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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
Folks, sometimes it helps to remind ourselves. Notice, again, the OP:
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.
See how understanding is pivotal? KFkairosfocus
March 4, 2019
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re 94: Vivid writes,
FYI there have been critics that have visited this site that don’t accept the laws of logic as self evident and real truths.
I know nothing about that.hazel
March 4, 2019
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Hi vivid. Let me take it line by line: 1.
We have in hand a demonstration by example of a self evident truth.
Well, as Dave and I have been pointing out, the demonstration of “false propositions exist” is a logical deduction from the even more self-evident truth the of the law of non-contradiction. But I certainly take the three laws of logic as self-evident truths, by virtue of which they are the starting axioms of our system of logic. 2.
If one truth exists, truth exists.
I think all the consequences of the laws of logic are true in the same way that ““false propositions exist” is true: as a consequence within the world of logic 3.
If one self-evident truth exists, self evident truth exists.
Yes, but once you’ve established the three laws, I’m not sure how many more self-evident truths there are. There are a number of beginning axioms in math and geometry that are considered self-evident, but this can get on problematic, as we have found that in some cases you can assume a different axioms and get a different logical system which has its own truths. 4.
If one necessary truth exists, necessary truth exists.
I’m not sure how “necessary truth” differs from “self-evident” truth. 5.
If one warranted, credible truth exists and is accepted by one person, knowledge exists.
I assume that a “warranted, credible truth” is one established within the logical systems of logic and math, so once such are known by someone, knowledge exists. 6.
If the truth is warranted to certainty, certain knowledge exists.
Yes: there are many many facts in logic and math that we have certain knowledge of. 7.
If the truth is necessary, knowledge of necessary truth exists. If the truth is warranted to self evidence, known self evident truth exists.
Again, I’m not sure what all this means, especially “warranted to self evidence”. I consider consequences which flow logically from beginning principles, as kf quoted Copi about at 83, as necessary. Since they derive their necessity (maybe that is what he means by “warranted”) from the beginning self-evident truths, perhaps that is what he means by “warranted to self evidence”, but I’m not sure. 8.
Schemes of thought that deny such are therefore in that respect falsified.
I know of no “scheme of thought” which denies the laws of logic or the logical consequences which flow from them. 9.
Of course, as one SET in question is that error exists and another closely linked one is that false propositions exist, then this also implies that we must be prudent in our investigations and claims.
I’ve already said I agree with that.hazel
March 4, 2019
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Hazel “If “such” refers to the proposition that “false propositions exist”, then I don’t think anyone has denied that from the beginning of the thread.” The “such” is quite clearly the implications he spells out in the first paragraph of 72. Do you deny the implications? If so what is it specifically do you object to? Vividvividbleau
March 4, 2019
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Hazel “But the laws of logic have already been accepted as real truths.” FYI there have been critics that have visited this site that don’t accept the laws of logic as self evident and real truths Vividvividbleau
March 4, 2019
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re 92: If "such" refers to the proposition that "false propositions exist", then I don't think anyone has denied that from the beginning of the thread.hazel
March 4, 2019
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Hazel In 72 KF summarizes his thought process with this conclusion and I think this is what he is asserting. It seems that everyone is in agreement here. “ Schemes of thought that deny such are therefore in that respect falsified. “ Vividvividbleau
March 4, 2019
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This is all a little silly. Consider the first law of logic, the law of non-contradiction, F = “for any proposition P, P and ~P cannot both be true.” F is true, as it is the first axiom of logic. Therefore ~F is false. Therefore, false propositions exist. For the life of me, I don’t see how this leads to anything other than “so what”? kf says it establishes that there are real truths. But the laws of logic have already been accepted as real truths. We don’t even need to go through all this about the proposition “false propositions exist” (although we can) because all we need to do is show an example of a false proposition, which I just did.hazel
March 4, 2019
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KF,
DS, kindly note the distinction between an explanation and a deduction.
Eh? It's a straightforward proof. You assume ~E and show that this implies E.daveS
March 4, 2019
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And yet Copi says, "To determine whether an inference is correct, the logician examines those propositions that are the initial and end points of that process and the relationships between them." And yes, it is a stepwise logical deduction process. Back at 5, you wrote the following stepwise logical argument, although it wasn’t very clear.
