Is logic undoubtable? What can we know for certain?
I couldn’t find another topic about this, I hope I’m not redundant
My question for you is: can we be certain that the laws of logic are valid? Or is logic to be taken as an absolute a priori?
What I am trying to say is that many ethical beliefs can be logically deemed ideas taken as true without any rational thinking (if I say that all man are equals, I am expressing essentially a belief and not a certain thing) and that, i believe, is the base of every kind of relativism (we cannot know for certain that killing is wrong or that helping people is good, we just believe they are) yet, whenever we think or we doubt something we cannot do it without the laws of logic.
Can we, so to say, ”trust” the laws of logic? Are they absolute or rather just to be taken as if they were?
And my second question for you is: can absolute relativism be logically acceptable?
Taking the laws of logic as true, is it possible to consider everything relative without contradiction? I mean, if I say that ”everything is relative”, then the fact that ”everything is relative” is not relative anymore, it is absolute, and if I say that even that is relative, so that ”even that everything is relative is to be considered as relative” I’m still considering the relativism of the relativism of everything as absolute, thus contradicting myself.
I sincerely hope you understand my questions, I tried my best and I’m not a native speaker.
I’ll be waiting for your answers
Have a nice day
My question for you is: can we be certain that the laws of logic are valid? Or is logic to be taken as an absolute a priori?
What I am trying to say is that many ethical beliefs can be logically deemed ideas taken as true without any rational thinking (if I say that all man are equals, I am expressing essentially a belief and not a certain thing) and that, i believe, is the base of every kind of relativism (we cannot know for certain that killing is wrong or that helping people is good, we just believe they are) yet, whenever we think or we doubt something we cannot do it without the laws of logic.
Can we, so to say, ”trust” the laws of logic? Are they absolute or rather just to be taken as if they were?
And my second question for you is: can absolute relativism be logically acceptable?
Taking the laws of logic as true, is it possible to consider everything relative without contradiction? I mean, if I say that ”everything is relative”, then the fact that ”everything is relative” is not relative anymore, it is absolute, and if I say that even that is relative, so that ”even that everything is relative is to be considered as relative” I’m still considering the relativism of the relativism of everything as absolute, thus contradicting myself.
I sincerely hope you understand my questions, I tried my best and I’m not a native speaker.
I’ll be waiting for your answers
Have a nice day
Comments (88)
My opinion is logic isn't perfect. It can't fully describe our experience. I think it's safe to say that classical logic ran into trouble in quantum physics. There are, I daresay, a lot of weird (read ''illogical'') stuff going on in the quantum world. With classical logic only we'd be forced to deny many quantum-level ''facts''.
This is a very difficult position for those who must face it. Do we reject fundamental laws of logic like the law of noncontradiction or do we reject the results of quantum experiments?
Logic still needs a lot of work. Perhaps there is no ONE system of logic that'll work in ALL situations. We may need to develop different systems for different situations or issues. I think that's the general direction of efforts in logic.
Also, your paradox about ''everything is relative'' applies here because you seek evidence that will show you that you can trust logic. Isn't that already trusting logic? I mean to ask for justification for logic you're pre-assuming logic to be jusified.
Id you were to deny logic any trust then even that would require justification. It's a vicious cycle.
Logic: Is an extrapolation of how we think about relations; there are different species of logics, with incompatible axioms, etc.
Ethics: ethical foundations have nothing to do with logic and ethical utterances are not true or false.
Is it not true that, in order to achieve scientific progress, and knowledge in general, that a certain morality is required? A society cannot progress towards the truth unless they value it, and are open to change and willing to subject their ideas to criticism.
If you value truth, then there are objectively better ways to act.
As for the other subject I think you raise an interesting issue, since you said that classical logic ran into trouble because of quantum experiments results (and I assume you are referring to the particle wave duality and its implications) I want to ask you: do you think that logic (and if you want philosophy itself) should submit to scientific results?
Because I think there would be a bit of stuff to deal with.
I’m referring to the fact that science holds many philosophical ideas as true and proceeds without explaining them, for example science believes there is something outside thought, which, philosophically, is not certain at all. So, the implications of scientific experiments, which rely on philosophical concepts, can be used to change those philosophical concepts?
P.S. Don’t worry, I’m not trying to prove quantum physics wrong, I’m just asking.
Yet, I sincerely don’t understand what your point is with the different and incompatible logics.
Besides, for scientific progress (which I believe you think as ”good”) a lot of things we generally don’t see as moral has been done.
If you value knowledge, then only certain moral systems will support that value. Are they objectively good? I'm not sure that question is answerable. Are they objectively better? They are, in exactly the same way that General Relativity is better than Aristotle's theory of gravity.
