Is Logic "Fundamental" to Reality?

MindForged

So this is something I've thought about awhile, but it will take some doing to try and explain what I'm asking properly. This will sound like a religion-related question at first, but it's not. A bit of backstory too, hope that doesn't annoy anyone.

So years back when presuppositional apologetics was the rage in the whole religion and God arguments, I recall hearing these guys arguing that the applicability (or in their words, "inescapability") of logic was because logic is part of God's nature or something to that effect. At the time, I dismissed this as nonsense spouted by people who hadn't take a single course in formal logic or higher mathematics. Over time I got bored with the whole atheism discussions and thankfully stopped thinking about such things. However, I began noticing that even atheists would make the same argument as these Pressupotionalists. But instead they would subsitute "reality" for "God"; logic apparently was "inescapable" because reality is logical.

Usually this is described logic being part of the "fabric" of reality (whatever that means). My issue with these sorts of arguments comes from a number of angles.

Like just as a preliminary remark, which logic is fundamental to reality? Assuming those using this sort of argument realize that a whole panoply of logical systems exist, this is often immediately assumed to be Classical Logic (terrible name, it's not from the classical period~). Which to mean reeks of having an assumption and trying to cake that assumption into the world itself to avoid having to justify holding this assumption. Perhaps that is the correct logic but that's not immediately obvious.

However, my real confusions begin here. In what sense is logic supposed to be fundamental to reality? Obviously it's not supposed to be some purely empirical matter (e.g. go find a logical object), since while logic can be thought of in several ways (norms of argumentation, study of formal languages, theories of logical consequence, etc.) it's not supposed to be about anything in particular. It seems logic can be used to do things that we assume are physically (or even metaphysically) impossible. So take first-order classical logic. The argument from explosion is taken to show why a contradiction cannot hold, because otherwise trivialism would follow (every proposition would be true). By how is such a reductio to be interpreted when talking about reality? That if a contradictory situation could arise, everything would occur? What about reality's structure would make this so? In explosive logics, that absurdity is caused by a set of inference rules, but is there a metaphysical analogue to inference rules?

One possibility that came to mind is that this argument is supposed to say there is an isomorphism between the "structure" of reality and the algebra of some particular logic. But then I suppose this gets us back to the issue with there being all sorts of different algebraic logics (Boolean algebra, Heytin algebra, etc.), and we even know that some Non-Classical Logics can be constructed purely within their own meta-theory (e.g. Paraconsistent semantics). And further, are we to understand this isomorphism as necessary, that the only way reality can possibily be is such that its structure is isopmorphic with the algebra in question?

I'm rambling, sorry I've gone on for so long. In a way, I can kind of see what might drive this sort of view about logic and its relation to reality. I mean, it seems true that "If it's raining, then there are clouds in the sky" allows me to truthfully determine that "there are clouds in the sky" when it's raining. So it seems like there's SOMETHING there that makes the connection between these truths necessary. But damn I just can't quite make the leap because I either can't understand it (because logic and reality seem like different domains) or else it becomes unclear how we can pick which logic is to be metaphysically priviledged.

I suppose there are likely similarities with my questions and old problems in the philosophy of mathematics. My own view ends up treating logic more as a tool which, depending on the rules we adopt, can be useful to some resolving some problem or understand something we find interest in. So we construct systems wherein we manipulate symbols according to a set of rules we specify, which we think are correct for the domain. Of course, this is probably because I'm a logical pluralist of some sort (instrumentalist?), so maybe someone would find my questions folly because they have a different view about logic.

apokrisis

...logic apparently was "inescapable" because reality is logical...Usually this is described logic being part of the "fabric" of reality (whatever that means). — MindForged

Isn't this confusing logic and causality, strictly speaking? Of course, the two are related.

We think of reality as being fundamentally reasonable or intelligible because there are certain emergent structural truths that appear to have the force of rational necessity.

