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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
hazel, Yes, I definitely agree on the second point, and perhaps also on the first. The term "self-evident" seems to be used in a number of different conflicting ways, so I use it reluctantly.daveS
March 1, 2019
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H, pardon, but self evident does not mean axiomatic. It does mean that a claim C is such that once stated to a person of suitable experience and understanding, s/he will immediately see that it is so, must be so and must be so on pain of immediate patent absurdity once denial is attempted. That obtains for this case. Similarly, 2 + 3 = 5 is self evident -- || + ||| --> ||||| -- but 971^2 = 942,841 is necessarily so but is not self evident. Besides, in schemes of thought axioms need not be self evident. KFkairosfocus
March 1, 2019
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Dave, I like that you framed the statement in terms of logical propositions. I have some comments, and am interested in your response, if you wish. 1. That the proposition "False propositions exist” is true follows quickly and logically, as you and kf have shown. However, I think this misuses the word "self-evident", because this is a deduction (albeit a simple one), not an axiom. A=A is self-evident, and an axiom of logic. I think the word "self-evident" is used in so many ways that it is better to find other ways to describe things. 2. The phrase "error exists" doesn't distinguish between logical error and error about the world, and your statement does. 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.hazel
March 1, 2019
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DS, that is a useful reworking. F = false propositions exist. The denial ~F implies it is false to claim that a false proposition exists. This is or implies an assertion that is true or false, i.e. a proposition. So the latter implicitly affirms what it tries to deny, and is necessarily false -- that's stronger than one or the other is false. The same consequences follow, and doubtless there are many other cases that show the same thing. KFkairosfocus
March 1, 2019
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VM, unfortunately, the silliness addressed is out there in our world. Actually, it has long been so, as say the prophet Isaiah challenged 2700+ years ago:
Isa 5:20 Woe (judgment is coming) to those who call evil good, and good evil; Who substitute darkness for light and light for darkness; Who substitute bitter for sweet and sweet for bitter! 21 Woe (judgment is coming) to those who are wise in their own eyes And clever and shrewd in their own sight! 22 Woe (judgment is coming) to those who are heroes at drinking wine And men of strength in mixing intoxicating drinks, 23 Who justify the wicked and acquit the guilty for a bribe, And take away the rights of those who are in the right! [AMP]
A few centuries later, Plato spoke in The Republic on the parable of the cave, whereby we can see a systematically distorted perception of reality that is resistant to correction. He also wrote the parable of the Ship of State, which I now excerpt:
It is not too hard to figure out that our civilisation is in deep trouble and is most likely headed for shipwreck. (And of course, that sort of concern is dismissed as “apocalyptic,” or neurotic pessimism that refuses to pause and smell the roses.) Plato’s Socrates spoke to this sort of situation, long since, in the ship of state parable in The Republic, Bk VI:
>>[Soc.] I perceive, I said, that you are vastly amused at having plunged me into such a hopeless discussion; but now hear the parable, and then you will be still more amused at the meagreness of my imagination: for the manner in which the best men are treated in their own States is so grievous that no single thing on earth is comparable to it; and therefore, if I am to plead their cause, I must have recourse to fiction, and put together a figure made up of many things, like the fabulous unions of goats and stags which are found in pictures. Imagine then a fleet or a ship in which there is a captain [–> often interpreted, ship’s owner] who is taller and stronger than any of the crew, but he is a little deaf and has a similar infirmity in sight, and his knowledge of navigation is not much better. [= The people own the community and in the mass are overwhelmingly strong, but are ill equipped on the whole to guide, guard and lead it] The sailors are quarrelling with one another about the steering – every one is of opinion that he has a right to steer [= selfish ambition to rule and dominate], though he has never learned the art of navigation and cannot tell who taught him or when he learned, and will further assert that it cannot be taught, and they are ready to cut in pieces any one who says the contrary. They throng about the captain, begging and praying him to commit the helm to them [–> kubernetes, steersman, from which both cybernetics and government come in English]; and if at any time they do not prevail, but others are preferred to them, they kill the others or throw them overboard [ = ruthless contest for domination of the community], and having first chained up the noble captain’s senses with drink or some narcotic drug [ = manipulation and befuddlement, cf. the parable of the cave], they mutiny and take possession of the ship and make free with the stores; thus, eating