I don't know if you are familiar with Rene Descartes but I based my questions mostly on his solutions.
But if you were trying to say that if you want X you need to do Y, then I agree with you.
P.S. You mentioned gravity, but what if there is nothing outside thoughts and everything we experience is an illusion? What if I don't exist?
Aristotle and Einstein would have wasted their time on an illusion
Depends on what is meant by logic.
If by logic we mean rationale or reason then it becomes subjective and dependent on perspective. This is because we can rationalize or reason out anything depending on the factors we give precedence to over others (priority), or in accordance with how we evaluate significance and meaning.
If by logic we mean the principles which govern the working of reality, then we refer to laws which are absolute in their unity and harmony and which cannot be transcended (altered or undone) by any phenomena because they are strict and unyielding in their domains.
Then, where would the thoughts and illusions exist?
As BrianW stated above:
What do you mean by logic?
It has various incarnations such as:
Syllogistic logic
Propositional logic
Predicate logic
Modal logic
Informal reasoning and dialectic
Mathematical logic
Philosophical logic
Computational logic
Non-classical logic
I find it a bit difficult to handle each of these fields of logic as a one size fits all general notion called logic.
Meow!
G
Even if I were to look at reality with the eye of an empirist or a materialist I'd still have a hard time calling "unyielding" quantum physics.
But by logic I was referring to classical logic, Aristotle's laws, for example, A is A, A is not B and there is not a third option, tertium non datur, and the recent addings like De Morgan's work.
Should have been more precise then, my bad
Certainty in knowledge is impossible, worthless, and damaging. What you are seeking is an authority, to certify certain truths. There is no such thing.
We are saying that A is A and also B, but it cannot be anything else
Not explicitly. I used "the principles which govern the working of reality" because reality applies to everything that is, regardless of conditioning.
I believe the laws of logic as derived by Aristotle to be valid and comprehensive. They are:
Quoting Towers
Then in what sense do they exist, and how do they relate to a Plato who also has a material presence?
I believe the significance of the materiality or immateriality of objects/subjects is dependent on their practical value. That practical value can make immaterial factors to be empirical and material factors to be theoretical. For me, the conditioning does not exclude the unity of everything just like in our lives we employ both the material and immaterial.
How do you know that?
So basically it sounds as if you are concered with how we have such things as Modus ponens and other valid arguments (inference)?
If so, in this case I'd say you can use a truth table to justify it.
Modus ponens p ? q
The other rules of inference follow that same sort of means of validation. It's not all too difficult to justify them as reliable tools with which one can infer conclusions and such. Perhaps the application of these tools of logic is another kettle of fish.
Meow!
G
By practical I mean having utility or being functional, and both the material and immaterial have proved to be that.
Quoting Towers
I find that logic to work in all cases.
Meow!
G
As far as I know the laws of logic, the rules of syllogisms, an introduction in deduction and induction are not taught in primary school, and because of this I think a lot of people don't know how to reason or use logic well.
Personally, I run into problems that logic has. But if you know modus ponus, for example, you can reduce the errors in your logical thought processes. If you didn't know them however, logic could lead you into confusion and conclusions that are not substantiated by deductive validation.
I really do think if we gave primary school classes on logic there would be less religious participation. This is of course a hypothesis, a logical argument on its own. Our logic skills correlated with religiosity? I digress.
I did enjoy reading the ideas of some people here about non-classical logic. I will not get into that in this reply.
Just imagine how different things would be if indeed these were taught and we included an understanding of logical fallacies (such as argumentum ad passiones or hasty generalizations)?
I somehow think Facebook and Reddit would be far less of an addictive frustrating entertainment. ;)
Meow!
G
Anyway the A is A and not B is a bit of a deal with Quantum physics, like ThaMadFool said before, how do we fix it?
Right.
Quoting Towers
I haven't met any deal to speak of.
My point is that in everyday life we use logic to understand relations of events, the road's wet so it must've rained and if it is very cold outside lakes will freeze. So, if we are presented a relation of events that does not follow that pattern we call it wrong, if you touch ice you do not get burned (I realize these are terrible examples but they'll do)
But you can never use logic on logic, to prove it right nor wrong so can we trust it? And how do we know? Is logic the correct instrument to measure the world around me, if it exists?
What are the limits of it?
My second point, the one you didn't understand was only about trusting logic as an absolute tool a priori, without explanation, as I believe that we cannot express thoughts without one absolute at least.
This is very confused, sorry, I hope you understand
The law of identity just states that A is A. The law of non-contradiction states that A is not and cannot be Not-A (the Not-A could be anything from B to Z as long as it's not A). The law of excluded middle states that A is A and cannot be Not-A, or anything in between. As far as I'm concerned there is no sense of conflation.