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
Here’s the same argument, more straightforwardly, in proof by contradiction form: Let F = “false propositions exist” Assume ~F is true: “false propositions do not exist”, which is to say “all propositions are true.” Therefore F is true. Thus contradicting our assumption that ~F is true. Therefore F is true. (Wrote this before I saw Dave's post. I have no idea what purpose kf has saying this is an explanation, as if that somehow adds to the conclusion. And his recent P.S. doesn't make sense, including the idea that "direct understanding", whatever that is, adds something to, much less is a substitute for, logical deduction.)hazel
March 4, 2019
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DS, kindly note the distinction between an explanation and a deduction. By what it is, a proposition Q carries with it the entangled counter-assertion ~Q of coupled, opposed T/F value. So, to assert there are no false propositions directly fails on insightful explanation. Passing on to E, the assertion carries with it its counter ~E by simply being a proposition, where again, on insightful inspection, ~E must fail. I am not saying that one cannot construct a chain of claims to show a SET would follow on some premises or other but instead that on understanding it -- which may require explanation to build understanding -- one sees that it is so, must be so, and must be so on patent absurdity if denied. In both cases discussed, the false proposition undermines the meaning of what a proposition is. KF PS: In the usual case, the argument to a proposition may be ultimately less plausible than directly understanding, e.g. it will often involve the inescapable use of the proposition or may be abstruse, etc.kairosfocus
March 4, 2019
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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.
Isn't this a logical deduction? "Assume ~E. Then the proposition 'error exists' is erroneous. Hence ~E is false, therefore E is true".daveS
March 4, 2019
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H, Copi shows that I am using the term proposition in the generally understood way: an assertion say Q that is assignably T or F, which will automatically bear with it its own antithesis ~Q (of coupled opposite value ~T or ~F) -- do I need to say, "entangled" to make the point clear? In that light, the proposition that no propositions are false is by insightful inspection necessarily false. This pivots on what a proposition is, rather than a chain of argument. I repeat, an explanation is not a stepwise logical deduction process. KFkairosfocus
March 4, 2019
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To be clear, these are propositions within the realm of logical systems your sources are talking about.hazel
March 4, 2019
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I don't disagree with Copi, and I have no idea why you think I might. I have certainly not said anything different than what Copi is describing.hazel
March 4, 2019
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F/N: I cite Copi from my copy p 5:
"Inference is a process by which one proposition is arrived at and affirmed on the basis of one or more other propositions accepted as the starting point of the process. To determine whether an inference is correct, the logician examines those propositions that are the initial and end points of that process and the relationships between them. Propositions are either true or false, and in this they differ from questions, commands and exclamations. Only propositions can be either asserted or denied . . ." [Intro to Logic, Macmillan, 1990.]
In short, a proposition is what is asserted or implied by a thought, utterance, belief or doubt, etc, that is assignably T or F. Where obviously for any Q there is its denial ~Q by antithesis. The error of the proposition, There are no false propositions is then patent on the meaning of what a proposition is. Effectively, there is no possible world W in which some proposition Q is, that Q is false, where Q stands for any proposition whatsoever -- as in, no propositions are assignably False under any circumstances in any world. Explanation is not in this sense an inferential process but a drawing out of meaning and understanding. If you disagree with Copi et al (in effect, the field of scholarship), on what a proposition is, kindly explain. KF PS: Went digging, 14th Edn 2014 (mine is 8th) with now two co authors not just one:
Propositions are the building blocks of our reasoning. A proposition asserts that something is the case or it asserts that something is not. We may affirm a proposition, or deny it—but every proposition either asserts what really is the case, or it asserts something that is not. Therefore every proposition is either true or false. [p. 2]
kairosfocus
March 4, 2019
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Yes, kf, no one is arguing that there is any weakness in the logical demonstration that "false propositions exist" is true.hazel
March 4, 2019
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H, so far as I understand a proposition is by definition an assertion that is assignably T or F. It is part of the meaning of asserting Q that there is an alternative ~Q that is denied; I believe this is called antithesis. One will be T and the other F, part of the background. This brings up the part about being of suitable experience and understanding to see what is "in" a claim. In the relevant case, there is a special claim such that the denial is recognisably the one that is false, as it in fact undercuts part of the meaning of what a proposition is. KFkairosfocus
March 4, 2019
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KF (#76), Certainly we know today that trisecting some angles with compass and straightedge is impossible.daveS
March 4, 2019
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kf, you write, " Q is asserted, ~Q denies it, a proposition being assignably T or F by meaning, one or the other must be false. Here, False propositions Exist is denied, and we see that it is the denial which is false." That is a logical deduction. I don't know why you call it an explanation, any more than any logical or mathematical proof is an explanation. And yes, some SET exist: the laws of logic, for example, so the set of SET is not empty. But, as I write above,
Fine, but that doesn’t establish what those others are. Each one is a separate issue. So I agree that “this also implies that we must be prudent in our investigations and claims.”
