Is Logic "Fundamental" to Reality?
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.
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.
Comments (89)
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.
Quoting 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.
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:
Quoting 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.
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.
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.
No.
Though logic is part of Reality, there's no justification for saying that it's fundamental to Reality.
Michael Ossipoff.
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.
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.
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.
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.
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.
Well, if Harry Potter were written well...
My taste leans towards Tolkien. 8-)
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.
[quote=Eugene Wigner] 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.[/quote]
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.
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,
That's basically the view I mentioned that I hold when I think about logic.
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?
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
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?"
Do they say that an object is not what it is? That an object is not identical to itself?
Quoting 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.
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:
[quote='Krause & da Costa']
"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"
[/quote] (I can forward this paper if you can't get it from sci-hub)
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?"
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".
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.
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".
Quoting 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".
Quoting 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.
Come on Mcdoodle, let's have that cup of tea. :D
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.
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.
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:
[quote='litewave']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.[/quote]
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.
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.
I know, I know, you can feel me wavering can't you? I must stop agreeing with Wayfarer about things :)
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.
OK, no fancy schmancy tea then. Just regular tea.
Not finding "word salad" in a dictionary, I'll just guess that it means words that don't constitute a sentence, or maybe a sentence that doesn't have a meaning, or a large collection of sentences that doesn't say anything.
But my words were a sentence, one sentence. And each of its clauses has an explicit declarative meaning.
Shall I separate the statements in the clauses?
1. Logic isn't fundamental to Reality.
Many agree with that.
2. Logic is fundamental to metaphysical-reality.
Not everyone believes that metaphysical reality is all of Reality. The statement that logic is fundamental to metaphysical reality is explicit. I didn't explain it or justify it, The OP didn't ask for that. He asked a yes or no question.
3. Logic is what what-metaphysically-is is constructed of.
You could replace "constructed of" with "consists of", if that would be clearer.
As I said, I didn't explain or justify that statement, because explanations and justifications weren't asked for.
But it's a clause with a straighforward declarative meaning.
Maybe what StreetlightX was confusedly trying to say was that i didn't explain what I meant, or make any effort to justify it. As stated above, explanations and justifications hadn't been asked for.
Then I'll briefly here give a bit of explanation, in case StreetlightX has seen any of my posts about that:
I suggest the following:
Any fact about this physical world implies and corresponds to an if-then fact.
For example:
"There's a traffic roundabout at the intersection of 34th & Vine."
"If you go to 34th & Vine, then you'll encounter a traffic roundabout."
Additionally, any fact in this physical world is at least part of the "if " premise of some if-then statements, and is the "then" conclusion of other if-then facts.
For example:
A set of hypothetical physical-quantity values, and a hypothetical relation among them (called a "physical law") are parts of the "if " premise of an if-then fact.
...except that one of those quantity-values can be taken as the "then" conclusion of that if-then fact.
Obviously, a quantity-value can be part of the "if " premise of some if-then facts, and the "then" conclusion of other if-then facts.
There are infinitely-many complex systems of such inter-referring if-then facts.about hypotheticals.
Inevitably, there's one system, among those infinitely-many logical systems, that has the same events and relations as your experience. There's no reason to believe that your experience is other than that.
I call that your life-experience possibility-story.
I can't prove that the objectively, fundamentally, existent physical world that Materialists believe in doesn't superfluously exist, as an unverifiable, unfalsifiable brute-fact alongside of, and duplicating the events and relations of, the if-then system that I've described.
We're used to declarative, indicative grammar, and it's convenient. But, as described here, this physical world can be described entirely by conditional grammar. Maybe we're too willing to believe in the grammar that we use..
Instead of one world of "is", infinitely-many worlds of "if".
This suggestion (but maybe referring to mathematical/logical structure, but not explicitly about if-thens, and not stated from the subjective point-of-view) was apparently first made (in the West at least) by the physicist Michael Faraday, in 1844.
Michael Ossipoff
Actually, the Platonic analysis of this apparently obvious point, was that no object truly is, on account of it being an appearance only, without inherent reality (following Parmenides.) But this is not so with 'ideal objects' such as numbers, which really are what they are; so A=A is certain, but when it comes to the sensory or phenomenal domain, there are actually no 'A's as such, but only representations in material form. That in a nutshell is the difference between phenomenal and noumenal objects.
What is confusing is that having generally rejected the kind of critical realism that the Platonist tradition offered, we start nowadays from an assumption of naive or scientific realism, which is to accept that the 'objects of perception' have real or inherent existence in their own right. We hardly even know what it would mean to question that sense. Whereas the Platonist tradition actually provided a perspective within which the apparent certainty of sensory perception might be critically questioned.
When you claim that object X has property P and object X does not have property P, you violate LNC by holding both the proposition "object X has property P" and its negation as true. And you simultaneously violate Law of Identity because you claim that object X is something it is not - that it has a property that it doesn't have. Such an object is absurd and cannot exist in reality. In this sense, reality is logical (logically consistent). Or do you think that reality contains objects that have and simultaneously don't have the same property?