This is how we reacted to the early discoveries of maths. Behind the accidents of the material world there was another world of inevitable formal necessities. Mathematical forms you could not escape as an ideal limit on being.

Eventually this did lead to mathematical logic - the "geometry" of computational, permutational or deductive form. And those syntactic shapes appear to be reflected in the material operations of the actual world. They seem to encode something about natural causality.

So there is a relation between logic and causality. But it remains a weakly expressed one. More work would need to be done to show if logic in fact describes natural necessity.

This is a live debate. Some folk simply presume Turing Universal Computation proves the physical world to be computable. One kind of mathematical model speaks to the true causal structure of existence.

But anyway, my point is that it is the causal structure of the material world that is the target here. And the mathematics of logic seem our best models of that. So it is easy to make the step of claiming reality is actually a product of logical necessity.

There certainly seems something in that line of thought. But also a lot of potential pitfalls to address.

But then I suppose this gets us back to the issue with there being all sorts of different algebraic logics (Boolean algebra, Heytin algebra, etc.), and we even know that some Non-Classical Logics can be constructed purely within their own meta-theory (e.g. Paraconsistent semantics). — MindForged

Yeah. And all these also presume some shared metaphysics. They presume an atomism about reality. So they really only can address material and efficient cause. They struggle to address formal and final cause.

So if you believe Aristotle - reality is a system involving all four causes - then you can see why mainstream logics, in being atomistic rather than holistic, might struggle to give a full account of the causal structure of reality. You can see the major problem that arises.

I'd mention ontic structural realism here. It leverages the maths of permutation symmetry and symmetry-breaking. Fundamental physics has show how that is the maths that best describes the logic/causality of the Big Bang universe.

So there is a connection to be made for sure. Our theories of mathematical necessity would seem to model the fundamental structure of existence in a way that makes its causal organisation seem completely reasonable or intelligible. We are getting there - with traditional logics perhaps having far less to do with the holistic picture than folk were expecting.

Wayfarer

↪MindForged

I think a good place to start that question is historically, and in particular, in relation to the history of philosophy, with the Greeks, and with the Parmenides. Parmenides is regarded as the starting point of the metaphysical tradition, and the kinds of questions he asked, the way he asked them, and the answers he came up with, are of profound importance for the subsequent development of the tradition. The other fundamental elements came from Plato's theory of Forms and Pythagorean numerical philosophy. These were among the fundamental elements that became incorporated into Aristotelian philosophy and then handed down, and also developed, through subsequent schools, particularly Neo-Platonism.

One major factor in the historical account, is that much of those traditions were then incorporated in the philosophical theology by the three 'Semitic religions' (i.e. Judaism, Islam and Christianity). As this happened, so-called 'pagan' conceptions of 'The One' and 'nous' were incorporated in theology and treated as attributes of God. In saying all this, I'm glossing over a subject which could easily occupy several years of full-time study in ancient and medieval philosophy. But it's a background factor which I think too many people don't take account of nowadays. Because, up until the early modern era, all philosophy was 'religious' in a sense, in that there was an implicit expectation that the kind of knowledge that philosophy provided was somehow 'salvific'. (This is the subject of the life work of French historian of philosophy, Pierre Hadot.)

So if you asked this question to any philosopher in the classical tradition, up to and including Hegel:

In what sense is logic supposed to be fundamental to reality? — MindForged

You would probably receive an answer along the lines of the idea that philosophy was concerned with the nature of the 'logos' of the Universe as a whole; after all, it was Hegel who said 'the real is rational'.

