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Logic and First Principles, 12: The crooked yardstick vs plumb-line self-evident truths

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Let’s propose a silly example, that a certain Emperor (maybe, just before he went out in his new invisible clothes) decides that a certain crooked stick is now the standard of length, straightness, uprightness and accuracy, a crooked yardstick. Suddenly, what is genuinely such things will be deemed the opposite. And then, suppose that somehow he and his publicists persuade the general public to accept the new standard. Will they not then find that those backward fuddy duddies that hold up their old yardsticks are ignoramuses and obstacles to progress and harmony?

Are we then locked into a war of competing imposed definitions and redefinitions? (That would for sure be a manipulator’s paradise.)

That’s where a plumb-line might help:

A plumb-line

Here, we see something that is naturally straight and upright, which will then clearly correct the crooked yardstick. It will even vindicate the fuddy duddies, even though the progressives won’t like it.

So, now, let us lay on the table a key concept: there are self-evident first truths (including inescapably true claims) that can and do serve as plumb-line tests for various truth claims. And thus, such truths can allow us to sift through various worldview or ideological alternatives and schools of thought. Which then allows us to think, decide and act with greater soundness.

For simple example the Josiah Royce proposition, E = error exists, is undeniably true. To see that, try to deny it, ~E. That in effect claims it is error to propose E. So E must be true.

Is this a trivial result?

No, as E is an example of self-evident truth, of truth, of objectively warranted truth (thus knowledge), indeed of truth warranted to undeniable certainty (thus certain knowledge). Such immediately sweeps away radical skepticism, relativism and subjectivism, as well as a raft of linked common notions.

Likewise, for any distinct A — say, a bright red ball on a table — we see that the world can be dichotomised W = {A|~A} thus showing the triple first principles of right reason, Identity, Non Contradiction and Excluded Middle:

Here, A is itself in light of its particular distinct characteristics. No x in W can be both A and ~A. Any x in W will be A or else ~A. These laws are inescapably certain, indeed, any argument to object to them must rely on distinct identity and its corollaries to make an intelligible point. A classic case in point is a remark by St Paul:

1 Cor 14: Yet even lifeless things, whether flute or harp, when producing a sound, if they do not produce distinct [musical] tones, how will anyone [listening] know what is piped or played? And if the [war] bugle produces an indistinct sound, who will prepare himself for battle? So it is with you, if you speak words [in an unknown tongue] that are not intelligible and clear, how will anyone understand what you are saying? You will be talking into the air [wasting your breath]! [AMP]

This is again, hardly a trivial result. Ever so much of the modern skepticism towards reasoned thought pivots on dismissiveness towards precisely these three laws of thought. Where, BTW, Quantum Physicists rely on just these laws in order to do their work.

Similarly, if we look at the world partition W = {A|~A} we see that A is itself, a unit distinctly different from the complex unity ~A, thus we find unity and duality. Where too the partition is empty and there is nothing in W but outside A and ~A, thus, nullity. This sets up the natural numbers, integers, rationals, reals, continuum, and even by using vector rotation, complex numbers. That is a non-trivial consequence.

Likewise, identity and the logic of being allow us to see how inductive reasoning and causality can be grounded.

So, too, as arguably there are self-evident, plumb-line moral truths, moral forms of radical skepticism, relativism and subjectivism, as well as a raft of linked common notions are also swept away. This re-opens the issue of intelligible laws of our morally governed nature, framing thought, speech, behaviour and law. Indeed, Cicero is back:

—Marcus [in de Legibus, introductory remarks,. C1 BC]: . . . the subject of our present discussion . . . comprehends the universal principles of equity and law. In such a discussion therefore on the great moral law of nature, the practice of the civil law can occupy but an insignificant and subordinate station. For according to our idea, we shall have to explain the true nature of moral justice, which is congenial and correspondent [36]with the true nature of man. We shall have to examine those principles of legislation by which all political states should be governed. And last of all, shall we have to speak of those laws and customs which are framed for the use and convenience of particular peoples, which regulate the civic and municipal affairs of the citizens, and which are known by the title of civil laws.

Quintus [his real-life brother]. —You take a noble view of the subject, my brother, and go to the fountain–head of moral truth, in order to throw light on the whole science of jurisprudence: while those who confine their legal studies to the civil law too often grow less familiar with the arts of justice than with those of litigation.

