We have achieved a plateau of effort here, i.e., what we initially set out to accomplish. There is still much to comprehend and comment about though. We will leave red text as-is for about a month, then reset it. Subsequent updates will use our multi-bar code which we inaugurated in our Quantum Pendulum page. We have now made updates which make this page, from our perspectives, ready for consumption. If you want a brief summary of our effort here see this, and this. Also, see other minor red text changes.
Jammer's work ALREADY helps us stimulate some great affects. Check our QELRs of point, line and circle based upon our latest quanton: a quantum fuzz¤n. Also take a peek at our most recent (August, 2004) Fermionta,which our work here in Jammer helped stimulate.
Our commentary derives from pp. 341-416 of Jammer's TPoQM. (Notice that Dirac's famous text has an analogous, (quantum ) heteronymic (e.g., TProQM vis-à-vis TPhoQM) mnemonic for his, The Principles of Quantum Mechanics. We shall assiduously avoid confusion in that regard. That should be our only reference to Dirac in this web page.)
Jammer breaks Chapter 8 of TPoQM into seven sections:
As you can see, Jammer's approaches and analyses are almost wholly mechanical. To our way of thinking quantonically, only von Weizäcker treads near avatars quantum, yet his approach is still objective (in his usages of mathematics as symbolic and formal representations of a n¤nformal, n¤nmæchanihcal quantum ræhlihty) . We felt that if only Weizäcker could uhsæ anihmatæ, ihncludæd-mihddle quantonic scrihpts he would swerve nearer what we intend.
But to be honest and fair and as transparent as we know how to be, "quantum logic" is an oxymoron!
Why?
'Logic' is about two-valuedness of verity versus falsity. 'Logic' is bivalency: dialectical bivalency, digital bivalency. Doug - 31Jan2006.
Logic is classical. Classical logic is formal, mechanical. Quantum reality (i.e., Doug's Quantonics hermeneutics of it) is neither classically formal, nor classically mechanical. As Rabelais might say, "quantum logic is coquecigrues (an avatar of a memeo which classically appears as an absolute absurdity; see Rosebush)!" Classical logic reifies yu! And, classical logic has no wu. Indeed, classical logic drives wu out, disembodies wu! Now there's a Geertzian "anti anti" if we ever saw one. Quantonics is inventing quantum philosophy, as we go. Here we see another justification of our sense of need to accomplish that. Coquecigrues is a Rabelaian avatar, genuinely. Coquecigrues: A reembodiment.
See [François] Rabelais (1495-1553), Gargantua and Pantagruel, Book I, Ch. 49, 'How Picrochole in his flight fell into great misfortunes, and what Gargantua did after the Battle.' Readers should worry that Britannica's [un]Great Books, Volume 24, Rabelais is a useless resource here. Ugh! See our above Australian link and search for <Rabelais coquecigrues>.
Quantum reality offers naught similar classical notions of logic and reason. Bergson explained: reality is neither stable nor objectively independent. Classical reason and logic require both stability and independence. Classical logic is flat. SOMland is a Flatland.
We went to our Cambridge and Oxford Dictionaries of Philosophy. We searched for: imaginary, i, conjugate, conjugation, complex (in any sense of conjugation), wedded, orthogonal, and so on... Classic philosophy has no (appears to have no) means of entering discussions of quantum~coquecigrues! (Will someone who speaks French please tell~show us how to pronounce coquecigrues? We guess it is something like kawkseegruh.)
Relevant comments appear in Heisenberg's The Physical Principles of the Quantum Theory, "It is instructive to compare the mathematical apparatus of quantum theory with that of the theory of relativity (Reminder: Add link here to Hoffmann's TSSotQ, Act II comparison of QM and R. That review is due end of August, 2007 or sooner. Doug - 6Aug2007.). In both cases there is an application of the theory of linear algebras. One can therefore compare the matrices [vis-à-vis Schrödinger waves] of quantum theory with the symmetric tensors of the special theory of relativity. The greatest difference is the fact that the tensors of quantum theory are in a space of infinitely many dimensions, and that this space is not real but imaginary [~wu, what we call quantum~nonactuality; we failed to mention here, when we first wrote this treatise in May, 2004, that Quantonics' n¤nactuality is not classically conservative, rather it represents unlimited potential...if we show our quantum~reality quanton(n¤nactuality,actuality) in Cantonese it might look like this: quanton(wu,yu)...in Autiot it looks like: quanton(Aleph,Yod)... and those both illustrate, almost ad oculos, why we call quantum~l¤gihc "coquecigrues"... Doug - 4Nov2006, 27Oct2014]." Start of first paragraph of Chapter IV. Our brackets.