Now, that kind of expression can't help but sound 'religious' to us, at least partially because Christianity incorporated (some might say, purloined!) the notion of 'the Logos' which then became identified with 'the Word', meaning 'the Bible', or with Christ himself. But the original Platonistic conception of 'logos' (which is the root of 'logic') was not at all 'theistic' in that sense. Nevertheless it was sort of religious, because, again, 'Plato was clearly concerned not only with the state of his soul, but also with his relation to the universe at the deepest level. Plato’s metaphysics was not intended to produce merely a detached understanding of reality. His motivation in philosophy was in part to achieve a kind of understanding that would connect him (and therefore every human being) to the whole of reality – intelligibly and if possible satisfyingly.' (Nagel, Secular Philosophy and the Religious Temperament)

I think one of the hallmarks of the modern and post-modern period is the loss of this sense of the connection between logic and reality. I suppose one of the milestones in that is the development of non-Euclidean geometry (which accompanied the discovery of the Theory of Relativity), paraconsistent logics, and the like. Whereas in the classical outlook, it was assumed that logic and reason were somehow woven into the fabric of the cosmos, which is very much the native view of the Western philosophical tradition, now it began to be felt that these are internal to the workings of the mind, or rather, hominid brain, which is after all the product of evolutionary biology (as is everything! This is the subject of a book, Max Horkheimer's The Eclipse of Reason.)

I think nowadays the popular view of logic is overwhelmingly that it is in some sense a human invention, the product of the brain, rather than being 'objectively' real. But I also think it's deeply vexed question.

Cavacava

↪MindForged

I don't believe there is any necessary correspondence between logic and the world. The principal of sufficient reason cannot be proved because there is no way to confirm that the structure of thought is the same as the structure of the world. Only contingencies and probabilities can be known, I think chance is prior to the law of non-contradiction.

If what we experience is only available to us by means of our thoughts, which we order, filter, remember, change and modify according to some well worn logic then it is not surprising that people believe in a mimetic correspondence between reality and appearance.

Andrew M

In what sense is logic supposed to be fundamental to reality? Obviously it's not supposed to be some purely empirical matter (e.g. go find a logical object), since while logic can be thought of in several ways (norms of argumentation, study of formal languages, theories of logical consequence, etc.) it's not supposed to be about anything in particular. — MindForged

Going back to Aristotle, logic was an empirical matter. For Aristotle, particular things were considered to be an inseparable composite of matter and form (hylomorphism). So logic just was the method of investigating and discovering the nature of reality (i.e., its form).

On an Aristotelian view, logical rules emerge naturally from our interactions and experiences in the world. That is, we observe, make distinctions, and find those rules that enable us to organize what we observe and to act purposefully in the world (including the LNC, ethical rules, and what have you).

It requires a different philosophical mindset that involves understanding the world holistically. That is in contrast to the familiar dualistic sense that sees matter and form as fundamentally separate and then struggles to see how they could possibly relate.

Michael Ossipoff

↪MindForged

Is Logic "Fundamental" to Reality?

No.

Though logic is part of Reality, there's no justification for saying that it's fundamental to Reality.

Michael Ossipoff.

Xav

I agree I think logic is a helpful tool for decision making and discovery but it cannot govern the universe as it is useless without some degree of assumption. You should read a book called Zen and the Art of Motorcycle Maintenance, there's a quote in it which says "the number of hypothesis for any given phenomenon is infinite" which is true. Assuming absolutely nothing, you can give any explanation for any observed behavior. There is no possibly way to eliminate every other possible correlation to rainfall and you can never completely confirm that rain only falls when there are clouds in the sky.

Logic and science has been experimentally proven to be correct but I see no reason that it wouldn't be out dated like every religious ideology of its time. Logic is a very helpful tool for accurately predicting the universe from the limited perspective of a human, but to truly understand the universe would be to completely simulate the universe and be the universe. The only fundamental of the universe is that it is what it is.

Caldwell

logic apparently was "inescapable" because reality is logical. — MindForged

A good observation. You must be referring to a hyper-classical school of thought. I'm not sure if they necessarily wanted to mechanize reality. Their tendency is towards determinism but, perhaps, with exuberance (and here now I am sympathetic) logic was thrown in for good measure.

