• creativesoul
    2.9k
    All the predictions of logic are true? What the hell is that supposed to mean? Predictions are neither true or false when posited.

    All logical conclusions are called "true" if they result from reasoning/argument that follows the rules of correct inference. Logic is the rules of correct inference. Calling something "true" doesn't make it so, even when we're calling the conclusion of a valid argument "true". Validity does not equate to truth. Logical truths are a misnomer.

    Logic doesn't find truth.

    Logic presupposes truth. It's utility is to preserve it. The rules of correct inference are justified - if we must talk like that - solely by virtue of how well they work.

    True conclusions do not logically follow from false premisses. False conclusions do not logically follow from true premisses.
  • Dfpolis
    156
    All the predictions of logic are true?creativesoul

    Who claims his?
  • Aleksander Kvam
    213
    I used to think logic was the same as common sense... :sad:
  • creativesoul
    2.9k


    Argument A:
    1. If ALL the predictions of logic are true then logic is justified
    2. ALL the predictions of logic are true
    So,
    3. Logic is justified

    Argument A is NOT circular and is a valid application of modus ponens.
    TheMadFool
  • MathematicalPhysicist
    12

    We justify Logic by Logic.

    Now, that's Logic for you!
    :-D
  • MindForged
    315
    Logic is a statement of fact/in relation to fact. If there is any error, it cannot be logic/logical.BrianW

    Logic has nothing to do with facts and there relation. Facts refer to ways the world is. Logic specifically deals with (primarily) the logical consequence relationship, nothing to do with the empirical world. (At best one might bring up abstract objects)

    We might be a little more explicit and say it is the science of correct thinking about reality -- because we want it to be salve veritate -- if our premises reflect reality, then we want "correct thinking" to be such that our conclusions will necessarily reflect reality.Dfpolis

    This seems incorrect. Logic has many uses which either have nothing to do with reality or else is used in a way we might not reason about reality. So just take this website. Now I'm assuming it uses SQL as its database language. If so, then this website operates according to a Non-classical logic. But many propose we ought to reason about reality using classical logic. In which case, we have an example of using at least two logics in different domains, irrespective of reality itself. This is ignoring much of mathematics as well, such as the very useful Constructive Mathematics (based on intuintionistic logic) which rejects the Law of the Excluded Middle.


    that it is impossible to both be and not be at one and the same time in one and the same way (the principle of contradiction) and that a putative reality either is, or is not (the Principle of Excluded Middle). Thus, these principles are not a priori, not forms of reason, but a posteriori understandings that are so fundamental that once we come to grasp them, we understand that they apply to all being.Dfpolis

    Identity violations: See non-reflexive logics and quasi-set theory.

    Excluded Middle violations: see Intuintionistic logic.

    Non-contradiction violations: see Dialetheism.

    Whether you accept these or not, statements like "so fundamental that once we come to grasp them, we understand that they apply to all being" are just question begging. Sure, if I accept all your definitions for "truth", your preferred inference rules, your semantics/metatheory, then yes they follow. But that simply makes the nature of the disagreements have an obvious location of disagreement (e.g. in the semantics and such).

    Working through the valid forms of syllogism with this understanding, we can see how the role of identity in propositions, together with the principles of being, justifies themDfpolis

    It's weird that you would bring up syllogisms when we know that Syllogistic Logic has the wrong set of valid arguments for a whole slew of things. Like this is invalid in Classical Logic (Frege's logic) but was regarded in Syllogistic as valid:

    All winged horses are horses.
    All winged horses have wings.
    Ergo some horses have wings.

    The point being that people can believe you hold the incorrect view about the principles of existence just as much as they can believe (sometimes correctly) that you hold the incorrect logic.
  • Banno
    3.1k
    Meh. Logic is the mechanics of justification. Move on.
  • Christopher A
    9
    It's not hopeless to criticise a set of rules built on a simplistic understanding of the world. In Quantum Mechanics, A is not necessarily just true OR false, it can be both at the same time. Physicists had to create new language (read logic) to work with it. It's also very likely that non-locality will win as the most likely interpretation of QM. Even causality is not secure in QM interpretations. So the classic logic rules may be shown to be very situational.
  • Blue Lux
    286
    If logic is not about reality... Then it is? Imagination?
  • Blue Lux
    286
    If logic is a method to knowledge, then logic is subject to what knowledge is subject to, namely an interrogation.
    What is logic? A system by which facts are ascertained? What are these facts? But... What is it that logic represents or illustrates? That which eludes a superlative representation? Yes, logic is therefore abstraction.
    But this abstraction has its placeholders and aspects of existence can be substituted so to assume a logical intelligibility, but never does logic have anything to do with truth, absolute truth, only a truth that is imaginary.
    Knowledge is only as if it were knowledge.
  • Dfpolis
    156
    We might be a little more explicit and say it is the science of correct thinking about reality -- because we want it to be salve veritate -- if our premises reflect reality, then we want "correct thinking" to be such that our conclusions will necessarily reflect reality. — Dfpolis

    This seems incorrect. Logic has many uses which either have nothing to do with reality or else is used in a way we might not reason about reality.
    MindForged

    Of course "logic" can be defined in many ways, so it is not one thing, but many related things. That is why I defined what I meant by logic: the science of correct thinking (about reality). That is what I am offering to justify.

    Of course, this does not mean that classical logic is unrelated to other forms of "logic." You raise he example of SQL. To apply SQL, we must first realize that, given our actual goals and the reality we are considering, SQL can be applied and doing so will advance our goals. This, of course, is thought about reality, and if our forms of thought did not yield true conclusions, the application of SQL would be irrational.

    In the same way, you mention "Constructive Mathematics (based on intuintionistic logic) which rejects the Law of the Excluded Middle." Yet, if, in criticizing the proof of a theorem in Constructive Mathematics I were to say that in addition to an axiom you used applying or not applying there was some other possibility you had not considered, surely you would object. So, while you may construct a system which makes no internal use of the principle of excluded middle, in reasoning about that system, you would use the principle.

    Second, whenever we apply any scientific principle to a particular instance, we necessarily use the syllogism in Barbara. Let p be a scientific principle and q describe sufficient conditions for the application of p. Then we think as follows:
    All cases such that q are such that p.
    A is a case such that q.
    Therefore A is a case such that p.
    So, when we apply mathematical or cybernetic algorithms, the reasoning justifying their application is quite Aristotelian.

    Identity violations: See non-reflexive logics and quasi-set theory.MindForged

    I've said while we can think of impossible states, there can't be impossible states. You have not provided a single example of a real state violating the ontological principles of identity, contradiction or excluded middle.

    statements like "so fundamental that once we come to grasp them, we understand that they apply to all being" are just question begging.MindForged

    No, it is not question begging. It is an experiential claim to which you have provided no counter example or rebutting argument.

    Sure, if I accept all your definitions for "truth", your preferred inference rules, your semantics/metatheory, then yes they follow. But that simply makes the nature of the disagreements have an obvious location of disagreement (e.g. in the semantics and such).MindForged

    No. Definitions of terms point to aspects of reality that can be experienced and analyzed. So, the question is not about the self-consistency of semantic relations, but about the adequacy of my account to our experience of reality.

    All winged horses are horses.
    All winged horses have wings.
    Ergo some horses have wings.
    MindForged

    As I said, logic is not about the consistency of language, but about salve veritate thinking. To save truth, you must start with truth. "All winged horses are horses" is not a truth, but an equivocation. "Winged horses" are not "horses" in the sense living equine creatures, which is the sense of "horses" required by the conclusion. In the same way, there is no true statement in which "the present king of England" is taken as having a substantive reference.

    It speaks poorly of those who educated you in logic that you are unable to spot so obvious an equivocation. Correct thinking is not about matching letter sequences or manipulating word strings. It is about using conceptual representations rationally.
  • MindForged
    315
    If logic is not about reality... Then it is? Imagination?Blue Lux

    Logic is about graphing out a particular consequence relation by accepting some set of axioms and inference rules. You can understand this as the relation between particular abstract objects (model theory) or as sequences of proofs (proof theory). There are other conceptions of logic, but most of those (such as the "rules for correct reasoning") make use of these in a normative setting or else they have fallen by the wayside (most professionals don't place primacy on logic regarding thinking anymore).
  • Blue Lux
    286
    And this is thus reality? Or... Something else?
  • MindForged
    315
    That is why I defined what I meant by logic: the science of correct thinking (about reality). That is what I am offering to justify.Dfpolis

    That's the problem though. Presumably there is only one reality, but we know there are many logics so there seems to be an inherent problem with your definition. Namely, the contradiction with having multiple correct ways of thinking about reality based on different, inconsistent logics.