Marcus. —Your observation, my Quintus, is not quite correct. It is not so much the science of law that produces litigation, as the ignorance of it, (potius ignoratio juris litigiosa est quam scientia) . . . . With respect to the true principle of justice, many learned men have maintained that it springs from Law. I hardly know if their opinion be not correct, at least, according to their own definition; for “Law (say they) is the highest reason, implanted in nature, which prescribes those things which ought to be done, and forbids the contrary.” This, they think, is apparent from the converse of the proposition; because this same reason, when it [37]is confirmed and established in men’s minds, is the law of all their actions. They therefore conceive that the voice of conscience is a law, that moral prudence is a law, whose operation is to urge us to good actions, and restrain us from evil ones. They think, too, that the Greek name for law (NOMOS), which is derived from NEMO, to distribute, implies the very nature of the thing, that is, to give every man his due. [–> this implies a definition of justice as the due balance of rights, freedoms and responsibilities] For my part, I imagine that the moral essence of law is better expressed by its Latin name, (lex), which conveys the idea of selection or discrimination. According to the Greeks, therefore, the name of law implies an equitable distribution of goods: according to the Romans, an equitable discrimination between good and evil. The true definition of law should, however, include both these characteristics. And this being granted as an almost self–evident proposition, the origin of justice is to be sought in the divine law of eternal and immutable morality. This indeed is the true energy of nature, the very soul and essence of wisdom, the test of virtue and vice.

So, then, are we willing to acknowledge the problem of crooked yardsticks and the value of plumb-line, self-evident truths in our thinking, arguing, deciding and doing? END