Streetlight

It's true that - as @Wayfarer says - the ancient philosophical conception of Logos was that which was expressed by the universe in its unfolding, but it's also the case that those who invoke a 'universe governed by logic' are more often than not not referring to any such conception, and have no idea what they think they are talking about.

Michael Ossipoff

But I should add that, though logic isn't fundamental to Reality, it's fundamental to metaphysical-reality, and is what what-metaphysically-is is constructed of.

Michael Ossipoff

Streetlight

But I should add that, though logic isn't fundamental to Reality, it's fundamental to metaphysical-reality, and is what what-metaphysically-is is constructed of. — Michael Ossipoff

Word salad.

Wayfarer

↪StreetlightX

(Y)

Banno

Would @MindForged be surprised that an axe cuts wood so well?

Logic (and mathematics) sets out how we can use words and other symbols. It's groups of grammatical rules. Yep, there are lots of different logics. It should not be a surprise that the one we worked out first works well in our everyday experience. Geometry started with Euclid; that's the geometry best for building and dividing blocks of land. Non-Euclidian geometries were a fun exercise for mathematicians until General Relativity. Now we use it to make our GPS work.

We choose the grammar for the job at hand, just like we choose an axe or a saw.

mcdoodle

I'm a logical pluralist of some sort — MindForged

Me too. Nelson Goodman's 'Ways of world-making' might appeal to you as it does to me. He argues (as I remember it) against a univocal this-is-how-reality-is logic, but also against wiffly waffly woo. Any world we imagine needs intellectually to fit together by, as Banno puts it, choosing the grammar for the job in hand. (It seems to me this applies to the Harry Potter universe as much as to our variants on relativity or how participatory research can happen in social science)

Any logic one applies leaves great remainders of the ambiguous, contradictory, unknown, unknowable and misunderstood, for a pluralist. But of course there's still room in there for mystical Oneness underlying everything, although that's not my cup of tea.

Banno

It seems to me this applies to the Harry Potter universe as much as to our variants on relativity or how participatory research can happen in social science — mcdoodle

Well, if Harry Potter were written well...

My taste leans towards Tolkien. 8-)

Sam26

It's an interesting question. It seems to me that when we say that logic is fundamental to the universe, then we're saying something about how we talk about the universe, or how we describe and make sense of the universe. Logic is a language that's used as a tool to reason, to correctly reason.

In another sense there seems to be something built into the universe that lends itself to logic or mathematics. I would think that any possible universe is governed by rules, and by rules that have some consistency, at least generally. I would say that for any possible universe there are fundamental rules or laws that allow us to use logic to describe that universe. One could also argue that the fundamental rules or laws that govern any universe, IS the logic that's part of the reality of that universe. So maybe in that sense one could argue that logic is fundamental to any possible universe. It's hard to see how this wouldn't be the case.

Wayfarer

One of the very first things I learned about on philosophy forums was Eugene WIgner's The Unreasonable Effectiveness of Mathematics in the Natural Sciences. It's not an elegant piece of writing, but makes an interesting point. Also worth noting that 'Wigner was awarded the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles" which are prime examples of the kind of 'unreasonable effectiveness' he describes.

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. — Eugene Wigner

litewave

Logic is fundamental to reality in the sense that every object in reality is what it is and is not what it is not. In other words, every object in reality is identical to itself and different from other objects. And when the identity and difference of objects is established, all true propositions about them are logically consistent. This is basically the law of identity or non-contradiction. Without this law, reality would be absurd and even the difference between existence and non-existence would be erazed. I have no idea what that would mean.

Even the logic systems that relax the law of non-contradiction in certain situations, like the paraconsistent logic, would not work without the law of non-contradiction - because they need to specify - non-contradictorily! - how the law of non-contradiction is relaxed. They just seem to block the spreading of contradictions to other parts of an information system to save the whole system from becoming worthless. If they completely abandoned the law of non-contradiction they would be worthless because they would automatically negate whatever claim they would make.