Thus one may educe Quantonics' choice to use coquecigrue in place of "quantum logic." Quantonics' new quantum philosophy uses coquecigrue while assiduously avoiding classical 'logic.'
Topic
As you may intuit by Jammer's section titles' words this is a formal work, e.g.,
See Logic and What is Logic?, Classical vis-à-vis Quantum Complementarity, for discussion of Value see our Bases of Judgment and What is Wrong with Probability as Value?, for Many-Valued see our heterogeneous, for Algebraic see Bergson on radical mechanism and duration, Axiomatic, and Generalizations. See Doug'a CeodE 2012 QELR of Value.
See Logic and What is Logic?, Classical vis-à-vis Quantum Complementarity, for discussion of Value see our Bases of Judgment and What is Wrong with Probability as Value?, for Many-Valued see our heterogeneous, for Algebraic see Bergson on radical mechanism and duration, Axiomatic, and Generalizations.
See Doug'a CeodE 2012 QELR of Value.
Let's commence our section-by-section commentary...
1. - The Historical Roots of Quantum Logic
Supporting our list of bullet comments, Jammer tells us that all interpretations (of course excepting Quantonics) find their bases in an assumption. That assumption is that any interpretation of quantum mechanics (QM) should encompass one or more of these "components," which he describes in detail in Section 1, Chapter 8, of TPoQM. These are part of Quantum Logic's "historical roots," according to Jammer:
Jammer's "Components"
Jammer shows us how current theories of quantum mechanics (QM) run into what he calls "an impasse."
Jammer says Theory is physical, must be physical.
Jammer says Theory decomposes into our following list: Formalism, Relations, and Picture.
Classical assess: stability independence excluded-middle EOOOness H5Wness lisrability causation certainty EEMDivity observation : Theory
See mechanics.
Quantum assess: animacy c¤mplementarity included-middlings BAWAMings H5Wings lisrings affectati¤nings umcærtainty EIMAivityings c¤¤bsfection : Thæ¤ry
Jammer explains that QM's Formalism is mathematical.
Jammer says, "If a certain theory T leads to an impasse,..., it is not necessarily its mathematical formalism as such nor the meaning of its extralogical concepts that may have to be modified; it may equally well be the logic underlying the formulation of T which has to be revised." This represents what is called a quantum logical approach. It is mechanical.
In Quantonics, we see formalism, and thus mathematics as quantum philosophies' greatest impediments to understanding QM.
Classical assess: stability independence excluded-middle EOOOness H5Wness lisrability causation certainty EEMDivity observation : Formalism
See form.
Quantum assess: animacy c¤mplementarity included-middlings BAWAMings H5Wings lisrings affectati¤nings umcærtainty EIMAivityings c¤¤bsfection : Æmærqancy
See emerq.
Jammer says QM's Theoretical set of Relations are "Epistemic Relations."
Most logicians distinguish epistemic (anthropocentric belief) and alethic (fact and truth) logics. It is Quantonics view that belief emerges and evolves where fact and truth are expected to be immutable, stable and independent. Latter is classical. Former appears, to us, more quantum but for its innate "epistemic" anthropocentricity.
Classical assess: stability independence excluded-middle EOOOness H5Wness lisrability causation certainty EEMDivity observation : Relations
Classically, mechanically, materially, substantially, objectively, relations can only be formally 'interactive,' due an assumption (an axiom) of exclusion based upon Aristotle's 'axiom' of 'excluded-middle.'
Quantum assess: animacy c¤mplementarity included-middlings BAWAMings H5Wings lisrings affectati¤nings umcærtainty EIMAivityings c¤¤bsfection : Ihnterrelati¤nships
Quantum reality's middle is included! Quantons in reality compenetrate, interpenetrate, comfuse, entangle, superpose, con(m)dense, coinside, co-here, etc.
N¤ formal rules, tools, axioms, suppositions, normatives, unequivocations, nonprevarications, maths, etc. can classically define, n¤r classically describe quantum reality! N¤næ of those, n¤r their spawn can adequately represent 'classical relations' in quantum reality! 'Classical relations' do n¤t 'exist' in quantum reality!!!
Classical assess: stability independence excluded-middle EOOOness H5Wness lisrability causation certainty EEMDivity observation : Picture (i.e., QM's classical mythos)
Classically 'physical' implies mechanical, material, substantial, objective, formal, etc.
Quantum assess: animacy c¤mplementarity included-middlings BAWAMings H5Wings lisrings affectati¤nings umcærtainty EIMAivityings c¤¤bsfection : Æmærs¤s
Quantum reality, an emersos, is flux. Flux can emersce many affectings, some of which only appear 'classically, state-ically physical.'