Comments
Math Guy @ 64- “purely immaterial beings existing in a non-physical world” would be directly with all of the immaterial information there is, including all mathematics. They would all be super duper versions of Srinivasa RamanujanET
March 4, 2019
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hazel,
One example that always fascinated me: the three trisectors of the angles of any triangle intersect in an equilateral triangle! Isn’t that cool?
Yes, that is very interesting. Is this the theorem? It's surprising that it was discovered only a little over 100 years ago.daveS
March 4, 2019
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MG, it seems we are visiting old grounds. I take it from the non-reaction to the bulk of substance I summarised in 52 above, that it is clear that there is good reason to accept that there will be abstract structures and quantities that are necessarily present in any possible world as part of its framework. From the point we reach Z, we have direction and size, thus vectors. The step of the rationals plus infinitely continued converging power series of rationals gives us abstract continuum, R. The first rotation of R, by i*R gives us planar space. Modifying, the ijk unit vectors give us 3-d rotations and a 3-d vector space that is a continuum. Along the way, we may readily extend to the transfinites. Let me add: just recognise w as order type of the unending succession of naturals: {0,1,2 3 . . . } --> w A field can be understood as a quantity that is assigned values across a domain of space, i.e. at each point in a relevant region, it assigns a value. Sometimes, a scalar (temperature, local air pressure, local air density, potential such as a voltage etc, popping across to physics) or a vector (e.g. gravity, electrical, magnetic fields, flow fields for fluids etc). So, we can assign fields to conceptual spaces and readily observe them in the physical world. While I am at it, space itself has measurable properties connected to electromagnetism etc. which in that case set the propagating speed of electromagnetic waves. Fields are inevitable in abstract logic model worlds, as part of the core facts of structure and quantity that are antecedent to axiomatisations. They are seen in our world, working integrally with many spatially extended physical phenomena, which can be seen as ways in which objects influence space around them. A massive object notoriously distorts the space-time fabric, giving rise to gravitational phenomena. This is in fact the root of General Relativity, and it is why we accept that on the grand scale, our world dies not follow the abstract structures of a Euclidean space. But under relevant local circumstances, we can use familiar models that fit Euclidean expectations. So yes, fields are real and space is real. Similarly, the mobius strip shows that objects in space can and do exhibit quantitative and structural properties that do not depend on our axiomatisations and calculations to be real and even empirically demonstrable. We already saw that there are transfinitely many core basic mathematical facts that are tied to the bare possibility of a world, as they are part of the framework for such to be of distinct identity. So, too, I have no doubt that Godel was right: there are ever so many facts of Math unreachable by sufficiently complex axiomatic systems, that are coherent, and that there is no constructive process to establish a demonstrably coherent axiomatic system. So, bot, we must work by faith having learned of our limitations and there is in principle an escalating, endless hierarchy of mathematical systems that cannot exhaust the span of mathematical facts. Coming back to focus, it is important that we have confidence in the significant intelligibility of reality, that we see and accept that there are self-evident first truths, that there are truths, that some can be warranted so as to be knowledge, that some are so warranted beyond rational doubt, including that humbling truth: error exists. From this, we can see that in all of our explorations we find ourselves inescapably under government of duties to truth, right reason, prudence, fairness etc. Indeed, such is inextricably entangled with our life of responsible, rational, significant freedom. This points onward to the need to bridge the IS-OUGHT gap, which, post-Hume we know can only be done at world root. I have long since pointed out that to do so, there is but one serious candidate: the inherently good, utterly wise creator-God, a necessary and maximally great being. One who is arguably the prime, ultimate mind and who is worthy of our loyalty and of the reasonable, responsible service of doing the good that accords with our manifest nature. Of course, objectors are free to put up an alternative under comparative difficulties across factual adequacy, coherence and balanced explanatory power: ________ . The main purpose of this OP and thread has been to move the game forward, to the point where we find truth (real, objective truth not strongly held opinions), warranted truth, self-evident and certain truth reasonable, credible, acceptable. Where, arguably, such does involve a core of moral truths and instructive test cases. This, as radical hyperskepticism, subjectivism and relativism run riot all across our civilisation, wreaking havoc as they go. It is time for a sea-change, KFkairosfocus
March 4, 2019
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Hazel (and Rob Sheldon, for that matter) We use infinite and continuous vector or tensor fields to great effect in physics. For instance, the "zero point field" describes the behavior of virtual particles, modeled via Feynman diagrams. The gravitational field seems to be almost as mysterious. Do fields exist?math guy
March 3, 2019
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ET@63 I must disagree. Unless the “purely immaterial beings existing in a non-physical world” are capable of grasping all aspects of infinite sets (such as the integers) so as not to be bound by finite processes (like our current mathematical proofs), then Gödel's theorems imply an infinite hierarchy of formal systems, each containing true results that are unprovable in lower systems. The complexity of provably verifiable truths (i.e. theorems) form an infinite chain. Just like ordinal numbers, there is no "final most complicated theorem".math guy