    Yet, if, in criticizing the proof of a theorem in Constructive Mathematics I were to say that in addition to an axiom you used applying or not applying there was some other possibility you had not considered, surely you would object.
    So, while you may construct a system which makes no internal use of the principle of excluded middle, in reasoning about that system, you would use the principle.
    Dfpolis

    This is exactly what I was talking about when I brought up the metatheory/semantics point. You are simply assuming the Principle of Excluded Middle in your metalanguage and then pointing out how it then appears in the object language. No, using Intuintionistic Logic does not mean accepting reasoning about constructive proofs with Excluded Middle. As I said, this and other Non-classical logics have their own metatheories that make do not accept Excluded Middle. Excluded Middle is not false in constructive mathematics, it simply cannot be placed within the scope of the universal quantifier in proofs (so it's application in infinite domains is invalid). You are simply question begging the principle at hand.

    So, when we apply mathematical or cybernetic algorithms, the reasoning justifying their application is quite Aristotelian.

    I sincerely hope I don't sound rude, but are you kidding me? You do realize that a simple conditional is valid in damn near any logical system, right? I could just as easily say scientific reasoning is Intuintionistic by your lights.

    I've said while we can think of impossible states, there can't be impossible states. You have not provided a single example of a real state violating the ontological principles of identity, contradiction or excluded middle.Dfpolis

    Bro, I didn't give everything at once to avoid a massive post. Aside from the fact that logic isn't about reality, take:

    Identity violations: Check Newton da Costa's work (based on work by early pioneers in quantum mechanics) about indistinguishable quantum objects. That is, objects that are such that they are *ontologically* indistinguishable (it's not an epistemic limitation), non-individuated objects. Schrodinger himself explicitly endorsed this, hence the old phrase that quantum objects had "lost their identity".

    Excluded Middle: nothing here, not my wheelhouse. However, ironically Aristotle disagrees with you. He believes there are metaphysical violations of Excluded Middle: contingent statements about the future (his sea battle argument).

    Non-contradiction: The Liar paradox. No, it does not have an obvious or simple solution. Professional logicians have no standard resolution. That aside, the LP (if a sound argument) violates non-contradiction. And if one is, as I am, a Platonist about mathematical and other abstract objects like propositions, one is (as I am) committed the accepting the existence of inconsistent objects from what seems to be an argument from commonly accepting rules for reasoning.

    No, it is not question begging. It is an experiential claim to which you have provided no counter example or rebutting argumentDfpolis

    It's question begging. You made the argument that in even assessing e.g. Constructive Mathematics one has to use Excluded Middle because you think it results in an situation where you're... violating Excluded Middle.

    No. Definitions of terms point to aspects of reality that can be experienced and analyzed. So, the question is not about the self-consistency of semantic relations, but about the adequacy of my account to our experience of reality.Dfpolis

    I'm not sure you understood my point. You said this:

    "Thus, these principles are not a priori, not forms of reason, but a posteriori understandings that are so fundamental that once we come to grasp them, we understand that they apply to all being."

    All this really says is that "once you assume my definitions of the relevant terms and their scope of application is global in all possible domains, you'll see they apply to all of reality" (It's essentially defining your way to victory). The only difference is you're (intentionally or not) cloaking it under language of discovery as opposed to assumption. As it happens, people can and have put forth reasonable objections to your views about these "a posteriori understandings". On a related note, we have definitions for things which do not exist in reality so I don't really know why you're insisting on thinking about definitions in that way.

    As I said, logic is not about the consistency of language, but about salve veritate thinking. To save truth, you must start with truth. "All winged horses are horses" is not a truth, but an equivocation. "Winged horses" are not "horses" in the sense living equine creatures, which is the sense of "horses" required by the conclusion. In the same way, there is no true statement in which "the present king of England" is taken as having a substantive reference.Dfpolis


    No. The argument I gave there is *valid* in Aristotelian Logic, having the form: All A's are B's, All A's are C, Therefore some B's are C. It's not an issue of language, you have simply run into one of the issues with Aristotelian logic: it has syllogisms it deems valid but which can take one from true premises ('All winged horses are horses') to false conclusions ('Some horses have wings'). Take up existential import with Aristotle, modern logics don't have this issue.

    It speaks poorly of those who educated you in logic that you are unable to spot so obvious an equivocation. Correct thinking is not about matching letter sequences or manipulating word strings. It is about using conceptual representations rationally.

    Lame insult aside, its clearly not an obvious equivocation given Aristotle created this issue.
  • MindForged
    315
    Not if you're talking about "the world" when you say "reality". If you're an anti-realist about abstract objects then you'll probably think logic in a pragmatic or instrumentalist way. So then logical systems are useful in various aspects of reality but it's not about or part of reality.
  • Blue Lux
    286
    Logic is as it is used, correct? And so it is in a sense about reality, right? Unless... Logic has a mind of its own?
  • MindForged
    315
    No. The use of something is not the thing itself. A tool is not the same as what you use the tool for, to give an example.
  • Blue Lux
    286
    But what would logic be if it were not in its truth its meaning? And its meaning is in its function right? Or am I off?
  • wellwisher
    163
    The left side of the brain processes data using a schema similar to logic; 2-D cause and affect. The right brain uses a different schema that is more spatial. Logic was not invented, but rather the natural data processing of the left brain was made conscious and copied. This is why it feels natural. However, the brain also uses a 3-D schema to complement logic and bring it to higher awareness. Logic, by itself can be half baked. This can be seen within specialization.

    Picture yourself in the woods, where the trees and brush is dense. One can look around and draw logical conclusions based on what it sees. We may even try to extrapolate beyond where the dense forest obscures our view. This may all appear reasonable, but it may be way off base and one may never know if true.

    The 3-D side of the brain is like someone up on the hill looking down at the forest below. They see the bigger picture, but not all the details seen by logic. From the hill one can see the larger patterns in the fauna that can't be seen from below, when one is stuck in a small section of trees trying to extrapolate the larger patterns.

    The brain goes back and forth from the big picture to the little picture to develop the middle from both ends. Human logic tends to stay in the weeds trying to expand outwards. If the theory meets with exceptions, we add a wildcard called random, instead of revise the theories anchored in the weeds. The reason we do this is, humans have yet to develop a collective way to simulate the 3-D side of the brain. The extra dimension is not processed via human language, but rather via a natural language that is felt with subtle sensations and feelings; intuition.

    Development of pseudo 3-D logic could be done via a generalist style education. This is were we learn the basics of many places in the forest; all the specialties, without getting bogged down in the weeds. Then we try to connect all the apparently unrelated specialities, to form a bigger picture. Once the bigger picture is set, this becomes the goal of the specialities. The people on the hill can the patterns below better than those in the weeds. Those in the weeds head toward patterns even if this may not seem logical in the weeds.
  • Pattern-chaser
    208
    The left side of the brain processes data using a schema similar to logic; 2-D cause and affect. The right brain uses a different schema that is more spatial.wellwisher

    You say this like it's accepted wisdom, tested and proven over millennia. But it looks to me like an unjustified assertion, an implication of knowledge that we don't possess. I think there is a great deal more to human brains than you have considered here. And that's before we make the move from brains to minds.... :wink:
  • MindForged
    315
    I don't understand what you're saying. Whatever one thinks about logic, we're going to use it where and when it's useful. We use it to derive truths from other truths.
  • Dfpolis
    156
    Presumably there is only one reality, but we know there are many logics so there seems to be an inherent problem with your definition.MindForged

    There is no problem with my definition. I am not denying that "logic" can have many meanings. I'm specifying the meaning I'm using.

    Namely, the contradiction with having multiple correct ways of thinking about reality based on different, inconsistent logics.MindForged

    I defined what I am talking about as the "science of correct thinking." The "logics" you are thinking of do not study thinking. Mostly, they study systems of symbolic representation and manipulation. So, while they may be correct ways of thinking about various formal systems, they do not study the structure of correct thought, as does classical logic.

    You are simply assuming the Principle of Excluded Middle in your metalanguage and then pointing out how it then appears in the object language.MindForged

    No, I am not.

    First, I am not even discussing language. I am discussing thought that may or may not be expressed in language.

    Second, I am not "assuming the Principle of Excluded Middle." I am finding that, when I reflect on the understanding of existence I have abstracted from my experience of reality, I see that some conjectured state must either be or not be. This is not an "assumption," but a finding. Futher, it is not a finding about about language, or even about thought. It is a finding about reality.

    As I said, this and other Non-classical logics have their own metatheories that make do not accept Excluded Middle.MindForged

    I am not denying that, because I am not discussing systems of symbolic manipulation and their metatheories. I am confining myself to the study of thought, and specifically, thought that is necessarily salve veritate. This requires us to look at the relationship between thought and reality, not the relationship between systems of symbolic manipulation and their corresponding metatheories.