Quoting MindForged
I am sorry but your quote didn't explain why the authors believe that particles don't have identity. It just says that they don't have identity and that in many situations one cannot distinguish particles of the same kind. And I am not sure what they mean by "cannot distinguish particles of the same kind". Do they mean that the particles are exactly the same? But if the particles have different positions at the same time then they can be distinguished by their position, so position is a property that gives them distinct identities, even though all of their other properties are the same.
Quoting MindForged
Actually, reality or existence in the most general sense includes all consistently defined objects - that is objects that have an identity. Objects that don't have an identity - objects that are not what they are, that don't have properties they have - are nonsense, so these are not included in reality.
Quoting MindForged
Completely rejecting LNC means that you believe not only that there is at least one true proposition which also has a true negation, but that you also believe the opposite: that there is no true proposition which also has a true negation. As you see, such a belief is absurd and self-defeating. Even as you try to get rid of LNC, you still have to hold on to it. You can utter a contradictory statement, such as "there is a triangle that is not a triangle" (and at the same time hold on to LNC by regarding the statement as true rather than true and false), but I don't think you can find such a triangle in reality. I see no reason to admit such absurd objects in ontology.
Quoting MindForged
A contradictory sentence is meaningless in that it doesn't correspond to any object with an identity. And an object without an identity is an absurdity. I don't even think it's an object; it's nothing.
Quoting MindForged
This sentence says that it has the property of falsehood and simultaneously says (implicitely) that it doesn't have the property of falsehood. Even though a part of it ("This sentence") refers to itself, the sentence as a whole (with the predicate "is false") doesn't refer to anything; it doesn't correspond to itself because it characterizes itself as both false and true when in fact it is just false (like any contradiction).
I can imagine that a person is unsure whether someone is dead or alive but I haven't met a person who believed that someone is both dead and alive.
But an appearance or representation is still identical to itself, no? An appearance of a triangle is an appearance of a triangle, not an appearance of a circle.
We call 'reality' what makes sense to us, what else? Logic is the formalization of that 'making sense'. Beyond that, it's not clear to me what you are asking about.
Quantifying over the properties of an object is a second-order task, it's not relevant to the LNC which requires only 3 things: negation, conjunction and variables. Identity is not bound up with it. Again, you're equating equality with 3 separate notions. A contradiction is not the assertion that an object has a property "X" and lacks that property, it's the assertion that a proposition holds and it's negation holds. Again, FOL without identity exists while retaining the LNC, because equality is not defined in the language. I don't think this is disputable unless we pretend that logic doesn't exist. I believe Wittgenstein writes about it (but doesn't develop it further, thankfully Hintikka did) in the Tractatus.
Well yea bro, I'm not gonna quote the entire paper. I named the paper at the end of the quote and offered to send to the PDF of the paper in question if you couldn't access Sci-Hub (it's having issues right now). And the quote I gave stated what it meant: the particles are, under this view, *metaphysically* indistinguishable and yet they are not identical. Reading the paper would really help, it goes over this in greater detail than appropriate in a forum post.
"objects that are not what they are"
That's not what a contradiction is, why do you keep saying that? You could probably *derive* a contradiction from the assertion that "X !== X" but that's not the Law of Non-contradiction. Further, your original objection on this point was that because it does not "correspond to reality", which I assumed was physical reality since that was what I asked about in the OP.
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.
— MindForged
Well this is the easiest thing in the world. I did not mention "completely rejecting the LNC" because Dialetheists don't completely reject it. They don't believe ALL contradictions are true, only some. So you were simply misreading what was said (I did, after all, specify that only one exception was a requirement for dialetheism). And also, to call the belief therefore "absurd and self-defeating" is either a meaningless designation or else it's question begging. If "absurd" or "self-defeating" simply mean "contradictory" then that's a bad way to argue for one's position.
This doesn't follow and it ignores the compositionality of meaning. If "It is raining" has meaning, and it's negation "It's not case that it's raining" are meaningful, then "It's raining and it's not the case that it's raining" is meaningful. Confusing "meaningless" and "false" (or even "necessarily false") is an error. Meaningless statements, by and large (if not always), are not truth-apt, they cannot be false. Identity has nothing to do with this.
I mean let's just demonstrate this. Take an open question in mathematics; I'll be unoriginal and use Golbach's Conjecture (GC). Either GC is the case or it's not the case (for the sake of argument). So if tomorrow we discover the GC is true, surely it must be necessarily true and those saying it was false were necessarily incorrect. Were those who were wrong about the GC uttering a meaningless assertion just because the GC turned out to be necessarily true? Of course not, because a meaningless proposition cannot even e given a truth-value, because it cannot even be interpreted. Contradictions can be interpreted, and that's precisely the reason they are necessarily false.
That's not the case. Just take relational semantics. There is a proposition "P such that "P" relates to truth and "P" relates to falsity. This is perfectly coherent and understandable in modern mathematics. Also, properties of objects don't "correspond to themselves". "This sentence" refers to the ENTIRE sentence, not to the phrase "this sentence". To not understand what sentence it refers to is to be blind, because there's only one such sentence there. It can even be made more explicit:
[The sentence in brackets is false.]