March 3, 2019
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daves, I would think that if we were if we were "purely immaterial beings existing in a non-physical world" then we would know everything. There would be nothing to pursue.ET
March 3, 2019
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BB, technology long preceded significantly sophisticated mathematics, but rudimentary mathematics is part of our day to day existence. KFkairosfocus
March 3, 2019
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Not very far, although "formalized" is a broad term, and so is "rudimentary technology", as technology usually has gone hand-in-hand with other advances such as trade, exploration, war, etc. That's what I think.hazel
March 3, 2019
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Hazel and Dave, I have a question that I would be interested in your response to. Could a technology develop without some form of formalized mathematics? Very rudimentary technology would be possible, but how far could it be extended without mathematics?Brother Brian
March 3, 2019
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Agreed, Dave: math is a delightful and fascinating field irrespective of any application to the physical world. One example that always fascinated me: the three trisectors of the angles of any triangle intersect in an equilateral triangle! Isn't that cool?hazel
March 3, 2019
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ET, We wouldn't necessarily require it. Perhaps we would pursue mathematics as a recreational activity.daveS
March 3, 2019
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DS, I suppose we often find vaguely mechanical contrivances easier to understand. KFkairosfocus
March 3, 2019
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SB, the current resort to infanticide under false colour of law speaks volumes. Notice, I now start with moral government of our reasoning and discussion. Even the most cynical know that we are guided by duties to truth, right reason, prudence, fairness etc. They just hope to exploit it. KFkairosfocus
March 3, 2019
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Hi daves- What makes you think that mathematics would require developing "if we were purely immaterial beings existing in a non-physical world"?ET
March 3, 2019
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PS to my #50: A Universal Turing Machine in Minecraft This also leads me to wonder how mathematics would have developed if we were purely immaterial beings existing in a non-physical world. What would they think of Turing machines and the lambda calculi?daveS
March 3, 2019
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KF @43, Yes, the objective moral law is self-evident *in itself* and *to those* who have not been [a] psychologically harmed, [b] brainwashed, [c] or morally weakened as a consequence of forming immoral habits. Also, fallen human nature temps us to shirk the responsibility of submitting our ego to the authority of binding moral truths. Our natural desire is to prefer our own desires over the truth. Subjectivism, Hyperskepticism, Relativism, Idealism, Nominalism, Communism etc, are all just different ways of denying the moral authority of the divine lawgiver so that we can be a law unto ourselves.StephenB
March 3, 2019
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H & DS, Bottomline is, that we can see that there are possible worlds holding distinct identity. As I outlined earlier, this leads to the effects of that distinct identity where any possible world W is distinct from close neighbours due to at least one characteristic A (which may be reduced descriptively to a proposition). The world partition then shows that nullity, unity and duality are necessary corollaries of W being a distinct possible world. Apply von Neumann's construction and N follows thus Z, Q, R, and using rotating vectors C. In short, embedded structure and quantity are part of the fabric for any possible world. Which is to say such core mathematical entities are necessary beings, they did not begin to exist, they cannot cease, they are not dependent for their abstract reality on our reflection or conception. Their properties are independent of our spinning out abstract structural and quantitative logic-model worlds. Indeed, the utility of that in key part is that exploring such a world brings out such framework entities which will then be in any world, including ours. Other more specific features will extend to our world to the extent that there are in common characteristics. This sort of perception of real abstract entities inextricably part of any distinct world is sometimes called Mathematical Platonism. I add: thus in regards to certain core mathematical entities, properties, structures etc, we discover them, we do not invent them. The set C is an example where we thought we invented then found that a vector-rotation view naturally yields the key results. (This then invites in the complex exponentials approach with all its richness, where also the ghost of Fourier beckons.) I suspect the label is triggering, it is the substance that counts. I am pointing out that mathematical abstracta are necessarily embedded in the framework for any world, forming part of the logic of being. I am not imagining some sort of cloudy world out there with perfect cases of nullity, unity, duality, etc. So, while there is but one null set -- separate recognitions of it can obviously find no distinctions so it is all one and the same: { } --> 0 -- I don't think there is some ideal world repository out there where that abstractum is somehow concretised so that a sufficiently visionary person may somehow catch a glimpse like an Astronomer peering through a telescope. I do think that such realities are eternally contemplated by God as a facet of omniscience [God is the greatest possible Mathematician and Logician, Reason himself], but that is separate. I add, nope, I don't think there is some ethereal scroll or codex with perfect, complete Mathematics