    So, when we apply mathematical or cybernetic algorithms, the reasoning justifying their application is quite Aristotelian.

    I sincerely hope I don't sound rude, but are you kidding me?
    MindForged

    I note that you did not comment on the syllogism I offered in evidence. Is your claim, then, that to apply a principle to a concrete case we do not need to recognize that the concrete case meets the conditions of application? Or perhaps that we can validly apply principles that are not thought of as universal? Or perhaps you want to claim that if the conditions of application can be stated in words that can describe, in another sense, the case at hand, we can still rationally apply the principle to that case?

    Check Newton da Costa's work (based on work by early pioneers in quantum mechanics) about indistinguishable quantum objects. That is, objects that are such that they are *ontologically* indistinguishable (it's not an epistemic limitation), non-individuated objects. Schrodinger himself explicitly endorsed this, hence the old phrase that quantum objects had "lost their identity".MindForged

    You see not to understand the Principle of Identity. it does not make contingent claims about reality, saying, for example that electrons are individually identifiable or even that they are individuals. What is says is: "Whatever is, is." So if it is the case that electrons are not individuated, then that is the case.

    Now, do you have an actual example of a violation of the Principle of Identity?

    Aristotle disagrees with you. He believes there are metaphysical violations of Excluded Middle: contingent statements about the futureMindForged

    I am sorry, but this does not contradict my position, but a confirms it. The reason the linguistic expression of the Principle of Excluded Middle does not apply to future contingents is that they do not exist. Since they have no being, there is no justification for applying a principle founded in our understanding of existence.

    Non-contradiction: The Liar paradox.MindForged

    Again, my position offers a simple solution to the Liar paradox, Jourdain's paradox and other conundrums based on the notion of "truth value." It simply shows that "truth value" is an ill-defined construct. Actual truth, however, is not. The liar who says "I am lying" is making no statement about reality. Therefore, what he says cannot be either adequate to or inadequate to the referenced reality. So, the concepts <truth> and <falsity> have no application.

    The same applies to Jourdain's paradox. You may recall that it is a card that says on one side "The statement on the other side of other card is true," and on the other "The statement on the other side of other card is false." Jointly these sentences make no claim about reality, and so, again, the concepts <truth> and <falsity> have no application.

    So, we see that founding logic in a reflection on being provides us with a simple solution to problems for which, as you point out, "Professional logicians have no standard resolution."

    And if one is, as I am, a Platonist about mathematical and other abstract objects like propositions, one is (as I am) committed the accepting the existence of inconsistent objects from what seems to be an argument from commonly accepting rules for reasoning.MindForged

    I am sorry to see you committed to so many errors.

    No, it is not question begging. It is an experiential claim to which you have provided no counter example or rebutting argument — Dfpolis

    It's question begging. You made the argument that in even assessing e.g. Constructive Mathematics one has to use Excluded Middle because you think it results in an situation where you're... violating Excluded Middle.
    MindForged

    The assertion of first principles is not question begging. Every line of argument, to avoid circularity, must have first principles. That does not mean that those principles cannot be justified. it only means that they they cannot be deduced. They can, for example, be justified by an appeal to experience. My claim, which you refuse to address, is that the principles of being are abstracted, a posteriori, from our understanding of existence.

    You have tried, but failed, to provide counter examples. If you have more to offer, please do so. If you have no more to offer, show how the principles cannot be based on our experienced-based understanding of reality. Claiming that experienced-based knowledge is "question begging" will not do.

    You said this:

    "Thus, these principles are not a priori, not forms of reason, but a posteriori understandings that are so fundamental that once we come to grasp them, we understand that they apply to all being."

    All this really says is that "once you assume my definitions of the relevant terms and their scope of application is global in all possible domains, you'll see they apply to all of reality"
    MindForged

    Note that while my claim addresses what can be known from our experience of reality, your reply fails to address what we can know from experience. it is, therefore, nonresponsive.

    we have definitions for things which do not exist in reality so I don't really know why you're insisting on thinking about definitions in that way.MindForged

    Of course we can't define things into existence. Rather, definitions point to the aspects of reality we're discussing. They suggest that our dialogue partners look in that direction in the hope that they will see what we see. If they do look, and see that we are wrong, they can do us the service of pointing out our error. However, if our partners refuse to look, because they believe there is nothing to see, there is no more we can do.

    The argument I gave there is *valid* in Aristotelian Logic, having the form: All A's are B's, All A's are C, Therefore some B's are C.MindForged

    What you refuse to grasp is that classical logic is not concerned with linguistic forms, but with correct patterns of thought. Aristotle spent a great deal of time pointing out fallacies -- many of which (such as the equivocation in your example) use apparently correct linguistic forms to mask manifestly incorrect thinking.

    Take up existential import with Aristotle, modern logics don't have this issue.MindForged

    That is why they cannot resolve paradoxes such as the Liar and Jourdain's.

    As for Aristotelian existential import being an "issue," make your case.

    its clearly not an obvious equivocationMindForged

    I spotted it instantly. Are you claiming that "horse" is univocally predicated in "some horses have wings" and "winged horses have wings"?

    Also, you have not applied the little you know about Aristotelian logic. You claim to know about existential import in Aristotelian logic. If so, you know that "All winged horses have wings" is false because it lacks existential import. So, you should have seen that not only does your syllogism have an undistributed middle (because of equivocation) but also that its major premise is false.
  • MindForged
    315
    There is no problem with my definition. I am not denying that "logic" can have many meanings. I'm specifying the meaning I'm using.Dfpolis

    And I provided an issue that falls out of using that definition.

    Mostly, they study systems of symbolic representation and manipulation. So, while they may be correct ways of thinking about various formal systems, they do not study the structure of correct thought, as does classical logic.Dfpolis

    You are avoiding the issue though. What defines correct thinking? That is determined by articulating some formal set of rules, i.e. a logic, and arguing that such a system ought to be reasoned in accordance with. And really, there's a reason your conception of logic has fallen out of use amongst logicians. That being that there's a difference between logic (a set of symbols and rules regarding their transformation) and the normative roles we give to a certain set of those rules (the correct rules for reasoning, or if you prefer, thinking). The modern development of logic does not treat that latter definition as the base of logic. I mean as a first observation, people do not think in accordance to the rules Aristotle believed were correct. In fact, humans seem to (reasonably) assume that correct thinking is rather domain-dependent. Classical logic says from a contradiction everything follows and yet it would be impossible to actually reason that way in everyday life (just recall how often you come across conflicting information).

    Second, I am not "assuming the Principle of Excluded Middle." I am finding that, when I reflect on the understanding of existence I have abstracted from my experience of reality, I see that some conjectured state must either be or not be. This is not an "assumption," but a finding.

    A finding which even your own apparent source (Aristotle) disagrees with. And again, reflecting on your own experience does not entail finding a necessity because your experience does not encompass the whole of how reality can be. (this will come up later, so I'm saving it).

    I note that you did not comment on the syllogism I offered in evidence. Is your claim, then, that to apply a principle to a concrete case we do not need to recognize that the concrete case meets the conditions of application? Or perhaps that we can validly apply principles that are not thought of as universal? Or perhaps you want to claim that if the conditions of application can be stated in words that can describe, in another sense, the case at hand, we can still rationally apply the principle to that case?

    Ok, you somehow missed the part of that response where I explicitly responded. I'll summarize: The syllogism you made was followed by you claiming that the justification is Aristotelian. My response was that your argument is valid in basically every logic. Ergo it wasn't resorting to Aristotelian assumptions.


    You see not to understand the Principle of Identity. it does not make contingent claims about reality, saying, for example that electrons are individually identifiable or even that they are individuals. What is says is: "Whatever is, is." So if it is the case that electrons are not individuated, then that is the case.

    Now, do you have an actual example of a violation of the Principle of Identity?

    Ok, this is not an argument on your part. I gave you an example of a (potential) empirical violation of the Law of Identity. Your response was simply to claim that Identity is necessarily true (in the world) therefore my example is off the table because it posits the Law of Identity is only contingently true (only holding for some objects). Again, you are either question begging about Identity being true or else your assuming identity can only be conceived of one way with no debate (which is probably just question begging since, again, people can disagree on the correct account of something). So for instance, we could define Identity such that it applies to some class "M", indirectly limiting what it applies to and yet retaining the principle where it seems to apply.

