Friday, March 13, 2009
A Rejoinder to Tyro on existence, identity, non-contradiction, and the Laws of Logic
Since Sye will need to deal with personal matters until next week, I'm going to offer a slightly different theme than the normal religious nature of my blog. In the "Peanut Gallery" thread, Tyro made a few interesting and challenging comments, and I think they're significant enough for everyone to have their own voice in the matter. Tyro's comments, and my responses, will follow in the Comments section of this post. Keep it clean, kiddos!
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>>Tyro
ReplyDelete//What does identity & existence mean at a quantum level? For fermions, we have the Pauli Exclusion Principle which states that no two fermions with identical properties may occupy the same state. That's well and good and at least allows the definition to continue but there is no corresponding principle for bosons. Two photons may have identical properties and occupy the same space & time. There is no way to distinguish between the two.
In what sense then do bosons have this identity property?//
I'm not quite sure what you meant with this question; you carefully and (as far as I can recall) accurately outlined the nature and identity of quantum mechanical behavior, and then you asked how they have identity.
You may be challenging the notion of identity by asserting that spacial separateness is absolute and must be inherent in the identity of all that exists. So, at most, all you've done is dispelled absolute separateness for bosons; it does not follow that the Law of Identity is false, nor even that absolute separateness fails for everything else (it is the case for fermions, as you point out).
//And as I've asked many times before and which no one has ever answered, how do you apply this to complex, macroscopic objects? Every second I'm a different person. Replace a carbon atom in my liver with a different carbon atom and I'm a different person. Your definition rejects all attempt at nuance. It looks like your definition is radically at odds with all of our working definitions of identity which is stable in the face of small, "insignificant" permutations. How do you reconcile your black-and-white absolutist definition with what we use in our normal lives?//
I reconcile it with the fact that we use concepts in everyday normal lives, and concepts themselves have an identity: they are, roughly, epistemological recognition of similarity between constituents of existence by virtue of links of perceptual quality and omission of the quantity of these qualities observed in the particulars.
My definition of *concept,* surprisingly, has already been given by you here: it rejects nuance. That's the identity of concepts. That's what measurement-omission means. Nuance is tied to particulars (individual percepts); to demand that a concept include all descriptions of all perceptions of all members of that concept in reality is a contradiction in terms. It's like saying you and I cannot both be human because you're not exactly identical in every way to me. So you're just confusing particulars with conceptual abstractions of particulars here.
To make this more concrete, let me continue by answering your later challenge:
//1) The sky on day A is blue (true)
2) The sky on day B is blue (true)
3) The colour of the sky on day A and B are different (true)
4) By (1) and (2), Colour(A) = Colour(B) AND Colour(A) != Colour(B)//
This argument commits the fallacy of equivocation. Premise (1) and Premise (2) refer to the concept "blue," while Premise (3) equivocates "blue" to refer to the particular *percepts,* not the *concept* of blue assumed to be the definition in the first two premises.
The error here is an epistemological one, and is not a challenge to the laws of logic. The percept "Blue sky on day A" and the percept "Blue sky on day B" are drawn together by the concept "blue," whose range of "shading" is omitted in the contextual assumption of a normal, sunny midday.
So how can two particulars, who differ in at least some nuance, not be contradictory when you apply a concept to them (spacial or temporal separation of existence almost always works to serve as a basic nuance or "measurement omission")? The answer is because it is the *identity of the epistemological concept* to omit the relevant nuances.
You wanted a mapping. This is not formal, but I will do so: let R be the set of all that exists outside a given particular human's content of consciousness, let C be the set of concepts (in the epistemological sense) and let P:R->C, P(r)= c where r is a particular existent in R and c is a particular (existent) concept in C, i.e. the action of the identity of a particular human's consciousness upon the identity of the reality-constituent r. Presuppose your example, i.e. let r1 be Sky A and r2 be Sky B (elements of R) and let c1 be the concept "clear blue sky at noon at my house" with measurement shade-nuances between the bleakest witnessed particular winter clear blue noon sky and the brightest witnessed particular summer clear blue sky above this guy's household omitted. So the mapping will be P(r1)=P(r2)=c1.
What if he sees a cloudy sky? He's presumably seen this at noon before, so there's no contradiction if that's what he sees; the mapping goes to another concept c2, or "cloudy sky at noon," with measurements on cloud cover omitted (from a couple cirrus to impending stormclouds, say).