written out in perfect symbolism so that a visionary can inhale incense then go to the library, don magically translating spectacles -- an extension of virtual reality goggles I suppose -- and read it all. I have also been struck by the Mobius strip. Cut three strips of paper, make one common loop and two with a half twist. Cut the ordinary loop and one M-loop going around, in the centre. The first will separate into two loops, the second as you know doubtless will become a single, double length loop with several twists. Now, cut the third going around, 1/3 way across. It will separate into a narrower mobius loop interlocked with a longer loop. Those properties are independent of our expectations, ideas, understanding, axiom systems or whatever. They directly, empirically show how certain structural and quantitative properties are embedded in the fabric of our world. There are many other cases. Most recently I looked at how hearing exploits a mechanical implementation of a transform to the frequency domain. Where the Fourier Transform is about as abstract a thing as we will ever meet. KF PS: SEP, supplement to article on Mathematical Platonism:
Supplement to Platonism in the Philosophy of Mathematics Some Definitions of ‘Platonism’ Dummett 1978b, p. 202: Platonism, as a philosophy of mathematics, is founded on a simile: the comparison between the apprehension of mathematical truth to the perception of physical objects, and thus of mathematical reality to the physical universe. Dummett 1991a, p. 301: Platonism is the doctrine that mathematical theories relate to systems of abstract objects, existing independently of us, and that the statements of those theories are determinately true or false independently of our knowledge. Field 1989, p. 1: A mathematical realist, or platonist, (as I will use these terms) is a person who (a) believes in the existence of mathematical entities (numbers, functions, sets and so forth), and (b) believes them to be mind-independent and language-independent. Gödel 1995, p. 323 [Platonism is] the view that mathematics describes a non-sensual reality, which exists independently both of the acts and [of] the dispositions of the human mind and is only perceived, and probably perceived very incompletely, by the human mind. Maddy 1990, p. 21: [Realism or platonism is the view that] mathematics is the scientific study of objectively existing mathematical entities just as physics is the study of physical entities. The statements of mathematics are true or false depending on the properties of those entities, independent of our ability, or lack thereof, to determine which. Parsons 1983, p. 273: As is customary in discussing the foundations of mathematics, platonism means here not just accepting abstract entities or universals but epistemological or metaphysical realism with respect to them. Thus a platonistic interpretation of a theory of mathematical objects takes the truth or falsity of statements of the theory, in particular statements of existence, to be objectively determined independently of the possibilities of our knowing this truth or falsity. Shapiro 1997, p. 37: [Realism in ontology or platonism is the view that] mathematical objects exist independently of mathematicians, and their minds, languages, and so on. Resnik 1980, p. 162: Let us call an ontological Platonist someone who recognizes the existence of numbers, sets, and the like as being on a par with ordinary objects and who does not attempt to reduce them to physical or subjective mental entities.
The main SEP article summarises:
Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. Just as electrons and planets exist independently of us, so do numbers and sets. And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, so are statements about numbers and sets. Mathematical truths are therefore discovered, not invented.
PPS: Let me add, that information and energy look to me like similar embedded abstracta that have structural and quantitative properties. Angular momentum is similarly a vector that produces astonishing effects yet is decidedly not concrete. PPPS: Let me further add, I am viewing Mathematics as having two aspects, a study and a substance. That is as (the study of) the logic of structure and quantity. I think both are distinct and important. The mobius strip for example is independent of our study but exhibits embedded structural and quantitative properties which historically helped to launch topology.kairosfocus
March 3, 2019
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H, this thread is part of a general exercise on logic and first principles, which I have become convinced is necessary because the root disagreements and contentions are worldviews driven, not science. In this context science comes in fairly late. In that context, hyperskepticism, subjectivism, relativism and the like are major cultural forces. An important minority could be termed neural illusionism or the like where consciousness is viewed as an illusion. And yes, part of that has been the attempt to dismiss first principles of reason. Way back when I looked at boolean algebra I recall being taught that there was nothing special about the triple cluster LOI, LEM, LNC, such was just part of the seventeen laws, and of course at bottom truth tables could be trotted out. It is only on considerable reflection that I came to realise that there is more to the story. I don't know if you realise that my sliding scale treatment of what knowledge is -- with degrees of warrant, certainty and credibility/reliability -- is a deliberate weak form i/l/o how we speak of scientific, historical and common sense knowledge claims. Similarly, the weak, inquiry form form of the principle of sufficient reason and causality etc. KFkairosfocus
March 3, 2019