Now there's no way to avoid recognizing the referent. We can even do this purely formally like Tarski did:
~True(x) <=> T
The predicate "is false" is part of the sentence being referred to here. If your issue is with self-reference, well, I think you're up a creek there. Even classic and groundbreaking work in mathematics treats self-reference as a coherent concept (such as Godel numbering used in Godel's Incompleteness Theorems). I mean, "This sentence has five words" is equally self-referential and yet the predicate "has five words" is clearly the case about the sentence. Or "This sentence is an English sentence", etc. Heck self-reference crops up in everyday dialogue as well (Kripke has some classic examples of this phenomena) and few treat these as incoherent.
It is - but when we say that 'one triangle is the same as another' that is an intellectual operation - we're able to say 'this shape is the same as that one' because of the rational ability to abstract and compare types. In fact we're able to categorise it as 'a triangle' on the basis of the same ability. So in this case, it is ideas that are being compared, not objects as such. So again, what is 'a triangle'? It is not an object per se - an object is this or that triangle, a particular - but what a triangle really is is a plane surface bounded by three straight lines.
The reason I mention it, is that according to this analysis, objects, per se, only have real identity as instances of forms. That is what enables reason to operate on them.
It means that there are scenarios where you can have two (or more) particles that can't be physically distinguished, even in principle.
To see this, have a look at the Hong–Ou–Mandel effect. Figure 1 shows the four quantum states in superposition when two photons enter a beam splitter at the same time, one photon entering from above and one photon entering from below. (The minus sign for states 3 and 4 represents the phase shift for the lower photon reflecting from the lower side of the beam splitter.)
On a classical analysis, it would seem that on repeated runs of the experiment, each state should be observed a quarter of the time. However under quantum mechanics when (and only when) two states in superposition are physically identical, they interfere. What is actually observed is that the two photons always emerge together on either the upper or lower side of the beam splitter (i.e., either state 1 or 4). This means that states 2 and 3 always destructively interfere and so must therefore be physically identical, in principle. Which means there is no physical information identifying each emerging photon uniquely with one or the other of the entering photons. Thus raising an issue about our understanding of identity.
Even if identity is eventually determined to be preserved, I find considering such possible objections and potential revisions to be useful for a number of reasons. I never find arguments to the effect of "axiom X is inescapable and even denying it affirms it" compelling. Most of the time such arguments just assume the axiom in the metalanguage and use that assumption to claim the axiom will appear in any language whatsoever, even though it only appears in the corresponding object language because it's being assumed in the first place...
That logic could improve so much with the advent of Classical Logic via Frege, and improve over the prior Aristotelian Logic, motivates me to try not to assume that whatever logic is dominant at present is infallible or some such. That said, I'm mostly satisfied with some of the answers I got in this thread, thanks~
So please give me an example of a contradiction, and we'll see if it violates the identity of some object.
Quoting MindForged
It might help if you explained the reason why you think quantum particles don't have identity to someone who is a layman in physics. For me, two objects (particles or whatever) are identical (metaphysically indistinguishable, that is, one and the same object) iff all of their properties are the same (including e.g. their position in space). This is just the principle of identity of indiscernibles or indiscernibility of identicals. So how is this violated in QM?
Quoting MindForged
That's why I said that they still need LNC even though they relax it in certain situations. In ontology I wouldn't relax LNC at all because it would mean to accept the existence of objects without identity (with violated identity.)
Quoting MindForged
I clarified that by "meaningless" I meant that the sentence doesn't correspond to any object with identity. What object does the sentence "It's raining and it's not the case that it's raining" (as a whole) correspond to? There exists no such state of weather; it would be an absurd state of weather.
Quoting MindForged
What do you mean by "relates to truth"? Simply that it "is true"? Your above proposition seems to mean that something is true and not true, which is a contradiction.
Quoting MindForged
I agree. The phrase "this sentence" refers to the entire sentence. But the entire sentence as a whole doesn't refer to anything, because there is no sentence that is both false and true. The entire sentence says it is both false and true, but in fact it is just false (like any contradiction).
Quoting MindForged
This sentence as a whole refers to itself because it indeed has five words.
Both particulars and universals are objects because they are identical to themselves and different from what they are not.
So at the beginning of the experiment the two photons are not identical because they have at least one different property - position in space: one is above the beam splitter, the other is below.
Quoting Andrew M
So at the end of the experiment both photons have the same position in space? If so, can we say they are just one photon? I guess not, because there is energy of two photons there, not of one. So the two photons must be numerically different. But what is their distinguishing property then? I think their distinguishing property is their different position in an abstract space where even photons with all the same physical properties are distinguished. I don't know how to call it, perhaps primitive particularity or "thisness".
Whether the two photons at the end of the experiment can be distinguished by physicists seems to be an empirical problem, not ontological. Also, whether each photon at the end of the experiment is the same photon as it was at the beginning of the experiment is a question of the preservation of identity through time. Identity doesn't have to be preserved in time; an object can be annihilated, or merged with another object, or separated from another object at some point in time. But at each point in time an object is identical to itself and different from other objects.
It's raining and it's not the case that it's raining. I'm sserting a proposition and its negation both hold, not that there is some object which has and lacks a property (that *is* a contradiction).