David Bohm claims that quantum flux manifests itself holographically, as animate, EIMA "holomovement[ings]." Our brackets. We tend to agree, but need more effort here to assess potentia for hologrammings to be and portray all of quantum reality, both nonactuality and actuality, their isoflux and flux. It appears now that Bohm is right on if holo issi n¤t just photonic. Doug - 31Oct2004.
Quantons aræ anihmatæ, EIMA pihcturings ¤f ræhlihty.
See animate, EIMA.
Jammer tells us that many new forms of QM logic are called "multi-valued logics." Observe how this is still and yet a classical objective view of QM logic. How? A good example is what they intend by "multi-valued." Don't they mean multiple discrete single observation values, measurable and stoppable hold-still values? Quantonics' version would change that "multi-valued AKA fuzzy" active voice pasticity to participating plural present participle nowistic (affective) and futuristic (anticipative, expectational) "many valuings, many coobsfectings, and many signatureings."
Jammer drops countless names of multi-value logicians, both obscure (e.g., Siger of Brabant and Duns Scotus) and not (Peirce, Zawirski, etc.), regardless they nearly all share analytic formal mechanism. One, Zwicky, who may not have realized his suggestion to abandon Aristotle's 'law' of excluded-middle was an abandonment of formal mechanism. Bell quotes Zwicky, "The conceptual difficulties in quantum mechanics may be interpreted as due to the peculiar inconsistencies of this theory which in certain respects conforms with our principle of flexibility, whereas in other respects...quantum mechanics and the relativity theory are based on very antiquated notions. It should also be clear from our discussion that the recent controversies regarding the absolute truth of uncertainty principle versus causality are quite futile, as scientific truth intrinsically cannot be absolute." Quote appears on pages 345-6. Our bold.
Jammer writes that Zwicky's ideas were not well accepted by Margenau. Margenau apparently did not intuit paradigm shifting of physical 'laws' as many truthings and quantum evolution of betterings. Margenau essentially claimed that logical validity finds its bases in physics as an empirical science. To us that is blatantly Aristotelian, like saying, "A is A because A is A." Elsewhere we show how Margenau's beliefs tend toward and favor formal mechanics.
2. - Nondistributive Logic and Complementary Logic
Jammer tells us that a first penetration into a qualitative quantum mechanical 'logic' was suggested by Jon von Neumann in his 1932 masterpiece Mathematical Foundations of Quantum Mechanics. See p. 253 of Beyer's 1955 translation. Jammer quotes von Neumann exactly, "the relation between the properties of a physical system on the one hand, and the projections on the other, make possible a sort of logical calculus with these. However, in contrast to the concepts of ordinary logic, this system is extended by the concept of 'simultaneous decidability' which is characteristic for quantum mechanics." Readers please be (quantum~) aware that classical temporal simultaneity (i.e., ideal mechanical isochrony) and quantum coherent simultaneity (e.g., everywhere uncertain phasicity) are entirely omniffering comcepts. Coherent peaqlos may cohere across ensembles of PNFings. Doug - 25May2007; thanks to DMD and a reader in Boston for stirring this addendum. See Doug's QELR of simultaneity.
Aside on Quantonics' Simultaneity Resources: See Doug's QELR of simultaneous, See these comments in Doug's review of Banesh Hoffmann's The Strange Story of the Quantum: "Did we say simultaneously?" Quantum Cohera as Quantum Simultaneity Measurement is Always Uncertain simultaneous motions north and east we have an electron in a combination state See these comments in Doug's review of Einstein, Podolsky, and Rosen's 1937 EPR paper: Simultaneous Measure of Position and Momentum Doug - 1Apr2008. End aside on Quantonics' Simultaneity Resources.
Aside on Quantonics' Simultaneity Resources:
Doug - 1Apr2008.
End aside on Quantonics' Simultaneity Resources.
Von Neumann's 'simultaneous decidability' and 'simultaneous measurability' offer classical notions of what we call 'many truths,' a kind of heterogeneous incommensurability. This is a tell that von Neumann was on a better track, yet he still retained his mechanical legacy, as we shall see. One problem: his 'simultaneity' implies homogeneous temporality, and quantum reality demands heterogeneous timings.
Later, von Neumann and Birkhoff wrote a paper describing a 'phase space' G with states represented by points P. Propositions like a then are subsets Sa of G. Propositions expressing measurements in G can thus be certain. Further,
Our red bold highlights show extreme classical predilections of Birkhoff and von Neumann. See our QELRs of state, point, measure, certain, uncertain, true, and equals. Also see our QELPs.