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hazel, Those views are very close to mine, I believe. I have been trying (with limited success) to read about automated reasoning and automated theorem proving lately, and it has reinforced some of these views. Some of the sources I am looking at explain a concept verbally, then implement that concept in a programming language, which gives one a very concrete understanding of what is going on. As an example, one could build a computing machine which actually does compute the billionth decimal digit of pi (of course some already exist). In principle, this machine could be built out of legos or even 2 x 4s. Provided the machine is built correctly, the output of this machine, when it finishes the computation, is an objective "fact", independent of our minds. That is, if the physical universe operates as I understand it to. And I believe any other mathematical "fact" should be amenable to the same sort of mechanical verification. [Edit: By "fact" I mean "theorem" here; I don't expect mechanical verification of axioms or choice of logic].daveS
March 3, 2019
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Hi Dave. I don't know whether you (or I) want to reopen a can of worms, but here goes. After some thought, I had concluded last fall that my position is that mathematical truths exist within the logical symbol systems which we have developed to express them, but not in some eternal, pre-existing Platonic realm. Within those systems, the force of logic creates truths that exist (the one billionth digit of pi, base 2, for instance), that we could potentially discover, at least in theory. They are objective in the sense that anyone following the laws of logic and utilizing the proper math would reach the same conclusions. They are either unequivocally either true or false, even if we don't which at this point. More broadly, I also think that in general abstractions exist in our minds, and in the verbal and written systems we use to express them. I'm not interested in re-arguing this with kf, but I thought I'd share my basic view on these issues.hazel
March 3, 2019
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Kf writes, “We can see this in for example how we are agreeing that truth is real and can be objective. … Similarly, the force of the undeniable truth, error exists, has led to recognition that hyperskepticism, radical subjectivism and radical relativism are not tenable … These are important points of progress.” If you are referring to me (and probably Dave), all we have agreed upon is that in the world of logic, it is proven that “false propositions exist” is true, that the laws of logic and associated mathematical structures exist, and we can use mathematics to understand the world, at least to some extent. I don’t think we have agreed that these logical truths are “real and objective” in the same way you do (although what that way is is not clear), or have the same implications as you think they have. Also I don’t think whatever you mean by “hyperskepticism, radical subjectivism and radical relativism” has even been addressed, other than in your rhetoric, unless you mean not accepting the laws of logic, which I don't think is true of anyone.hazel
March 3, 2019
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hazel,
We discussed a whole bunch of this last fall, Dave, and I’m pretty sure I am one of those that kf doesn’t think falls in the minority that he thinks you are in. However, I think you would need to know more about what kf means about the existence and nature of abstract, objective truths before you agreed that you agreed with him about these matters.
Thanks, that's interesting. I should also admit that if someone pressed me on what I mean when I say the integers or real numbers actually exist independently of our minds, I don't know that I could make a convincing case.daveS
March 3, 2019
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H, okay, I think it is 36 that I somehow must have connected to you. KFkairosfocus
March 3, 2019
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kf, you write concerning Gab, "you also discussed and I noted to you as a result". No, I never discussed Gab until you mistakenly identified me as the person who had brought it up. See posts 32, 34, and 36.hazel
March 3, 2019
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H, you also discussed and I noted to you as a result -- I do not like what Gab seems to be doing here though I understand frustration at say Wikipedia's moderators. Empowering unmoderated trollery and apparently tracking people all over the web opens up serious cans of worms, I add. I note, too, that while agreement is important, acknowledgement is not the same as establishment of truth. It is the establishment of key truths that can serve as plumb-lines to check socially agreed or imposed yardsticks that is the pivot of the OP. Hence, the story of the silly Emperor. KFkairosfocus
March 3, 2019
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SB, thanks for your ever insightful points. You are quite correct to point out that error addresses those of logic and those regarding entities that are real, whether concrete or abstract. I have also noted that given logic of being and the metaphysical import of the principle of identity, if a proposed entity such as a square circle has contradictory core characteristics it will be impossible of being. This thread is serving as a forum for clarification and for building some key points of agreement. We can see this in for example how we are agreeing that truth is real and can be objective. That which says of what is that it is, and of what is not that it is not is true. Similarly, the force of the undeniable truth, error exists, has led to recognition that hyperskepticism, radical subjectivism and radical relativism are not tenable (though, doubtless, they are still very common or are even dominant views on the ground . . . having been drummed into us by the media and education systems). These are important points of progress. I note, too, that no one has actually extrapolated from or directly inferred from, that truth exists to therefore moral truths exist. What I did was to note that in discussing and arguing (even about the import of error exists), we mutually, implicitly and even intuitively recognise that our reasoning is morally governed by duties to truth, right reason, prudence, fairness etc. This is inextricably entangled with inferring, judging, rationality in general and is of course echoed in our typical understanding that knowledge must have truthfulness or at least credible truthfulness as a