MindForged

↪Banno

Logic (and mathematics) sets out how we can use words and other symbols. It's groups of grammatical rules. Yep, there are lots of different logics. It should not be a surprise that the one we worked out first works well in our everyday experience.

That's not quite right. Classical logic is not the logic we first worked out, classical logic is the logic created by people like Frege and Boole in the late 19th century. At best one might say that about Aristotelian Logic or whatever work the Indian grammarian Panini was doing, but it's practically universally accepted that Classical Logic was a definite improvement over prior logical systems. That said, I agree when you say,

Geometry started with Euclid; that's the geometry best for building and dividing blocks of land. Non-Euclidian geometries were a fun exercise for mathematicians until General Relativity. Now we use it to make our GPS work.

We choose the grammar for the job at hand, just like we choose an axe or a saw.

That's basically the view I mentioned that I hold when I think about logic.

MindForged

↪Sam26

In another sense there seems to be something built into the universe that lends itself to logic or mathematics. I would think that any possible universe is governed by rules, and by rules that have some consistency, at least generally. I would say that for any possible universe there are fundamental rules or laws that allow us to use logic to describe that universe. One could also argue that the fundamental rules or laws that govern any universe, IS the logic that's part of the reality of that universe. So maybe in that sense one could argue that logic is fundamental to any possible universe. It's hard to see how this wouldn't be the case.

But I think, as I say in the OP, my issue with this is: Is the suggestion that the same rules apply to every possible world? In other words, even though we know there are all sorts of algebras for different logics, what's the rationale for saying only one of these systems can be mapped onto a possible world?

MindForged

↪litewave

Logic is fundamental to reality in the sense that every object in reality is what it is and is not what it is not. In other words, every object in reality is identical to itself and different from other objects. And when the identity and difference of objects is established, all propositions about them are logically consistent. This is basically the law of identity or non-contradiction. Without this law, reality would be absurd and even the difference between existence and non-existence would be erazed. I have no idea what that would mean.

This is not an obvious truth. Take Identity. There are known systems of logic which lack the Principle of Identity or even change the law itself. Namely, take a look a Non-Reflexive logics and quasi-set theory, mostly associated with Newton da Costa. The stated point of these formal systems is the claim that issues in quantum mechanics may require changing identity or else what we think it applies to. You can have the Law of Non-contradiction without the Law of Identity, as these logics have the LNC without identity. Or heck, there's a version of classical logic without identity; aptly called "first-order classical logic without identity".

I'd recommend Graham Priest's book which has some discussions about other potential issues where identity may come into question (issues regarding the nature of instantiation, from what I recall): One. That said, Identity is fine with me. I just mean to say you can work without it, or at least work with an altered or restricted version of it

Even the logic systems that relax the law of non-contradiction in certain situations, like the paraconsistent logic, would not work without the law of non-contradiction - because they need to specify - non-contradictorily! - how the law of non-contradiction is relaxed. They just seem to block the spreading of contradictions to other parts of an information system to save the whole system from becoming worthless. If they completely abandoned the law of non-contradiction they would be worthless because they would automatically negate whatever claim they would make.

Well this is just false.The way that (dialetheic) paraconsistent logics deny the Law of Non-contradiction is simple. They merely give a case wherein (according to them) there is a proposition which is true and its negation is true as well. A typical case is the Liar sentence. Denying the LNC as a tautology does not "automatically negate whatever claim they would make", they simple give an example they (dialetheists) believe shows the LNC to fail to be a tautology. For the dialetheist, the whole point of removing the principle of explosion is that it prevents the true contradiction from trivializing the logic, so what you say here seems incorrect.

Heck, paraconsistent logics have even been done within their own meta-theory (meaning consistency is not a requirement), such as here: "What is an Inconsistent Truth Table?"

litewave

There are known systems of logic which lack the Principle of Identity or even change the law itself. — MindForged

Do they say that an object is not what it is? That an object is not identical to itself?

