164 thoughts on “The Rules of Right Reason”

1. The fundamental principles of right reason must be accepted as axioms for the simple reason that they cannot be demonstrated.

   That is a foolish reason for accepting anything as an axiom.

   It is frustrating to see people pontificate about logic, and then plainly demonstrate that they don’t understand it.

   Now I’m no logician, but I am capable of seeing that if we assume those axioms are true, we can construct a logical language in which useful conclusions can be drawn, and useful computations performed.

   That’s much better.

   I am inclined to say that those rules of logic are not axioms at all, but are instead methodological principles. They are prior to being able to have axioms. And, as is often the case with methodologies, we accept them on a pragmatic basis – because they turn out to be useful.

2. The Law of the Excluded Middle: For any proposition, either that proposition is true or its negation is true.

   I propose that Barry Arrington has stopped beating his wife.

   I propose that the tide is coming in.

   I propose that it will be Spring in just over a month.

3. It’s so much worse than they realize!

   For one could, after all, ask just why we *must* accept these ultimate presuppositions? And if you scratch beneath the surface, I strongly suspect, the response will be, “because Aristotle said so!” And indeed he did. But then, what makes that gesture anything more than an “appeal to authority”? (Which, last time I checked, was a fallacy.)

   What Barry (and others) don’t want to recognize is that logic is a science, or a kind of science, and that there have been advances in logic since the 3rd Century BC. We have a lot more logical techniques in our tool-kit than Aristotle did, and we have a lot more ways of thinking seriously about logic than Aristotle did. (Aside: using modern symbolic logic, it can be shown that each of Aquinas’ “Five Proofs” for the existence of God is invalid.)

   And the idea that logical systems are methodologies, to be evaluated according to their use, can be found explicit in two of the greatest logicians of the 20th century: Rudolf Carnap and W.V.O. Quine.

   That’s not to say, of course, that “anything goes” — but it is to say that a great work has been done, and still needs to be done, in explicating the difference between basic rationality (“playing the game of giving and asking for reasons,” as Wilfrid Sellars puts it) and any logical system, Aristotelian or otherwise.

4. Every kid knows this; but what can one say about the following sentence?

   “This sentence is FALSE.”

   One might also ask whether whatever rules of logic one wants to invoke have to say anything about the real world. Clearly they don’t.

   But if one is making assertions about the real world and presuming to use that logic to make one’s points, shouldn’t one also demonstrate that the assertions and conclusions reflect reality? Name the form of logic that assures that one is talking about reality.

5. I’d also like to point out that there’s a big revolution happening in logic (what? huh?): that the choice of a formal language determines what kinds of objects can be referred to in that language.

   Aristotle’s argument for the law of non-contradiction, for those who take the time to look it, already presupposes his metaphysics — that what we’re talking about are objects (“substances”, he would say) and their properties. And of course he needs to build the case this way, because there were in ancient Greece philosophers who denied both “the law of non-contradiction” and the substance-property ontology — the most famous case being Heraclitus.

   And today, though “quantum logic” was a short-lived project, the big lesson is: what logic you’re committed to and what ontology you’re committed to go hand-in-hand. Many logicians of the 20th century (Carnap, Quine, Putnam, Dummett) would agree with “eigenstate”: if we’re not talking about substances-with-properties, then the principles of non-contradiction and the excluded middle might very well *not* apply!

6. In addition to all of the excellent points made thus far, it’s important to note that Barry is avoiding the core issue raised by at least two of the people he banned. I’ll quote Petrushka’s response since it was the first I found:

   I accept the definitional foundation of logic.

   I also accept the findings of physics which make the concept of physical existence rather complicated. That just means that physical is not the same as the ideal, just as a physical circle is not an ideal circle.

   I thought this was something generally agreed upon. I thought it was the foundation of Plato’s thought.

   But to answer the specific question, in formal logic, the moon cannot both exist and not exist.

   The question faced by physics is somewhat different.

   No one who was banned was disputing the rules of formal logic. Barry’s refusal to acknowledge the distinction between the rules of logic and regularities identified by empirical observations of reality makes his claim that he is not deliberately suppressing dissent ring hollow.

   He has every right to run UD as he wishes, but observers have every right to point out his mendacity and hypocrisy.

7. In all the years I debated on UD these rules never came up while discussing ID issues. They only arose in the context of the fundamentals of religion when proponents wanted to argue that these rules were prior to all reasoning therefore God exists. In any normal discussion you don’t find yourself invoking the LNC!

   Neil is absolutely right they are more like descriptions of how we reason than axioms. There is a really interesting debate to be had about their status. In what sense are they true if you cannot define the conditions under which they are true? But it is not essential to use them to have a rational debate.

8. And, let it be noted, StephenB wanted to use them in order to make a fallacious argument! For what he wanted to give was the “kalam argument”:

   (1) all events must have a cause
   (2) the origin of the universe was an event
   (3) therefore, something must have caused the universe.

   The reason why this is fallacious, I think, is because there’s some equivocation going on here, and the correct version is:

   (1*) all events within space and time must have a cause.
   (2*) the origin of the universe is the origin of space and time

   and since the origin of space and time could not have taken place within space and time, the revised premises show that the sought-after conclusion cannot be derived.

   P.S.: I’ve been a lurker at UD for a long time. I participated for a while, but I was banned for uncivil language. The banning was entirely appropriate. I lost my temper and said something quite rude. But I continue to lurk there, because I have an intense (and not fully rational) interest in the evolution/creation debate. I promise to behave myself here!!

9. Note that the three laws of thought cannot be proven. They are either accepted as self-evident axioms – or not. The fundamental principles of right reason must be accepted as axioms for the simple reason that they cannot be demonstrated. There is no way to “argue for argument” and it is foolish to try to do so. If one’s goal in arguing is to arrive at the truth of a matter, arguing with a person who rejects the law of idenity is counterproductive, because he has rejected the very concept of “truth” as a meaningful category.

   Axioms are not proveable. If they were subject to proof, they wouldn’t, couldn’t be axioms. Axioms are necessities. What they are necessary for depends on the goal. If one wants to converse in English with other humans using propositional claims, then the semantics for ‘true’ and ‘false’ demand a necessary distinction between them — ‘true’ is not ‘false’.