and drinking, they proceed on their voyage in such a manner as might be expected of them [–> Cf here Luke’s subtle case study in Ac 27]. Him who is their partisan and cleverly aids them in their plot for getting the ship out of the captain’s hands into their own whether by force or persuasion [–> Nihilistic will to power on the premise of might and manipulation making ‘right’ ‘truth’ ‘justice’ ‘rights’ etc], they compliment with the name of sailor, pilot, able seaman, and abuse the other sort of man, whom they call a good-for-nothing; but that the true pilot must pay attention to the year and seasons and sky and stars and winds, and whatever else belongs to his art, if he intends to be really qualified for the command of a ship, and that he must and will be the steerer, whether other people like or not-the possibility of this union of authority with the steerer’s art has never seriously entered into their thoughts or been made part of their calling. Now in vessels which are in a state of mutiny and by sailors who are mutineers, how will the true pilot be regarded? Will he not be called by them a prater, a star-gazer, a good-for-nothing? [Ad.] Of course, said Adeimantus. [Soc.] Then you will hardly need, I said, to hear the interpretation of the figure, which describes the true philosopher in his relation to the State[ --> here we see Plato's philosoppher-king emerging]; for you understand already. [Ad.] Certainly. [Soc.] Then suppose you now take this parable to the gentleman who is surprised at finding that philosophers have no honour in their cities; explain it to him and try to convince him that their having honour would be far more extraordinary. [Ad.] I will. [Soc.] Say to him, that, in deeming the best votaries of philosophy to be useless to the rest of the world, he is right; but also tell him to attribute their uselessness to the fault of those who will not use them, and not to themselves. The pilot should not humbly beg the sailors to be commanded by him –that is not the order of nature; neither are ‘the wise to go to the doors of the rich’ –the ingenious author of this saying told a lie –but the truth is, that, when a man is ill, whether he be rich or poor, to the physician he must go, and he who wants to be governed, to him who is able to govern. The ruler who is good for anything ought not to beg his subjects to be ruled by him [ --> down this road lies the modern solution: a sound, well informed people will seek sound leaders, who will not need to manipulate or bribe or worse, and such a ruler will in turn be checked by the soundness of the people, cf. US DoI, 1776]; although the present governors of mankind are of a different stamp; they may be justly compared to the mutinous sailors, and the true helmsmen to those who are called by them good-for-nothings and star-gazers. [Ad.] Precisely so, he said. [Soc] For these reasons, and among men like these, philosophy, the noblest pursuit of all, is not likely to be much esteemed by those of the opposite faction; not that the greatest and most lasting injury is done to her by her opponents, but by her own professing followers, the same of whom you suppose the accuser to say, that the greater number of them are arrant rogues, and the best are useless; in which opinion I agreed [--> even among the students of the sound state (here, political philosophy and likely history etc.), many are of unsound motivation and intent, so mere education is not enough, character transformation is critical]. [Ad.] Yes. [Soc.] And the reason why the good are useless has now been explained? [Ad.] True. [Soc.] Then shall we proceed to show that the corruption of the majority is also unavoidable, and that this is not to be laid to the charge of philosophy any more than the other? [Ad.] By all means. [Soc.] And let us ask and answer in turn, first going back to the description of the gentle and noble nature.[ -- > note the character issue] Truth, as you will remember, was his leader, whom he followed always and in all things [ --> The spirit of truth as a marker]; failing in this, he was an impostor, and had no part or lot in true philosophy [--> the spirit of truth is a marker, for good or ill] . . . >>
(There is more than an echo of this in Acts 27, a real world case study. [Luke, a physician, was an educated Greek with a taste for subtle references.] This blog post, on soundness in policy, will also help)
The problem is real, indeed the fable of the Emperor's new clothes is quite similar. In more recent times, one can argue that Fascism, Nazism and Communism were large scale political delusions, and more. Yes, it is silly to fall into systematic irrationality but that has been of concern for thousands of years and is unfortunately again highly relevant in our day. KFkairosfocus
March 1, 2019
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I find it easier to understand if we rephrase the argument. Consider the proposition "False propositions exist". Then clearly either "False propositions exist" or its negation "False propositions do not exist" is a false proposition.daveS
March 1, 2019
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I was gonna write something, but this is so SILLY that's not worth the effort.vmahuna
March 1, 2019
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Logic and First Principles, 12: The crooked yardstick vs plumb-line self-evident truthskairosfocus
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