- https://en.wikipedia.org/wiki/Wave–particle_duality
Therefore, from A is A, we get quantum entity=quantum entity. The conditioning does not alter the identity. Also, the only problem in that query is the means of defining a quantum entity. They (quantum entities) are and have always been what they are. That we can't distinctly determine their nature does not mean they're illogical, only that our methods thus far have not been successful.
But still, my point was, apart from trusting logic, which still is a question to me, what can we know really?
Can we reduce our knowledge without answering "because yes" to something and stopping there?
We don't really know much, we believe
Everything I know starts with "I" and then "I AM". I may not know everything about myself but the only certainty I have is that "I" am, regardless of whether the nature of my existence is real or illusion. My knowledge is just a relationship between my experience of "I" and that which is not "I". For me, logic is just the path of least chaos or the tool of best fit, so I trust it implicitly.
If I had said something like that, which I have before because I think it’s true, I would have used a few dozen more words, which wouldn’t have made it any better.
This needs to be disambiguated otherwise it's not coherent to my ears. Validity is a property of a logical *system*, not to the axioms of that system. Validity, roughly speaking, refers to the set of possible argument forms that can be made given some set of logical rules, known as the logical consequence relationship. Now, perhaps by 'valid' here what you mean is "true". But that's not the domain of logic at all, logic stands independent of truth. We know there are lots of logical systems: Classical logic, intuitionistic logic, Paraconsistent logic, many-valued logic, etc etc. Asking if any of them are "true" is something you need to thing about making sense of first before asking that question.
What would it mean for a logic itself to be true? To me that's either an incoherent suggestion or else it has to mean something about the structure of a universe mapping on to the abstract relationships sketched out by some particular logic. And the latter of those is necessarily relative to a specific world anyway. There's really nothing a priori here. But what should be clear is that in any case logic and (physical) reality are not about the same thing. It's a case of the abstract vs the material.
Quoting Towers
Trust them how? The logical consequence relationship is an abstract object and that by definition can't change, whether you understand logic semantically or syntactically. That seems a pretty good thing to trust, as it's not like it can randomly change or something. "Absolute" is a term I would avoid here. There's way too many things that can be taken to mean and most of them wouldn't be true.
Quoting Towers
Logical consequence is already defined relatively. An argument is relative to a set of logical rules specifying which Propositional transformations can be performed. Intuitionistic logic does not permit double negation elimination while classical logic permits it. The issue you're running into is a failure to state things correctly. I wouldn't necessarily say "Everything is relative", but in this context I would say "Every valid argument is relative to a set of rules specifying them as valid". That's a true statement and doesn't create any contradictions because I'm not saying every statement is relative or something off like that.
Quoting Towers
One should note that Aristotle did not use classical logic, he created and used Syllogistic logic. Classical logic is a poor name because it was created in the 1870s by Frege and considers a different set of arguments to be valid than what Aristotle did, so they are different logics for sure.
But I think you misunderstand my question, maybe my level of English is not as good as it should be for this, I only meant to bring about a question that may be wrong in its own roots:
Whatever logic you may want to refer to, whatever you prefer to use or even whatever you want to call it, how do you know it is the best tool to analyze relations between things?
I mean, putting aside names and even concepts, whenever you formulate thoughts you must use some kind of logical process, right? Any kind, Jack is a boy, therefore he is not a girl.
So, for those who say that endless logics work on endless different system, which one is to use when?
Because by saying that neither of us can be nor wrong nor right because everyone uses a logic that suits his system and this whole thing makes no sense at all.
For those who say that classical or Syllogistic logic is the one, how do you know?
Most of you agree that there is nothing absolutely true, ontologically I mean, like God for the Christians or The Idea of Good for Plato, yet logic works always and it is always right, thus absolute, how is that? You believe it is.
In regard to the second question, I see no problem with the logic of absolute relativity. Perhaps there are absolute truths, it is even likely... But how can knowledge of them be claimed by fallible logic?
If they're incompatible then we're obviously not dealing with certainty for them.
Try to imagine any situation that violates the law of non-contradiction. My sense is that I just can't do it. I can't even understand what A and NotA both obtaining is supposed to involve. Some people say that various physics results should be interpretted as involving such a situation, but I think even the people who defend that interpretation will admit that they have absolutely zero idea what it means. I think it is unintelligible, and won't be made any more intelligible by inventing pretty new logical symbols and defining their relations to other symbols.
Non-contradiction is, in that way, a necessary condition of intelligible thought. Of course you can invent abstract systems that violate it, by defining various symbols in various ways, but substitute symbols for actual concrete things and what you get is meaningless.