   LNC, then is axiomatic — necessary, that is — for propositional dialectics. But for other goals and enterprises — say, a computing system that uses machine-based learning algorithms to make market-beating investment decisions — fuzzy logic or multi-way logic frameworks are needed, and the “bitwise truth” of {true|false} is counterproductive to that goal.

   That doesn’t mean that the humans programming such a system have forsaken the LNC or Boolean logic. Manifestly, they haven’t, and use it all the time (just as I’m using it right here, right now) toward their communications goals, and how they think about the world around them in propositional terms. It does mean understanding axioms and logical frameworks as tools toward ends, and deploying fuzzy logic for a financial prediction platform in no way is problematic for the LNC as the transcendental requirement for propositional discourse — or whatever you want to build on top of a classical logic foundation.

   This distinction has eluded Barry, though, and show he has a fundamental misconception about axioms being “true”. They are not true or false. The aren’t “self-evident”, where “evident” has any bearing on “true” (or false). They are only necessary toward some end.

   And they are definitional. They are not empirical or attached to the real world by necessity. Many axioms we employ are useful precisely because their use enables the construction of models that perform well. But declaring an axiom tells on nothing about the extra-mental world beyond what is transcendentally necessary to conceive and express the axiom (which is different than what the axiom itself states). Barry’s post reflects a simplistic and misconceived understanding of what and axiom is and how it functions in the service of logic.

10. Patrick: Barry’s refusal to acknowledge the distinction between the rules of logic and regularities identified by empirical observations of reality makes his claim that he is not deliberately suppressing dissent ring hollow.

    He is insisting that logic be understood (or, actually, misunderstood) in a way that licenses those cosmological arguments for the existence of God, as well as other creationist bogus reasoning.

11. Has anyone made the case that Rules of Right Reason, or LNC, or whatever actually distinguish between people supporting ID and people criticizing it? Like Mark, I don’t recall these being an issue in debates about evolutionary biology. (Note I’m not asking about the origin of the Universe, or about quantum fluctuations, or about where the principles of logic originate).

12. Contradictory statements can be both true depending on scale of observation/point of view.

    Morality is a prime example: An action is immoral or moral depending on the person’s morality. This of course is what they would want to negate, and thus establish ‘rules’ which don’t match reality.

    It’s a shallow attempt at absolutism over relativism.

13. In my view the differences in this discussion turn on the following distinction.

    StephenB wants to argue that it is impossible for the moon to simultaneously exist and not exist. The proposition “The moon exists” and the proposition “the moon does not exist” cannot be simultaneously true, due to the resulting violation of the LNC. Therefore, by the lights of classical logic, “The moon simultaneously exists and does not exist” must be false. Further, any analogous statement regarding any other entity, quantum or otherwise, must also be false. To state otherwise is to abandon all rationality.

    However, I would argue not that “the moon simultaneously exists and does not exist” is false, but rather that, within the framework of classical logic, it is unintelligible. It is not impossible that the moon simultaneously exits and and does not exist; rather, that statement is simply unintelligible. Were someone to insist that “the moon simultaneously exists and does not exist” in a conversation about actual astronomical bodies I simply would be unable to unpack what is meant.

    Propositions that are unintelligible are neither true nor false. Further, the negation of an unintelligible proposition is not a true proposition, but rather another unintelligible proposition. Therefore, the negation of “the moon simultaneously exists and does not exist,” namely, “the moon doesn’t simultaneously exist and not exist” is equally unintelligible.

    With respect to the relationship between the LNC and quantum phenomena such as superposed states, the question therefore becomes, “have we have discovered phenomena that are unintelligible within the framework of classical logic?” Obviously the answer is yes, which is why the implications of quantum mechanics, when expressed in ordinary human language, and reasoned over employing classical forms of reasoning, are so difficult to grasp. Hence the statement often attributed to Feynman, “If you think you understand quantum mechanics, you don’t understand quantum mechanics.”

    Yet the mathematical and empirical foundations generating this unintelligibility are unassailable.

    Does it follow from the observation that we have discovered quantum phenomena that are stubbornly unintelligible when expressed verbally due to violations of the classical LNC that quantum phenomena cannot exist? It does not. Indeed, when stated this way, it strikes me as a startling hubris to insist a priori that a system of logic devised by Aristotle must be capable of expressing every possible true state of affairs, and that phenomena that are inexpressible within that system therefore cannot exist.

    This, of course, is the conclusion that StephenB and BarryA strive to avoid, as it exposes leaks within what they suppose to be an airtight argument compelling belief in the existence of God.

    So we return to BarryA’s test question. “Can the moon exist and not exist at the same time and in the same formal relation? The answer to this question is either ‘yes’ or ‘no.'”

    My response to BarryA is that he is mistaken to assert that the only answer to this question is “yes” or “no.” Indeed, the correct answer to his question is, “this is not an intelligible question.”

14. Reciprocating Bill,

    I’m not sure anything more needs to be said!

    Thanks, Reciprocating Bill 🙂

15. Elizabeth:
    Reciprocating Bill,

    I’mnot sure anything more needs to be said!

    Thanks, Reciprocating Bill

    I don’t know about that but I think RB’s comment deserves its own thread.

16. Reciprocating Bill,

    I don’t get it. Why is “The moon exists and does not exist” unintelligible within the framework of classical logic? It has the form “A & ~A”, and sentences of that form are provably false within that framework.

17. Reciprocating Bill:
    In my view the differences in this discussion turn on the following distinction.

    StephenB wants to argue that it is impossible for the moon to simultaneously exist and not exist. The proposition “The moon exists” and the proposition “the moon does not exist” cannot be simultaneously true, due to the resulting violation of the LNC. Therefore, by the lights of classical logic,“The moon simultaneously exists and does not exist” must be false. Further, any analogous statement regarding any other entity, quantum or otherwise, must also be false. To state otherwise is to abandon all rationality.

    However, I would argue not that “the moon simultaneously exists and does not exist” is false, but rather that, within the framework of classical logic, it is unintelligible. It is not impossible that the moon simultaneously exits and and does not exist; rather, that statement is simply unintelligible. Were someone to insist that “the moon simultaneously exists and does not exist” in a conversation about actual astronomical bodies I simply would be unable to unpack what is meant.