hazel
March 4, 2019
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KF (#76): Yes, agreed.daveS
March 4, 2019
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H, no. There is not a deduction at work but an explanation. Q is asserted, ~Q denies it, a proposition being assignably T or F by meaning, one or the other must be false. Here, False propositions Exist is denied, and we see that it is the denial which is false. KF PS: I laid out several corollaries of one SET being recognised for what it is. One such is that if a SET exists, then self evident truth -- a category -- exists, i.e. it is meaningful and non-empty.kairosfocus
March 4, 2019
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DS, so far as I gather, there were things they tried but could not do with said instruments (famously, squaring the circle). It was Algebra that provided a criterion for the rule. Of course, there is a trivial case of trisection, the 60 degree thirds of a 180 degree angle. There may be others e.g. as derived from it. But there is no general construction such as for bisection of an angle. I suppose an infinite chain of chosen bisections will converge on trisection, but the final value would require transfinitely many steps. KF PS: To construct 30 degree parts of a right angle, construct the perp bisector of the line and then do 60 degree angles, one on each leg of the right angle. That should work. But the trisection of 60 degrees is apparently not possible on such tools. Relax the rules and other things become possible.kairosfocus
March 4, 2019
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PPPS: Let me clip the opening remarks from No. 10 in this series:
One of the issues we must face is whether there is enduring moral truth that can be warranted to such a degree that it rightly governs our thoughts, words (especially in argument) and deeds. Where, given that we have an inner voice (conscience) that testifies to duty under moral law, as well as an inescapable sense of duty to truth, right reason, prudence, justice, uprightness etc., if that intuition is false, then our whole inner life becomes tainted by grand delusion. A lot is at stake, in short. A quick first answer is, that we may recognise that grand delusion is self-referential, incoherent, self-falsifying — a case of reduction to absurdity. That is, we see the inescapability of being governed by moral truth as part of the same first principles that we cannot prove but must accept on reasonable responsible — note the self-reference! — faith, for all proofs, all arguing must start from such.
kairosfocus
March 4, 2019
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Actually, kf, "false propositions exist" is a logical deduction. Calling it self-evident in this case only means that it's a simple deduction. The laws of logic are self-evident. No one denies this. Your argument is that if one self-evident logical truth exists, then other can. Fine, but that doesn't establish what those others are. Each one is a separate issue. So I agree that “this also implies that we must be prudent in our investigations and claims.”hazel
March 4, 2019
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KF, Well, trisection definitely was studied by the ancient Greeks, and methods for trisection were known. They of course didn't know it was not possible using only compass and straightedge.daveS
March 4, 2019
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H, I did not leap without warrant, I drew out the implications of an established point. We have in hand a demonstration by example of a self evident truth. If one truth exists, truth exists.If one self-evident truth exists, self evident truth exists. If one necessary truth exists, necessary truth exists. If one warranted, credible truth exists and is accepted by one person, knowledge exists. If the truth is warranted to certainty, certain knowledge exists. If the truth is necessary, knowledge of necessary truth exists. If the truth is warranted to self evidence, known self evident truth exists. Schemes of thought that deny such are therefore in that respect falsified. Of course, as one SET in question is that error exists and another closely linked one is that false propositions exist, then this also implies that we must be prudent in our investigations and claims. KF PS: I note, that logic of being is one class of logical investigation and that one result is that if a proposed entity Q is such that two core characteristics x and y are in contradiction then Q cannot exist in any possible world, i.e. it is impossible of being, e.g. a square circle. Logical considerations can and do have existential import. PPS: Also, once we find moral SETs, we can draw out a framework for moral knowledge. This was already discussed at no 10 in this series. It has been outlined above, starting with that reason and discussion inescapably pivot on known duties to truth, right reason, prudence, fairness etc. In addition as moral abuses exist, what they violate exists. E.g. it is self evidently wicked to kidnap, bind, sexually torture and murder a child for one's pleasure. From which, much can be drawn out. There has been no leap from certain simple truths to moral truths, further relevant considerations have been repeatedly brought to bear. Cf: https://uncommondescent.com/ethics/logic-and-first-principles-10-knowable-moral-truth-and-moral-government-vs-nihilistic-manipulation/kairosfocus
March 4, 2019
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DS, trisection was not something doable with compasses, unscaled straight-edge and dividers -- one of the rules of classical Geometry, so this would not have been explored in classical times. KFkairosfocus
March 4, 2019
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re 65 to MG. This thread is about the significance of the fact that "false propositions exist" can be shown to be logically true. As kf said at 66, all the stuff about how math can describe the real world is "old ground" from previous threads. kf writes, "The main purpose of this OP and thread has been to move the game forward." But that hasn’t happened. Kf jumps from "false propositions exist" to claiming we can “ 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.” But I can’t see how he has justified that leap. Logical truths exist. I think we all agree on that. Then what? What is one other logical truth that follows from “"false propositions exist"? Just asserting that other truths logically exist doesn’t establish what those truths are, or why they are true.hazel
March 4, 2019
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Yep, Dave. I found out about it 20 years or so ago while teaching high school geometry. I spent a lot of time trying to prove it by using equations based on 180° in a triangle, and found out later that can't be done. I don't now why that approach doesn't work. Wikipedia did not exist at the time!hazel
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