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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
Yupkairosfocus
March 7, 2019
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KF, Ah, I think I know what you are talking about now.daveS
March 7, 2019
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DS, the exchanges were real enough, tracing to certain views on Popper. I hope that is not a trigger. KFkairosfocus
March 6, 2019
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KF, Perhaps I wasn't present during those exchanges. In any case, I don't doubt the importance of inductive reasoning.daveS
March 6, 2019
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DS, I am recalling all too well long exchanges on the subject of the credibility of inductive reasoning and its resulting weak sense knowledge, which dominates the real world. In seeing the exchange that developed above, it seems to me important to see that inductive reasoning will also naturally arise and lead to a next stage that perhaps was unanticipated. That seems to be significant. Of course, the overall unreality and disconnect from self-sacrificial behaviour in honor/shame cultures make ET's point far more practically relevant. One take-away for me is that induction is something that needs a bit more. Just what, I am not yet sure, but I think it is connected to double-standards of warrant linked to induction. For one, consider the alphanumeric code observed in cell based life, a language phenomenon. KFkairosfocus
March 6, 2019
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KF,
The silver lining, I guess, is that it seems to reveal that there is a problem with how we respond to induction and to weak sense knowledge
I don't think anything of the sort has been revealed, has it? We all use inductive reasoning all the time. We are forced to. We can barely survive without it. We can't do empirical science without it.daveS
March 6, 2019
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H, DS posed a logic puzzle which is hardly RW, which I mistakenly thought could be briefly answered, allowing the thread to go back to focus. The silver lining, I guess, is that it seems to reveal that there is a problem with how we respond to induction and to weak sense knowledge . . . which is what science gives precisely because of its inductive character. Which, is where this series began. The significance of plumb-line, self-evident truths remains. KFkairosfocus
March 6, 2019
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daves:
It’s a logic puzzle.
And as I said- the first argument would stand. It would be highly illogical to try to determine the color of your eyes given that such knowledge leads to your committing suicide.ET
March 6, 2019
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I haven’t paid any attention to this puzzle: I dropped out when it seemed kf didn’t want to talk about applying logic to the real world, but that is exactly where the discussion has gone anyway; At 145 Dave wrote,
There was some back and forth above about using logic to reason about abstract things vs. using it to reason about things in the “real world”. I think this puzzle shows that we really only reason about abstractions, ultimately. That is, we have to form an abstract model of the situation on the island. Hopefully a sufficiently accurate model; that can be difficult to do because the “real world” is not a blocks world whose state can be described with mathematical precision.
I absolutely agree with this. Once we make a model and use it to deduce conclusions, we then re-examine the world to see if those conclusions are borne out. If they are not, we revise our model. As as been noted, our model will include premises and other facts that we think are true, via induction, as well as definitions we think are sufficiently clear. But our model is always “fuzzy” in some ways, so our conclusions about the real world are always provisional, with some degree of uncertainty. Kf writes,
PS: deductive reasoning in valid ways can also arrive at false conclusions. The issue is the truth of relevant premises, and that is normally established in ways that are shot through with inductive experience.
Yes, as I said above.hazel
March 6, 2019
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Anyway, FTR, I'm not saying that inductive reasoning is of a lower class than deductive reasoning. ENDdaveS
March 6, 2019
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DS, in a bit of a hurry but this is pivoting on what is knowledge. Knowledge, first is not equal to certainty or theoretical scientific knowledge and general factual knowledge on experience and report are not knowledge. In this context, deduction is normally not independent of induction and induction is intricately tied to deduction too. So, it is reasonable on this case to hold that the islanders empirically know a law that eyes they are aware of on island are blue or brown. On the givens we know that such an inductive conclusion is not just cogent but accurate. It is on this if not A then B pattern that the islanders will operate. I repeat, inductive knowledge is not a second class, second rate form of knowledge. KF PS: deductive reasoning in valid ways can also arrive at false conclusions. The issue is the truth of relevant premises, and that is normally established in ways that are shot through with inductive experience. Indeed, the concept of a background of experience and understanding is going to imply just such. PPS: Further eye colours would not affect the fate of the blues, but they would make a huge difference for the others. For they would then have uncertainty on their own eye colour.kairosfocus
March 6, 2019
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PS to #146:
Again, we know there are only two eye colors present. The islanders don’t ever know that in this particular instance of 100 blue-eyed and 900 brown-eyed islanders.