    I agree, but have to point out that this would be the substance of StephenB’s objection: “the moon simultaneously exists and does not exist” is nonsensical, and thus, irrational, in his (and Barry’s, others’) view. You are pointing to the same understanding I was with StephenB, that the unintelligibility is a function of the applicability of classical logic. That’s anathema for StephenB, as you point out below. But “that’s unintelligible” is very much what would StephenB would say in the same point of the conversation about the moon.

    Propositions that are unintelligible are neither true nor false. Further, the negation of an unintelligible proposition is not a true proposition, but rather another unintelligible proposition. Therefore, the negation of“the moon simultaneously exists and does not exist,” namely, “the moon doesn’t simultaneously exist and not exist” is equally unintelligible.

    Here is the major point of departure, I think, for StephenB and Barry. It’s a given, per their understanding, that when you have unintelligibility, it’s not a limitation of classical logic (there aren’t any, it’s believed), but a failure to develop coherent propositions. All paradoxes are by definition merely apparent, in this view.

    With respect to the relationship between the LNC and quantum phenomena such as superposed states, the question therefore becomes, “have we have discovered phenomena that are unintelligible within the framework of classical logic?” Obviously the answer is yes, which is why the implications of quantum mechanics, when expressed in ordinary human language, and reasoned over employing classical forms of reasoning, are so difficult to grasp. Hence the statement often attributed to Feynman, “If you think you understand quantum mechanics, you don’t understand quantum mechanics.”

    Yet the mathematical and empirical foundations generating this unintelligibility are unassailable.

    Right. QM is fundamentally problematic to classical logic. Which is not, UD management claims notwithstanding, any kind of rejection of the LNC (this post I’m writing can’t happen with out it, at all). Nature at quantum scales is not just “hastily framed”, or otherwise insufficiently developed in our analysis of it such that we might say we are just not articulating our terms well, or framing the proposition in a consistent and meaningful way. The empirical support and math models for QM dismiss that complaint.

    Does it follow from the observation that we have discovered quantum phenomena that are stubbornly unintelligible when expressed verbally due to violations of the classical LNC that quantum phenomena cannot exist? It does not. Indeed, when stated this way, it strikes me as a startling hubris to insist a priori that a system of logic devised by Aristotle must be capable of expressing every possible true state of affairs, and that phenomena that are inexpressible within that system therefore cannot exist.

    Hence my complaint to StephenB that has assigned “magical powers” to the LNC. A logical framework has been confused for a metaphysical imperative. Reality must, exhaustively and universally conform to Boolean logic. Just because it must.

    So there.

    This, of course, is the conclusion that StephenB and BarryA strive to avoid, as it exposes leaks within what they suppose to be an airtight argument compelling belief in the existence of God.

    You may be right about that, although what I see needing defense for their apologetic is the law of causality/PSR — often couple with Aristotle’s laws of logic, but external to those rules.

    Obviously, if the LNC is available, then not only do theistic arguments fail, ALL arguments fail, for the the LNC is transcendental to all of that kind of discourse. But setting Barry/StephenB’s strawmen aside about the dismissal of the LNC, how does the universality, the “non-magicalness” of the laws of logic towards the intelligibility of all phenomena hold up theistic arguments for God? Not saying that’s not a dynamic here, I’m just not seeing the syllogism that gets undercut.

    My understanding about the objection is that this is more basic than that. StephenB’s theism follows from his simplistic and brittle notions of rationality — that really is beholden to the simple rules he uses to process propositions. People with such commitments I think viscerally object because empiricism getting mixed in makes things messy, complex to think about. Once Nature is consulted as to how things really are, “philosophizing by definition” doesn’t work anymore.

    So we return to BarryA’s test question. “Can the moon exist and not exist at the same time and in the same formal relation? The answer to this question is either ‘yes’ or ‘no.’”

    My response to BarryA is that he is mistaken to assert that the only answer to this question is “yes” or “no.” Indeed, the correct answer to his question is, “this is not an intelligible question.”

    That was a hell of a post, almost like something that Diffaxial guy would have posted at UD if he’d been allowed to stick around. “Not an intelligible question” would have received a more immediate banning than my answer did. Which is not a flaw in your answer, but a flaw in the posing of the question. It’s easy to “demagogue” an answer like yours, or mine, though, because there is a classical interpretation of “exist”, one that doesn’t take heed of QM, that provides an unequivocal “no”.

    That’s why the test is formulated that way. If Diffaxial had replied with “not an intelligible question”, Diffaxial would be charged with eschewing the LNC, and rationality altogether. Theirs was a litmus test for affirming the plenopotentiary powers of classical logic to render any and all features of reality intelligible.

18. Sotto Voce:
    Reciprocating Bill,

    I don’t get it. Why is “The moon exists and does not exist” unintelligible within the framework of classical logic? It has the form “A & ~A”, and sentences of that form are provably false within that framework.

    They are resolvable only in a syntactical sense. If I write, in C++:

    
bool moon_exists = true;
bool moon_both = (moon_exists && !moon_exists);


    moon_both will be set to false, just by virtue of a Boolean AND operation. It’s intelligible (and compilable) syntactically, but only syntactically. Consider this, then:
    
bool moon_exists = true;
moon_exists = false;


    Now, moon_exists has the value false after these two statements have executed. Why, because moon_exists has a single, discrete value, either 1 or 0, and cannot be both. “A & ~A” is a statement that demands that moon_exists as a single, discrete value, has two different, exclusive values (1 and 0) at the same time.

    Given that, would you still say it’s intelligible for me to say that that variable, mapped to some discrete set of bits in memory in my computer, has both a “1” value and a “0” value in it at the same time?

    On classical logic, that’s a contradiction, an incoherent statement. True and false cannot be semantically preserved agains the And (&) Operator when you have a ‘true’ on one side, and a ‘false’ on the other side, and both referring to the same proposition.

19. Yup. Rule 1: Reality invariably makes sense within the confines of Aristotelian logic. Rule 2: Where reality does not, see rule 1.

20. Sotto Voce: I don’t get it. Why is “The moon exists and does not exist” unintelligible within the framework of classical logic?

    Here’s how I would put that.