PA
Yes, even the law of non-contradiction can be intelligibly doubted: see Dialetheism
The a priori status of logic has been under attack for quite some time (as you can see above, even the sacrosanct non-contradiction is not safe). This is true even of the so-called "laws of thought," which is what you must really mean when you talk about logic, because formal or mathematical logic is as diverse and open-ended as mathematics.
I don't need to invent new symbols or anything to give a semantics to a logical system which, yes, intelligibly violates Non-contradiction. Let's note something first. Define what you mean by "intelligible" here in a non-question begging way, such that it's not just a substitute for "consistent". Otherwise all you're saying is that an inconsistency has to be inconsistent, which, well, yes.
Now, just take the standard, classical propositional logic and make the following modifications. Drop (or in some way weaken) the Disjunctive Syllogism inference that way the Principle of Explosion is no longer a valid argument. Then, replace the truth-functional semantics with truth relational semantics. What this means is that instead of a proposition relating to only one truth value they can relate to any number of them. Thus, a true contradiction (that is, a proposition which is true and has a true negation, a dialetheia) is simply some proposition P such that P relates to the value 'true' and P relates to the value 'false'. This is perfectly mathematically coherent and uses well understood math (hell, relations are used in everyday language as well).
Semantics don't stand independently of a logic but are created to understand, so it would be more than silly to say the above is meaningless. Forget physics, I've no idea if such Paraconsistent logic and dialetheism will ever be used there. Maybe to solve the Liar paradox, or the vagueness paradoxes, or for alternative set theories, or perhaps for some fundamental ontology or mereology if you want something metaphysical (particularly when discussing the concept of nothingness). There's possible uses, but whether or not these uses pan out has nothing to do with a circularly defined notion of intelligibility. There's no such thing as an indubitable logical axiom, or one which contravening entails unintelligibility. Perhaps if it entails trivialism then we can dismiss it but that's why Paraconsistent logic exists, so that potential violations of the LNC do not entail that every proposition is true.
Haven't you shot yourself in the foot?
After all, providing reasons (in this case to prove logic is untrustworthy) means you already trust logic to do its job of finding the truth.
Perhaps that's the beauty of logic, right? It doesn't exempt even itself from its courts.
Note that @PossibleAaran said that the idea of A and not-A obtaining is unintelligible. This follows Aristotle's use of the LNC as a rule for thinking about the world.
Per physics, it's possible for an electron to be in a quantum superposition of spin up and spin down. But the term "superposition" has a clear mathematical meaning and there is no implication that the electron is in a contradictory state.
It is really the idea of contradictory states obtaining in the world that is unintelligible (so it seems to me).
I don't see this. If one has a coherent but inconsistent logic with the appropriate semantics, and they have a theory about the world which best explains the data which requires reasoning by that logic, then it seems to me there would a case for intelligibly understanding inconsistent states of the world.
I'm not saying this is actually the case. As far as I can tell, since physics uses the standard math formalism it's going to necessarily make use of the underlying logical principles there so contradictions cannot be intelligibly added because it would result in trivialism. But that's a case of the logic and theory causing that, not whether or not the LNC necessarily applies to the world itself.
Suppose you have a logic that could represent a switch that is both on and off in the same sense and same respect. Can you visualize or simulate a scenario where such a switch would operate? That is the test of intelligibility. It seems to me that that exercise would require changing how the switch is represented such that its states were consistent.
An analogue of what you're asking however has been suggested by Newton da Costa as a potential interpretation of superpositions as being potential contradictions (though this is difficult to understand for me and seems to require a deep dive in QM formalisms that I cannot do).
So let's take an easier approach. I take it for granted that people can (and most often do) have inconsistencies in their set of beliefs (one's internal maps of where things are located are often inconsistent with other such mental maps, for example). Take the hypothetical switch you mention and put it under the control of a reasonably advanced A.I. which tracks the behavior of a hypothetical person with an inconsistency in their beliefs. Presumably this switch would operate once such a scenario was observed when a person was mistakenly operating under these contrary beliefs. The switch then, could be represented by three states. 0 for false, 1 for true and 0.5 for both. If the A.I. determines the subject is showcasing their inconsistent beliefs 0.5 would be the value indicated when queried.
Or are you asking the switch to be an inconsistent physical object? I'm not sure the representation of the logic is supposed to have all the same properties of the formal system. By way of example, standard computers do not instantiate the exact model of classical logic since classical predicate logic has a model that is infinite, where clearly no actual machine can be made to represent that.
Yes smart people deny the law of non-contradiction, but even they do so only because it solves certain paradoxes and not because any of them can imagine any concretely obtaining contradiction. When it comes to thinking concretely about the world, and not about abstract formal systems, my sense is that there is just no choice but to think under the law of non-contradiction. It is indubitable in that sense, whatever we say about the liar paradox.
my reply to your post is the same as Andrew M's, so I'll move to your latest post if you don't mind.
