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
Logic is a statement of fact/in relation to fact. If there is any error, it cannot be logic/logical. — BrianW
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
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
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 them — Dfpolis
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
Identity violations: See non-reflexive logics and quasi-set theory. — MindForged
statements like "so fundamental that once we come to grasp them, we understand that they apply to all being" are just question begging. — MindForged
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
All winged horses are horses.
All winged horses have wings.
Ergo some horses have wings. — MindForged
If logic is not about reality... Then it is? Imagination? — Blue Lux
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
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
So, when we apply mathematical or cybernetic algorithms, the reasoning justifying their application is quite Aristotelian.
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
No, it is not question begging. It is an experiential claim to which you have provided no counter example or rebutting argument — Dfpolis
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
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
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.
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
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
Namely, the contradiction with having multiple correct ways of thinking about reality based on different, inconsistent logics. — MindForged
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
As I said, this and other Non-classical logics have their own metatheories that make do not accept Excluded Middle. — MindForged
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
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
Aristotle disagrees with you. He believes there are metaphysical violations of Excluded Middle: contingent statements about the future — MindForged
Non-contradiction: The Liar paradox. — MindForged
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
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
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
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
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
Take up existential import with Aristotle, modern logics don't have this issue. — MindForged
its clearly not an obvious equivocation — 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. — Dfpolis
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
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.
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?
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?
"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."
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.
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.
I am sorry to see you committed to so many errors.
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.
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.
Of course we can't define things into existence. Rather, definitions point to the aspects of reality we're discussing.
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.
That is why they cannot resolve paradoxes such as the Liar and Jourdain's
I spotted it instantly. Are you claiming that "horse" is univocally predicated in "some horses have wings" and "winged horses have wings"?
I provided an issue that falls out of using that definition. — MindForged
You are avoiding the issue though. What defines correct thinking? — MindForged
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
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
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
A finding which even your own apparent source (Aristotle) disagrees with. — MindForged
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
My response was that your argument is valid in basically every logic. Ergo it wasn't resorting to Aristotelian assumptions. — MindForged
I gave you an example of a (potential) empirical violation of the Law of Identity. — MindForged
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
This might contradict Relativity — MindForged
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
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
At this point you cannot even use modern logical systems, nor even modern mathematics based on those systems. — MindForged
As it happens, your experiences (even ones you may think must be true) can be incorrect. — MindForged
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
That's not what I said. Pegasi do not exist. That does not mean I cannot define a meaning for "Pegasi". — MindForged
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
Classical logic is the logic Frege created in the 1870s, Aristotle used Aristotelian logic. — MindForged
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
"All winged horses are horses" is obviously true unless you make the (now discarded) Aristotelian assumption about existential import. — MindForged
Otherwise we have this infinite class of perfectly analyzable statements (in ordinary language) and yet we cannot reason about them meaningfully. — MindForged
And a logic like that is so weak as to be inadequate in modern mathematics. — MindForged
I have already said. Let me be more precise: forms of thought that are salve veritate, not accidentally, but essentially. — Dfpolis
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.
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.
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.
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.
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.
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.
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 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."
You can redefine "exists" if you wish, but doing so will not change what I mean by the term.
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.
So, you want me to seriously consider that I may never have encountered existence? I'm not following you down that rabbit hole either.
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.
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.
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.
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
Thank you for your faith claim.
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
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
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
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
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
Explosion didn't become standard in logic until Frege created classical logic. — MindForged
The way people form their concepts of being an existence are not the same. — MindForged
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
The particles in question are, quite possibly, not identical to themselves — MindForged
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.
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
Can people defensibly have different accounts of an idea which goes by the same name? — MindForged
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
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
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
if you cannot accept truth-values then you cannot even use modern mathematics. — MindForged
Rudeness begets rudeness my friend, and you have a habit of using it and pretending it didn't happen. — MindForged
Kripke gives examples in "An Outline of a Theory of Truth", — MindForged
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
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
Yea, one which we can say true things about. — MindForged
"All winged horses are horses" should come out as true — MindForged
"Sorry mate, it's no longer true that zebras are black and white because, obviously, there are no zebras anymore!" — MindForged
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 — MindForged
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
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
"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
First, if you "create" a system without foundational reflection, there is no reason to think its principles of inference will besalve veritate.
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.
Your syllogism has an undistributed middle, and the conclusion, while true, is invalid.
You mean there was no Principle of Pseudo-Scotus before Frege?
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.
It does no such thing. "Whatever is" assumes no specific structure to reality. It applies to whatever is actually the case.
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 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.
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."
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.
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.
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, 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.
Or lets take a "problem" from the quantification article for Wikipedia:
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.