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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
re 31 to Dave and 37 to Brian: I certainly don't see how the logical deduction that "false propositions exist" or the logical development of the number system extrapolate to there being objective moral truths. These don't seem connected to me, and I don't see how the metaphor of plumb lines or crooked yardsticks adds anything to any argument that they are.hazel
March 2, 2019
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Self evident truths and objective moral truths may exist but there are no ways of proving them.Brother Brian
March 2, 2019
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Dissenter isn't the same. It's more akin to Disqus but where you can't be censored. It is a Gab product though.True that Gab can be quite nasty. Anyway, keep the fight. (Just saw another Dissenter comment on the Wiki ID article. This might be fun)tribune7
March 2, 2019
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H, I laid out the significance again, just above. In an age of radical skepticism, relativism and subjectivism, showing that there are truths, intelligible truths, warranted truths, knowledge and even certainty and self-evident truth is an important plumb-line check against some fairly crooked yardsticks: radical skepticism, subjectivism and relativism are undercut. A limited but important result, one that actually breaks the momentum of some major trends of how people have been led to think in this day and age. BTW, you may recall that I earlier showed that warrant comes in degrees, as does certainty. Specifically, scientific explanatory constructs do not -- rpt., NOT -- rise to even moral certainty. KFkairosfocus
March 2, 2019
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Trib, longtime no see. Never heard of that stuff before. I gather Gab can get pretty hairy and nasty. I gather it is like Twitter, in which I have no interest. BTW, are they tracking you everywhere you go, showing you comments on the page? That would be a deal-killer for me. Thanks, though. KFkairosfocus
March 2, 2019
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Hi Dave, I, like you I think, don’t see how proving the proposition that “false propositions exist” leads to certainty about any propositions about the world, much less about morality, or to the existence of “objective” truths other than those which reside in mathematical and/or logical system. In particular, you ask,
And are we still dealing with the same level of certainty we have about the truth of the proposition “error exists”?
I think the answer is no, we’re not, as I’ve mentioned. Propositions about the real world are a different kind of thing, established in a different way, and provisional in comparison to mathematical/logical propositions. Also, you said
FTR, I accept the LOI, LNC, LEM. Regarding the bit about {A | ~A}, I don’t follow how this “sets up” things such as the real number system. However I do accept that all those mathematical structures exist, and we can use mathematics to understand the world, at least to some extent. I’m not a radical skeptic, relativist, or subjectivist, fortunately.
Kf then writes of you,
DS, in the particular regards of interest, you seem to be one of the apparent minority who accept that there are objective truths, that such can be intelligible, that they can in certain cases be warranted sufficiently to be knowledge, that such truths embrace abstracta [specifically entities of structure and quantity] and more.
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. And FTR I also “accept the LOI, LNC, LEM. …[and that] all those mathematical structures exist, and we can use mathematics to understand the world, at least to some extent.hazel
March 2, 2019
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Don't want to hijack the thread, KF, but you might want to do a post on Gab Dissenter which allows commenting on any post on the web. I've already put a comment on the article for Intelligent Design on Wikipedia. You have to have Dissenter to be able to see it. It's described here: https://www.pscp.tv/w/1yNxaOpVWPQGj You can download it here: https://dissenter.com/downloadtribune7
March 2, 2019
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KF, Yes, I'm not so sure there is an objective moral code which exists independently of our minds.daveS
March 2, 2019
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DS, in the particular regards of interest, you seem to be one of the apparent minority who accept that there are objective truths, that such can be intelligible, that they can in certain cases be warranted sufficiently to be knowledge, that such truths embrace abstracta [specifically entities of structure and quantity] and more. I have not seen enough to take it that you acknowledge moral government of our rationality and that there are thus inescapable moral truths, which sets up a context for objectivity of certain moral truths, i.e. objective albeit limited moral knowledge. The plumb-lines above are about sorting out some seriously crooked yardsticks in our civilisation. KFkairosfocus
March 2, 2019
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KF, Thanks for typing that out. At this point I'm not persuaded I need to make any changes to my worldview, however.daveS
March 2, 2019
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DS, Possible world W has to have in it some distinct feature A that marks it separate from nearby neighbours, say W' and W". Let us call it A and partition W = {A|~A}. A is a case of unity that must be present for a distinct world W, leaving the cluster of other features as complex unity ~A, which is a different unit. Thus, duality is necessarily present. As W has nothing between or beyond those two, we see nullity also -- the partition is empty. We see here 0, 1, 2, thus by succession N, thence Z, Q, R, and even C (considered as a set of vectors of rotation from the polar axis). We are not leaping from Math to induction, or objective morality, we are laying out further cases and classes. As was earlier explored, induction and analogy, as well as causality turn out to flow from distinct identity and properties in common, even when there is distinction. LOI is actually extremely powerful, once recognised as saying A is itself i/l/o its core characteristics that give it its distinct, specific, particular