    If objects are not ontologically individuated, they are not self-identical. To be self-identical is to be (though not the best phrasing) the same as oneself and different than every other thing (to be individuated, essentially). That's what is referred to when Schrodinger was talking about in "Science and Humanism", such objects may if fact lack any ontological individuation and thus have no identity:

    "When you observe a particle of a certain type, say an electron, now and here, this is to be regarded in principle as an isolated event. Even if you observe a similar particle a very short time at a spot very near to the first, and even if you have every reason to assume a causal connection between the first and the second observation, there is no true, unambiguous meaning in the assertion that it is the same particle you have observed in the two cases. The circumstances may be such that they render it highly convenient and desirable to express oneself so, but it is only an abbreviation of speech; for there are other cases where the 'sameness' becomes entirely meaningless; and there is no sharp boundary, no clear-cut distinction between them, there is a gradual transition over intermediate cases. And I beg to emphasize this and I beg you to believe it: It is not a question of being able to ascertain the identity in some instances and not being able to do so in others. It is beyond doubt that the question of 'sameness', of identity, really and truly has no meaning."

    Now I don't care if you accept this as actually being the case (I doubt I would even accept it), but we know that it is at least possible for this to be the case.

    I am sorry, but this does not contradict my position, but a confirms it. The reason the linguistic expression of the Principle of Excluded Middle does not apply to future contingents is that they do not exist. Since they have no being, there is no justification for applying a principle founded in our understanding of existence.

    This might contradict Relativity so I don't see how you aren't just picking and choosing what to accept based on principles that only hold in limited experiences and generalizing them to everything needlessly. It's not obvious that the future doesn't exist, or at least, you've no experience on which to say anything about it.

    Again, my position offers a simple solution to the Liar paradox, Jourdain's paradox and other conundrums based on the notion of "truth value." It simply shows that "truth value" is an ill-defined construct.

    At this point you cannot even use modern logical systems, nor even modern mathematics based on those systems. Most of pure maths don't even have referents in the world by which they could be made "really true" or whatever.

    I am sorry to see you committed to so many errors.

    Says the guy who cannot even accept truth values (and therefore none of modern maths and logic). Cute.

    That does not mean that those principles cannot be justified. it only means that they they cannot be deduced. They can, for example, be justified by an appeal to experience. My claim, which you refuse to address, is that the principles of being are abstracted, a posteriori, from our understanding of existence.

    That's not what you did. When I brought up a possible empirical violation of Identity,you simply claimed that because Identity is not contingent, but rather necessary, the example must be incorrect. Just saying "Such and such are my first principles because they're abstracted from my experience" does not entail they are necessary truths, or indubitable, or whatever. As it happens, your experiences (even ones you may think must be true) can be incorrect or else not justified to the extent that you treat them as applying to everything.

    Note that while my claim addresses what can be known from our experience of reality, your reply fails to address what we can know from experience. it is, therefore, nonresponsive.

    Your claim makes an assumption that from your experience you have found some necessary portion of reality, but note you've given no argument that it is actually necessary or how you know it to be so other than by saying "Upon reflection".

    Of course we can't define things into existence. Rather, definitions point to the aspects of reality we're discussing.

    That's not what I said. Pegasi do not exist. That does not mean I cannot define a meaning for "Pegasi". In fact, given you understand what "pegasi" means you can't really dispute that. Definitions do not always point to actual things, sometimes they just point to ideas or concepts.

    What you refuse to grasp is that classical logic is not concerned with linguistic forms, but with correct patterns of thought. Aristotle spent a great deal of time pointing out fallacies -- many of which (such as the equivocation in your example) use apparently correct linguistic forms to mask manifestly incorrect thinking.

    Classical logic is the logic Frege created in the 1870s, Aristotle used Aristotelian logic. And what you refuse to accept is that the argument I gave is valid in Aristotelian logic.

    That is why they cannot resolve paradoxes such as the Liar and Jourdain's

    Oddly enough, despite no standard solution existing there are many potential solutions to such paradoxes (reworking the T-scheme, using a different truth-bearer besides sentences, etc.). And the Liar-type paradoxes have nothing to do with existential import, because the arguments don't have any quantifiers in them so your response here makes no sense.

    I spotted it instantly. Are you claiming that "horse" is univocally predicated in "some horses have wings" and "winged horses have wings"?

    You seem to have mixed up the point. That being that "All winged horses are horses" is obviously true unless you make the (now discarded) Aristotelian assumption about existential import. Otherwise we have this infinite class of perfectly analyzable statements (in ordinary language) and yet we cannot reason about them meaningfully. And a logic like that is so weak as to be inadequate in modern mathematics. That's why Frege had to invent the theory of quantifiers in the first place, traditional logic wasn't up to the job of parsing out how mathematicians were reasoning.
  • Dfpolis
    156
    I provided an issue that falls out of using that definition.MindForged

    I disposed of.

    Which
    You are avoiding the issue though. What defines correct thinking?MindForged

    I have already said. Let me be more precise: forms of thought that are salve veritate, not accidentally, but essentially.

    That is determined by articulating some formal set of rules, i.e. a logic, and arguing that such a system ought to be reasoned in accordance with.MindForged

    Not quite. It is observing that if you're reasoning, and want the truth of your premises to guarantee the truth of your conclusion, your reasoning needs to reflect the principles of being. Adhering to certain forms is one way of doing this.

    That being that there's a difference between logic (a set of symbols and rules regarding their transformation) and the normative roles we give to a certain set of those rules (the correct rules for reasoning, or if you prefer, thinking).MindForged

    Since you admit there is a difference, between what you call "logic" ("a set of symbols and rules regarding their transformation") and the science of correct thinking, let us agree that what I am discussing is not what you call "logic"

    Let us also agree that mere fact that two areas (correct thought vs the transformation of symbolic forms) differ is not a reason for the study of one to be more in vogue than that of another.

    Classical logic says from a contradiction everything follows and yet it would be impossible to actually reason that way in everyday life (just recall how often you come across conflicting information).MindForged

    From a contradiction, anything does, in fact, follow. And yes, we are told conflicting things. ( I would not call both conflicting statements "information" because they cannot both reduce what is logically possible.) Does the mere existence of conflicting claims warrant treating contradictory statements as equally true? Hardly.

    Do you think that the existence of conflicting claims is new -- that the people of Aristotle's time were not beset with half truths, misunderstandings, rumors, myths and outright lies? If they were, then there is no more reason now to ignore the study of correct thinking than there was when Aristotle taught invented logic.

    Of course if you are not interested in truth, Aristotelian logic can be of little use. I want to be able to deconflict incompatible claims. I see the goal of philosophy as providing us with a consistent, experienced-based framework for understanding reality -- resolving the conflicts you find so overwhelming as to justify giving up on correct thought.

    A finding which even your own apparent source (Aristotle) disagrees with.MindForged

    Please! I've already dealt with this absurd claim.

    And again, reflecting on your own experience does not entail finding a necessity because your experience does not encompass the whole of how reality can be.MindForged

    Of course my "experience does not encompass the whole of ... reality. It does not need to. As with many lacking a adequate background in perennial philosophy, you are confusing induction on the Hume-Mill model with abstraction. Hume-Mill inductions are not reliable because, to reach a universal conclusion, they must add an assumption (that all other cases are like those already encountered), to the data. Abstraction is quite different, It does not add to the data, it removes some notes of intelligibility, fixing on others to form actual knowledge. So, to form our concepts of <being> and <existence>, all we need to do is remove any notes of intelligibility that specify the particularity of the being we are encountering.

    So, it is completely immaterial that we have not encountered all possible beings, or even all actual beings. All that is required to apply our understanding of being is that anything to which we wish to apply it be able to evoke the concept <being> -- and all reality is.

    My response was that your argument is valid in basically every logic. Ergo it wasn't resorting to Aristotelian assumptions.MindForged

    Let's be clear. The syllogism only reflects a valid thought process in words. Aristotelian logic is not about verbal forms. It is about the ways of thinking expressed in those forms. (See Henry Veatch, Intentional Logic.) So, no, the form of thought is not addressed in non-intentional systems of "logic." They only deal with rules of symbolic manipulation.

    I gave you an example of a (potential) empirical violation of the Law of Identity.MindForged

    That is precisely the point. Your example has nothing to do with the Principle of Identity we are discussing. To continue to pretend that it does, after I have shown you its utter irrelevance is arguing in bad faith.

    Your response was simply to claim that Identity is necessarily true (in the world) therefore my example is off the table because it posits the Law of Identity is only contingently true (only holding for some objects).MindForged

    My response was that granting the facts you put into evidence does nothing to show that "Whatever is, is" is false. Please do not distort my position. If it is the case that electrons are not indiviualizable, then it is the case that electrons are not indiviualizable. (BTW, I have no reason to doubt this.)

    Nor is it useful to pretend that the Principle of Identity is something else. I am not following you down a Trumpian rabbit hole, so I am skipping the rest of your comments on identity.