Well this is just false.The way that (dialetheic) paraconsistent logics deny the Law of Non-contradiction is simple. They merely give a case wherein there is a proposition which is true and its negation is true. — MindForged

And do they say that it is true that there is such a case? If so, then they are employing the law of non-contradiction.

MindForged

↪litewave

Do they say that an object is not what it is? That an object is not identical to itself?

The POI says that for every "x", x stands in a symmetrical, transitive and reflexive relation with itself. I think stating the the way you have is somewhat misleading because it ignores how exactly identity is understood and how it is applied. In the case of Non-reflexive logics and quasi-set theory as they relate to quantum mechanics, you misunderstand. To restrict the domain of application of the POI means that the objects is question are metaphysically (not epistemically) indistinguishable. Or to quote the paper in question:

"Quantum mechanics raises some ontological issues which are hard to deal with in simple terms. More than one of those issues concern the relationship between quantum mechanics and logic, and here we shall be dealing with a particular aspect of one such logical problem. We begin by recalling the infamous Problem of the Identical Particles. According to a widely held interpretation of non-relativistic quantum mechanics, there are many situations in which one cannot distinguish particles of the same kind; they seem to be absolutely indiscernible and that is not simply a reflection of epistemological deficiencies. That is, the problem, according to this interpretation, is seen as an ontological one, and the mentioned indiscernibility prompted some physicists and philosophers alike to claim that quantum particles had "lost their identity", in the precise sense that quantum entities would not be individuals: they would have no identity. Entities without identity such as quantum particles (under this hypothesis) were claimed to be non-individuals."

-"Classical Logic or Non-Reflexive Logic? A case of Semantic Underdetermination" — Krause & da Costa

(I can forward this paper if you can't get it from sci-hub)

And do they say that it is true that there is such a case? If so, then they are employing the law of non-contradiction.

You don't seem to understand what the Law of Non-contradiction is. The LNC says that either a proposition "P" is the case or the negation of "P" is the case, not both. Merely using the concept of truth and saying there is a case where the LNC fails does not employ the LNC. Let's make this simple with the example I mentioned (don't debate the example here if you wish to contest it; there is already a thread on this is the logic section):

"This sentence is false."

There's not question of what the referent here is. It specifies an object (itself), a sentence, and asserts that the sentence is not the case. But if the sentence is not the case, then what the sentence says is not the case. But the sentence says, of itself, that it isn't the case. So it's true. But it's truth entails its own falsity as well. Yes it's a contradiction, but it follows from relatively simple principles that are not obviously incorrect.

Your argument would hold that contradictions cannot even be uttered, which is patently silly otherwise we wouldn't even know what the LNC is. You need not accept the Liar sentences as counter-examples to the LNC, but your own argument about the LNC does not work. Accepting at least one violation to the LNC does not commit one to the view that every contradiction is true (that's why these proponents suggest using a paraconsistent logic).

Again, the following paper is quite thorough and is relatively easy to understand, even for those with little to no background in formal logic: "What is an Inconsistent Truth Table?"

Uneducated Pleb

In what sense is logic supposed to be fundamental to reality? — MindForged

Personally, I think this sentence sums up the confusion perfectly. Logic is reified into "something" as a class itself, then applied to another class of things which then act as properties of "reality".

"Reality", as I take it to mean here, is the sum total of what there is and how it all interacts. To state there is something "fundamental to reality" creates a false distinction - for how can one part of "reality" be fundamental and another part be secondary for "reality"?

Logic (as well as mathematics), from my pov, are simply human symbols that condense and represent the structural processes of how "things" interact. The list of "things" being represented can be (somewhat) arbitrarily picked based off peceived degree of relation, but the interactions will always be the same assuming that "things" for the process share the relevant degrees of relation. Those paramaters are the "brute facts" of Nature, or "reality", or Cosmos, or whatever name you give to the concept of the totality of things.