Because particles can share all their physical properties, yes, including what space they occupy (see the link to a relevant effect that a previous user posted). And come on, just gesturing at Leibniz's Law does nothing different than gesturing at the Law of Identity. The Indiscernability of Identicals will fail if identity is not part of the language or if it fails to be applicable to some class of objects (see the paper I mentioned, it goes over this in a way physics laymen are more likely to understand, even giving an analogy IIRC)
I don't think you understood me. Accepting that not all contradictions are true is *not* the LNC, that's simply a rejection of Trvialism. That's not using the LNC, because rejecting the LNC does not entail accepting all contradictions.
Well that doesn't make sense then since each conjuct does have a referent. If you don't mean "meaningless" just use a different word. Heck, we even have a proper term for this in logic: False. Of course the situation is false, but you were going beyond that for some strange reason. Contradicions are false, not meaningless (lacking a *physical* referent is irrelevant).
Truth assignment in logic is a relation (usually a function, but not in this case) between a proposition and a semantic value. In other words, a proposition is true when some proposition (or whatever truth bearer you have in mind) relates to the value "true" (pRt), and it's false if it relates to the value "false" (pRf). I'm aware it's a contradiction, that's the whole point. One can give a perfectly coherent semantics for how a contradiction holds, using the techniques of modern math.
That's ridiculous. The sentence clearly has a reference: itself. If it didn't have a reference it couldn't have a truth-value. Both Classical Logicians and Dialetheists agree that contradictions have the proeprty of being false (Dialetheists believe they are also true, as explained above). Saying that "the sentence doesn't refer to anything because there is no sentence which is true and false" entails rejecting that a contradiction is even a thing at all, which is ludicrous. The contradictory sentence exists. If on your view it is simply false, the sentence exists so saying the sentence lacks a referent is gobbldygook (non-existent things cannot have a proeprty like falsehood.)
That is completely ad hoc. Self-reference doesn't prevent a sentence from having a truth-value, being contradictory doesn'r stop it from having a truth-value (a contradictory sentence is a false sentence after all) and both the Liar sentence and "This sentence has five words" have clear referents.
It's an ontological issue bearing on identity, not an empirical (epsitemic) one. As per the article linked, the photons are completely physically indistinguishable.
My proposal is just an emotional equivalent to the logical argument: that there are many situations in life where one holds two possibilities to have equal weight, and must live with that fact, which to a logician is 'contradictory'.
To me the issue also happens in some supposedly binary choices in ethical dilemmas, where there is no right answer: there the important thing is to commit, one way or the other, and live with the consequences. I think many consequentialist thought-games are like that, where one is supposed to add up likely deaths from this action and compare with likely deaths from an alternative: that isn't how ethical choices happen, it's just a logician's game empty of serious human meaning.
By asserting this contradiction you are also asserting an object ("it"/weather) has the property of raining and does not have the property of raining. Since the identity of every object is determined by its properties, you are asserting that the object is not identical to itself. By asserting a contradiction, you violate the identity of an object.
Quoting MindForged
Ok, I automatically also assumed the principle of explosion. So, you can reject LNC and accept only some contradictions as long as you block the principle of explosion in some way and thus prevent contradictions from spreading to all other statements. Blocking the principle of explosion seems an arbitrary act but I guess it can be useful in some situations like where you don't want contradictions to contaminate a whole information system - it's a pragmatic solution designed to prevent spreading of false information but with no implications for ontology (reality). In ontology I reject all contradictions because contradictions refer to absurd objects without identity.
Quoting MindForged
The sentence "This sentence is false." exists but it doesn't refer to itself. Only a part of it ("This sentence") refers to the sentence. Compare with the sentence "My dog is not a dog.": a part of the sentence ("My dog") refers to my dog but the sentence as a whole doesn't refer to anything because there is no dog that is not a dog.
Identity regards the properties of an object, LNC regards whether some proposition is the case or is not the case. Again, if you drop equality out of classical logic, you get First-Order Classical Logic without Identity, which still retains LNC. You keep switching between metaphysics and logic without recognizing the difference. LNC doesn't make reference to identity at all, nor does Identity entail LNC (otherwise such a logic could not exist, yet it does).
Well I mentioned Paraconsistency in the OP so it didn't come out of nowhere (there'd be no reason to advocate for a true contradiction unless you dropped explosion). And it's not arbitrary to do this; if you accept the Liar as a sound argument you need to eliminate or restrict an inference rule that generates explosion.
I don't know what you're trying to say here. Only the phrase "this sentence" has a referent, the entirety of a sentence can't have a referent. The sentence you gave is simply a contradiction, it's not false because it lacks a referent, and besides which that sentence isn't even self-referential. It's false because it's a contradiction, all of which are necessarily false (even under Dialetheism). "This sentence is false" has a referent in any way that one defines what a referent is. Your argument would entail that "This is an English sentence" either lacks a referent or is false, which seems ridiculous.
But what is a proposition? It is a statement that assigns a property to an object. So when you deal with propositions you can't avoid dealing with objects and their properties and thus with identity of objects. So tell me an example of a contradictory proposition that doesn't violate the identity of some object.
Quoting MindForged
Liar is a contradiction so I regard it as false.Quoting MindForged
Take the sentence "My dog is black". This sentence as a whole has a referent in reality. The referent is the fact that my dog is black.
Um, that's incorrect. A proposition is just an object, whose ontological status will depend on what view you adopt about abstract objects. A statement is not the same thing as a proposition, though they are related.