    This might contradict RelativityMindForged

    No, it does not. The Sea Battle (on earth) tomorrow is in the future in all frames of reference.

    Since you brought it up again, her is what Aristotle actually says:
    This is the case with regard to that which is not always existent or not always nonexistent. One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good. — Aristotle, De Interpretatione, 9

    The reason Aristotle give is exactly that I gave, i.e. that because the case is not actual (does not exist) neither proposition can "be either actually true or actually false."

    It's not obvious that the future doesn't exist, or at least, you've no experience on which to say anything about it.MindForged

    You can redefine "exists" if you wish, but doing so will not change what I mean by the term.

    At this point you cannot even use modern logical systems, nor even modern mathematics based on those systems.MindForged

    I do not base the math I use on symbolic logic, as no mathematical system reducible to arithmetic can be shown to be self-consistent. I justify my mathematics by abstracting its foundations from reality -- thus guarantying its self-consistency.

    Still, I wonder why you are not commenting on my simple resolution of the "insoluble" paradoxes, or jumping in with an actual defense against my charge that "truth value" is an incoherent concept. "Cute" is not a counterargument.

    As it happens, your experiences (even ones you may think must be true) can be incorrect.MindForged

    So, you want me to seriously consider that I may never have encountered existence? I'm not following you down that rabbit hole either.

    you've given no argument that it is actually necessary or how you know it to be so other than by saying "Upon reflection".MindForged

    I invite you, and all readers, to make a similar reflection and determine whether or not your understanding of <being> justifies the principles we've been discussing. I can only lead you to the standpoint, orient you, and bid you to look. I cannot put the insight in your mind.

    That's not what I said. Pegasi do not exist. That does not mean I cannot define a meaning for "Pegasi".MindForged

    I was not talking about your example, but responding to your claim that I had made my case true by definition.

    Rather, definitions point to the aspects of reality we're discussing.

    ... Definitions do not always point to actual things, sometimes they just point to ideas or concepts.
    MindForged

    Quite right, they do not always indicate some reality. I was imprecise. I should have said they specify concepts that may or may not be instantiated.

    Still, unless we are discussing ideas or concepts, they do not just point to ideas or concepts. The definition of "Pegasus" is not the definition of an idea, but of a mythical beast.

    Classical logic is the logic Frege created in the 1870s, Aristotle used Aristotelian logic.MindForged

    Yes, symbolic logicians have appropriated "classical logic" for a class of propositional "logics." In some sources, Aristotle's logic is the first example of a "classical" logic," and you have used the term to include the kind of logic I am discussing. ("Classical logic says from a contradiction everything follows.") Still, I don't want to confuse you, so I'll say "Traditional Logic" -- which has a long history of development after Aristotle.

    That said, you have once again pettifogged instead of addressing my point, viz. that traditional logic is not primarily about linguistic forms, but about correct thinking, and the alternatives you raised look no deeper than the surface of formal expression.

    And the Liar-type paradoxes have nothing to do with existential import, because the arguments don't have any quantifiers in them so your response here makes no sense.MindForged

    I did not say the sentence of the Liar paradox had existential import. I said that that the concepts of <truth> and <falsity> did not apply to the sentence because it made no reference to reality.

    Stepping back, you're so dogmatic in your commitments that you will not even discuss the merits of my solution. instead, you employed the Trumpian tactic of raising other issues (T-schemes, existential import, etc) to distract from my proposal.

    "All winged horses are horses" is obviously true unless you make the (now discarded) Aristotelian assumption about existential import.MindForged

    1. No, it is not true. Truth is the adequacy of what is inthe mind to reality, and your claim adequates to no reality.

    2. You were trying to show the outright stupidity of Aristotelian logic, but you could only do so by violating its canons, specifically by ignoring the requirement that Universal affirmative propositions have existential import. That is shabby at best. It is like a high schooler trying to reject algebra by "proving" that 1=2 -- forgetting that there isw a prohibition against divideing by zero.

    Otherwise we have this infinite class of perfectly analyzable statements (in ordinary language) and yet we cannot reason about them meaningfully.MindForged

    Again, you are closed to my fundamental point. Traditional logic is not about sentential or any other form of symbolic manipulation, It is about correct thinking. There is no explicit or implicit contradiction in requiring existential import of universal affirmative judgements about reality. If you think there -- have at it.

    And a logic like that is so weak as to be inadequate in modern mathematics.MindForged

    Thank you for your faith claim.

    1. I've already shown you that you cannot rationally apply axioms without the line of thought reflected by the syllogism in Barbara.
    2. Nothing in traditional logic prevents you from postulating axioms of whatever sort and working out their consequences. The axioms can specify any of the systems of symbolic manipulation that so amuse you. So, understanding how to think correctly can do noting but help you think correctly about the several systems you choose to call "logics."
  • MindForged
    315
    I have already said. Let me be more precise: forms of thought that are salve veritate, not accidentally, but essentially.Dfpolis

    You're not being precise at all. You're simply saying that a certain set of rules are necessarily correct but have no reason for believing so that isn't contentious. Anyone can say that, actually showing it has been my repeated argument against you.

    Not quite. It is observing that if you're reasoning, and want the truth of your premises to guarantee the truth of your conclusion, your reasoning needs to reflect the principles of being. Adhering to certain forms is one way of doing this.

    This is incorrect. Logic is the enterprise of creating a system which preserves truth by not resorting to "principles of being" (which, again, you do not have some inherent claim to the correct principles of being without argument) but to principles of inference.

    Let us also agree that mere fact that two areas (correct thought vs the transformation of symbolic forms) differ is not a reason for the study of one to be more in vogue than that of another.

    This doesn't make any sense. The reason the symbolic side is more in vogue is precisely because the normative role of logic requires first having your inference rules and axioms laid out first. It's exactly akin to having your moral principles laid out before declaring to know the moral status of every act.

    From a contradiction, anything does, in fact, follow. And yes, we are told conflicting things. ( I would not call both conflicting statements "information" because they cannot both reduce what is logically possible.) Does the mere existence of conflicting claims warrant treating contradictory statements as equally true? Hardly.

    If you accept the Principle of Explosion then you do not accept syllogistic logic. In Syllogistic, one cannot derive any arbitrary conclusion from inconsistent premises, e.g.

    Some As are Bs
    No Bs are As
    Therefore, All As are As

    What warrants accepting contradictory claims is that you might well have good reason to believe both and possess no (current) means of picking one over the other. This happens in everyday life (conflicting statements from trustworthy friends) to even science and mathematics (the early calculus was known to be inconsistent, but people just rolled with it for a couple centuries until limits were hammered down). Explosion didn't become standard in logic until Frege created classical logic. That's why Syllogistic is often regarded as a paraconsistent logic.

    So, to form our concepts of <being> and <existence>, all we need to do is remove any notes of intelligibility that specify the particularity of the being we are encountering.

    This is exactly the same problem you make in multiple different ways. People
    Do not form always the same concepts of being and existence.

    Let's be clear. The syllogism only reflects a valid thought process in words. Aristotelian logic is not about verbal forms. It is about the ways of thinking expressed in those forms.

    Aristotelian logic does not map to the "ways of thinking". In fact, probably no logic does to any degree of usefulness (otherwise developing AI would be much easier).

    That is precisely the point. Your example has nothing to do with the Principle of Identity we are discussing. To continue to pretend that it does, after I have shown you its utter irrelevance is arguing in bad faith.

    Yes it does. The particles in question are, quite possibly, not identical to themselves (it's a question of science and not one solved by recourse to abstraction from everyday experiences). To pretend that's not the argument I was making is a lie. Or you just refuse to read the Schrodinger quote again. That's a neat move.

    My response was that granting the facts you put into evidence does nothing to show that "Whatever is, is" is false. Please do not distort my position. If it is the case that electrons are not indiviualizable, then it is the case that electrons are not indiviualizable. (BTW, I have no reason to doubt this.)

    It does show that. If "Whatever is, is" holds for quantum objects as well (take Schrodinger's case of electrons) then they necessarily must be ontologically individuated. If they cannot be individuated, they are not self-identical. This does not mean you cannot say true things about such objects, simply that you cannot say they are identical to themselves.

    Nor is it useful to pretend that the Principle of Identity is something else. I am not following you down a Trumpian rabbit hole, so I am skipping the rest of your comments on identity.

    This is silly and borderline ridiculous. Can people defensibly have different accounts of an idea which goes by the same name? Obviously so, just look at *any* disagreement in terminology. Intuitionists believe classical logicians incorrectly define Excluded Middle for instance.