What if he sees a green sky with two suns and a gigantic floating purple eye overhead instead? This is not a contradiction, either; the concept mapping P would not apply, as he has not learned this concept yet (although P might map to the "HOLY SHIT" concept). His memory stores the particular, and unless the new particular is an arrangement of previous concepts and current observable causality from which he can generally deduce implied relevant omissions and thus a concept from the singular particular, he's got to see at least one more instance of this kind of sky to start building his new concept, c3, the "HOLY SHIT" noon sky, say.
Now, as an aside, you may harp on "blue." There is no particular "blue" in reality, like there is no particular "four feet three inches" in reality; they are necessarily attached to different percepts. What we are discussing here, though, is abstractions from abstractions: "blue" is abstracted as a standalone concept by seeing other particulars from a different concept possessing this same measurable quality (sapphires, say). One can then, from the concept "blue sky at noon" and "pretty blue gem" recognize the similarity in the abstraction and abstract away another concept. Much of complex mathematics works this very same way.
I will add some other comments below, but this ought to clear up (I hope) some confusion and perhaps supply an answer to your challenge that you can analyze.
>>Whateverman
ReplyDelete//If so, then perhaps we need a better understanding of just how universal this law of non-contradiction is, and why it applies in some situations and not others. What are the criteria by which we may know its applicability?//
You've made an excellent point here. What you have illustrated, perhaps a little unwittingly, is the fact that the *Law of Identity* precedes the Law of Non-Contradiction. We must, after all, know the identity of the subject before we can even know what's there to contradict.
For instance, suppose you were to tell me "there is no way you can ever make a square circle." But then I could *establish an identity* of "distance" to mean "the greatest value of the x or y coordinate in absolute value," which is useful in mathematically theoretical measure theory, instead of "the square root of the sum of the squares of x and y" as is typical. Then if you were to graph all points of distance 1 from the origin (the definition of a circle of radius one) you would trace out a square! This shows that, for analysis of *particulars* or *particular concepts,* you must know their identity before stating *particular contradictions* that could occur.
The entire situation with Quantum Mechanics directly illustrates this need. As I mentioned above, all it does is show that several concepts applicable to the context of the reality available nakedly by the nature of our percepts unaided by instrumentation do not apply to the context of the microscopic word that needs huge-ass expensive machines to observe.
This has been rampant in those equivocating physics exactly with metaphysics and excluding any notion of logic from reality, the basis from which logic is accounted. The best example of this is saying, very roughly, "all individual particles behave quantum mechanically and change on observation, therefore, the moon doesn't exist when we turn our back from it because the moon is comprised of all these weird particles." This is the Fallacy of Composition, pure and simple. Those advocating this theory would have to definitively prove that no combination of these individual particles can entail, by virtue of their individual identities, the causal result in a structure which loses the quality of quantum mechanical probability. It's the same as asserting that water cannot be fluid at room temperature because its exact constituents (hydrogen and oxygen) are individually gas particles at room temperature.
And, even if one can show the quantum-mechanical must apply to everyday stuff like the moon, one would have to show likewise why *one's percepts* behave the same and define the nature of the particular at the "normal, everyday" level, unless one enjoys affirming the consequent. Furthermore, the definitive effect of percepts on particulars in our macrocosmic reality may be impossible to notice in a human context without special instrumentation - Newtonian mechanics is absolute, for instance, **in the context** of what Newton and his contemporaries could possibly detect with the identities of human perception and the quality of their perception-enhancing instruments during their time.
Remember throughout all of this that we have identity ourselves, as do our body's instruments of perceiving reality.
Darrin,
ReplyDeleteThanks for responding in such detail. I don't have the philosophical background that you have and I've never heard of anyone talk about logical laws being existence before so please pardon me if I miss something elementary. It's all new to me and I'm fumbling in the dark :)
You may be challenging the notion of identity by asserting that spacial separateness is absolute and must be inherent in the identity of all that exists. So, at most, all you've done is dispelled absolute separateness for bosons; it does not follow that the Law of Identity is false, nor even that absolute separateness fails for everything else (it is the case for fermions, as you point out).
If there is no way to tell one photon from another, not even in principle, how can we distinguish one from another? I don't think there is a way, even if we include its position in space and time. How can we say that one photon is different from another, or that one photon here and now is the same as a photon somewhere in the past? Photons surely exist and under many circumstances one photon may be distinguished from another through spacial & temporal separation but not always. If we can't distinguish two apart, how can we have a fixed, permanent concept of identity?
I'm trying to flesh out what it means when you say that identity is existence. It's not clear that photons have identities yet they still exist. In my round-about, poorly explained and poorly conceived way I guess I'm asking for what it would take to falsify this claim so I know better what you're not saying. (I don't have as much philosophy background so I'm probably missing a lot of the nuance and connotations as I double-check concepts with Wikipedia and dictionaries.)