    “The moon exists” and “the moon does not exist” cannot both be part of the same logic argument. However, that has no empirical implications.

    When describing the observed world, “the moon exists” and “the moon does not exist” might both be incorrect descriptions of reality. Perhaps we think “the moon exists” is close enough for practical purposes. Then fine. You can use that in logic. But you should keep in mind that your logic depends on a premise which is merely “close enough for practical purposes.” Most of the time, that works well enough. Sometimes it leads to problems such as show up in the sorites paradoxes.

21. Hi RB,

    However, I would argue not that “the moon simultaneously exists and does not exist” is false, but rather that, within the framework of classical logic, it is unintelligible.

    Like Sotto Voce, I think that “A & ~A” is quite intelligible within the framework of classical logic. It is certainly unsatisfiable, in that it remains false regardless of what A represents, but that doesn’t make it unintelligible.

    Consider the statement “x is an integer and x^2 +2 = 0.” We can see immediately what that statement means. It is perfectly intelligible, and each of the substatements is perfectly intelligible. We can see that it will be true if both of the substatements are simultaneously true. It just turns out that there is no single value of x that makes both of them true, so the statement is always false.

    Likewise, “A simultaneously exists and does not exist” is intelligible. It consists in simultaneously asserting that “A exists” and “A does not exist”, each of which is an intelligible substatement. It just so happens that the two substatements cannot be true simultaneously, so the statement is always false.

22. Over on Uncommon Descent (and elsewhere) there are interminable and ultimately futile debates about whether religions or secular ideologies have been responsible for more deaths over human history. Like many others, I take the view that both sides are missing the point. The real danger is in absolutist or totalitarian thinking. Once people come to believe that have got hold of some absolute truth, be it religious faith or political ideology, it can be but a short step to thinking that they are entitled by that knowledge to do almost anything in its furtherance.

    The driving force behind those movements is the human craving for certainty in a world that in many ways still mysterious and dangerously unpredictable. I see the same need behind this insistence on the rules of right reason (and the existence of objective morality) by the likes of Barry Arrington and StephenB. They want some kind of bedrock certainty on which to ground all their other cherished beliefs.

    The problem they have is in trying to elevate what are essentially modeling languages to the status of scriptural certainties.

    We have formal systems in which a statement such as “A cannot be simultaneously A and not-A” is true by definition. The tricky bit comes when we start assuming the formal truths of the model take precedence over the reality of what is being modeled.

    The question about the existence or otherwise of Jupiter reminded me of a little illustration from a book by Paul Davies (I think, although I could be wrong) He wrote along the lines that saying “I have some coins in my pocket” can be re-phrased as “There exist some coins in my pocket” but what, if anything, does it mean to say “There are non-existent coins in my pocket”? Non-existent coins like a non-existent Jupiter actually means nothing. The problem is that our language allows us to state a name or label that implies “non-existent Jupiter” has a different ontological status from just nothing. This puts us in danger of falling into the fallacy of reification, of inferring (wrongly) that, because we have word for something, that something must exist out there somewhere.

    I would agree with the proposition that Jupiter, if such a planet exists, cannot both exist and not exist at the same time, nor, as I understand it, is that contradicted by quantum superposition since that refers to the possible alternative states of an entity that exists as more than just a word and does not imply something that both exists and doesn’t exist at the same time.

    The problem for Arrington et al is that such a position simply doesn’t enable them to go where they so clearly want to go. All that is really being stated is the tautology that existing things exist. There is still no way to logically derive a moral code from that assumption and it certainly provides no basis for an objective morality, whatever that might mean.

23. Well, Sotto Voce and Keiths have clearly put their fingers upon something problematic about my post above, although Eigenstate and others have gone some distance to rescue some of what is right about it. I overstate my case vis intelligibility and formal logic as pointed out above (knowing something about formal logic would help). I think a better formulation lies somewhere in the neighborhood of the notion that “intelligibility” as I am construing it refers to the level of utterances in a social context and what people wish to accomplish with those utterances. People “do things with words,” and upon encountering someone uttering assertions that must be false regardless of empirical content, one would be right to wonder just what they are doing with those words.

    That’s all the self-deprecation I can do in one day, so be nice.

24. People “do things with words,” and upon encountering someone uttering assertions that must be false regardless of empirical content, one would be right to wonder just what they are doing with those words.

    Yes. If someone walks up to you and says “Barack Obama is and isn’t the President,” you’ll assume she’s trying to convey something subtler than the assertion of an obvious falsehood. On the other hand, if she says “the statement ‘Barack Obama is and isn’t the President’ is false”, you’ll infer that she’s saying something about logic, and that the President was just a handy prop.

    That’s all the self-deprecation I can do in one day, so be nice.

    That, and your willingness to actually listen to criticisms of your views, puts you miles ahead of StephenB and Barry Arrington.

25. Well, this has been an enlightening thread (as opposed to all the feedback I’ve gotten at UD.) I get involved in these things to learn – I am no expert – and try to put my thoughts into words. Sometimes I get in over my head.

    But I’ve really enjoyed all these comments, and understand a whole bunch of things better. I particularly liked these two comments, from above someplace.

    Aristotle’s argument for the law of non-contradiction, for those who take the time to look it, already presupposes his metaphysics — that what we’re talking about are objects (“substances”, he would say) and their properties.

    and

    My understanding about the objection is that this is more basic than that. StephenB’s theism follows from his simplistic and brittle notions of rationality — that really is beholden to the simple rules he uses to process propositions. People with such commitments I think viscerally object because empiricism getting mixed in makes things messy, complex to think about. Once Nature is consulted as to how things really are, “philosophizing by definition” doesn’t work anymore.

26. The root of classical logic is the attempt to divide the universe into discrete groupings or objects. We look at a puffy cloud moving across the sky, and see it as distinct from everything else around it, but if we look more closely, we see its edges are vague, and our one cloud might merge with other clouds. Similarly, with every other object. Some are more distinct that others, but all are artificial or utilitarian constructs, a consequence of human cognition.