Jammer, "A physical quality was now defined by Birkhoff and von Neumann as the set of all experimental propositions equivalent to a given experimental proposition." All of this allowed Birkhoff and von Neumann classical notions of 'partial ordered systems.' Their approach retained compatibility with classical mechanics.
Where have we seen 6 before? Does this sound familiar? "We are in It and It is in us." That is an expression of an included-middle! This is a good tell of a better track.
But what kind of included-middle have Birkhoff and von Neumann invented? A classically mechanical included-middle, whose point and propositional middles cannot be included due their innate mechanicity. Points and propositions are classical lisr objects! They did not say P_{1} in P_{2} and P_{2} in P_{1}, did they? Quantum points, which we call "fuzzons," have arbitrary probability propositions (and (e.g., ~spatial, temporal, energy~mass, etc.) distributions and likelihoods). Classical points ideally do not. (For two fathomable exemplars see our quantum versions of line and circle.)
Their complementation is classical ideal objective negation. Quantum c¤mplæmæntati¤n is massively (scope of reality) subjective. (See Bergson's Negation is Subjective. Also ponder how interpretation/heuristic/hermeneutic of e^{}i as -1 offers one of an unlimited number of metaphors of how quantum c¤mplæmæntati¤n is subjective.)
Conclusion? Birkhoff and von Neumann concluded that quantum logic is still mechanical but different from classical logic. Where classical logic is a Boolean lattice, quantum logic is an orthocomplemented modular lattice. They made some tiny progress but failed massively via retention of mechanicity.
Our reactions in our May, 2004 notes concluded:
Karl Popper refuted Birkhoff and von Neumann's paper, however, in our view Popper's own system of thought is questionable: it is mechanical, it assumes complementarity is objective and exclusive, it assumes falsifiability, and it assumes logic may be unambiguous. We accept none of those assumptions. To our ways of thinking, Popper just "didn't get it." Popper's negation is objective. Quantum reality is always ambiguous and thus not mechanical and not analytic due its up to Planck rate animate EIMAness. See our 2004 Bases of Judgment.
Abner Shimony, in 1971, offered his suggestions as a potential solution to Birkhoff and von Neumann's difficulty of interpretation of conjunction and disjunction of propositions:
Jammer discusses Martin Strauss' modified logic for quantum mechanics next. Strauss adheres some pretty silly stuff, claiming that von Neumann's use of probability theory is questionable due classical complementarity. He claims the unitarity of any metric is necessary to ensure that "meaningless questions have no meaningful answers." We nearly laughed out loud when we read this bilge. To us, all questions imply some comtext(s) and some answer(s). His Ph.D. dissertation claimed that Birkhoff and von Neumann's paper offers metaphysical propositions whose bases demand physical situations which cannot confirm or contradict them. He felt denouncing distributivity abandons two valuedness. Though he did not grasp it well, he is right! Dialectic is our problem! We have to abandon dialectic (two valuedness) in order to commence understanding and describing quantum reality!
In this section 8.2. Nondistributive Logic and Complementary Logic, Jammer's acknowledgment of Patrick Suppes approach, to us, comes closest to what we consider quantum better. It essentially says quantum reality is waves and waves are probability (and likelihood) distributions. Bravo! Suppes approach still has some problems in its assumption of closure, and quantum complements as classically objective elements.
We reaffirm baselines: quantum reality is nondistributive (as well as noncommutative, nonfactorizable, etc.; note that quantum associativity is vastly omnifferent and omniffering classical associativity, so in that sense quantum reality is non classically associative also; see EIMA and associate) and quantum complementarity is inclusive via macroscopic spatially and temporally arbitrary wave function probability (pastings), plausibility (nowings), and likelihood (futurings) di(omni)stributions. Lack of grasp of these baselines contributed significantly to troubles encountered by and in quantum logicians' efforts.
This section (8.2.) offered us significant growth in understanding some important memeos plus growth in our own innovation of better quantum memes and memeotics.
3. - Many-Valued Logic
Jammer begins this section in a review of Paulette Février's "tri-valent" logic. Paulette sees a need for novel notions of disjunction and conjunction, but she stays with classical legacy objectification, quantification, uni-global context, dissociativity, etc. She, as most others, fails to grasp dialectic as classical logic's primal thorn. Yet she was one who said that quantum logic is "non Aristotelian."
Jammer talks about Hans Reichenbach next. Reichenbach tackled probability as an approach and weighed its value dealing with indeterminacy and pondered its massive philosophical issues. He attempted to apply probability to logical propositions. In Quantonics this works if one throws out dialectic, e.g., dichon(A, B) vis-à-vis quanton(C,D), where C and D are quantons and A and B are dyadic classical objects.