    This is the case with regard to that which is not always existent or not always nonexistent. One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good.
    — Aristotle, De Interpretatione, 9

    The reason Aristotle give is exactly that I gave, i.e. that because the case is not actual (does not exist) neither proposition can "be either actually true or actually false."

    I'm honestly trying not to laugh because your point doesn't make any sense. I said Aristotle gave this argument as a metaphysical example of where the Law of the Excluded Middle does not apply. Your response is to say that the rules are different there. Well, yea, that's what I was saying. Aristotle does not believe that particular rule applies to potential events in the future. But Aristotle does not assert time negates the application other principles (e.g. Non-contradiction) but that one specifically. So it's not posited as a domain where logic does not apply.

    You can redefine "exists" if you wish, but doing so will not change what I mean by the term.

    Ah the good ol' "My definition is inherently the default one". As a matter of fact, I don't believe I redefined "exists" at all, as the ontological status of the future isn't obvious (whatever you may insist, philosophy doesn't tend to settle such matters).

    I do not base the math I use on symbolic logic, as no mathematical system reducible to arithmetic can be shown to be self-consistent. I justify my mathematics by abstracting its foundations from reality -- thus guarantying its self-consistency.

    I didn't suggest you were a Logicist. My point was simply stated and obvious: if you cannot accept truth-values then you cannot even use modern mathematics. Mathematicians do resort to such formalisms when necessary, and they use these concepts.

    Still, I wonder why you are not commenting on my simple resolution of the "insoluble" paradoxes, or jumping in with an actual defense against my charge that "truth value" is an incoherent concept. "Cute" is not a counterargument.

    I believe I said "cute" in reply to you saying "I'm sorry you are committed to so many errors", which was equally as much a non-argument. Rudeness begets rudeness my friend, and you have a habit of using it and pretending it didn't happen.

    That aside, the notion of truth-value isn't what causes the Liar paradox, it's having a semantically closed language and a language which uses Tarski's T-scheme. You can construct contingent Liar paradoxes by pure reference to real world things (Kripke gives examples in "An Outline of a Theory of Truth", which you can find online (it's on the first few pages)). So even by the criterion you gave it doesn't do anything about the paradoxes.

    So, you want me to seriously consider that I may never have encountered existence? I'm not following you down that rabbit hole either.

    No, I'm saying that "reflecting" upon it does not by virtue of magic entail you have developed an adequate understanding of it. It's not a rabbit hole, it's just not how you do philosophy unless it's with sycophants.

    Still, unless we are discussing ideas or concepts, they do not just point to ideas or concepts. The definition of "Pegasus" is not the definition of an idea, but of a mythical beast.

    Yea, one which we can say true things about. If your definition of truth is just what we can point at and think about correctly then a lot of normal things people says is either nonsense (because we think we're speaking truthfully of non-existent things) or your definition fails so fundamental adequacies (e.g. "All winged horses are horses" should come out as true). I mean, imagine if zebras vanished tomorrow and we then said "Sorry mate, it's no longer true that zebras are black and white because, obviously, there are no zebras anymore!"

    I did not say the sentence of the Liar paradox had existential import. I said that that the concepts of <truth> and <falsity> did not apply to the sentence because it made no reference to reality.

    I've already addressed this point when I brought up contingent, empirical examples of the Liar paradox forming in natural language exchanges (just read the Kripke paper I referenced otherwise this is pointless).

    Stepping back, you're so dogmatic in your commitments that you will not even discuss the merits of my solution.

    No, I ignored the "merits" because the "cost" includes rejecting modern logic and mathematics which make crucial use of the concepts you're dispensing with, not to mention rendering innumerable natural language expressions as mistaken.

    You were trying to show the outright stupidity of Aristotelian logic, but you could only do so by violating its canons, specifically by ignoring the requirement that Universal affirmative propositions have existential import.

    Not the stupidity, the lack of usability. If it cannot even work for expressions such as that then its use of existential import (and the ill-defined notion of "correct thinking") just aren't worthwhile to keep.

    Again, you are closed to my fundamental point. Traditional logic is not about sentential or any other form of symbolic manipulation, It is about correct thinking

    Yes I've addressed this. In doing so it leaves itself unable to do basic reasoning and so as a theory of "correct thinking" it leaves much to be desired. Classical logic, whatever issues I may take with it in certain domains, does not have this issue (and, at the first-order level) is not susceptible to the self-reference paradoxes.

    Thank you for your faith claim.

    Oh stuff it. Without a theory of quantifiers (which we get in classical logic) one cannot, for instance, distinguish between the condition for the continuity of a function and the condition for uniform continuity. The difference is the placement of just two nested quantifiers and Syllogistic has no way to even formalize this. Once Frege had done his work we found out theat hitherto mysterious difference. And that's just one example, doubtlessly historians of logic know others.
  • Dfpolis
    156
    You're not being precise at all. You're simply saying that a certain set of rules are necessarily correct but have no reason for believing so. Anyone can say that, actually showing it has been my repeated argument against you.MindForged

    i am ceaselessly amazed how I can explain my position repeatedly, and spark no glimmer of understanding. You asked "What defines correct thinking?" I defined the term, saying "forms of thought that are salve veritate, not accidentally, but essentially. "Rules." were not mentionde.

    Your reply doesn’t address a word of my response. Instead, you put in my mouth something I did not say. Further:
    1. You didn’t ask for a justification, but criticize me for not giving one here.
    2. I have previously given a justifying argument, but you claim I’ve given no reason for my position. Whether you agree with my reasons or not, saying I have given none is a lie.
    3. In a good faith dialog, the partners do their best to understand one another, asking for clarifications when needed. They then respond, to the best of their ability, to what is actually said. You are not doing me that courtesy.

    Moving on:

    Logic is the enterprise of creating a system which preserves truth by not resorting to "principles of being" (which, again, you do not have some inherent claim to the correct principles of being without argument) but to principles of inference.MindForged

    First, if you "create" a system without foundational reflection, there is no reason to think its principles of inference will besalve veritate. Since truth is the adequacy of our thought to reality, any foundational reflection must include an understanding of reality, of being.

    Second, the principles of being are not my personal discovery, nor are they limited by finite domain of human experience and cognition. Rather, just as our understanding of unity applies to anything that can properly elicit the concept <one>, so the principles of being apply to anything that exists.

    Third, as first principles, they cannot be the conclusion of a more fundamental deduction. Still, we can examine the processes by which we come to them, and I’ve offered such an account. You have chosen not to criticize my account, nor have you offered viable counterexamples to the resulting principles.

    You’ve made hand-waving remarks about the unreliability of human cognition. I could make similar, but substantiated, objections to the beliefs of symbolic logicians – say to Hilbert’s program and its demise at the hand of Goedel. Of course humans make errors. I've made plenty, but the strength of communal research lies in its power to identify errors and correct the processes leading to them. So, if you have a specific criticism of my abstractive justification of the principles of being, please spell it out.

    The reason the symbolic side is more in vogue is precisely because the normative role of logic requires first having your inference rules and axioms laid out first.MindForged

    That is a good reason to begin with an examination of correct thought, as Aristotle did. It is no reason to "create" rules of inference that lack an adequate foundation in human thought or in the reality it seeks to reflect.

    In Syllogistic, one cannot derive any arbitrary conclusion from inconsistent premises, e.g.

    Some As are Bs
    No Bs are As
    Therefore, All As are As
    MindForged

    Your syllogism has an undistributed middle, and the conclusion, while true, is invalid.

    Consider:
    Some Americans are Hispanic.
    No Hispanics are pure Irish.
    We can draw no conclusion linking "Americans" and "pure Irish" from this data, so your "syllogism" is formally invalid. Substituting "American" for "pure Irish" does not make it a valid form.

    What warrants accepting contradictory claims is that you might well have good reason to believe both and no (current) means of picking one over the other.MindForged

    With reasoning like this, no wonder we disagree! Knowing the truth of neither, warrants neither.

    I have no good reason for believing p if I have a good reason for believing ~p. Why? Because reasons for belief do not work in isolation, but in the aggregate.

    The "shaky" foundations of the calculus before the theory of limits was developed is not an example of your claim. No one using calculus in that era doubted that it was a reliable tool. No physicist used it despite thinking it was "false." Mathematicians recognized that its foundations needed work, but did not simultaneously believe it was well-founded.

    Rational people do not accept contradictions. If they can't decide, they suspend judgement.

    Explosion didn't become standard in logic until Frege created classical logic.MindForged

    You mean there was no Principle of Pseudo-Scotus before Frege? In which of Frege's Latin works did he write "ex falso sequitur quodlibet"? Or "ex contradictione sequitur quodlibet? Was it in Die Grundlagen der Arithmetik: eine logisch mathematische Untersuchung über den Begriff der Zahl? Oh, wait, that was in German, like the rest of hie works, wasn't it? Have you read anything about logic before Frege?