This argument commits the fallacy of equivocation. Premise (1) and Premise (2) refer to the concept "blue," while Premise (3) equivocates "blue" to refer to the particular *percepts,* not the *concept* of blue assumed to be the definition in the first two premises.
I don't think this is equivocation, no. It certainly presents challenges when put into modal logic but I don't think equivocation is the issue.
I think the problem is that "blue" isn't a simple, single-value. We may say there is a "true blue" which is pure and fully saturated but we can add blacks, whites and even other colours to take it to aquamarine, azure or other shades while still being recognizably "blue". Not pure-blue, but still blue (or blue-ish which is what we mean). As the shade changes, we start hedging and saying it has "hints of blue" and maybe even "blue tinged". At some point we stop calling it blue but what's key is that there is no sharp line dividing blue from not-blue.
You can try to rephrase the issue by talking about the colour of the sky being in the blue category but you'll still hit the problem where this artificially sharp container will have shades which are virtually indistinguishable from shades which are outside. If one is in the "blue" category, surely the other must be.
We hit the same sort of problem in many aspects of life. Heating systems, driving (e.g.: break force & timing), and certainly morality. Many questions can't be answered with simple yes/no or true/false answers but are instead on a continuum. We can talk about skies growing bluer or darker, we can gently apply breaking gradually instead of using full force all the time.
If we wished to reason logically about these issues, how much gets lost if we confine ourselves to modal prepositional logic? Why wouldn't we use a logical system more suited to it such as fuzzy logic? You'd argued that I was using equivocation which isn't a concept that really applies to modal prepositional logic, but does relate to how reality is mapped. We've started using another logical system which allows us to say that we're capturing some aspects but missing others, a concept not possible with only true/false values. Clearly there are different mappings, some more useful than others. If a logical system is universal and absolute, does it really make sense to talk about different possible mappings? Shouldn't there be one and only one?
The very strictness & lack of nuance makes me think:
Remember throughout all of this that we have identity ourselves, as do our body's instruments of perceiving reality.
Really? Is this identity so strict that we have a different identity every second so that any given identity does not perceive, think or anything, it's just frozen in time?
If identity is fuzzy, then the same problem with the blue sky arises: where do we draw the sharp line?
If there is no way to tell one photon from another, not even in principle, how can we distinguish one from another?
ReplyDeleteThere is a significant difference between two photons being separate and our ability to distinguish such things. The first is an ontological concern and the second is an epistemological concern. It may be that the separateness of bosons may be epistemologically inaccessible, yet for it to be the fact anyway. This isn't simply a question of our *ability* to discern such things, but that such things may be separate, but indiscernably so.
Much of the concerns here are very similar to the problem of the heap. In such a scenerio, we drop a grains of sand one by one until the grains of sand become a 'heap' of sand. On my blog a few days ago in fact, I demonstrated the following mathematical proof of the non-existence of a heap:
1) A single grain of sand is not a heap of sand.
2) If N grains of sand is not a heap, then N+1 grains of sand is not a heap.
3) Therefore, by mathematical induction, for all natural numbers N, N grains of sand is not a heap.
If we want to reject this argument, we must reject one of the premises, which would presumably be 2. If we reject 2, however, we must accept that there is some particular N at which N grains of sand is not a heap yet N+1 grains of sand IS a heap.
Notice, however, that this proof says nothing about us being able to *know* what this N is. We merely have to accept its existence in principle. I would posit that in most cases of identity, this N (for whether it be grains of sand or atoms or properties or whatever) is indiscernable. But it *must* exist if we are to say that anything is distinct from anything else in a meaningful way. So, in short, the inability to point out exactly where colors are different on a spectrum or which atoms in particular are important to the identity of a physical object doesn't do much to undermine the fact that distinct identities exist and that there is a sharp line somewhere.
Identity is not fuzzy. It is a yes/no, true/false ontological matter. It is our epistemic situation that makes our situation difficult. Identity would only become a fuzzy matter if we were to claim that things are only different if we can distinguish them as being different, which I think is a bit of an assumption to make.
Sorry it took so long to get back to you guys here. Good questions!
