Hazel @116; In other words, you don't have an alternate explanation, you are simply rejecting the Platonic Realism explanation of what "exists in mind' means. IOW, under the category of what "exists in mind" means, there exists under discussion two sub-categories of explanation of (at least some) mental phenomena; (1) physicalism/materialism (such thoughts are generated by material forces) and (2) Platonic Realism - such thoughts represent things that objectively exist in a shared mental landscape, which we all can discover independently by exploring a bit in our mind. If I remember correctly from other threads, you have rejected both. Furthermore, you don't object to Platonic Realism based on an evidential or logical basis (in fact, I think you agreed to at least some of the evidence and logic), but rather because the enormity of what would reside in such a realm if true is something you cannot accept (if I remember correctly), which I'm sure you understand is not a logical objection. As I have said before, having a coherent theory of mind is not necessary to practically function and succeed in the world (in such terms as success is usually defined), but if you're going to enter into philosophical discussions about the nature of mind and thought and the like, it might be interesting to explore what it is that you do believe (via your own personal introspection) about what is going on when you think and imagine, about the nature the existence of universal mental forms and values and how it is they occur. Come up with your own positive ideas to present.William J Murray
January 16, 2019
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H, I note from another thread and suggest to you -- i/l/o the actual OP topic (talk about side tracks!), the painful subject of fallacies vs credible warrant thus substitution of opinion for objective truth -- that too often you have set up in effect a strawman target. Sorry if you find that objectionable or painful, but sometimes something has to be forced through resistance and even pain. For example, my primary point on this side-tracked discussion (red herrings for breakfast, anyone?) has always been that to get a distinct world, W -- any such world -- we must have the generic distinction A vs ~A. Consequently, we contrast and partition: W = {A|~A}. Instantly, we have two distinct entities so duality. A is a unit, and the dichotomy implies nothing inside the partition. Likewise W has nothing outside A and ~A. So, 0, 1, 2. Mix in succession and per von Neumann, the naturals, with Z, Q, R, C to follow, etc. Thus a flat space in which circles etc. All of this is inherent in the distinction of identity for any distinct world. So, these entities are necessary beings embedded in the framework for a world to exist. There is therefore a logic of structure and quantity embedded in any world and that is a substance of mathematics. Mathematics is not reducible to the culturally influenced study of effectively arbitrary conceptual entities we want to amuse ourselves by playing games with. Nor is it a mere clash of opinions, we have a demonstration on the table of necessary being mathematical entities which form a considerable body of facts on the ground antecedent to any axiomatisation that sets up an abstract, logic-model world. And I note that for many weeks, you have never presented a refutation of the core point. You have tried to convert it into a discussion of opinions and have posed on a different opinion. Indeed, you have effectively tried the rhetorical dismissal that I labour under the delusion that I have perceived an established, certain truth. At this point, my response is, that distinct identity is the core of logic, and its corollaries will be equally necessary, framework entities in any world. So, having shown that N, Z, Q, R and C (from the vector perspective you scarcley will acknowledge as valid) are such corollaries and/or constructions on such, I may freely draw conclusions on substantial matters. First, there is mathematical substance antecedent to our error-prone subjectivity, cultural influences and traditions at work in any possible world. This being a collection of propositions that for relevant purposes sufficiently describes a possible state of affairs for this or another world. Henceforward, core mathematical facts: CMF's. Such, also, patently being abstract but often serving as archetypes reflected in concrete specific particular entities, e.g. a 6500 C3 gear train which manifests several phenomena linked to circles. Imperfect reflection is valid reflection. Thus, I freely posit on such CMF's, that Mathematics is of dual character. Substantial and objective, as well as a study constrained by CMF's. Thus, a well supported good enough fer gvv'mint work definition: Mathematics is (the study of) the logic of structure and quantity. Going further, one may speculate as to how such abstract entities may have some existence. It is clear that nominalism is incoherent due to how abstracta are inextricably entangled in every act of serious conceptual thought. This particularly holds for evolutionary materialistic scientism -- which happens to be ideologically dominant and so must be addressed first or else one is open to the you set up a strawman objection. It then extends to fellow traveller ideologies commonly seen among today's educated classes, by the same token of entanglement. It extends to conceptualism, and to effectively any other species one cares to erect. Nominalism is dead. That means that we must address an abstract domain that collects relevant abstracta. Call it what you will, a neo-Platonic domain or whatever. Labels are not the issue -- nominalism being dead. Substance is. Going forward, we can take due note on the merits, holding that we have answered Wigner's challenge:
the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories. In order to establish the first point, that mathematics plays an unreasonably important role in physics, it will be useful to say a few words on the question, "What is mathematics?", then, "What is physics?", then, how mathematics enters physical theories, and last, why the success of mathematics in its role in physics appears so baffling. Much less will be said on the second point: the uniqueness of the theories of physics. A proper answer to this question would require elaborate experimental and theoretical work which has not been undertaken to date.