identity. Two neighbouring peas in the same pod are distinct, each being itself and not another. By contrast the Evening and Morning stars turned out to be a common planet. See linked. For moral knowledge, we exploit the inextricable entanglement of reasoning with its moral government through duties to truth, right reason, prudence, fairness etc. That is, the IS-OUGHT gap HAS to be bridged, which is only possible at world-root. Our existence as a rational responsible community is implicated. We are looking at inescapable truths of moral character. In that context, for human community, the self evident case of evil exploitation and destruction of a child for pleasure sets up a framework for drawing out the law of our nature, with broad implications. See linked. So, no, there is no leap beyond reason or prudence involved. And that step was addressed already, this OP is in effect setting a further stage, of how we go about reasoning in the face of crooked yardsticks backed up by power and influence. Thus the silly example that riffs on the fable of the Holy Roman Emperor's invisible new clothes. KFkairosfocus
March 2, 2019
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KF, Fair enough. FTR, I accept the LOI, LNC, LEM. Regarding the bit about {A | ~A}, I don't follow how this "sets up" things such as the real number system. However I do accept that all those mathematical structures exist, and we can use mathematics to understand the world, at least to some extent. I'm not a radical skeptic, relativist, or subjectivist, fortunately. How you make the leap from logic and mathematics to morality and so forth escapes me. I suggest we leave that for the 2nd or 3rd step. I believe that I am a reasonable person and understand the material world as well as the average layman. Is there anything you mention above which should cause me to change my views? And are we still dealing with the same level of certainty we have about the truth of the proposition "error exists"?daveS
March 2, 2019
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DS, it has already been explicitly laid out, several times from the OP on. Let me clip the OP:
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. [it's not a matter for opinions and agree/disagree, this is an established undeniably true point of knowledge] 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. . . . . [summary on the core, triple first principles of reason, LOI, LNC, LEM] 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. [see the weak argument correctives] 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. [--> framing a lot of the logic of structure and quantity as embedded in the fabric of any possible world, discussed previously] Likewise, identity and the logic of being allow us to see how inductive reasoning and causality can be grounded. [links in OP, the legitimacy of sound analogy is also implied] So, too, as arguably there are self-evident, plumb-line moral truths,[link in OP] 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 . . .
KFkairosfocus
March 2, 2019
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KF, I think everyone here accepts that 'error exists'. What's the next step in the sequence?daveS
March 2, 2019
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H, until people are willing to acknowledge objective truth and knowledge, principles of reason etc, it is futile to try to assume that acceptance and then build up consensus on what propositions are true, what ones are necessarily true, and how we may then frame reliable, credible bodies of knowledge. In short, we need plumb-lines and sound yardsticks, then we can address substance. KFkairosfocus
March 2, 2019
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DS, a modest effort but with rather relevant consequences given common perceptions regarding truth, knowledge, principles of reason, morality etc. In short, a case of a plumb-line. KFkairosfocus
March 2, 2019
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Thanks, Dave. Actually we did discuss the question of the nature of the existence of abstractions last fall: sorry you missed it.:-) But obviously the important question is which propositions are true, which, because some propositions can be false, always involves some work, as I commented on in in my third-to-last paragraph at 19.hazel
March 2, 2019
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hazel, I also believe that establishing that false propositions exist is a rather modest achievement. We all have known that from a very young age, I would wager. Well, perhaps a philosopher will jump in soon and question whether propositions actually exist, but I don't anticipate that.daveS
March 2, 2019
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H, the issue was clearly identified: establishing that there are knowable truths about the world, knowable to in this case certainty. In a world where there are such things as popular notions of hyperskepticism and more sophisticated radical relativism or subjectivism, that is already a significant corrective. It shows that such things, as a bloc, are falsified. If your worldview implies that truth beyond perception or opinion is meaningless or impossible, this is an answer. If your view is that truth is radically relative, this too is decisive. Thus, such serves to re-open minds to objective truth, warrant, knowledge. Of course that one of the pivotal certainties is that error exists, that should serve as a warning, leading to due prudence. This also highlights that naturally certain truths serve as means to correct crooked yardsticks, which are out there -- as was just exemplified. KFkairosfocus
March 1, 2019