As for a contradiction that doesn't violate identity, well, just post any arbitrary contradiction. I'll stipulate, for my example, that it's in a language which lacks equality, and therefore the semantics required for identity. "P & ~P". A contradiction and therefore false to be sure, but identity isn't required.
Well even dialetheists agree with that.
No, that's not what a referent is. A referent is what the sentence is about. The referent of "My dog is black" is the dog in question, not "reality". In exactly the same way, "This sentence is false" has a referent: itself. That's what "This sentence" is pointing at, so to speak.
A proposition, whatever its exact nature, assigns a property to an object. So propositions are inseparable from identities of objects.
Quoting MindForged
You still haven't given an example of a contradictory proposition that doesn't violate the identity of some object. "P & ~P" is not an example; it's a general symbol for a contradictory proposition.
Quoting MindForged
The sentence "My dog is black" is not just about the dog but also about the dog's relation to black color.
No, a proposition is just an object. An object doesn't assign properties to itself, an object is just something with properties.
I said the contradiction can be arbitrary, so it doesn't matter what you substitute for "P". The Golbach Conjecture is true and it isn't true.
You are shifting the goal post. The referent is what the sentence is about, the predicate tells us that the object in question is related to black. Your initial objection here was the claim the Liars lack a referent in reality. The Liar sentences have a referent (themselves) and that's just the way it is. It doesn't commit you to dialetheism so I don't see the issue acknowledging that. The Liar paradoxes are notoriously difficult to solve; even logicians (who study this phenomenon) don't have a standard resolution. The only agreement seems to be that no one has done a proper solution, and whatever the solution ends up being will necessarily be rather strange since all the non-strange/obvious "solutions" have failed.
When you say "The dog is black" you assign the property of blackness to the dog.
Quoting MindForged
Well, you have just said that an object (Goldbach Conjecture) both has the property of being true and doesn't have the property of being true. Again, you have violated the identity of an object.
Quoting MindForged
The sentence "The dog is black" is about the situation of a dog having the property of blackness. Its referent is not just the dog, and not just blackness, but the whole situation.
Quoting MindForged
The Liar sentence "This sentence is false" says that the sentence is both false and not false, so its referent is a situation where the sentence is both false and not false. But such a situation doesn't exist, because the Liar sentence is just false (like any contradiction). So the Liar sentence has no referent.
Yes, though that objection may not apply if the object language contains its own metalanguage as natural languages do. There presumably are implicit axioms in natural language arguments.
Quoting MindForged
Agreed. I don't have any objection to formal logics, including dialetheism, and agree they can be useful. But I also think logic is integral to both ordinary language and empirical investigation and this would be the sense that logic is seen as fundamental to reality. Which is why there is generally assumed to be a principled answer to how the liar sentence should be handled, including by dialetheists.
I'm aware. What you said, however, was that objects assign properties,; objects don't do anything. Objects have properties. If that's what you meant then there was a typo somewhere in your post.
That's a contradiction, not an identity violation. Without equality in the language identity isn't present within the language.
No it isn't that's not what a referent is. I hate to quote Wiki of all places but it states it plainly:
The referent of "The dog is black" is the dog in question, not "the whole situation".
The Liar sentence does not say it is both true and false. The Liar claims, of itself, that it is false. That the Liar is also true is entailed by it being false. Further, you are again confused about what a referent is. A referent is not the situation to which a proposition refers unless that's explicitly what some proposition refers to. I'll repeat an obvious example to demonstrate this:
[The sentence in brackets is false.]
The referent is itself, the only sentence in brackets. It's not referencing a "situation". The Liar has a referent, being a contradiction does not change that.
Yes, the two photons are initially in different positions. But the reason they are termed "indistinguishable" or "identical" is that if they somehow exchanged positions, this would make no physical difference (i.e., the quantum state would be identical).
Similarly at the end of the experiment they are measured in different positions - see Figure 3 of the earlier link. But at the time that they hit the beam splitter, their positions are also physically indistinguishable. (If they were not, then there wouldn't be interference. This is analogous to distinguishing which slit the photon passes through in the double-slit experiment.)
Quoting litewave
So any time that a photon interacts with something (say, the beam splitter or the detector), we could say that it is annihilated and created anew. But sometimes we want to consider the identity to have persisted (as with a photon in the double-slit experiment or things at a macroscopic level, such as humans). Even in the HOM experiment, there is some sort of continuity in that we started with two photons and ended up with two photons. But the history in terms of individual photon identity seems not to physically exist.
[quote='The Received View on Quantum Non-Individuality: Formal and Metaphysical Analysis']This is also connected with a second point. What exactly is meant when
we say that we deny a tautology (or a logical law, or a logical necessity)? In
denying that an axiom of classical logic is valid in general, don’t we have to
accept that this ‘axiom’ is false in at least one interpretation of an alternative
system in which the same formula may be expressed? Consider, for instance,
intuitionistic logic. In denying the validity of some instances of the law of
excluded middle, it is not the case that intuitionists accept its negation in its
place. However, they do accept that the law may be false sometimes (mostly
when we deal with infinite collections). For another example, consider some
paraconsistent logics, like those in da Costa’s Cn hierarchy. In denying the
Explosion Law, it is certainly not accepted as an axiom (or as logically valid
in the system) the negation of the Explosion Law, but some of its instances
must be false in some valuations. So, the argument could go, in denying the
universal validity of the reflexive law of identity in non-reflexive logics, are we
not committed to accepting that it may be false sometimes?