Note, how he focusses on Mathematics as study:
mathematics is the science of skillful operations with concepts and rules invented just for this purpose. The principal emphasis is on the invention of concepts. Mathematics would soon run out of interesting theorems if these had to be formulated in terms of the concepts which already appear in the axioms. Furthermore, whereas it is unquestionably true that the concepts of elementary mathematics and particularly elementary geometry were formulated to describe entities which are directly suggested by the actual world, the same does not seem to be true of the more advanced concepts, in particular the concepts which play such an important role in physics. Thus, the rules for operations with pairs of numbers are obviously designed to give the same results as the operations with fractions which we first learned without reference to "pairs of numbers." The rules for the operations with sequences, that is, with irrational numbers, still belong to the category of rules which were determined so as to reproduce rules for the operations with quantities which were already known to us. Most more advanced mathematical concepts, such as complex numbers, algebras, linear operators, Borel setsãand this list could be continued almost indefinitelyãwere so devised that they are apt subjects on which the mathematician can demonstrate his ingenuity and sense of formal beauty. In fact, the definition of these concepts, with a realization that interesting and ingenious considerations could be applied to them, is the first demonstration of the ingeniousness of the mathematician who defines them. The depth of thought which goes into the formulation of the mathematical concepts is later justified by the skill with which these concepts are used. The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess. However, this is not our present subject. The principal point which will have to be recalled later is that the mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity. [3 M. Polanyi, in his Personal Knowledge (Chicago: University of Chicago Press, 1958), says: "All these difficulties are but consequences of our refusal to see that mathematics cannot be defined without acknowledging its most obvious feature: namely, that it is interesting" (p 188).] The complex numbers provide a particularly striking example for the foregoing. Certainly, nothing in our experience suggests the introduction of these quantities. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius. [4 The reader may be interested, in this connection, in Hilbert's rather testy remarks about intuitionism which "seeks to break up and to disfigure mathematics," Abh. Math. Sem., Univ. Hamburg, 157 (1922), or Gesammelte Werke (Berlin: Springer, 1935), p. 188.]