    When we ask “Can Jupiter exist and not exist at the same time”, we are assuming that existence is a distinct category that can be applied to the object. Certainly, if anything is an object, then Jupiter qualifies. Jupiter does exist. (We did answer this in the affirmative on Uncommon Descent, but our comment disappeared into the æther of silent bannination.) However, if we ask “Can an electron exist and not exist at the same time”, well, it turns out that existence may not be a clearly defined dichotomy.

27. Josean: Contradictory statements can be both true depending on scale of observation/point of view.

    Right, Aristotle also covered this. You’ve two eyes and each sees a different image. Therefore there is no proper contradictory. Contraries, subcontraries, but not contradictories. This is all general abstract nonsense well older than the Christian religion.

    eigenstate: Right. QM is fundamentally problematic to classical logic.

    The only fundamental problem is the desire to stop asking questions. But if QM presents a dialetheia then there simply aren’t any more questions to ask. Or, that thing that’s claimed will happen if religious folks get a hold of science. QM only presents a problem for those that desire it present a problem, and doesn’t for those that don’t.

    Neil Rickert: “The moon exists” and “the moon does not exist” cannot both be part of the same logic argument.

    According to many here, and Graham Priest, they most certainly can.

    Seversky: The real danger is in absolutist or totalitarian thinking. Once people come to believe that have got hold of some absolute truth, be it religious faith or political ideology, it can be but a short step to thinking that they are entitled by that knowledge to do almost anything in its furtherance.

    This, simply this. And the weapon best-suited for self defense in these measures is logic for the sake of the reason and the refutation. And refutation needs the law of the excluded middle and the law of non-contradiction. Which is why those that are more interested in ideology than truth do their utmost to defray the LEM and LNC. The sort of folks that stick explosives in their shorts and catch a red-eye flight.

28. Maus: The only fundamental problem is the desire to stop asking questions. But if QM presents a dialetheia then there simply aren’t any more questions to ask. Or, that thing that’s claimed will happen if religious folks get a hold of science. QM only presents a problem for those that desire it present a problem, and doesn’t for those that don’t.

    So, Maus, why don’t you share your thoughts on the status of an electromagnetic field in the quantum state |0>+|1>, where |0> corresponds to no photon in the resonator and |1> corresponds to one photon. Such states are now routinely realized in experiments. See this paper for example: Quantum memory with a single photon in a cavity. The photon exists and not exists at the same time and in the same formal sense.

29. Maus,

    Welcome to TSZ, Maus 🙂 Pull up a chair!

30. There are several points to be made here.

    First, the focus on axioms is misplaced here. It is the logic equivalent of the habit that some people have of formulating all philosophical questions as “does X exist?” Logicians (at least those interested in the sorts of foundational issues at stake here) do not talk all that much about axioms, they talk about the rules of deduction. This reflects the fact that logic is, after all, concerned with what follows from what, rather than in enumerating logically true sentences. The logical calculi based on axioms and modus ponens (for some reason, this rule is left out in many discussions of logic, as if the axioms were of any use in and of themselves) are the oldest and crudest of the formal calculi in use. When trying to substantiate principles such as the law of the excluded middle, logicians use natural deduction or sequent calculi, which do not have any non-trivial axioms.

    Second, the three principles in the OP are, from a modern point of view, a hodge-podge of propositional and first-order logic, so it would be best to restrict ourselves to non-contradiction and the excluded middle. As for the principles supposedly depending on what an object is or what time is, they do not. Objects are, from the point of view of logic, roughly what singular terms designate. Modern logic does not presuppose some kind of pre-existing metaphysical understanding of objecthood, properties and so on. As for time, it makes no sense to rip the word “time” out the context of the phrase “at the same time as” and claim that understanding this phrase presupposes understanding what time is.

    Third, despite the fact that people keep repeating this, quantum logic questions neither the logical truth of “A or not A” (the LEM) nor the logical falsehood of “A and not A” (the LNC). What it questions is the equivalence of “A and (B or C)” and “(A and B) or (A and C)” (the distributivity of conjunction and disjunction). There are, of course, other logics which, for example, do not have “A or not A” as a theorem, such as intuitionistic logic.

    Fourth, the whole “game of giving and asking for reasons”, to repeat the term Carl Sachs used above, is a rule-governed activity. If you’re thinking of what you call “the rules of right reason” as some principles written down by some wise men in the olden days that only apply to some highly idealized situations, you’re thinking of them the wrong way. They are the very principles whose acceptance enables us to reason. Reasoning logically is precisely using what you call the rules of right reason. Although this may not be reflected by the connectives “and”, “or” and “not” in certain logics, it is for example constitutive of the acts of assertion and denial that you’ve made a mistake if you’ve both asserted and denied A. If you haven’t, then what you did simply cannot be called asserting and denying A. This sort of pragmatic principle of non-contradiction has nothing to do with whether A is a sentence about quarks, minds or tables.

31. Maus:

    This, simply this.And the weapon best-suited for self defense in these measures is logic for the sake of the reason and the refutation.And refutation needs the law of the excluded middle and the law of non-contradiction.Which is why those that are more interested in ideology than truth do their utmost to defray the LEM and LNC.The sort of folks that stick explosives in their shorts and catch a red-eye flight.

    Not quite getting your metaphors, but perhaps that is as well 🙂

    Logic is fine Maus, and we all make liberal use of classical logic. But the laws of classical logic are merely human tools – they are not written into the fabric of the universe, and there are other logics than classical logic which are more appropriate tools for certain questions.

    What question, relevant to the origin and evolution of life, do you think requires classical logic to elucidate, and where do you think those of us who accept evolutionary theory contravene classical logic?

    To put my cards on the table: I think Dembski violates the Law of Excluded Middle in his CSI concept. He defines anything other than Design as “not-design” but then implicitly defines “not-design” as processes that give rise to equiprobable patterns.

    Where do you think that “evolutionists” violate classical logic?

32. Maus: The only fundamental problem is the desire to stop asking questions. But if QM presents a dialetheia then there simply aren’t any more questions to ask. Or, that thing that’s claimed will happen if religious folks get a hold of science. QM only presents a problem for those that desire it present a problem, and doesn’t for those that don’t.

    I think you are using “fundamental” in a different sense than I am. You want to say it’s an important problem when people stop asking questions, and I’d agree. But in ‘fundamentally problematic”, I meant something different than “important” or “disabling”; I meant that parts of QM produce insuperable problems for classical logic at the base, at the lowest levels, and the foundation, beyond which there is nothing more to resort to in order to reduce or subdivide the problem so as to make it tractable.