As we have said in the previous section, in non-reflexive logics we do not
accept the negation of the reflexive law of identity. Also, we don’t have to accept
that it must fail in at least some interpretations. Rather, we adopt its restriction
in the form of its inapplicability. Here, ‘inapplicability’ is couched in terms of
identity not making sense, not being a formula, for some kinds of terms. [/quote]
In other words, Identity (arguably) not applying to a certain class of objects is not the same as saying "An object has a property and does not have that property".
So there is a language in which an object can have and not have the same property?
Quoting MindForged
The Wiki quote just says that the referent of the word "Mary" is Mary and the referent of the word "me" is me, with which I agree. But the whole sentence "Mary saw me" is a linguistic expression too, and its referent (meaning) is the situation that Mary saw me.
Quoting MindForged
The referent of the word "Dog" is the dog, the referent of the word "black" is black (color), and the referent of the sentence "The dog is black" is the situation that the dog is black.
Quoting MindForged
That's why I said in an earlier post that the Liar sentence says "implicitely" that it is true. But that doesn't matter. The meaning of the sentence is that it is both false and true, and that's what matters. That's why it is a contradiction.
In theory - and also in reality if the theory is correct - there are two photons throughout the experiment, not one photon. They are numerically different, so there must be a property that ensures that they are two photons and not one. I would say that this differentiating property is the position of each photon in an abstract structure of the theory, because it is the abstract structure of the theory (including the definition of energy of a photon as a product of Planck constant and frequency) that differentiates the situation into two photons.
But without identity there is not really an object. I don't know what it would mean that an object has no identity or what it would mean that the law of excluded middle does not hold. Paraconsistent logic and intuitionistic logic seem to characterize imperfect knowledge rather than objects in reality.
One can construct a language (easily in fact) where equality is not part of the language, ergo identity isn't. Your forumlation of identity is incorrect; that is simply a contradiction.
"Black" is not a referent though, it's a predicate, a proeprty an object may have or lack. In your sentence, the "dog" is the only referent in the sentence.
You're confusing a predicate with a referent, and you're mistaking a state of affairs (or "a situation") with a referent. A referent can obtain in some state of affairs, but the sentence you typed had only one referent.
That's certainly an implication of it. That said, it's referent is itself, it's not a situation. "false" is not a referent, so I don't know how your comparison with "My dog is black" is even relevant here, seeing as it's neither self-referential nor does the Liar lack a referent. What do you think self-reference even means? That a situation refers to itself? That's nonsense. Sentence can have references to themselves, not situations.
So you say, and yet the entire point of this view (non-reflexive logics and the referenced view in QM) is that it might be the case that you can have an object without an identity. That just makes your post question begging against an opposing view. I've told you what it could mean: That identity only holds for some objects and not others, which is sketched out via a restriction in the logic as to what identity applies to. If you're looking for an in-depth semantics as to how this can work, well, I already reference the papers. Here, I'll even link them:
Classical Logic or Non-Reflexive Logic? A case of Semantic Underdetermination
The Received View on Quantum Non-Individuality: Formal and Metaphysical Analysis
Otherwise just responding by importing Identity into the metalanguage is just ignoring how the objection is formulated and I'm not interested in that.
As for Paraconsistent Logic and Intuitionistic logic, I think you're incorrect. Or rather, your view about them is not what their proponents believe about those logics. Intuitionists certainly don't believe that their formalism is simply about "imperfect knowledge" or something. Michael Dummett certainly didn't believe that, and Graham Priest definitely believes true contradictions exist (even in the world itself).
Properties are objects too - they are something that is identical to itself and different from other objects. I see no reason why words could not refer to properties.
Quoting MindForged
Situations are objects too - they are identical to themselves and different from other objects. Situations are referents of sentences.
Quoting MindForged
"False" is a property, so it can be a referent.
Quoting MindForged
The sentence "This sentence is false" refers to a purported situation that includes the sentence, so in this sense it is a self-referential sentence. The part "This sentence" refers to the sentence itself.
Ok, I'll look into it.
...What? This seems like an incoherent view. A property is some entity which can be predicated of an object, not objects themselves. In "My dog is black", you are attributing the property of "blackness" to the referent "dog".
How are situations objects??? A situation (state of affairs) picks out how things are, it is not itself an object.
Falsity is a property, so it is not a referent.
You've misunderstood. "Self-reference" regards a sentence which asserts something about itself. My point is that if we agree that's what self-reference is, we have to agree that a referent is not a situation because situation cannot self-refer. That requires some sort of language and operations in the language. "This sentence is false" refers itself, "My dog is black" refers to a dog and then predicates the property of blackness to it.
And in so doing I am also referring to the property of blackness. The property of blackness is the referent (meaning) of the word "black".
Quoting MindForged
An object is anything that has an identity. In other words, it is something (as opposed to nothing). In my view "objects" without an identity are nothing (so not really objects).