Of course, the vector-rotation view actually does embed complex numbers in relevant physical contexts. Where the span from N to C is necessary so on exploring in an abstract possible world, we will readily extend necessary entities to any world and useful possible ones to any relevant one. Such as, gear trains. And so forth. KFkairosfocus
January 16, 2019
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H, QM is a capital example of mathematics deeply embedded in the experienced physical world as key substructure. KFkairosfocus
January 15, 2019
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MG, I use insomnia power. This week has been particularly busy with a cluster of meetings connected to moving MNI from hard-won breakthroughs to a redevelopment breakout. The unfolding brexit chaos is also material; I wonder how Mrs May soldiers on; but then I suspect no one else would do materially better -- and I see the just walk away and use WTO. More, later today -- solar energy initiatives -- so I will try to catch a nap or two. Y/day was sea port. Day before, annual financial aid mission. KFkairosfocus
January 15, 2019
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H, again, I already explained precisely why I started with physicalism and its fellow travellers, then extended to claimed non-physicalist forms of nominalism, including of course conceptualism. I noted how attempts to reduce mind to computational substrates fail to account for the substrates. They also fail to account for abstracta, which include logic, inference, propositions, numbers etc. It turns out that our rational discussion is inextricably entangled with reference to any number of abstracta so that we in effect cannot reason without such abstracta being implicitly accepted as accurately referring to realities. Realities that are not mere concrete entities or collections -- oops, abstractum -- and which are not merely arbitrary ideas or concepts -- oops -- going no further than somehow mutually agreed -- oops -- games -- oops -- that we play together. Games we call Mathematics that then inexplicably -- poof, magic -- apply effectively to concrete realities. (And, "reality" -- the world of entities in themselves as opposed to our error-prone perceptions -- is itself yet another abstraction in this context. Here comes that Kantian ugly gulch and fail again. As F H Bradley pointed out c 1897, s/he who imagines that one may mot know about reality in itself, has already proposed a knowledge claim regarding reality. Where, knowledge and propositions expressing same, warrant that supports the claim, etc are all again abstracta. ) If I were in a more light-hearted mood, I would chuckle; but you have objected to my noting such, so I refrain. Instead, I note that WJM is right to highlight, what do you mean by mind, noting too your tendency to confine to human ones. Let me clip what looks as close to describing mind as you seem willing to posit:
Some concepts, to some extent, are based on experiences with the physical world, and since we are all approximately alike in our sensory experience, share some commonality for that reason. However, the vast majority of our concepts are in large part brought to us through language, either verbal or written, and are thus held in common through learning with symbols. Thus, I don’t believe the fact that we share approximately common concepts with others is an argument that those concepts reside outside of us an archetype or some other type of independently existing abstraction. A few further thoughts on what I said above. Everyone’s concepts are unique no matter how much common substance they have
Do you see how many abstracta are involved? How many collections that do not reckon with the inherently abstract concept of such collection into a cluster -- a universal? How many linked propositions, another abstract commodity? How many assumptions rooted in inferred import of family resemblance? How much seems to parallel the physicalist appeal to computational substrates and seems to echo the Kantian ugly gulch? Etc? In short, you illustrate the inextricable entanglement I have pointed out already. If we are indisputably thinking, inferring, reasoning, warranting, and if such inextricably are entangled with abstracta, then it seems reasonable to accept the inevitable. As, not a demonstration, but as a start point: abstracta, whatever they will turn out to be ontologically, are an inescapable fact of rational thought. Where, likewise, ability to communicate and come to mutuality of sufficient degree on key abstracta is inescapable in being a community of minded -- whatever that is -- thinking practitioners. So, human thriving is also entangled, thus moral government too. Where, known duties to truth, right reason, fairness, prudence etc are prominent in discussion, argument, attempts to persuade, and are -- again -- inextricably entangled. Even knowledge is an abstractum. The logical import -- abstract, again -- is that the world of thought and its applicability to reality as experienced through embodiment and consciousness, intentionality etc (notice, the abstracta and collectives) are inescapably tied to the truthfulness of some propositions as well as to accepting that a great many abstract entities, such as sets, numbers, broader quantities and structures are real in some sense that transcends any particular human mind or community. That is, they are objective, which has in it openness to extension, adjustment or correction but entails having enough reliability to be routinely and confidently used. Including, hypothetically towards instantiating a design. For a circle, once we get to the reals and use i* to rotate, we have a conceptual, planar, flat space. In that space, we can readily specify circles as fulfilling the relationship: r^2 = x^2 + y^2, with translations and reflections and scaling allowing for arbitrarily many circles. Where in the r --> inf. , we have a straight line, where at any point along an arbitrary curve we can define a radius and centre of curvature (as well as extending such reflections to cumulative arc length). The relations of circularity and pi etc as