We could have been given various instances where there are 1, 2, 3, 4, and so on up to 1000 different eye colors, and it would not change the outcome---the blue-eyed people would all commit suicide at some point, and the remainder would never know their own eye colors.daveS
March 6, 2019
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KF,
DS, this is getting a bit tangential, but the givens as you link do state two colours are present on the island.
Again, we know there are only two eye colors present. The islanders don't ever know that in this particular instance of 100 blue-eyed and 900 brown-eyed islanders. We could be given the names, addresses, photographs, and eye colors of every islander, but it wouldn't change the outcome of the puzzle.
It seems there is an objection to inductive logic as though it were a second class level of suspect reasoning instead of a major means to knowledge.
I don't regard it as a second-class level of reasoning, just different. Such reasoning has a pretty important weakness: even correct inductive reasoning can lead to false conclusions. But sometimes it's all you have to work with. You can't always use deductive reasoning (which is one of its weaknesses).daveS
March 6, 2019
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KF,
The relevance is, that this puzzle shows how important it is to get start-points and steps of reasoning right, and it shows — by the online disagreements and puzzlement — just how hard it is to get our thinking straight.
There was some back and forth above about using logic to reason about abstract things vs. using it to reason about things in the "real world". I think this puzzle shows that we really only reason about abstractions, ultimately. That is, we have to form an abstract model of the situation on the island. Hopefully a sufficiently accurate model; that can be difficult to do because the "real world" is not a blocks world whose state can be described with mathematical precision. In this puzzle, some of the crucial information can be given only implicitly (or else one gives away the solution), which adds to the difficulty.daveS
March 6, 2019
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DS, this is getting a bit tangential, but the givens as you link do state two colours are present on the island. Next, we must credit basic sense of order, so a pattern observed without exception will be taken as established fact. It seems there is an objection to inductive logic as though it were a second class level of suspect reasoning instead of a major means to knowledge. That is itself an important issue if it is on the table, one relevant to ID and to Science in general. KFkairosfocus
March 6, 2019
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ET, It's a logic puzzle. We're supposed to deduce what we can from the given premises, even if they aren't consistent with typical human nature. No one believes that all Cretans are liars, yet it's productive to examine what follows from that statement (a famous paradox, in this case).daveS
March 6, 2019
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Look, guys, no one is going to work that hard just so they can commit suicide. "Oh no, if I know my eye color I must commit suicide. Let me follow the clues so that I can determine my eye color." Really? The first argument would stand or they would kill the traveler- argument #3.ET
March 6, 2019
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ET, To echo KF's post, imagine there are 10 total islanders, only one with blue eyes, and that they are standing in a circle where they can all see each others' eyes. The single blue-eyed islander can see everyone else's eyes, none of which are blue, so he can tell his own eyes are blue after the foreigner's statement. None of the other 9 islanders can deduce his or her own eye color with the available information.daveS
March 6, 2019
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KF,
There is a variant with a green eyed griot, which could drastically shift the dynamics — each person now being aware of a third option so the brown eyed cannot determine that by elimination if not blue then brown.
I haven't seen any versions of this puzzle where the islanders actually know there are only two eye colors. Certainly on this island, where there are in fact only two, each inhabitant knows there are at most three eye colors present.
it troubles me that it makes people repeatedly reflect on religious adherence in a very negative way, as though such were typically irrational, extremist and dangerous; fostering an invidious psychological association.