No, you are making a *reference* to the property of blackness, the *referent* of the sentence is the dog in question.
Even if it turns out to be the case that "No entity without identity" as the old mantra went, that doesn't entail that the reverse is true. This should be especially true for you given your previous statements about contradictions. Contradictions have properties (they are necessarily false, for instance), and therefore (on your view) they have an identity. So on your view there must be a contradictory situation, and hence, a contradictory object. That's why I think conceiving of a proposition as a "situation" is just a mistake. A state of affairs is not the same thing as a proposition.
When I am making a reference to the property of blackness then the referent is the property of blackness, no?
Quoting MindForged
A contradiction has an identity as a sentence (a string words) but it does not have a referent. A contradiction refers to a contradictory situation but there is no such situation, so a contradiction has no referent.
It's not the referent of the sentence, it's the referent of a word (although that's a bit misleading since "black" or blackness aren't objects). An object is not the same kind of thing as an aspect of the object.
It's not a situation, you can have a contradiction that makes no reference to a state of affairs (contradictions in math, for instance). You said anything with an identity is an object, the latter being something with properties. And it doesn't even have to be a string of words. Propositions aren't strings of words, and yet propositions can be contradictory.
Example?
Quoting MindForged
My understanding is that propositions are meanings of strings of words (if the string of words has a subject-predicate structure). In other words, propositions are referents of strings of words, or situations to which the strings of words refer. A contradictory string of words refers to a contradictory proposition/situation but such a proposition/situation would be an object without identity, which would be an absurdity, and therefore such an object doesn't exist and a contradictory string of words has no referent (meaning). We can talk about contradictory propositions or situations but ontologically they are nothing.
The problem is that quantum mechanics would seem to rule this out. The reason is that if there were a differentiating property such as position while in the beam splitter then, per figure 1, quantum states 2 and 3 would be physically distinct states and therefore would not destructively interfere (cancel out). But, as experiments show, they do.
(BTW, if the photons' positions were tracked to see how they individually traveled through the beam splitter then the interference effect would disappear and quantum states 2 and 3 would then be observed half of the time. This is analogous to the dual-slit experiment.)
So a different explanation is needed. One option is that the photons each have identity but are indistinguishable. A second option is that they don't have identity.
A third option is that the two photons merge into one photon (with higher energy) when they interact with the beam splitter and then subsequently split into two photons again. A fourth option is that the two photons are absorbed by the beam splitter (increasing its energy) which then subsequently emits two photons.
A fifth option is that the two photons actually do retain their individual identities throughout. But instead of the differentiating property being position, it is instead an index to relative branches in a very temporary world branching and merging. So both photons would be in the same spatio-temporal location in their respective branches and their interference effect would appear like the third or fourth options above. A bit like the bent-stick-in-water effect.
Disjunction introduction is a valid rule of inference and it is not a valid rule of inference. That's a contradiction yet clearly it's not making reference to a state of affairs. This is especially the case if you think logic is fundamental to reality, because then the validity of the inference rules varies in different states of affairs (or at least in different possible worlds), which seems to prevent logic from being fundamental.
A proposition is not a situation. The SEP summarizes this well:
As I said, a state of affairs is not a truth-bearer on most accounts of what a proposition is. Also, that you refer to a contradiction as an object (I agree it is) would seem to imply that it has properties (it does). But if it has properties, it cannot be "nothing ontologically".
I am not sure if you understood me. I was saying that the differentiating property of the two photons is their position in the abstract structure of the theory, not in physical space. According to theory (and also in reality if the theory is correct) the energy of one photon is E = hf, where h is Planck constant and f is frequency. So if in an experiment you measure frequency f and total energy 2hf, then theory tells you that there are two photons, not one. So it is the theory, the structure of its definitions and rules, that differentiates the stuff into two photons and thus gives each of them a separate identity. In this theory, in its abstract space or structure (and also in the corresponding abstract structure of reality), the two photons have a different position. But physicists cannot measure this position; it's not a position in physical space.
This contradiction is referring to a purported situation where disjunction introduction is a valid rule of inference and not a valid rule of inference.
Quoting MindForged
But if an axiom is valid (true) in one possible world and not valid (not true) in a different possible world then it is not a contradiction to say that the axiom is both valid and not valid. A contradiction arises when we affirm and deny something in the same sense, but here we are not doing it: were are saying that the axiom is valid in a possible world and is not valid in a different possible world. It would be a contradiction to say that an axiom is valid and not valid in the same possible world.
Quoting MindForged
I mean "situation" not as a fact but as an arrangement of an object and its property. Such an arrangement may hold in some possible world and thus be true in that world, and in another possible world it may not hold and thus not be true.
Quoting MindForged
Contradiction in the sense of a string of words without a referent has its identity as a string of words. But contradiction in the sense of the purported referent itself - a contradictory situation/arrangement/proposition - does not have identity (does not have the properties it has) and therefore does not exist in my view; it's ontologically nothing even though we can talk about it as if it were something.
OK, so granting that there are two photons throughout the experiment, are you saying that the property distinguishing the photons would not be physically measurable but still be physically real (a hidden variable)? Or not physically real and just part of the abstract structure (instrumentalist)? Or something else?