extended will obtain for Kzinti, angels and God. These relations would extend to more or less round objects, including gear trains for watches, fishing reels, bicycles and wheeled or tracked vehicle drive trains for one and all. (Does God favour Patek Philippe or Casio? Automatic or Quartz? Pope Francis goes for Casio quartz, US$ 12; unique among world leaders. Right now, I am a bit concerned that I have a time finding a battery for a Wenger quartz movement wristwatch., my favoured timepiece. Our best house clocks are all Casios BTW. And yes, there is at least one clock in every room of the house.) We see that abstracta credibly hold reality, especially relevant, rationally pondered structures and quantities. This is not mere individual or collective opinion, we have explored warrant, including logic of being. It being effectively undeniable that at least one world exists, we can assess possible worlds and find that on distinct identity, the naturals must exist as framework to any possible world. That generality of result transcends humanity. And yes, I know you tried to lock out such considerations some weeks ago. All that showed is a gap in your considerations. In that light, it is then reasonable to hold that there is a core of rationally accessible structure and quantity in this or any possible world. Such, being inextricably part of the framework for any distinct world to be. It is reasonable to ponder an abstract, shadow framework logic-world embedded in the fabric for any world, and term that core mathematical reality. And yes, that echoes Plato. And Augustine, who considered this a view into the contemplation of God, considered as root of reality, creator of this and any other actualised domains of reality. That is phil, it is enough for Math, that a core abstract intelligible framework necessarily obtains in this or any other possible world. We can be confident about the power of Mathematics. Wigner is answered. Which, is a big part of my context of thought. Further, we may extend from this core of necessary mathematical facts, creating various abstract logic-model worlds exhibiting structures and quantities. That is, we may ponder mathematical contingencies of more or less restricted scope, including designs for technological entities, theories of science, economic or financial models, statistical models, etc. Then, we may test and sufficiently confirm reliability and zone of applicability to use them confidently but responsibly. Where, too, going back to the OP, we can see how our thoughts can go amiss, and particularly, how important it is to see that just to think and operate as rational, responsible creatures, there are many core points that are inevitably involved and which must be taken as true beyond ability to demonstrate. For, demonstration itself relies on such. KFkairosfocus
January 15, 2019
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mathguy, I agree that human beings have some common cognitive abilities, and that children know how to use logic, just as they learn to speak. Rationality includes both the ability to learn, create, and use abstractions and the ability to manipulate them logically. Rationality is one of the main properties of human beings. I guess I've just been assuming that is part of the background of our discussion. Of course, people have to be taught formal logic, but the informal ability to reason from premise to conclusion is part of human nature. As to SETI, I've just talked about human minds, but if there are other minds like ours out in the world, it seems reasonable to me that they would develop some similar concepts, and thus we could establish some commonality by sharing something like a sequence of primes. I don't see how QM affects anything. Our understanding of QM, and the tools we have developed to explore it mathematically, are abstractions in our minds, just as the rest of math is.hazel
January 15, 2019
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There is lots more I'd like to say, but I have a day job which inhibits posting reams of material (unlike BA77 and Hazel, although BA77 tends to copy/paste from his vast and impressive collection). Nominalism, as per Hartry Field, cannot model QM, since the latter requires an infinite dimensional Hilbert space. On the other hand QM is the most successful scientific theory in history in that it perfectly models small-scale physics. QM is as "true" as any physical model could be hoped for (and its failed reconciliation with GR is most likely because our theory of gravity is lacking; cf the many discussions about dark matter). So using logical syllogism, nominalism cannot explain the physics that we observe and hence cannot be a correct model of reality.math guy
January 15, 2019
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Hazel @80 claims to accept logical reasoning (whose rules form a Boolean algebra used in computer architecture, an abstract non-physical entity). I claim it is false to suggest that all humans need to be taught rules of logic in order to use them, or even think about them. In fact, young children recognize logical implication early on, as witnessed by me (a parent). Let us examine the alternate position that abstract objects only exist in human minds. But JAD has already presented us with a gedanken experiment where SETI finally detects a nearby signal. We respond by sending pulses corresponding to an initial segment of the sequence of primes. Of course, ETI has no "human mind" with which to share our idea of primes and cannot make sense of our reply, even though ETI has somehow made a signal generator and sent intelligible signals across space to us.math guy
January 15, 2019
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kf quotes someone from the Wikipedia article on nominalism:
If the same concept is correctly and non-arbitrarily applied to two individuals, there must be some resemblance or shared property between the two individuals that justifies their falling under the same concept and that is just the metaphysical problem that universals were brought in to address, the starting-point of the whole problem (MacLeod & Rubenstein, 2006, §3d).