    The way people form their concepts of being an existence are not the same.MindForged

    Yes? Are you going to explain?

    Aristotelian logic does not map to the "ways of thinking". In fact, probably no logic does to any degree of usefulness (otherwise developing AI would be much easier).MindForged

    I suggest you read John Poisot's Ars Logica (translated in part as The Material Logic of John of St. Thomas) or Henry Veatch's Intentional Logic.

    Confusing AI, implemented in with instrumental signs infinite state machines, with human thought, which employs formal signs, betrays an inadequate grasp of material logic.

    The particles in question are, quite possibly, not identical to themselvesMindForged

    Really? If that’s what you think, you have completely misunderstood the text. Let's look at it:

    When you observe a particle of a certain type, say an electron, now and here, this is to be regarded in principle as an isolated event. Even if you observe a similar particle a very short time at a spot very near to the first, and even if you have every reason to assume a causal connection between the first and the second observation, there is no true, unambiguous meaning in the assertion that it is the same particle you have observed in the two cases.

    Note that the "identity" being discussed here is not that expressed by the Principle of Identity (“Whatever is, is”) -- which is unitary -- but a binary identity linking two cases. Using one as a counterexample to the other is equivocation.

    It does show that. If "Whatever is, is" holds for quantum objects as well (take Schrodinger's case of electrons) then they necessarily must be ontologically individuated.MindForged

    It does no such thing. "Whatever is" assumes no specific structure to reality. It applies to whatever is actually the case.

    Can people defensibly have different accounts of an idea which goes by the same name?MindForged

    If you mean by “accounts” explanations of the genesis of the idea, then, of course, the same idea can have a different genesis in different people. If you mean essentially different definitions[\i] of the same idea[\i], then no, because essentially different definitions specify essentially different ideas.

    If what you meant to ask was: Can one apply the same name, say “Principle of Identity,” to different ideas, then of course they can. The Principle of Identity in abstract algebra is not the Principle of Identity in ontology. Equating them can only lead to the fallacy of equivocation.

    I said Aristotle gave this argument as a metaphysical example of where the Law of the Excluded Middle does not apply. Your response is to say that the rules are different there. Well, yea, that's what I was saying.MindForged

    No, I did not say the "rule" is different. The "rule" is exactly the same. What is different is that future contingents do not exist, and so fail to meet the conditions of application for the rule -- which applies to all existential situations. This goes to the heart of what I am saying, and what you fail to see -- namely, unless you understand the foundational role of the principles of being, you cannot understand when the conditions of application for logic are met, and when they are not.

    I gave another example earlier, when I showed how simple it was to resolve the Liar and Jourdain's paradox if one understands the dependence of logic on being.

    The particles in question are, quite possibly, not identical to themselves (it's a question of science and not one solved by recourse to abstraction from everyday experiences). To pretend that's not the argument I was making is a lie.MindForged

    I have pointed out that unary and binary identity are different, If you cannot or will not grasp this, there is no point in my pressing the matter further.

    You can redefine "exists" if you wish, but doing so will not change what I mean by the term.

    Ah the good ol' "My definition is inherently the default one"
    MindForged

    Not at all. I am only saying that you cannot claim to rebut my position when you do not use my definitions. If I am talking about the associative property of fields and you argue that there is no such property in a corn field, what you're saying may be true, but it's entirely irrelevant to my position.

    if you cannot accept truth-values then you cannot even use modern mathematics.MindForged

    I do not reject all use of truth values. I simply see that they are not well founded for every well-formed formula. In other words that truth is a prelational, not na intrinsic property.

    Rudeness begets rudeness my friend, and you have a habit of using it and pretending it didn't happen.MindForged

    I admit to being rude to you. When I encounter an uncivil jibe, I sometimes post rude rejoinders. I will try to be more charitable,

    Kripke gives examples in "An Outline of a Theory of Truth",MindForged

    I suppose you are talking about this, from pp. 691f:

    Consider the ordinary statement, made by Jones:
    (1) Most (i.e., a majority) of Nixon's assertions about Watergate are false. Clearly, nothing is intrinsically wrong with (I), nor is it ill-formed. Ordinarily the truth value of (1) will be ascertainable through an enumeration of Nixon's Watergate-related assertions, and an assessment of each for truth or falsity. Suppose, however, that Nixon's assertions about Watergate are evenly balanced between the true and the false, except for one problematic case,
    (2) Everything Jones says about Watergate is true. Suppose, in addition, that (1) is Jones's sole
    assertion about Watergate, or alternatively, that all his Watergate-related assertions except perhaps (1) are true. Then it requires little expertise to show that (1) and (2) are both paradoxical: they are true if and only if they are false.
    — Kripke

    Note that "Everything Jones says about Watergate is true." is not a statement about the reality of Watergate, but one about Jones' statements. Similarly, "Most of Nixon's assertions about Watergate are false," is not a statement about Watergate, but about Nixon's locutions. Thus, it cannot be counted among "Nixon's assertions about Watergate."

    Since truth is the adequacy of our thought to reality, it is not intrinsic, but relational. Thus, not all statements have to be true or false. Some can be non-referential, having no relation to reality. and so neither true not false. Accordingly, if some of the subject statements are non-referential, it is a category error to assert that they are true or false.

    So, Kripke's paradox just like Jourdain's. While either statement here, or in Jourdain's paradox, could be ultimately referential, in the scenario given, they are not. We can confirm this by a thought experiment. If we change anything about Watergate not covered by Jones' excepted statements, the change will not alter the supposed truth or falsity of either Jones' or Nixon's claims. Thus, just as in the Jourdain case, the sentences, considered jointly, are unrelated to reality.

    The fundamental error here is assuming that truth and falsity can be assigned t statements which can't be cashed out existentially. The same principle shows the rationality of requiring universal propositions to have existential import.

    So, you want me to seriously consider that I may never have encountered existence? I'm not following you down that rabbit hole either.

    No, I'm saying that "reflecting" upon it does not by virtue of magic entail you have developed an adequate understanding of it
    MindForged

    I am not claiming to have an exhaustive knowledge of being. My understanding only needs to be adequate to justify the principles of being that underpin traditional logic.

    If you have a supperior way of justifying fist principles, please be good enough to share iit. If you believe my grasp of being to be inadequate, you need only show that one or more of the principles of being implicit in it (as stated -- not as extended by you) is false. So far, you have not.

    Yea, one which we can say true things about.MindForged

    No, one we can say conditionally true things about. The condition is what Aristotle called "the willing suspension of disbelief." If you impose this condition on a premise, then it remains imposed on any dependent conclusion. So, if you want to say "In an imagined world with Pegasi, some horses have wings," I would have no objection. But, that conclusion does not make your case.

    "All winged horses are horses" should come out as trueMindForged

    Only in the dissociated world of symbolic logic where "truth" does not mean adequate to reality.

    "Sorry mate, it's no longer true that zebras are black and white because, obviously, there are no zebras anymore!"MindForged

    Future contingents never had actual existence. Extinct animals had actual existence. We express this with past tenses. So, "Pterodactyls have wings (today)" is not true, while "Pterodactyls had wings (when they lived)" is true. Of course, common language isn't precise, so we have to consider the intention expressed, not just the words used. So, if someone says "Pterodactyls have wings," meaning "One characteristic of being a peterodactyl is having wings," she is speaking the truth, but imprecisely.

    No, I ignored the "merits" because the "cost" includes rejecting modern logic and mathematics which make crucial use of the concepts you're dispensing with, not to mention rendering innumerable natural language expressions as mistakenMindForged

    I already pointed out that this is baloney. There is nothing in traditional logic that prevents anyone from stating a set of axioms and working out their implications. Knowing traditional logic only means that they will be able to bring greater insight to the task.

    So, now that I've taken your fig leaf, and shown that there is no "cost," what is wrong with my solution?

    Not the stupidity, the lack of usability. If it cannot even work for expressions such as that then its use of existential import (and the ill-defined notion of "correct thinking") just aren't worthwhile to keep.MindForged

    So, you you think its "useful" to be able to prove that some living horses have wings? And believe that "salve veritate" thinking is not "worthwhile"? I am trying to be charitable here, but it's not easy.

    Perhaps you have in mind some theorem or empirical finding that cannot be arrived at using traditonal logic? I surely know none.

    Without a theory of quantifiers (which we get in classical logic) one cannot, for instance, distinguish between the condition for the continuity of a function and the condition for uniform continuity.MindForged

    Universal quantification:
    "For all n (a natural number), n has a successor." How is this more or less informative than "All natural numbers have a successor"?

    Existential quantification:
    "There exists an n such that n is q." How is this more or less informative than "some natural number is q"?