Depends on what you mean by "physical". Is "imaginary momentum" that a particle has in quantum tunneling "physical"? It cannot be measured, even in principle, but physical theory implies it is there.
That doesn't make sense. If, as you have said, that logic is fundamental to reality there is no possible situation where disjunction introduction is invalid. Speaking of "situations"/states of affairs in this way is a mistake. They are not the same things as propositions.
You already said that you believe logic is fundamental to reality in your first post, on the first page. So this precludes you from dealing with possible worlds where different inference rules hold. That was my point, the only way you could conceivably articulate your position goes against what you previously said. A proposition is distinct from a state of affairs, so you can have a proposition (which is an object) that is a contradiction, yet that doesn't entail there is some state of affairs (or a possible state of affairs) which corresponds to the contradictory proposition. After all, contradictions are necessarily false, even in dialetheism.
A situation (or state of affairs) is some way the world is that makes a given proposition true. It is not the arrangement of an object because objects are part of a state of affairs.
I've already dealt with this. Propositions aren't strings of words (that's a sentence) and yet they can have a referent in reality, and a truth value. Contradictory propositions (under most views) are precisly those propositions which cannot correspond to a possible state of affairs. They are not ontologically nothing, even on your view, because you said that have a property. If you say a contradictory proposition has no properties, that means they don't have the property of falsity. Which is just ridiculous because propositions are necessarily false, which is a property.
That's right. But there is also no possible situation where disjunction introduction is valid and invalid. Your contradiction referred to that situation.
Quoting MindForged
A situation/arrangement/proposition may be true in some possible world and false in another. And in the world in which it is true it is a fact. I assume that by "state of affairs" you mean a fact, and that is indeed different from situation/arrangement/proposition.
Quoting MindForged
Unless an axiom itself is self-contradictory (e.g.: "There is a circle that is not a circle"), there is no reason to prefer the axiom or its negation in ontology. They are both true but not in the same possible world (because if they were true in the same possible world they would constitute a contradiction).
Quoting MindForged
I agree that a proposition is distinct from a fact (state of affairs) and that a proposition is an object, but I don't think that a contradictory proposition is an object, because it would be a contradictory object - a referent (meaning) of a contradictory string of words. Contradictory objects lack identity, so they are absurd. And of course there is also no fact that corresponds to a contradictory proposition.
Quoting MindForged
Here is a misunderstanding. By a situation or an arrangement of object and property I don't mean a fact (state of affairs) but simply a proposition.
Quoting MindForged
I suppose that by the referent of a proposition you mean a fact. Ok. I'll just add that a proposition that is true in some possible world becomes a fact in that possible world. In other possible worlds this proposition may not be true and then it doesn't become a fact there. I regard a proposition as a kind of property that may be instantiated in some possible worlds (as a fact) and thus be true there and not instantiated in other possible worlds and thus be false there.
And I regard a proposition as a referent (meaning) of a string of words (sentence).
Quoting MindForged
Yeah, it's confusing. We can talk about contradictory propositions as if they were objects with a property called falsity but in fact they are not objects, and by characterizing them as (necessarily) false we mean that they cannot be true in any possible world - they cannot be instantiated as a fact in any possible world, which is not surprising, because they are simply nothing.
But a contradictory string of words (sentence) is something, an object with an identity; it just doesn't have a referent (meaning) because its referent is a contradictory proposition, which is nothing. A contradictory string of words is an object that has the property of (necessary) falsity because its meaning (a proposition) cannot be true in any possible world.
Yes, I regard it as physical.
The issue I'm thinking about with the HOM experiment is this. Suppose we name the two photons that are measured at the end of the experiment P1 and P2. Can P1 be identified with the photon that was originally above (or, else, below) the beam splitter? Or does that question have no physical meaning (as a question about ontology, not merely the inability to measure it)?
That interference occurs for the "both photons reflecting" and "both photons transmitting" quantum states implies the latter. Would you agree?
Well, since the two photons have no measurable differentiating property at the end of the experiment, not even a different position in physical space, we cannot find out which one was above the beam splitter at the beginning of the experiment and which one was below the beam splitter.
We might at least measure (if it is technologically feasible) whether their frequency didn't temporarily change during the experiment, to rule out that they temporarily merged into one photon (which would manifest as temporary doubling of frequency, since total energy should be conserved). If they merged into one photon and then separated again it seems that their identities were terminated at the merger and new photons came into existence at the subsequent separation. If there was no merger into one photon then the identity of the particles was preserved but since they have no measurable differentiating property at the end of the experiment we can no longer say which one is which.
The photons do have different positions in physical space at the end of the experiment (see figure 3 that shows the distinct photon pairs together either at the top or the bottom of the image).
The issue is only that the two photons could not have any different property while within the beam splitter. The observed destructive interference occurs because the "both photons transmit" and "both photons reflect" quantum states are identical and this entails that the photons are identical.
Quoting litewave
Yes. My guess is that such an experiment would only show evidence of the two photons and also destroy the interference effect in the process. If so, it would neither confirm or rule out the possibility. But it may still be a useful way to think about it. It at least shows how preserving identity can suggest a different physical model or interpretation.
Quoting litewave
Preservation of photon identity is ruled out by the observed destructive interference.