The kf adds,
So, is there or is there not an archetype in common that allows us to recognise the fiveness of say my right fingers and left toes, or those of my wife or mother?
This is a good question, and I’d like to share some thoughts. Each of us have a unique set of concepts in our mind, and they vary widely in how similar they are to other people’s. Some concepts, to some extent, are based on experiences with the physical world, and since we are all approximately alike in our sensory experience, share some commonality for that reason. However, the vast majority of our concepts are in large part brought to us through language, either verbal or written, and are thus held in common through learning with symbols. Thus, I don’t believe the fact that we share approximately common concepts with others is an argument that those concepts reside outside of us an archetype or some other type of independently existing abstraction. A few further thoughts on what I said above. Everyone’s concepts are unique no matter how much common substance they have. Paying attention to my own consciousness, I know that every concept I have has a cloud of peripheral associates that add to its overall meaning. Everyone’s overall cloud, then, is different based on their individual background and experience. An example: take the number seven. Almost all people over about the age of four understand it to be a certain number that can be used to count things. Some people also know it is a prime number. I now think about how 7^2 - 1 is a multiple of 24, and know why, but I didn’t know that a few weeks ago. That has expanded the cloud of knowledge around the concept. I also know you can’t construct a regular seven-sided polygon with a ruler and compass, but that you can using the seven 7th roots of 1 in the complex plane. These are things most people don’t know. Thus, the overall concept of seven, even though it shares a common core with others, exists in me differently, at least in some ways, then it does in anyone else. Of course, in math concepts can be formally defined. How most people learn that aspect of the concept is by being taught. The main reason we have a large body of shared concepts, both mathematically and otherwise, is that we are taught them, both formally and informally, through language. We share a lot of common sensory experiences, but the structure for applying abstractions to those experiences comes from sharing ideas through language and then building our own unique world of understanding in our minds. So i disagree with MacLeod and Rubenstein, quoted above, when they say, “If the same concept is correctly and non-arbitrarily applied to two individuals, there must be some resemblance or shared property between the two individuals that justifies their falling under the same concept,” We share the same concepts because we pass those ideas from mind to mind, and because both our minds and our sensory experiences share a great deal of a common human nature, but that doesn’t mean that the abstract property that we both, approximately, share, has a reality outside of our minds.hazel
January 15, 2019
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why can’t you get that into your head?
It's an interface issue. Most likely there is either too much SWR at the transmitter or receiver.ET
January 15, 2019
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kf, I have no idea how the ideas I'm an expressing have to do with physicalism. See my previous remark to wjm. Abstractions exist in the minds of human beings. As I said in 98, my position has nothing to do with physicalism and all those other things: why can't you get that into your head?hazel
January 15, 2019
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wjm, I mean "exists in my mind". I, right now, am contemplating Euler's Identity, e^(i*pi) = -1. I understand what it means and how it is related to the rest of the number system. It exists as a concept in my mind. I assume it exists in other people's minds who have studied the math also. I have no idea as to whether there is any larger mind, or Platonic realm, where it exists independently of those of us in whose individual minds it exists.hazel
January 15, 2019
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Hazel @ 108 said:
I start with and accept the experiential reality of my own consciousness and mind, and the experiential reality of there being an external world, including my own body, that is different from and separate from my mind. I don’t think that distinction is “functionally meaningless” if I can’t define what those terms mean.