ReplyDelete//If there is no way to tell one photon from another, not even in principle, how can we distinguish one from another? ... //
Light presupposes an existence of space-time. They would thus be distinguishable by position, as you stated. Even if they are identical and position is a nonessential, as you may be implying in this passage, that still does not mean they lack identity. They're just a bunch of identical identities ;)
//I guess I'm asking for what it would take to falsify this claim so I know better what you're not saying.//
It is not meaningful to falsify identity, since falsifying presupposes identity - i.e. it presupposes a possible method by which we could demonstrate that the identity of the constituents in our experiment are in reality not how we assert them to be in our epistemic context.
//...As the shade changes, we start hedging and saying it has "hints of blue" and maybe even "blue tinged". At some point we stop calling it blue but what's key is that there is no sharp line dividing blue from not-blue//
You're quite right. But this has to do with the specific way the perceiver was taught "blue" - for instance, it is very likely that most are taught the concept by pointing at the sky at noon, the eyes of babies, etc. The epistemic content of what one is taught and his value of integrating these similarities will determine where that person draws the line - and the line is usually drawn at a nonessential, i.e. a color in a paint folder or whatever. But so long as one presupposes that perceptual faculties are normal (i.e. that a person is not colorblind) then the structure of such faculties interact with the structure of objects in existence, with the effect of a percept - even though, for instance, my girlfriend calls her eyes "green" while I say they're "blue," (they are very much in this "grey area" of which you speak) then presuming that we both have healthy faculties, we still perceive the same *color* - our integrated tagging of this "grey area" is itself different in identity, though, entailing her calling it A and my calling it B. But we still have the same content of percept.
Morality is a different subject altogether, as it involves many deep questions which explore - sometimes to a depth inapplicable in reality (i.e. Age of Consent in relation to when a young person's faculties are proper, resolved by a standard that alleviates much courtroom tie-ups) - but many cases of morality are direct and obvious (i.e. theft, murder) from the identity of man interacting with the identity of a social context of other men.
// If a logical system is universal and absolute, does it really make sense to talk about different possible mappings? Shouldn't there be one and only one?//
As above, be sure not to go out too broadly here. You must take into consideration the metaphysical reality of the context of knowledge. But, at a basic level (i.e. the three "foundational axioms"), this is fundamental to all humans in any context and, yes, mathematically mappable, as my opening statement to Sye indirectly demonstrates.
//Really? Is this identity so strict that we have a different identity every second so that any given identity does not perceive, think or anything, it's just frozen in time?
If identity is fuzzy, then the same problem with the blue sky arises: where do we draw the sharp line?//
No - you may have misinterpreted what I meant here. I was discussing perceptual faculties such as the eyes, ears, etc. by which we fill the contents of our consciousness (i.e. the faculty that identifies reality).
Now, of course, the content of our consciousness changes with each (perceived) causal progression. But this does not eliminate our abilities to analyze and integrate this information into our knowledge!
Concepts are not permanent. They reflect my aforementioned point. One may build concepts based on the information received from new percepts that display similarity to the old percepts from which we integrated the previous concept. For instance, a child entering the sixth grade will (provided he or she is bright enough) integrate the new mathematical component "variable 'x' " when he or she is taught it, thus expanding mathematics beyond simple arithmetic. This does not mean mathematics qua mathematics changes - only the student's concept of it changes according to the identity of the context of the new aspects of reality he or she experiences that share this conceptual relation.
>>TKD
ReplyDeleteThe problem here is that the concept "heap" is dropped from its normal conceptual usage. "Heap" is a concept whose context of usage is to convey a collection of existents, yes, but it is also meant to convey that the exact numerical value is nonessential. For instance, if I were to tell you "I have a heap of admiration for CodewordConduit," what I mean by this is that I have a relationally greater admiration for her work. Or, if I were to point to a mound of sand on the beach and say "that's a heap of sand!" I mean that it's a localized collection of grains in a mound that is perceptually separable from an otherwise flat surrounding. Sitting out and counting how many grains so I can exact the concept would be to demand a non-essential - in fact, the way human beings conceptualize is by determining a proper range of measurement based on the identity of the percepts to which the name for the concept applies (the same goes for the "fuzziness" of blue). Where we draw the line is:
(a) Not essential, since the essentiality is the differentiation of the conceptual notion in the constituent percepts from the rest of reality;
(b) Nonetheless based upon the content of the percepts an individual has tied to the concept, and also upon the individual's choice of where to "end" the concept.
But (b) is not relevant - grey areas (outside of epistemically difficult "areas" like deep moral considerations, which take much intelligence and time) exist because that grey area demonstrates identities similar to the "other side of the grey" (this is why those much-coveted 64-crayon boxes had "blue-green," but the more basic ones our mothers and fathers bought us only had blue and green).