    The problems raised by QM are not a matter of desire; they are epistemic problems, logical problems that confound “classic” ways of building models. They inhere in the way we observe nature operating at the quantum level. I understand one can simply desire to avoid such problems by “thinking about something else”, but desiring to avoid them doesn’t make the problems — fundamental problems — go away.

33. olegt: So, Maus, why don’t you share your thoughts on the status of an electromagnetic field in the quantum state |0>+|1>, where …

    It’s behind a paywall so I’ll just run on the generalities rather than your specific link. I think it’s meaningless. I can, if you like, badly formulate an understanding of any well-known system such that it creates boggled nonsense like the Copenhagen crowd want us to swallow. The entire crux of the ‘QM contradicts contradiction!’ claim is that because we are ignorant, therefore dialetheias. Which, really, is right there with Cantor’s notion that ignorance makes the infinite more infinite: Which surely proves God with cardinals. Eh… The numeric kind.

    Elizabeth: Welcome to TSZ, Maus 🙂 Pull up a chair!

    Thanks for not hitting me with a stick! Sorry to hear about your sabbatical from the other joint and happy to know you’ve got your own.

    Elizabeth: But the laws of classical logic are merely human tools – they are not written into the fabric of the universe, and there are other logics than classical logic which are more appropriate tools for certain questions.

    Sure, and they don’t need to be written fabric of the universe. But they are relevant to how we speak, reason, and do math; thereby science and the rest of that rot. So to entertain the notion that the LEM and LNC are not the case requires disproving the Church-Turing hypothesis. That’s it, one piece of evidence as Einstein would have it. All anyone needs to do is produce a calculus that humans can compute but those nasty Aristotolean Intel chips will not.

    Elizabeth: What question, relevant to the origin and evolution of life, do you think requires classical logic to elucidate, and where do you think those of us who accept evolutionary theory contravene classical logic?

    Logic is only a formalism for reason, so if the origins of life don’t involve reason then it doesn’t involve logic. The only gross error, in a normative logic sense, is in claiming everything and both sides in a contingent system without adequately dealing with what the contingent conditions are. There are other minor points and that’s only the theory side rather than the belief side.

    Elizabeth: To put my cards on the table: I think Dembski violates the Law of Excluded Middle in his CSI concept. He defines anything other than Design as “not-design” but then implicitly defines “not-design” as processes that give rise to equiprobable patterns.

    There’s no problem with design/not-design as a dichotomy. The problem is the account of CSI itself. Which is addled at best and more often simply deranged. ID hasn’t been around long, so it’s not surprising that they’re still working things out. Of course, I’ve little interest in ID so they may have gotten a definition squared away recently for all I know.

    Elizabeth: Where do you think that “evolutionists” violate classical logic?

    By not using it. Same as the other side. It’s an issue of debate, refutation, and proof here but the largest individual flaws are equivocating and affirming the antecedent. The former is nearly impossible to avoid when dealing with poorly defined concepts of course. While the latter is just a common thing that people do when they already hold a belief in the topic they’re arguing. It’s a preaching to the choir problem. But it’s not a Darwinist thing, it’s a human thing.

34. eigenstate: The problems raised by QM are not a matter of desire; they are epistemic problems, logical problems that confound “classic” ways of building models.

    Right, they are epistemic problems, but not logical problems. We’re at a tiny level where we observe by not observing. Close your eyes, accelerate a 747 to a significant fraction of C, then slam it into a mountainside. (Because we like to construct 747’s with tornados, right?) Now reconstruct the Boeing and describe how it works. I bet you’d find it baffling and contradictory no matter how many airplanes you went through.

35. Monoid: Third, despite the fact that people keep repeating this, quantum logic questions neither the logical truth of “A or not A” (the LEM) nor the logical falsehood of “A and not A” (the LNC). What it questions is the equivalence of “A and (B or C)” and “(A and B) or (A and C)” (the distributivity of conjunction and disjunction). There are, of course, other logics which, for example, do not have “A or not A” as a theorem, such as intuitionistic logic.

    This conversation is tricky because, to use Kantian terms, analytic truth keeps getting conflated with synthetic truth. “A & ~A = false” is true by definition, analytically true. It’s not true by virtue of the statement’s correspondence to nature or extra-mental reality.

    Logic doesn’t “question” other logic. Logic is a self contained rule framework.

    I don’t know what ‘quantum logic’ is, but in any case, while LNC is analytically true, it is also so ubiquitously useful for making reality intellgible, that we are tempted to see the LNC as “metaphysically true”, somehow, rather than analytically true, and enormously, pervasively useful for deriving synthetic truths.

    So what happens is that quantum physics, the way nature operates at quantum scales, breaks (and thoroughly) Aristotelian metaphysics, the ancient idea that an “object” is a real thing, a distinct, and discretely extant (or not) thing, at the fundamental level. Now you have real physics, performative and precise models grounded in an unassailable surfeit of evidence, overturning many synthetic truths, or more precisely, rendering them simplistic and obsolete.

    Quantum physics, then, undermines, or at least complicates many of these synthetic truths, which in turn weakens the efficacy of the LNC as a “swiss army knife” logic tool for understanding all and any aspects of reality.

    The LNC remains as analytically true as ever — it’s a axiom, a given — but it’s powers, classically thought to be magical, metaphysically imperative, are now diminished in some areas of understanding reality (and these are the most fundamental ones!). LNC and LEM are still transcendental to our propositional thought and communication, so classical logic is not and cannot be overthrown for many (nearly all) of the domains where it’s effective, of more strongly, necessary for the enterprise to operate (like posting this post).

    “Quantum logic”, if I take that to mean “models for quantum physics”, does not question the LNC itself. It can’t, “questioning” doesn’t have any meaning in that context. But it does question the “universal applicability” of the LNC as a tool for rendering all parts of our reality intelligible.

36. Maus,

    If I am playing chess, I say to myself, what would happen if I moved my queen here, and then I go through the logic AS IF I had actually moved the queen.

    Whether the queen is physically there or not, my logical process is identical.

    Why?