    Or lets take a "problem" from the quantification article for Wikipedia:
    1 · 2 = 1 + 1, and 2 · 2 = 2 + 2, and 3 · 2 = 3 + 3, ...
    This sis supposedly problematic because it is infinite. But, it can be stated as a universal affirmative: "All natural numbers are such that 2 times the number is the sum of the number with itself."

    Admittedly, modern notation is far less cumbersome. Still, that is not a problem of principle, but of notation.
  • MindForged
    315
    "What defines correct thinking?" I defined the term, saying "forms of thought that are salve veritate, not accidentally, but essentially. "Rules." were not mentionde.Dfpolis

    You are unbelievable. I, again, repeat: What makes them (let's speak plain english) "correct thinking"? You haven't answered that, you simply said they are not accidentally so, but essentially so. No argument is given, you're just saying they are. Great argument.

    First, if you "create" a system without foundational reflection, there is no reason to think its principles of inference will besalve veritate.

    "Foundational reflection" will necessarily presuppose other principles. In the case of logic, all you'll end up doing is presupposing what constitutes "correct thinking", if it's even defined at all or explained what makes it so. And what do you know, you've done exactly that. There's no reason to think the rules you presuppose in entering such reflection are inherently correct.

    That is a good reason to begin with an examination of correct thought, as Aristotle did. It is no reason to "create" rules of inference that lack an adequate foundation in human thought or in the reality it seeks to reflect.

    The problem is such an examination will require reasoning. And correct reasoning (or form of thought, correct thinking, whatever) already presupposes a set of correct logical rules you are abiding by. You don't get around this by recourse to "reality" (an already contentious concept; people consider many different things part of reality).

    Your syllogism has an undistributed middle, and the conclusion, while true, is invalid.

    That. Was. Literally. My. Point. You claimed the principle of explosion is valid. My response was that it's not valid *in Aristotelian logic*, and I gave an explosive argument in Aristotelian terms but which is not valid because contradictions do not imply anything in traditional logic.

    You mean there was no Principle of Pseudo-Scotus before Frege?

    Interesting how you missed the words "standard logic". I didn't say Frege created the principle of explosion, I said it was not what you might call logical orthodoxy until Frege made it part of Classical Logic. The works of medieval logicians cannot in any way be said to have been the standard logic, ever. By Kant's time they had been lost to history and not even remembered.

    Really? If that’s what you think, you have completely misunderstood the text. Let's look at it:

    When you observe a particle of a certain type, say an electron, now and here, this is to be regarded in principle as an isolated event. Even if you observe a similar particle a very short time at a spot very near to the first, and even if you have every reason to assume a causal connection between the first and the second observation, there is no true, unambiguous meaning in the assertion that it is the same particle you have observed in the two cases. (Schrodinger)

    Note that the "identity" being discussed here is not that expressed by the Principle of Identity (“Whatever is, is”) -- which is unitary -- but a binary identity linking two cases. Using one as a counterexample to the other is equivocation.

    "Two case" as in two cases of observation, not two cases of different objects. Schrodinger goes to pains to make clear that the object is not self-identical despite the reasonable assumption of there being a causal connection between what one observes.

    It does no such thing. "Whatever is" assumes no specific structure to reality. It applies to whatever is actually the case.

    Identity entails that objects are individuated. If some object (or set of objects) lacks individuation conditions, then they are not self-identical.

    No, I did not say the "rule" is different. The "rule" is exactly the same. What is different is that future contingents do not exist, and so fail to meet the conditions of application for the rule -- which applies to all existential situations. This goes to the heart of what I am saying, and what you fail to see -- namely, unless you understand the foundational role of the principles of being, you cannot understand when the conditions of application for logic are met, and when they are not.

    I did not say the rule was different, I said the rules were different. I went on to say that, according to Aristotle (as per your quote), Excluded Middle does not apply to future contingents. Note that which you did not address: In the case of future contingents, we can still reason about them. Aristotle does not say Non-contradiction no longer applies, nor does he say that Identity fails to apply. But that Excluded Middle no longer does. That's why the received view is that Aristotle is suggesting a different logic for such instances, one where Excluded Middle is not a tautology. The primacy of ontology just makes this clear: Future contingents require dropping Excluded Middle to reason about them, but we keep the other rules to think correctly about them. So correct thinking, even on your view, is not captured by one set of rules or a single set of ways of thinking.

    I do not reject all use of truth values. I simply see that they are not well founded for every well-formed formula. In other words that truth is a prelational, not an intrinsic property.

    You earlier referred to them as an "incoherent concept". Anyway, I don't really get this. It's a common view that liar-type sentences are not well-formed, not that truth-values are not well-formed.

    Note that "Everything Jones says about Watergate is true." is not a statement about the reality of Watergate, but one about Jones' statements. Similarly, "Most of Nixon's assertions about Watergate are false," is not a statement about Watergate, but about Nixon's locutions. Thus, it cannot be counted among "Nixon's assertions about Watergate."

    Statements that people make are real. Statements made about other statements are common, e.g. "You're lying" or "Your words are untrue". But in this case, I've no idea how you came to that conclusion. If Jones only says Nixon is mostly lying about Watergate, and Nixon says everything Jones says about Watergate is true, then the issue is these cannot be jointly true and yet they *entail* each other. If your issue is just that it's about a locution (which in turn is about Watergate) then that's easily remedied:

    1) Jones: Most of what Nixon says about Watergate is false.

    2) Nixon: Everything Jones says about Watergate-related issues is true.

    The paradox is the same (what Jones says about Nixon watergate claims counts as "Watergate-related", surely).

    I am not claiming to have an exhaustive knowledge of being. My understanding only needs to be adequate to justify the principles of being that underpin traditional logic.

    You went beyond that, you said your understanding was sufficient to claim (as you did) that the principles are true essentially, rather than accidentally. My point is your experience doesn't generate anywhere near the justification for that. Experience is fine for generation provisional assumptions that go into your logic, but that's not what you've argued for. You think there is one correct way of thinking and that traditional logic corresponds to that thinking (correct me if I'm mistaken).

    No, one we can say conditionally true things about. The condition is what Aristotle called "the willing suspension of disbelief." If you impose this condition on a premise, then it remains imposed on any dependent conclusion. So, if you want to say "In an imagined world with Pegasi, some horses have wings," I would have no objection. But, that conclusion does not make your case.

    With the lack of conditionals in traditional logic I'm not even sure this is consistent with the logic being proposed. I mean, there's even a bit in Prior Analytics where Aristotle considers a conditional but deems it not a syllogism despite the conclusion following necessarily. But I'm not even sure how your example works. An imagined world is by definition non-existent so how are you reasoning correctly about it? After all, the principles which apply to existing things is not supposed to apply to that which has no being.

    There is nothing in traditional logic that prevents anyone from stating a set of axioms and working out their implications. Knowing traditional logic only means that they will be able to bring greater insight to the task.

    What I was saying was that if we take your view that truth-values are an "incoherent concept" (as you said), then modern maths/logic are not usable because they make crucial use of this and other concepts (conditionals), and dispenses with aspects of traditional logic (existential import is not assumed in quantifiers). And I don't see how traditional logic has done anything to further knowledge in these areas, it's mostly a curiosity post-Russell (Frege was mostly obscure, sadly).

    So, you you think its "useful" to be able to prove that some living horses have wings? And believe that "salve veritate" thinking is not "worthwhile"? I am trying to be charitable here, but it's not easy.

    No. It was an example of a type of reasoning which ought to be invalid as logic rightly concerned with forms of argument which always preserve the truth. In the traditional case, it only meets this criterion if we only talk about what we know to be true about reality, so it's application to hypothetical and mathematical cases becomes less useful.

    Perhaps you have in mind some theorem or empirical finding that cannot be arrived at using traditonal logic? I surely know none.

    I already pointed out examples of what I was talking about (e.g. uniform continuity vs continuity of a function).

    Or lets take a "problem" from the quantification article for Wikipedia:

    The problem the Wiki article mentions doesn't seem to have anything to do with the logic, but that syntactic rules are expected to be finite. Traditional logic had no theory for the quantifiers it used, the quantifiers weren't detachable, and that's in part why its application to mathematics was so limited and thus Frege had to develop a new logic. Prior, until the medieval logicians there was no real understanding of them, and even the medieval logicians treated quantifiers sort of like names. Frege made them clearer by making them a new kind of linguistic object.

    Put it this way. Mathematicians did not commit themselves to instantiating every object they reason about in mathematics, even before classical logic was created. Making sense of this is a bit part in why Frege created classical logic, because the mathematicians were clearly not assuming existential import in quantifiers the way traditional logic requires.
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