What I meant was that the phrase "exists in mind" was functionally meaningless in providing a contrasting alternative to Platonic Realism, which is what the post I was referring to was about. I didn't say it was functionally meaningless in terms of practically sorting out behavioral options and distinguishing broad classes of experience. Until you provide a way that something "exists in mind" other than platonic realism, even though you don't require such an explanation to live and function successfully, you haven't actually offered an alternative to Platonic Realism, which does offer an explanation of what "exists in mind" means. Exists in mind - but NOT Platonic Realism ... okay, so then what? "I don't know" is a perfectly fine answer, but neither "nominalism" or "conceptualism" mean anything unless one defines what they mean by "exists in mind".William J Murray
January 15, 2019
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H, it seems clear that a main form of nominalism is physicalism (and its fellow travellers); where the associated naturalism is known to be a major ideological motive in our time. So, it is entirely in order to show that this form of nominalism falls apart into absurdity. Then, once one accepts the reality of mind beyond epiphenomena and delusions -- if that is possible! -- of a computational substrate, then the problems of rejecting the reality of archetypes instantiated in cases are seen to also follow. One cannot even posit propositions, what is meant and asserted by a sentence of certain types. Logic follows, poof. Rational principles, poof too. If one says, no, we accept minds (and presumably their contents) -- and not merely computational substrates -- then one has accepted abstracta. There is no good reason to reject archetypes, which will include quantities and structures. The real issue is, what are these things that are not matter, motion and clumps of same. Let me again clip Wikipedia as a handy source:
In medieval philosophy, the French philosopher and theologian Roscellinus (c.?1050 – c.?1125) was an early, prominent proponent of nominalism. Nominalist ideas can be found in the work of Peter Abelard and reached their flowering in William of Ockham, who was the most influential and thorough nominalist. Abelard's and Ockham's version of nominalism is sometimes called conceptualism, which presents itself as a middle way between nominalism and realism, asserting that there is something in common among like individuals, but that it is a concept in the mind, rather than a real entity existing independently of the mind. Ockham argued that only individuals existed and that universals were only mental ways of referring to sets of individuals. "I maintain", he wrote, "that a universal is not something real that exists in a subject... but that it has a being only as a thought-object in the mind [objectivum in anima]". As a general rule, Ockham argued against assuming any entities that were not necessary for explanations. Accordingly, he wrote, there is no reason to believe that there is an entity called "humanity" that resides inside, say, Socrates, and nothing further is explained by making this claim. This is in accord with the analytical method that has since come to be called Ockham's razor, the principle that the explanation of any phenomenon should make as few assumptions as possible. Critics argue that conceptualist approaches only answer the psychological question of universals. If the same concept is correctly and non-arbitrarily applied to two individuals, there must be some resemblance or shared property between the two individuals that justifies their falling under the same concept and that is just the metaphysical problem that universals were brought in to address, the starting-point of the whole problem (MacLeod & Rubenstein, 2006, §3d). If resemblances between individuals are asserted, conceptualism becomes moderate realism; if they are denied, it collapses into nominalism.[10]
So, is there or is there not an archetype in common that allows us to recognise the fiveness of say my right fingers and left toes, or those of my wife or mother? That archetype is also found embedded in the logic -- notice how impossible it is to avoid speaking or reasoning in categories and using universals -- of there being any distinct world. That is, there is an abstract substance of structure and quantity we may call fiveness. It will be an in common property of any set of discrete things that will match the successive counting glyphs: 1, 2, 3, 4, 5. Those things may be concrete -- my fingers -- or abstract, the fingers of my late father. For that matter, I may conceive a plan without giving it physical instantiation, and of several competing plans, the logical performance of say C will lead me to give it approximate physical effect, say as the main gear train of a 6500 C3 fishing reel. Which, will embed pi. The distinctions we may make indicate distinct identifiable entities, some physical, some abstract. And no, I need not suggest a weird, independent world of forms separate from the mind of God and from the logic of being for worlds that are possible of instantiation. God, here, being reason himself. KFkairosfocus
January 15, 2019
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Math Guy @ 92, Thanks for the comment. Here is an interesting quote from a paper Penrose wrote:
Gödel appears to have believed strongly that the human mind cannot be explained in terms of any kind of computational physics, but he remained cautious in formulating this belief as a rigorous consequence of his incompleteness theorems. In this chapter, I discuss a modi?cation of standard Gödel-type logical arguments, these appearing to strengthen Gödel’s conclusions, and attempt to provide a persuasive case in support of his standpoint that the actions of the mind must transcend computation. It appears that Gödel did not consider the possibility that the laws of physics might themselves involve noncomputational procedures; accordingly, he found himself driven to the conclusion that mentality must lie beyond the actions of the physical brain. My own arguments, on the other hand, are from the scienti?c standpoint that the mind is a product of the brain’s physical activity. Accordingly, there must be something in the physical actions of the world that itself transcends computation. We do not appear to ?nd such noncomputational action in the known laws of physics, however, so we must seek it in currently undiscovered laws going beyond presently accepted physical theory. I argue that the only plausibly relevant gap in current understanding lies in a fundamental incompleteness in quantum theory, which reveals itself only with signi?cant mass displacements between quantum states (“Schrödinger’s cats”). I contend that the need for new physics enters when gravitational effects just begin to play a role. In a scheme developed jointly with Stuart Hameroff, this has direct relevance within neuronal microtubules, and I describe this (still speculative) scheme in the following.