    Because, logic works on assertions, not reality.

    The LNC, is a property of logic and therefore applies to assertions, not reality.

    If you try to assert the moon exists and the moon doesn’t exist, I would ask you how you could possibly manage to assert that since logic accepts only TRUE or FALSE, not BOTH.

    That is what the LNC means, you can’t have an assertion that is both TRUE and FALSE at the same time.

    It has nothing to do with reality at all.

    If you however, tried to tell me you are holding in your hand a quarter that both exists and doesn’t, I would say you were probably crazy.

37. I’d like to distinguish between any specific set of logical principles and the broader question of normativity as such (including both norms of action, or ethics, and norms of thought, or reasoning, although ultimately norms of thought *are* norms of action).

    For while there are multiple logics, different formal systems constituted by different rules, where the ‘choice’ of a logic is governed by pragmatic considerations, it is also the case, I think, that human beings are fundamentally norm-using creatures — creatures of rules and not merely of habits. As I see it, thinking of the logical spaces of thought and action as an evolutionary inheritance and as cultural developments amounts to a refinement, not a rejection, of Kant’s thought that norms are a priori.

    I suspect I’m not being all that clear. I’ll try again later. All I really wanted to do is suggest that there’s a rich middle ground between saying that logic is written into the very fabric of reality and saying that logic is an arbitrary, or nearly arbitrary, social convention.

    Carl

38. I think there is a difference between saying “logic is written into the very fabric of reality” and saying, as the UD denizens seems to think, that “logic determines the fabric of reality.” If we ignore the designer metaphor of the phrase “written into”, and merely state that “logic is in the fabric of reality”, as opposed to imposed upon reality from without, then we have the distinction that I quoted from Wikipedia that I liked:

    Aristotle disagreed with Plato about the location of universals. As Plato spoke of the world of the forms, a location where all universal forms subsist, Aristotle maintained that universals exist within each thing on which each universal is predicated.

    Reality comes first, and reality does have a nature. Our abstractions from it, even though they obviously are in respect to how we experience the world, are not just arbitrary conventions. The heart of science, and of a point I’ve been trying to make at UD, is that we test our abstractions by accepting a hypothesis as true, drawing out the conclusions, and then testing those conclusions back against the evidence in the world. This process tests not only the hypotheses themselves, as tentative assertions, but also the logic that we have developed to manipulate those assertions. Classical logic is well tested, and it has worked marvelously well, because it does fit (is an accurate abstraction from) reality as we have known it. However, as we learn more about reality, especially at scales far removed from our everyday existence, it should be no surprise (maybe it is a surprise, though) that the logical principles we abstracted from daily experience are no longer as useful.

39. eigenstate: Quantum physics, then, undermines, or at least complicates many of these synthetic truths, which in turn weakens the efficacy of the LNC as a “swiss army knife” logic tool for understanding all and any aspects of reality.

    If you burden yourself with an ontological commitment of occultic frou for your understanding of QM, yes. But there are far more than just one valid interpretation of QM. What’s being missed here is that the math is the math. The ‘difficulties’ are imported ontological appendages that are helpful for analogy or pedagogy. And that there exist several that are mutual exclusive and contradictory to one another.

    Toronto: Because, logic works on assertions, not reality.

    The LNC, is a property of logic and therefore applies to assertions, not reality.

    Sure, there’s no necessity for reality to dance my tune of Deepak Chopra’s. But I assume then that you have a piece of evidence, a witness, as to how reality violates the LNC; thus establishing that it doesn’t apply.

    The strict difficulty with such a witness is that we represent our internal states and understandings of reality, conscious and unconscious, to one another by producing assertions in language. So it’s a rather open question of how we could even tell that the moon both did, and did not exist simultaneously. That said, ex falso quodlibet is considered a valid and necessary inference rule in bog standard ‘classic’ logic within Philosophy. If you work the details out from there you might see why these discussions even need be had.

    Toronto: If you however, tried to tell me you are holding in your hand a quarter that both exists and doesn’t, I would say you were probably crazy.

    Of course I do. Have you seen what they’ve been doing to the currency during the economic downturn!?

40. Maus,

    Toronto: Because, logic works on assertions, not reality.

    The LNC, is a property of logic and therefore applies to assertions, not reality.

    //—————————————————————————————-

    Maus: “Sure, there’s no necessity for reality to dance my tune of Deepak Chopra’s. But I assume then that you have a piece of evidence, a witness, as to how reality violates the LNC; thus establishing that it doesn’t apply.”

    Reality doesn’t “violate” the LNC.

    They don’t interact at all because they are on opposite sides of a border.

    If you measure a resistor at 1 K but the coloured bands say it should be 10 K, no laws of physics have been violated.

    Someone simply asserted the wrong value for the resistor by applying the wrong identification bands.

    Your claim of interaction between the LNC and reality, regardless of direction, is just as wrong as claiming the coloured bands on a resistor have any interaction with physics or violation of Ohm’s law.

41. Maus,

    Maus: “Of course I do. Have you seen what they’ve been doing to the currency during the economic downturn!?”

    I stand corrected. 🙂

42. I guess I’m more willing to say that logic is, to borrow a phrase from Robert Brandom, our “semantic self-consciousness” — that is, logic makes explicit the normativity that is built into our ways of speaking. I don’t see why the natural world (as explained by scientific theories) must conform to the categories of Aristotle (however helpful they are in explicating ordinary experience).

43. Toronto:
    Your claim of interaction between the LNC and reality, regardless of direction, is just as wrong as claiming the coloured bands on a resistor have any interaction with physics or violation of Ohm’s law.

    Then you have in mind an instrument design that will trigger a result, measure, when it recognizes what it is measuring at the same time it fails to recognize what it is measuring.

    The point being that if such witnesses can be proven and shown then it is not a question of whether or not the LNC is sound. Reality will have shown that the LNC itself is false — violated. And that gives rise to a host of terribly non-trivial issues. Such as: Can we design a contradiction detecting machine? If we could, how would we interpret it’s results? How could we even speak of the results or rationalize them?

    What ever reality exists, or may exist, outside our brain case is meaningless if we cannot detect it or digest it. It’s as ‘real’, in the only sense of real we have, as paisely to Helen Keller.