Andrew asks us to imagine a switch which is both on and off at the same time, which I think is plainly inconceivable, as he notes. But your example is much more complex.
I take it that your aim is to describe a conceivable situation where a contradiction obtains. I'm not sure your example is really detailed enough. How does the switch work? The switch is hooked up to a person's brain and tracks their inconsistent beliefs. What exactly is the switch reporting? It "operates once a person is operating under contrary beliefs". Does that mean that the switch reports "true" when the person is operating under contrary beliefs? If so, why would the switch show 0.5? I don't get it. In any case, suppose that the switch does report 0.5. Where is the contradictory state of affairs? We have a person who has two different beliefs that contradict one another. Having the belief that A and the belief that -A is not a contradictory state of affairs, any more than having a blue pillow and a red pillow is. We also have a switch that is reporting "0.5", and that isn't contradictory either.
Regarding the charge that I used a question beginning notion of intelligibility, I didn't. Say that something is intelligible if and only if you can conceive how it would be.
PA
I can demonstrate what might be called psychological inconsistency, for example by holding a self-negating belief, such as "This sentence is false. Therefore it is true. Therefore it is false... etc", but this isn't any different from writing {-1, 1, -1, 1,...} as a consequence of iterating the equation x(t+1)=-x(t) starting from x(0) = -1.
This is hardly what one might call the semantics of logical inconsistency, which requires two incompatible statements to be held simultaneously. But this isn't imaginable by definition. At most, I can imagine a driver encountering two signposts for a town which point in opposite directions, and him being unable to make a decision. Or two people disagreeing as to which word applies in a situation. Or a computer program failing a software test.
So logical inconsistency at most refers to a syntactical convention of communication of which nothing else needs to be said. It has no significant implications.
Sort of. As I said, I don't take it as controversial that people have inconsistent belief sets. What is the switch reporting? Well let's make it simple. Say the subject reports believing some business is located in certain location relative to their home and they draw a map of how to get there. They believe the locations are correct. Now they repeat this drawing of different maps to different locations and again voice their belief that they are correct. But say some of the maps are inconsistent with others because they place various locales in slightly wrong locations, such that the maps cannot all be take to be true. Whatever program is combing through these maps will reach this contradiction and when queried about some business being at a particular location will throw out the value 0.5 since the underlying logic is three valued (this is essentially the logic underpinning the database language SQL, although it's not really for contradictions). Its not true that the location is correct because one map says it isn't, but it's true that it's there since another map says it is. So to resolve this in a normal computer it's easier to throw out that value rather than try to continue the computation.
Now, the reason I said "sort of" is because this isn't necessarily a physical contradiction because this is about ones knowledge. But it's hard to say because if one is a physicalist I'm not sure how one talks about sets of beliefs in the mind. Is it contradictory because it's in the mind? I don't know. But the point is that switch would operate in this case, whether or not the contradiction is a bona fide physical one. The machine implementing the logic need not have contradictory properties .
Quoting PossibleAaran
Are sets of beliefs not in the mind? The comparison to differently colored pillows isn't a legitimate comparison, they are not the same object. I take beliefs to be part.of the mind, and so if there's an inconsistency in ones beliefs (as there likely always is) then there's an inconsistency in the mind.
Quoting PossibleAaran
That's not really explaining what you mean though. Is conceivability defined in terms of consistency? If so, it's question begging for the LNC. If conceivability is defined in terms of mental pictures, that's not going to work since lots of actual states of affairs cannot be pictured and mathematics has it's own notion of conceivability (basically deduction). Conceivability needs to be defined minimally in terms of logical deduction used to understand a concept (or something like that), and that's just as available to inconsistency-tolerant logics as consistent ones. Paraconsistent logics have their own model theories that have contradictions in the metatheory.
Even if this is true it's not going to be a sufficient refutation of giving semantics to inconsistency. I cant visualize the expanse of a million miles, only a tiny scale of it. I can't visualize something infinite, much less point at it (perhaps space and time). But these are surely not refuted from possibility on that basis.
Quoting sime
That's not true. For one, the liar paradox is, well, a paradox. In other words, it is not the bald assertion of a contradiction, it's an argument from seemingly valid principles of reasoning which ends in contradiction, and the LP is just such an argument. It only requires 5 or so axioms and inference rules (capture, release, Excluded Middle, adjunction) to produce it. So the comparison to just a sequence of opposed values isn't the same.
That's not (just) psychological inconsistency if one accepts the argument, it's a logical inconsistency. If one wants appropriate semantics for a logic to maintain it, adopt a paraconsistent metatheory.