I agree. I also find the tired trope of the blue-eyed foreigner visiting a "tribe" of mostly brown-eyed islanders with weird religious practices somewhat cringeworthy. There is no need to include suicide in what is supposed to be an amusing puzzle. An update is in order.daveS
March 6, 2019
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ET, I add, in the n = 1 case, each islander is aware of the stranger's eye-colour, blue [similar to sky and sea]. All but one will be directly, observationally aware of one islander with similar eyes. That one would see no other islander with such eyes and on the presumption that the visitor spoke truthfully, would infer that s/he is the one with blue eyes. On this recognition being publicly shows (the story is loaded), every other islander would realise that his or her eyes are the other evidently available colour, brown. (There is a variant with a green eyed griot, which could drastically shift the dynamics -- each person now being aware of a third option so the brown eyed cannot determine that by elimination if not blue then brown.) The relevance is, that this puzzle shows how important it is to get start-points and steps of reasoning right, and it shows -- by the online disagreements and puzzlement -- just how hard it is to get our thinking straight. Hence, the value of plumb-line, self-evident truths that are naturally straight and so correct our crooked yardsticks. We are finite, fallible, morally struggling, too often ill-willed and polarised. It is no surprise that we speak of an is-ought GAP that needs to be bridged. KF PS: The puzzle brings out the challenges of logic in an empirical world, and it troubles me that it makes people repeatedly reflect on religious adherence in a very negative way, as though such were typically irrational, extremist and dangerous; fostering an invidious psychological association. I therefore note that in some honor/shame culture societies, suicidal defence of the community or of one's honour is an act of defending or redeeming honour. Some elements of this remain in our civilisation, it is no accident that the highest military medals are often awarded posthumously.kairosfocus
March 6, 2019
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F/N: Do I need to note that deductive chains often start from empirically, inductively inferred facts? KFkairosfocus
March 6, 2019
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ET, now you see part of why my argument pivots on each blue seeing 99 others. KFkairosfocus
March 5, 2019
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DS, While this is tangential to the main thread, it reveals on a side issue the patterns that often play out. KFkairosfocus
March 5, 2019
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When n=1, the single blue-eyed person realizes that the traveler is referring to him or her, …
What? The single blue-eyed person doesn't know he/ she is blue-eyed so he/ she wouldn't know who the traveler is referring to. The brown-eyed people would but they cannot discuss it. And, if the single blue-eyed person commits suicide and the other 999 observe it, then they will know they have brown eyes and have to follow the one.ET
March 5, 2019
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PS:
BTW, we are given as a fact that there are just the two colours, so the inductive inference is correct on our “god’s eye view.”
Yes, but it is not given that the islanders know there are just two colors. Neal in the stackexchange thread seems to assume that is the case. The brown-eyed people can never know for sure they have brown eyes, whereas the blue-eyed people can.daveS
March 5, 2019
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DS, I added somebody's comment at Math Stack exchange. Yes, I see the Mathematical induction case. I also see something much more direct, each person sees 999 others. Of these, if a person is blue-eyed, s/he will see 99 others with blue eyes. Thus, on the inference day 99 is critical and if that day passes without event it means there is another invisible blue. For each blue that can only be oneself (the only invisible eyes) so on day 99 the blues all know they are blues. Then, on seeing the 100 blues remove themselves, the browns can each see 899 other browns and no blues. Each brown now knows s/he is a brown, on the premise that those are for all they know, the two possible states. The removal rule then applies to the browns. The problem has a gap in the formulation as given. Notice, it pivots on world models. This is also an illustration of the logic of signalling behaviour that carries implicit information. KF PS: This side exchange is illustrative of how ever so many exchanges get locked up.kairosfocus
March 5, 2019
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KF, No, there is no inductive reasoning involved in this puzzle whatsoever. The solution is supported by a deductive proof showing that if the tribe had n blue-eyed people for some positive integer n, then n days after the traveller’s address, all n blue-eyed people commit suicide. We are given that there were 100 blue-eyed people and 900 brown-eyed people, hence we deduce that 100 days after the address, all 100 blue-eyed people commit suicide.daveS
March 5, 2019
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DS, it involves both induction and deduction. Already, on the expected day, an observation is made (as each blue sees 99 blues) and a conclusion is inferred (that each other blue sees 99 also), leading to the conclusion that there is for each blue one more blue invisible to him or her self, thus that final blue is oneself. Also, agreement or disagreement/majority opinion is not a sufficient criterion of warrant. BTW, we are given as a fact that there are just the two colours, so the inductive inference is correct on our "god's eye view." What happens is the framing focuses on the blues, but the browns can see and infer just as well. KF PS: At Math Stack exchange there is a comment: "The day after the blue-eyed people commit suicide, everyone else gathers in the square and commits suicide, leaving the stunned foreigner alone on the island. – Neal Nov 15 '12 at 23:06" https://math.stackexchange.com/questions/238288/is-there-no-solution-to-the-blue-eyed-islander-puzzle PPS: It seems there are multiple versions of the puzzle.kairosfocus
March 5, 2019
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The evidence in hand also suggests that solutions to the puzzle should involve deduction rather than induction. This puzzle is all over the web. Can you find anyone who shares your position?daveS
March 5, 2019
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DS, the evidence in hand is that eye colour comes in two varieties. Absent one, then the other. KFkairosfocus
March 5, 2019
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