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Hi Dave. At 11, you write, "Ok, we’ve established that false propositions exist." My question is, now what, and to some extent, so what? At 6, I wrote, “The phrase “error exists” doesn’t distinguish between logical error and error about the world, and your statement does,” and you agreed at 8. I think this is a critical distinction, because we ascertain whether logical propositions are false and whether propositions about the world are false, in different ways. Kf says the distinction is not important if all we want to do is claim that “the point that error exists is undeniably true”, but I don’t see that much more follows. Of course, as my moose/elk example, shows we can make errors in propositions about the world, and of course propositions in logic can be false: kf gave a classic example involving if P then Q. But the mere fact that such errors exists doesn’t tell us anything about what is actually true, either logically or about the world: it just warns us that we can be wrong. kf does say the fact “that errors exist, implies that certainly knowable and known truths exist, and can be warranted beyond responsible doubt.” This is true, but it offers no guidance by itself as to what statements are true, either logically or about the world: those have to be found on their own merits. Furthermore, those merits are established in different ways and have a different kind of truth value, depending on whether they are in the domain of pure logic or in the domain of knowledge about the world. And last, logical propositions are either true or false–there is no question of “reasonable doubt”, but in respect to propositions about the world, what constitutes “reasonable doubt” adds a whole new element to judging whether a proposition is true or false. So, in summary, I don’t see any huge significance in establishing the proposition that false propositions exist. I'd be interested in your thoughts on this, if you're interesting in returning and replying, (which I fully understand you might not want to do.)hazel
March 1, 2019
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The Benevolent and Protective Order of Deer?ET
March 1, 2019
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Everyone has his or her pet views or reality, but you'll find out when you die. (Or not.) --Homer Simpsonmike1962
March 1, 2019
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Oops: How about Johnny says to his wife says, "Look, there's a moose, dear" and his wife says "No, that's an elk, dear." Will that work as an example? :-) I was thinking about my experiences in the Colorado Rockies where both mule deer and elk are common, and sometimes newcomers confuse the two.hazel
March 1, 2019
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Johnny says, “Look at that deer”, and Billy correctly says,”No, that’s an elk.” Johnny was in error.
Except that both the American and European elk are both deer. :-)Bob O'H
March 1, 2019
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ScuzzaMan, What is the next step in the sequence?daveS
March 1, 2019
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"Which counts." Which is why some people refuse to take the next step in the sequence, and prefer to batter themselves senseless against the rock of the foundation, like a fly against a window, and with all the cognitive content thereof. They know. Most assuredly, they know. It isn't their being wrong that convicts them - it is that they know they're wrong, and persist anyway.ScuzzaMan
March 1, 2019
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DS, enjoy lunch. However, it's a little more than that. It is true that errors exist, implies that certainly knowable and known truths exist, and can be warranted beyond responsible doubt. That cuts a wide swath across a world in which radical relativism and subjectivism are often put forth as though they were well-founded. Manifestly, they aren't. Which counts. KFkairosfocus
March 1, 2019
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Ok, we've established that false propositions exist. I'm going to break for lunch.daveS
March 1, 2019
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DS, in our discussions, self-evident is used to describe a truth T that once stated to one of appropriate experience and insight will be seen as true, as necessarily true and as true on pain of patent absurdity on attempted denial. We can create a taxonomy of cases (especially on what sort of absurdity results) but the point is sufficiently clear and crisp to be useful. As a classic example, that one is conscious is manifestly so to oneself and to try to deny it instantly lands in the absurdity: and so who is aware of attempted denial? Likewise, attempts to deny the triple cluster of first principles of right reason immediately must use these in the attempt; they are inescapably true. And so forth. Such truths never amount to enough to form the basis of a worldview but serve admirably as plumb-lines to test the yardsticks we use. Which is crucial in avoiding the morass of manipulation, confusion, chaos, polarisation and outright deceit that seems more and more manifest in our dark day. KF PS: The parallel line postulate is often given as a counter instance. I note that such often involves context switching from a plane characterised by members of R x R. In that context, take y = mx + c, and set m constant for a family of lines. Vary c, c1 c2, c3 etc, these lines will have strictly equal separation for any given x value. This brings out the force of the point. I resort to this to draw out that the intuition that the axiom holds has in it an implicit space being spanned.kairosfocus
March 1, 2019
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H & DS, that error exists simply asserts that the set that collects errors is non-empty. By contrast the set of dreams of rocks is decidedly empty. Error, takes the force, a claimed truth that misses the mark of accurately describing reality. An error in or of logic counts as an error and an error regarding attempted description of the world counts as an error. For example, P => Q, Q so P is an error as P => Q is not an equivalence, so to claim P follows from Q is an error of reasoning. I note, too that if a claimed state of affairs X leads to a contradiction as X => y AND X => ~y, then we see that a logical result establishes an ontological falsification through a logic of being result. For example, if X were a square circle it would have circularity AND squarishness, which stand in mutual contradiction of core characteristics so the logic of being entails the ontological result that a square circle is impossible of being. Likewise, the Moon is made of Green Cheese is an error if meant as a truth claim, but that is an error of fact. I recall a Sci Fi novel that pivoted on the Moon being a disguised massive starship . . . logically possible but factually obviously false. No distinction is necessary for the purposes of the point that error exists is undeniably true. KFkairosfocus
March 1, 2019
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