Quoting sime
By what definition? If one thinks the contradiction you mentioned (the LP) is veridical, then they hold it to be true and false simultaneously because there's a purported proof that it is. It's only unimaginable or incompatible "by definition" if your definition of imagination has the requirement of consistency in the definition you're using. But that's the very assumption questioning the law of Non-contradiction is challenging so it can't be used to defend the LNC on pain of circularity.
This isn't like being certain you have five fingers. It's more like being certain the bishop moves diagonally. Validity is defined by logic. How could they be invalid?
Absolutely not. It contradicts itself in asserting its certainty.
I hear you lol. Logic is a dangerous and inaccurate gun, but I certainly didn't mean to imply that it ALWAYS misses it's mark. Lucky shots (probably) happen.
I would say I only mostly trust logic, but it certainly is limitted by the accuracy of one's knowledge. Something may check out logically with the knowledge one has and still be totally inaccurate in reality.
If logic were a pancea for human knowledge it seems like we would have more convincing answers for people's questions instead of many arguments that are not very convincing. At least it seems to point towards logic not being an innate talent... but I'm sure that doesn't shock anyone.
Am I mistaken in this understanding?
well maybe this is solvable by using different words for the two levels. Maybe someone could suggest a n empiricist who already did so.
How would our talk have much meaning without self-identity (of some sort or other), including the posts in this thread?
Seems mostly like the only justification to abandon identity would be if we found that in the world.
The validity of statements always depends on the premises, if I say, for example, that killing is right, and Bob killed John, then Bob did right, ok? Logic cannot define elements, just relations of elements, but, how can we prove right or wrong, if we can, those relations? I know I sound redundant and tautologic but is the validity of logic itself ”knowable”? Can we use logic on logic?
I hope you understand my question, I know it’s a bit odd and that I am not the best ad asking it.
The fruit of an apple tree cannot be an orange
As far as I can see, there is no actual contradictory state of affairs in this example. There is the computer and it's program. There are various maps which are drawn differently, and there is the person who drew the maps. None of this is contradictory, is it?
Quoting MindForged
Is it right that the idea is that the contradiction lies in what the person who drew the maps believes? That is, he believes both A and Not A. If so, I don't think the example really works. The content of my beliefs is contradictory, but there is still no actual state of affairs that is incoherent, is there? Let's try to make this clear. If you have found a case (instantiated in the real world) where the law of non-contradiction is false, then there must be some proposition you can state, about the world, which is both contradictory and true. What would that be?
Quoting MindForged
What I had in mind is simple imaginability. If it is at least humanly possible to actually imagine what things would be like if P, then I take it that P is intelligible. I am tempted to think that the mental pictures idea is a little crude, but let's run with it. What's wrong with the mental pictures definition? You say lots of states of affairs cannot be pictured. Could you give an example? I should note that the picturing need not be absolutely precise. I can't really mentally picture what the atoms which compose my laptop are like, but I can at least picture billiard balls interacting in certain ways, and perhaps picture billiard balls that have smaller parts that produce certain effects. I can picture that much, and I know that the atoms in my laptop are a bit like that.
As to the point about mathematics, I don't see why it is relevant. Let mathematicians define conceivability however they like for their purposes - I have no objection. But that they define it one way does not show that there is anything wrong with defining it another way for some other purpose than mathematics.
I suppose my view is just this. When it comes to thinking about the empirical world, if no human being can picture, even in simplified form, what the world would be like if P, then we can have no idea what it would mean for P to be true. In such a situation, we find something (NotP) indubitable - something which cannot be doubted because we have no idea what it even means to doubt it. I don't think there are many of these indubitable truths. There might even be only one of them; the law of non-contradiction.
PA
Yes, that's the scenario that is unintelligible.
Mental maps (and beliefs) are abstract representations of the world. We know that representations can be mistaken or inconsistent. But the maps are not the territory.
If we encountered a physical switch that seemed to be both on and off at the same time, we would want an explanation for what was really going on.
This is the case with QM where it seems like the switch is both on and off when you're not looking (due to observed interference effects).
Quoting Andrew M
States if affairs or physical objects cannot be either coherent or incoherent. It is beliefs, mental maps, or what have you, that can have such a quality as coherency.
Stealing money ($5) from parents for food when I was 8 years old.
Logical, I was hungry and there was the coin jar filled with coins and now I could eat.
Emotionally it is bad because people worked for it and it’s wrong.
So...do I just not take the money due to emotion instead of logically needing to eat?
It’s a tough question to answer.
The person's set of beliefs are, and beliefs are part of the mind. This would make minds the sort of objects that can have contradictory properties, no?
Quoting PossibleAaran
Are your beliefs not part of the world? It would seem strange to regard one's set of beliefs as a fundamentally different type of collection than other sets. Whether dualist or otherwise.