https://philpapers.org/rec/PENGTM If I am understanding him correctly Penrose does not believe that a computer could ever have the capability to derive any of Gödel’s incompleteness theorems. In other words, “proving” such theorems requires the insight of an intelligent conscious mind. (As I understand Gödel’s incompleteness theorems they’re proving that there are true statements in a given system of mathematics that are undecidable.) Whether or not they are “intelligent” computers clearly are not conscious or minds. Of course this view is not uncontroversial. However, this brings up another interesting question: could computers using advanced AI algorithms ever get to the point where they could independently solve unproven conjectures such as the twin prime conjecture (whether or not the set of twin primes is infinite,) the Goldbach conjecture or the Riemann hypothesis? In other words, we feed a problem into a supercomputer programmed with an advanced AI algorithm named Math Savant and after some processing it solves one of the unsolved conjectures in mathematics. This question, along with Penrose’s thesis, I think would make an interesting topic for an OP or a Mind Matters article. I am not a mathematician or a computer geek so presently I have no opinion one way or the other what a computer could do. Anybody else (like a mathematician or computer geek) have any thoughts?john_a_designer
January 15, 2019
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Ed George:
Actually he does that to anyone he disagrees with.
That is not true, Ed. But I understand why you would say it. It is what I do when people just ignore the evidence and arguments and prattle on regardless. People- I don’t care about their gender seeing that they choose to be willfully ignorant. And I don’t want to insult any gender by calling a willfully ignorant person by that type of pronoun.ET
January 15, 2019
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hazel:
I feel pretty comfortable with philosophies that support the distinction between mind and matter, and not so much to philosophies that don’t.
And I feel pretty comfortable with the reality and evidences that support the distinction between mind and matter, and not so much to philosophies that don’t. :cool:ET
January 15, 2019
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hazel:
ET has doubts about my gender.
Not really. But if saying that makes you feel good, then have at it.
It is telling, as kf would say, that if I used a man’s name he would not do that.
And yet I do so all of the time. It is what I do when people just ignore the evidence and arguments and prattle on regardless. People- I don't care about their gender seeing that they choose to be willfully ignorant. And I don't want to insult any gender by calling a willfully ignorant person by that type of pronoun.ET
January 15, 2019
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to kf: all your remarks about physicalism and evolutionary materialism, etc. have nothing to do with me, and I'm baffled why you can't get that. I read the Wikpedia article earlier. One line in there says; "Conceptualists hold a position intermediate between nominalism and realism, saying that universals exist only within the mind and have no external or substantial reality." That is probably closer to what I have been trying to describe.hazel
January 15, 2019
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To wjm at 106: I have enjoyed learning about some philosophical views, including yours. However, as was a key point in my discussion with Gpuccio, I start with and accept the experiential reality of my own consciousness and mind, and the experiential reality of there being an external world, including my own body, that is different from and separate from my mind. I don’t think that distinction is “functionally meaningless” if I can’t define what those terms mean. Given how given they appear to my experience, I’m willing to consider their existence as undefined aspects of my views. (This is somewhat analogous to how geometry starts with some undefined terms like point, line, and plane.) I feel pretty comfortable with philosophies that support the distinction between mind and matter, and not so much to philosophies that don’t.hazel
January 15, 2019
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H, Wikipedia, that humble but handy reference, gives us a point of reference:
Nominalism From Wikipedia, the free encyclopedia Jump to navigation Jump to search In metaphysics, nominalism is a philosophical view which denies the existence of universals and abstract objects, but affirms the existence of general or abstract terms and predicates.[1] There are at least two main versions of nominalism. One version denies the existence of universals – things that can be instantiated or exemplified by many particular things (e.g., strength, humanity). The other version specifically denies the existence of abstract objects – objects that do not exist in space and time.[2] Most nominalists have held that only physical particulars in space and time are real, and that universals exist only post res, that is, subsequent to particular things.[3] However, some versions of nominalism hold that some particulars are abstract entities (e.g., numbers), while others are concrete entities – entities that do exist in space and time (e.g., pillars, snakes, bananas). Nominalism is primarily a position on the problem of universals, which dates back at least to Plato, and is opposed to realist philosophies, such as Platonic realism, which assert that universals do exist over and above particulars. However, the name "nominalism" emerged from debates in medieval philosophy with Roscellinus. The term 'nominalism' stems from the Latin nomen, "name". For example, John Stuart Mill once wrote, that "there is nothing general except names".