44. Addenda: It just occurred me what it must be like to be a Darwinist arguing in an ID room. “Because it works, damnit! Quit making crap up!”

45. Maus: If you burden yourself with an ontological commitment of occultic frou for your understanding of QM, yes. But there are far more than just one valid interpretation of QM. What’s being missed here is that the math is the math. The ‘difficulties’ are imported ontological appendages that are helpful for analogy or pedagogy. And that there exist several that are mutual exclusive and contradictory to one another.

    Oh, the good old chestnut But there are many interpretations of quantum mechanics! Have you ever wondered, Maus, why actual textbooks on quantum mechanics invariably teach the Copenhagen version? Because the other ones aren’t taken seriously by physicists. Philosophers like to play with them. Physicists, not so much. In fact, a popular view among physicists is that there is one standard quantum mechanics (Copenhagen) and the rest are useless philosophical appendages.

    The reason for such brazen favoritism is that all the other interpretations have severe problems. Two of the more respectable interpretations, Bohm’s theory of hidden variables and the multi-world interpretation (MWI), suffer from the problem of the preferred basis. Bohm’s theory explicitly prefers coordinates to momenta. The MWI does not state which basis it prefers, but it must choose one by its very definition.

    The problem is particularly severe for the simple case of a single spin or angular momentum. Do we prefer the basis states with definite projections of spins onto the x-axis, y-axis, or z-axis? Or any of the countless other axes? There is no answer to this.

    Bohm’s interpretation has additional problems, in particular the strongly unphysical nature of its hidden variables: they travel faster than light and violate causality.

    So forget it. Philosophers might enjoy playing with interpretations of QM, but in physics we just stick with the standard version.

46. Maus: Reality will have shown that the LNC itself is false — violated.

    I’m sorry, but this makes no sense at all. The LNC is not about reality, and reality is not capable of showing that the LNC is false.

47. Maus,

    ” Toronto: Your claim of interaction between the LNC and reality, regardless of direction, is just as wrong as claiming the coloured bands on a resistor have any interaction with physics or violation of Ohm’s law. ”

    //————————————————

    Maus: “Then you have in mind an instrument design that will trigger a result, measure, when it recognizes what it is measuring at the same time it fails to recognize what it is measuring.”

    No.

    What I claim is that the LNC, a property of the human originated tool we call logic, does not interface with reality, ..at all.

    Reality cannot violate the LNC because it is us humans, who came up with the process of logic, a means of dealing with “models” of things that we assert, whether those assertions reflect our current definitions of reality, or consist of a game of chess played in our heads.

    Reality did not come up with math, spelling, poetry or logic, (which includes the LNC), but we did.

    I hope this makes it clear that I don’t believe that the LNC has anything to do with reality.

    People have to deal with reality, logic deals with assertions.

48. olegt: Have you ever wondered, Maus, why actual textbooks on quantum mechanics invariably teach the Copenhagen version?

    The most printed book of all time is the Holy Bible. Have you ever wondered, olegt, why that is? And don’t pull out the old chestnut that there are many version of it.

    If I am to accept your argument as valid and sound then it is certain that you have by now converted to Christianity. I’m just going to hazard the wager that you have not. Perhaps you’d like to try something other than argument ad gutenberg.

    Neil Rickert: I’m sorry, but this makes no sense at all. The LNC is not about reality, and reality is not capable of showing that the LNC is false.

    Then it is just as certain that Darwinism is not about reality, and reality is not capable of showing that Darwinism is false. Or insert whatever theory you prefer in place. The LNC gets its roots in discussions about reality and theories about reality. That it is imported into various logical system on the basis of our experiences with reality does not happen to divorce it from them.

    Toronto: What I claim is that the LNC, a property of the human originated tool we call logic, does not interface with reality, ..at all.

    Reality cannot violate the LNC because it is us humans, who came up with the process of logic, a means of dealing with “models” of things that we assert, whether those assertions reflect our current definitions of reality, or consist of a game of chess played in our heads.

    So it has nothing to with reality except our models of reality, how we understand reality, and counterfacutals based on our prior experience with reality. Therefore there is absolutely no connection between the LNC and reality. It’s absurd.

    Do I have that right?

    Toronto: People have to deal with reality, logic deals with assertions.

    Fair enough. You’ve made your assertion that I need to deal with reality without assertions. Your mission, should you choose to accept it, is to assert that to me without an assertion. Just to keep it real.

49. There’s an important difference between (a) the relationship between assertions and the world and (b) the relationship between assertions and other other assertions. The former are questions of truth; the latter are questions of reasoning. They are not separable, but they are distinct.

    In a classical logic, the law of non-contradiction (and a few others) holds as rules about how assertions may be related to one another. (For one thing, it explicates the rules governing the use of conjunction, negation, and implication.) Whether there are useful non-classical logics is an interesting philosophical question that we needn’t worry about here.

    But even if we reject non-classical logic, and just stick with classical logic, it must be stressed that logical principles are empty, in the sense that since they govern all assertions, they don’t indicate anything about which particular assertions are true or false. Logic tells me nothing about whether P is true or false; it only tells me that if I assert P, then I should not assert ~P, and conversely. In order to know whether I should assert P or ~P, I need to go beyond logic alone and examine the world. Put slightly otherwise, logic tells me what I should do once I’ve got a set of commitments, but it doesn’t tell me what I should be committed to — it doesn’t guide me as to which concepts apply to which experiences.

    Now, here’s the thing, and it’s worth bearing in mind: there are normative constraints on which concepts apply to which experiences. It’s not will-nilly. But classical logic itself is not a theory of those normative constraints. In other words, one would have to go beyond logic (which is really just semantics) into epistemology, where notions of justification, truth, and evidence are central. You can’t do epistemology without logic, of course, but you can’t just have logic do the work of epistemology, either.

    Carl

50. Maus,

    Communications software is layered.

    You have a physical layer, a network layer, a link layer, etc.

    The application doesn’t know whether the data is coming from the Ethernet port or wireless connection, and it also doesn’t care.

    Saying the application doesn’t care is not the same as saying, “no layer cares”.

    If you can’t understand this, talk to kairosfocus and get his help in understanding it.

    Once you do that, we can move on to how and why logic is layered too.