Quoting PossibleAaran
I think you're trying to have it both ways here. You say it need not be precise but then what you're saying implies some unimaginable things can still exist despite not being properly conceived of. Conceiving of a useful alternate picture isn't really conceiving of the thing itself, just an analogue that suffices for some explanations but fails others. Examples could include any example of unobservables in scinetific theories, fields, geometric objects that are of infinite size (like a Euclidean plane), huge distances (can one really picture the expanse between Earth and the Sun???), etc.
Quoting PossibleAaran
Well the point is there's no real way (even in principle) to conceive of nearly anything large or strange in mathematics. Infinite sets? Nope. Or just large numbers, even (say 10^10^10 amount of anything at all, totally indistinguishable pictorally from 10^10^11 of something else). Or weird algebraic objects like groups or rings. Conceivability in math is really about have a way to construct or prove things about these objects by means of formally established rules of proof. The mental picturing theory just can't work for anything outside of everyday finite counting and even then it hits a limit. To me conceivability needs to include this otherwise it's fundamentally incomplete a view, so the inconsistent objects do make it on if standard mathematics does.
Then in that case I don't think it can exist. As I said, i doubt inconsistent physical objects can exist (though I'm unclear how to regard the mind), but this seems distinct from the abstract objects I mentioned previously.
But...
names, variables, and so on can be given an interpretation. So logic does define its elements.
As is validity.
...of the logical system being used. My bolding. Logic defines validity.
If logic defines validity, what defines logic? Experience of events maybe? I still can't get it, how do we understand that logic is valid?
Because sorting out what is valid and what is not valid is what logic does.
I suppose where ever it is not supported by empiricism, as ultimately even mathematics is merely theory/philosophy in the language of math until it can be proven as applicable to reality. We know 1+1=2 because of all the situations we have observed where this is true; not because we figured it out logically. True we may have come to the conclusion using logic-- but logic that is based on empiricism and must be shown to be empirically true before it can be considered as logically sound AND true in practice.
Ultimately logic in itself does not prove truth, valid logic does. This is why in math class we are expected to show our work--to prove our conclusions are not only correct but were reached following valid logic and not merely by luck. Logic is only universal if it can be empirically shown.
Whose logic? Suppose my logic tells me differently than yours, thus leaving us in a situation where we both claim logic but do not agree? If logic establishes validity shouldn't our logic align as say our senses of sight and touch often do when we agree on the color and firmness of a rock? It seems that disagreements on objective reality presupposes invalid logic on one end or the other unless truth and validity are meaningless.
The sheer fact of having to show your logic to prove it brings it into the realm of empiricism--in that you are making your logic experienceable to another being using written or spoken media--in my opinion. Unobservable logic from you is nothing more than thought to me, so how can you prove your logic as valid without providing the experience of proof of it's validity?
What separates logic from opinion? (Hint validity)
In a nutshell I am saying that sorting out what is valid from what is invalid is what PROOF does, and something being logical to either you or me does not constitute proof that our logic is based on valid premises, or we would never have different conclusions on a matter such as whether logic can deduce the facts of reality from that which is untrue.
For example...
Then you're using a different logic and will have to determine which logic is to be applied. But outside very deep disagreements in technical math and philosophy the difference in what arguments are considered valid aren't going to have an impact in everyday life. Classical logicians and constructivist logicians are going to agree on basically everything outside mathematical logic discussions, for example.
Quoting Carmaris19
Um, a logic establishes the validity of an argument given a set of axioms and inference rules, it says nothing of our experience in the world being correct or not. If I see a color and say it looks more red than orange, and my brother says it looks more orange than red, we have surely not therefore made a fundamental disagreement about logic.
Yet experience may not always be reliable, not to mention that experience itself may not exist.
You say that logic determines validity but remember that if a camera is broken the photographs too will be flawed.
I "trust" logic, Syllogistic logic on top, and I understand that without logic we can't really think, so taking out logic isn't really gonna get us far, not to mention that, technically, the only answer to my question would need to be illogical, since saving logic with logic is tautologic (it is like saying "that it is because it is") but I'd reject an illogical answer.
I think you are missing something extraordinary. Not just validity, but proof, is dependent on logic. Logic is the structure of validity and proof.
Even your doubting logic assumes a logical structure.
The switch being on and off is an example of an inconsistent state of affairs. The SEP entry for States of Affairs gives the example of Paul's having squared the circle.
Also paraconsistent logicians accept or at least consider the existence of inconsistent physical objects.
As @MindForged already told you, you are misusing the term "validity." A valid conclusion is a conclusion that is reached by following (some) rules of logic. Logic itself cannot be valid or invalid.