Under physicalism, there are no abstracta, just stored signals in some computational substrate that likes to call itself -- oops -- an individual mind. It is not too hard to see that such physicalism falls apart under the force of self-referential incoherence and GIGO. Evolutionary materialism self-falsifies and takes its fellow travellers down with it. Where, of course, on such failed premises -- oops, there are no premises as there are no propositions (as abstract a thing as we can get) -- there is no logic of being and no logic of structure and quantity as there is no logic, just signals in some GIGO-driven substrate that somehow assembled itself from cumulative noise and whatever mechanical cascades of events obtained. There is no logic, of course radically self-refutes. We cannot have a REASON to believe there is no right reason as there are no principles, there is no right and there is no reason. Utter confused chaos. And before we get there there is no answer -- oops, that is a logical commodity -- on such premises (oops) to how we get to functionally specific, coherent, complex organisation and associated information for us to have computational substrates. Perhaps, we have a modest version, where there is mind. But as WJM highlighted, what then is mind? Surely, not just another name -- oops, an abstract commodity again -- for a GIGO-limited computational substrate that will happily process nonsense nonsensically until the system crashes. Far better, to start with undeniable fact 1: the self-aware, conscious mind that perceives, reflects, reflects on itself, infers, reasons, understands, accesses and uses abstracta and in our cases is embodied. Where, I on reflection chose to type out these reflections, character by character. Among those abstract entities and processes is reasoned judgement under principles of reason, logic. The logic that tells me that a world with distinct identity, W, will have distinction, W = {A|~A}. so also, duality, unity, nullity. Thus, by way of the von Neumann construction the naturals. Further, integers, rationals, reals, complexes and other vectors and similar structures. Thus also abstract space where a circle of rad r centred on origin has r^2 = x^2 + y^2, and we can make any circle in the space by applying a vector displacement and a scaling. Where, we may proceed similarly to other figures. We may observe a circumference C and a diameter D = 2r, leading to pi = C/D, a transcendental real number. These are indeed abstracta but by logic will necessarily be present in any possible world, and will affect possibilities and actualities in any such world. For example, in ours, ponder the ways relevant structures and quantities affect a gear train in a fishing reel, a watch or a car. So, what are these abstracta? Not, traces on paper or ion gradients -- oops, another abstract commodity -- in nerve cells. Such may be associated, but very similar ion gradients readily mean something else. Oops, meaning is another abstraction. Just like man, woman, mind, truth, love. The candidate to beat is: something contemplated by a mind. Which, in the context of roots of a world, points to eternal mind. Which, in turn seems to be the real problem. Ideological commitment to block any shadow of Him with whom we wish to have no dealings. Never mind the resulting utter incoherence. But, I have not been primarily interested in debates over theism, just with the nature of Mathematics. KFkairosfocus
January 15, 2019
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Hazel, My point is that the phrase "exists in mind," especially in contrast to "not found in the physical world", is functionally meaningless unless one explains what those terms mean. In contrast, I (and others) have provided an explanation of what is meant by the phrase "exists in mind." You say you are offering an alternative to what others here mean by that phrase, but do not explain how it is different. Until you explain the distinction, you haven't actually offered an alternative at all.William J Murray
January 15, 2019
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