criterion -- we cannot properly know what is manifestly false, though we may err and believe it. So, we know first that truth is actual and then that it is in some cases not only intelligible but warranted so objective. And in the process of reasoning, we recognise another class of truths: truths regarding duties, in this case inescapable truths on the duties of rationality. Inescapable, on pain of instant, vicious absurdity that would destroy reason and discussion toward truth and sound reasoning. In short, we have here cases of inescapable and so self-evident truths of moral character, moral truths. Absent these, rationality collapses into chaos. Where, too, they are not subject to proof -- the attempt to prove or disprove or simply discredit already implicitly turns on the duties in question. They are part of where our proofs come from. Beyond, we have other self-evident moral truths that more directly shape or test our yardsticks of conduct. I have commonly used concrete manifestly undeniable evils as instructive test cases. For example, it is manifestly wicked to kidnap, bind, sexually assault and murder a child for one's pleasure. From this, we may build a considerable body of moral knowledge that is relevant to society. That is the point you drove at in writing:
We would have to say something like this: Moral violations exist, therefore moral truth exists. This would qualify as a self evident truth. Even people who deny objective moral truth complain – routinely and illogically – that they have been the victim of a moral violation.
Moral violations exist only if moral duties are true and binding. So, justice [a narrow form of the duty of fairness] and our recognition of its violation show that moral truths that are sufficiently objective to frame moral knowledge also exist. Justice of course is closely tied to rights (which require being in the right), and leads on to how moral truth and moral government reflect the law of our nature and guide the framing of civil law. Or at least, should guide such framing. KF PS: I note that deer is used in two senses, as a reference to particular species and as the wider family, Cervidae (in turn, distinct from Antelopes). We thus must recognise the principle of definition on what is common and what is different, genus-differentia -- now very important in computing given the object paradigm. Also, there are differences of local or regional names. Due to mistakes in the 1600's, what Americans call a Moose is what historically Europeans called an elk. The elk of North America has been known to inter-breed with the Red Deer of Europe (this happened when both were introduced to New Zealand). The picture is complicated. In the USA, deer refers to the white tail or the black tail or the mule deer. The black tail seems to be a sub-species of the mule deer. Your statement is true in the North American sense, once we reject the secondary use of "deer" to denote the family of related species. Ambiguity is ever the foe of clarity.kairosfocus
March 3, 2019
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Hazel
The phrase “error exists” doesn’t distinguish between logical error and error about the world, and your statement does.
The statement "error exists" applies to both the realm of internal logic and the realm of extra-mental reality. Each realm is in perfect correspondence with the other.
If we just look at “error exists” as a statement about the world, then of course it does: Johnny says, “Look at that deer”, and Billy correctly says,”No, that’s an elk.” Johnny was in error. The difference here is truth within the world of logic and truth about the world.
Johnny errs both ways, both logically and metaphysically. Logically, an elk cannot be a deer because if violates the law of noncontradiction. Metaphysically, an elk cannot be a deer because it violates the law of identity. The logic of mind always corresponds to the logic of the universe. It is impossible for something to be logically true and metaphysically false. On the other hand, we cannot say that since logical and metaphysical error exists, it follows that moral truth exists. We would have to say something like this: Moral violations exist, therefore moral truth exists. This would qualify as a self evident truth. Even people who deny objective moral truth complain - routinely and illogically - that they have been the victim of a moral violation.StephenB
March 2, 2019
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Kf, you write, “H, thanks re the commenter add-in, I don’t think I will go there. That was Tribune that mentioned that, not me. I agree with you that I wouldn’t want anything to do with it. Also, I am sure everyone in this discussion accepts the laws of logic as true, and necessary components of arguments both within math and logic and about the world. I don’t think that is in question.hazel
March 2, 2019
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H, thanks re the commenter add-in, I don't think I will go there. I note also we are not looking at a derivation but an explanation as to why false propositions must exist. There is no extrapolation to moral truths, but there is a recognition of another bit of inescapability on pain of absurdity. In arguing, we depend on implicit acceptance of duty to truth, right reason, prudence, fairness etc, denial of which duties is instantly, viciously absurd. This is instantly known moral truth, regarding our actually being bound by such duties. What is then interesting is how such can be adequately sustained in a post-Hume world. Which requires bridging the IS-OUGHT gap at world root level. KFkairosfocus
March 2, 2019
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BB, that is precisely the point, self-evident truths are where many proofs must start from, and in other cases they serve as plumb-line tests. For key example( as Epictetus pointed out) if one asks to prove the first principles of logic, the proof would have to use them, and we can add that the attempt to deny or dismiss such will also necessarily involve using them. They are inescapably true. Proofs depend on such, and so are necessarily weaker. KFkairosfocus
March 2, 2019
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