See, we can say what it means for a sentence (for example) to be inconsistent. I don't think it is possible to say what it means for an object or a state of affairs to be inconsistent - without looping back to the language that we use to describe that object/state of affairs. So yes, you can sort of attribute inconsistency to things, but that attribution will be parasitic upon language, thought, reason. Of course, things and talk of things are hard to separate anyway, except that if we are realist to any extent, we accept that there is a one-to-many relationship between them. That is, there is one thing, but our relationship to it is through thinking/talking about it, and there can be more than one way to do the latter - including dialetheic ways.
Take the superposition state in quantum mechanics, for example. One way to talk about it is through the use of the quantum mechanical formalism, and there is nothing inconsistent about that - it's just straightforward linear algebra. But sometimes people feel that the mathematical formalism doesn't give us the feel, the intuitive understanding of what the thing is, and they try to accommodate it in more familiar, human-scale classical terms. Or they are actually committed to the view that, at least for macroscopic things like cats, such terms should always apply, quantum formalism be damned. One way or another, they can end up talking about the superposition state using a deliberately inconsistent model. Does it make the subject of their description itself inconsistent? Yes, as long as they are talking about it in that particular way, and with the understanding that the inconsistency awes itself to that particular conceptualization.
A tip of the pointy hat from the back of the room.
That seems equally true when attributing any state to things, such as that the switch is on. Do switches really have state or is that just a conceptual projection by humans onto a world that has no intrinsic structure?
Quoting SophistiCat
Yes, though dialetheic realism would seem unintelligible. It's worth noting that Aristotle's main version of the LNC was about the nature of the world and not propositions (i.e., it is impossible for the same thing to belong and not to belong at the same time to the same thing and in the same respect [Metaph IV 3 1005b19–20]).
Quoting SophistiCat
Do you mean the person-on-the-street's mistaken intuitions about QM? Even if so, people don't usually think of themselves as referring to their own conceptual models. The subject of ordinary discourse, as with physics discourse, is the world itself (albeit with the understanding that claims are provisional).
Conversely, Bohr's famous quote may be apt here: "It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature."
First, I recognize I was using the word validity wrong, my mistake. I was using validity as a reference to the truth of the basis of one's logic-- not whether the conclusion matched the stated axioms. I'm a rookie.
However, if validity does not equate to truth, what good is it to say a conclusion is logical? That may well be true, but if the conclusion (or axioms) are false then what good is the logic? As the classic example: all cows are purple, Socrates was a cow, therefore Socrates was purple is valid logic, but untrue and irrelevent to reality. This is why I had a bit of terminology mix-up.
Color was a bad example (which was why it was coupled with the firmness of the rock and not a stand alone example).
Suppose maybe we disagreed about whether a rock would break a certain window. What amount of logic will conclude this disagreement? We can discuss our logic til the cows come home--but only throwing a rock against that window will settle the debate because my experience of windows may be different than yours after only experiencing bulletproof glass or what have you while you are referencing regular glass windows.
Tim wood, I follow you right up to the invention of logic. Without your empirical observations you never had a need or how to invent it, so you haven't disconnected them.
I'm not in doubt of the quality of good logic, I'm in doubt of how a person knows they have good logic. I simply posit that it must be put to the test or it is just a theory.
Touche on logic to interpret (and project) your experience--It just seems that something's amiss when you use logic to interpret your experience when it is experience that both grants you the ability to logic and is the basis you use as proof of your logic's truth.
Surely you see the danger of both interpreting now and projecting in the future with the same tool--if not I will inform you--that your present (possibly incorrect) perception is now your basis for claims of both reality now and reality tomorrow, and your incorrect notions today will affect what patterns you both look for and perceive tomorrow, resulting in possible affirmation of fouled logic. This is why one (or all) must prove their perceptions are true to know that their logic represents truth.
While empiricism may be a method of forming logical conclusions it must be distinguished from simple logical arguments (such as the purple cow Socrates) which have no bearing on reality. Thus we have empiricism not being the same as just logic. One can make all sorts of clever arguments with logic alone, empiricism can (at least attempt to) weed out both untrue axioms and conclusions (neither cows nor Socrates are purple--though there may have been a cow named Socrates).
Validity is one thing, but philosophy is the love of wisdom, not the love of validity. Wisdom in my opinion equates to truth of claims, not validity of logic (which seems to only equate to a clever argument). Don't get me wrong, I do like a clever argument, and it does take wisdom to create one--but I prefer that the conclusions are true in regard to things I am going to form beliefs around.
Not at all. Is my bedroom contradictory because it has a red pillow and a different not red pillow in it? The pillows/beliefs are distinct objects. It would be different if there were 1 belief that was both P and -P, but there is no such case.
PA