When the logic, or mathematics, don't seem to fit the empirical reality, it is because how the "things" defined are not truly linked in the ways the process (or equation or premise) being imposed upon them actually relate. Hence we have discovered non-Euclidean geometry or paraconsistent logic and all the other different systems needed to reorient our own assignation of properties of things considered to be in relation. It also seems to explain the odd little artifacts, like the "principle of explosion". That is like exploring a process of relation occuring in a "vacuum". The process holds to a structure, but without the "things in reality" to constrain the imposed structure of the process itself, the "result" is therefore not relevant to anything actually in "reality".

Even though the systems we use change according to the arena of "things" being arranged, the rules of interaction must follow a process of relation (apparently, as "brute fact" observation of reality).

You can have an abstract mathematical certainty (or logical one) that has nothing to do with empirical "reality".

But, can you have an empirical, "real" object that does not follow ANY mathematical or logical relation to anything else?

If there is such an object or thing that does not follow ANY mathematical or logical relation to anything else, then how could one even perceive of it empirically or even in abstraction? It would effectively be like some sort of a "singularity of a singularity" and completely outside of "reality". It could have no relation to anything else logically and hence potentially be unable to be thought of and in an empirical sense, if the object has no logic or process of relation, then it would be unrelated to anything in "reality"...hence a true "unknown and unknowable".

MindForged

↪Uneducated Pleb

"Reality", as I take it to mean here, is the sum total of what there is and how it all interacts. To state there is something "fundamental to reality" creates a false distinction - for how can one part of "reality" be fundamental and another part be secondary for "reality"?

I can mostly jive with what you're saying. However, here I think there's something one might argue. To say that something is reality is "more fundamental" than something else would, I suppose, mean that the "less fundamental" thing is ontologically dependent on the more fundamental thing. So I suppose the argument could be that "logic is fundamental to reality" means that logic (of some sort) forms the final ground upon which everything else in reality is dependent on in order to be.

Whether this works or not, I don't know. It just came to mind as the possible intended interpretation of this sort of argument. Though I don't think it flies for reasons I gave in the OP.

litewave

That is not the principle of identity. The POI says that for every "x", x stands in a symmetrical, transitive and reflexive relation with itself. — MindForged

By the principle of identity I mean that an object is identical to itself: that it is what it is. That's what this principle has meant since ancient Greece:
https://en.wikipedia.org/wiki/Law_of_identity

When you violate this principle of identity you also automatically commit a contradiction and when you commit a contradiction you automatically violate this principle of identity: you say that object X is not object X, or: "Object X has property P" AND "Object X does not have property P".

To restrict the domain of application of the POI means that the objects is question are metaphysically (not epistemically) indistinguishable. — MindForged

If two objects are metaphysically indistinguishable then they are one and the same object. Can two electrons in quantum mechanics be distinguished? Well it seems they can; they can be distinguished by at least one of their properties - by their position in space. It also depends on how you define "electron".

"This sentence is false." — MindForged

I don't claim you can't utter contradictions like this one. But contradictory sentences don't correspond to any object in reality. They are just a string of words that doesn't correspond to anything in reality. They have no meaning.

Sam26

But of course there's still room in there for mystical Oneness underlying everything, although that's not my cup of tea. — mcdoodle

Come on Mcdoodle, let's have that cup of tea. :D

MindForged

↪litewave

By the principle of identity I mean that an object is identical to itself: that it is what it is. That's what this principle has meant since ancient Greece:
https://en.wikipedia.org/wiki/Law_of_identity

When you violate this principle of identity you also automatically commit a contradiction and when you commit a contradiction you automatically violate this principle of identity: you say that object X is not object X, or: "Object X has property P" AND "Object X does not have property P".

I know what identity is, I was spelling out the properties of the identity relation, which is what the principle is. To "violate" the law of identity does not entail violating the Law of Non-contradiction. The LNC asserts that a proposition cannot be true and its negation be true as well. The Law of Identity tells you how to know when a seemingly distinct objects are in fact identical (when they share all their properties). That is why one can remove the law of identity from their formal logic and yet retain the LNC. Again, there is a version of *classical* logic which ditches identity and yet the LNC is still provable. Identity and LNC are not bound together, that's some weird Aristotelian view, not a view in modern logic.

If two objects are metaphysically indistinguishable then they are one and the same object. Can two electrons in quantum mechanics be distinguished? Well it seems they can; they can be distinguished by at least one of their properties - by their position in space. It also depends on how you define "electron".

That's an assumption (one which I would share), but it's not obviously the case given certain possibilities in quantum mechanics. I already quoted the relevant paper explaining this up above, but thus far you seem to have avoided acknowledging anything I've linked.

I don't claim you can't utter contradictions like this one. But contradictory sentences don't correspond to any object in reality. They are just a string of words that doesn't correspond to anything in reality. They have no meaning.

Well that's a silly view. Lots of things don't correspond to reality, yet they are true. There are an infinite number of mathematical truths that don't correspond to anything in reality yet I doubt you'd deny them or claim they were meaningless. And you *did* say you can't utter contradictions. Just look:

And do they say that it is true that there is such a case? If so, then they are employing the law of non-contradiction. — litewave

You asserted that if Dialetheists argue there is a true contradiction (that the LNC is not true) then they are thereby employing the LNC. This could only be the case if the notion of a "contradiction" assumed the LNC, which doesn't make any sense. Rejecting the LNC simply means you believe there is at least one true proposition which also has a true negation. Nothing in the prior sentence assumes the LNC, it is literally in direct violation of it, because it's proposing that a contradiction holds.

The sort of argument you're trying to make is just question-begging; you're trying to sneak the LNC into the meta-language as a means of claiming it's inescapable in the object language.

Also, it's just false to say contradictions have no meaning. Even in Classical Logic, contradictions do have a meaning. The thing is that their meaning is such that they cannot be true in such a logic (or indeed, in any logic besides a dialetheic logic). Being contradictory isn't sufficient for meaninglessness. A meaningful sentence is meaningful if it's components are meaningful. If "P" is meaningful, and "Not-P" is meaningful, "P & Not-P" will be meaningful. The conjunction will simply be false though, not meaningless.

And besides, the sentence "This sentence is false" seems perfectly meaningful and it has a referent in reality (the very sentence itself, as that's what it specifies). After all, an equally self-referential sentence like "This sentence has five words" is meaningful. These questions aren't easy, but besides that, I've taken us on a tangent from the OP. Dear lord, lol.

mcdoodle

Well, if Harry Potter were written well...

My taste leans towards Tolkien — Banno

Ah, well I'm not much of a one for either of them as stylists.

I'm about to study a module which begins at the Tractatus and logical atomism and so I'm thinking about how much of the world of the imagination, emotion and ethics 'The world is everything that is the case' leaves out, from Rilke to Rowling or TSEliot to Tolkien. What a strange idea positivism is.

mcdoodle

Come on Mcdoodle, let's have that cup of tea. — Sam26

I know, I know, you can feel me wavering can't you? I must stop agreeing with Wayfarer about things :)

mcdoodle

contradictory sentences don't correspond to any object in reality. — litewave

I went to a play last week about a long-missing man and the family's reactions. The programme featured an interesting article about how people cope with a loved one who has gone missing. Some say he has been seen here and there; some say the evidence all points to death. The phenomenon is known as 'ambiguous loss': it seems that the most balanced human reaction is to embrace the contradiction, i.e. to accept that the missing person is both alive and dead, like Schrodinger's cat. It seems to me much human reality is like that: we embrace opposite possibilities and live with them. How else can we go on? Everything's gonna be all right, isn't it? What do you mean, I won't live forever?

In this sense human understanding is more complex and difficult than this binary 'reality' people speak of.

Is Logic "Fundamental" to Reality?

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