Reichenbach did not recognize this primal quantum meme and went on to apply legacy classical thing-king to his own three valued logic. Part of his legacy is an assumption that classical mathematics are appropriate to use in a novel "quantum logic." To his credit he did recognize that quantum reality is hermeneutic and demands as Philip R. Wallace so astutely put it, "interpretation involves according primacy to subjective memes over objective notions." (Slightly paraphrased to adapt Quantonics' bent.) Classicists expect a single OGC interpretation of reality and conclude that quantum reality's many interpretations thus are a "problem." Rather, heterogeneous interpretations are, instead, a quantum tell: a huge quantum opportunity. Classicists carry similar idiocy over into their notions of 'measurement.' Likewise quantum measurement is heterogeneous, polychronic, pragmalogical, incommensurable, etc. All, to classicists, "absurd prevarication and equivocation." "Nonsense."
Essentially, Reichenbach innovated this: trichon(true, mu, false). His critics responded, quintessentially, "tertium non datur."
Reichenbach was far ahead of his peers in several ways. He saw a need for metalanguage preference over classical objective language. Kurt Gödel would agree. We agree. (A great example here is Gödel's provability as above 'proof,' a metalinguism for 'proof.' )
Almost no one liked Reichenbach's approach...
On Pauli, Jammer shows how Pauli favored "Status quo is the way to go."
On Bohr, Jammer shows that Bohr kept putting quantum logic back in SOM's box via his exclusive and dialectical and bogus versions of (to satisfy Einstein, what Bohr called "exclusive") quantum complementarity. (quantum~flux everywhere~included~middle associates~interrelates quantum~flux; only classical 'concrete' may be "exclusive" - Doug - 9Jul2006)
Born called Reichenbach's approach "a game with symbols." Born claimed that mathematics are "capable" of describing quantum mechanical reality. Trouble is, quantum reality is not mechanical. Classicists use analysis, mechanics, and mathematical formalisms to try to force quantum reality into their dialectical 'concrete' thing-king.
Result? "Back to Copenhagen I."
Von Weizsäcker's infinite valued logic is better than any three valued approach, but von Weizsäcker, like many of his colleagues, via his apparent assumption of analytic stoppability, failed to see quantum reality as emergent and unstoppable process. If von Weizsäcker had assumed a Planck rate, recursive, animate EIMA quantum reality his approach would be similar Quantonics' approach. Bundles of metavectors could be much like our fuzzons. Even so, he too was rejected for his ideas.
This section is interesting, but for us it just doesn't go anywhere. That's very likely appropriate since science's entrenched notions tend to reject almost anything novel, unless science itself is in crisis. Most times novel ideas are viral to science's current paradigm.
Doug - 10Sep2004.
4. - The Algebraic Approach
We took no notes on this section. It is short. Mathematics are objective, formal, and mechanical. They are dialectical and Aristotelian. As such they are essentially useless in any study of a non mechanical quantum reality.
5. - The Axiomatic Approach
Jammer focuses on Mackey's axiomatic approach.
Let us just synopsize Mackey's axioms' (1 through 9) sprinkled classical dependencies and assumptions:
Jammer's piece d'resistance, though, comes on p. 394, "If, however, all measurable properties (observables) of a quantum system are taken into consideration objectifiability becomes impossible within the framework of classical logic." This sentence agrees with our Quantonics perspectives and begs a question, "Why did we wade through all that algebraic and axiomatic crap?"
On page 395, Jammer continues, "Mittelstaedt was led to study the validity of logic in nature and in particular, in that part of spatiotemporal reality which can be described by the statements of quantum theory..."
This section ends with all theoreticians jumping back in SOM's classical, dialectical, logical box. Hans Lenk disputed Mittelstaedt's work and Jammer ends this section thus, "Mittelstaedt's alleged misconception was for Lenk just another argument for his general contention that all attempts, carried out so far, to show on philosophical grounds that classical logic has to be supplanted by some form of quantum logic in order to become adequate for modern physics have failed." Pure classical thing-king, folks.
This was all transpiring during 1950s-1960s. Philosophers of this time period still believed that "truth values of logical propositions are time independent," and that "measurement can be verified." Lenk accused "that Mittelstaedt confused the temporal order of measurement processes with the logical order of different stages in [] dialogue."
These 'philosophers' and 'scientists' failed to ask and attempt to answer, we believe, primitive and protoproemial questions, "Whatings, whenings, whereings, whyings, whoings, and howings issi quantum realityings?" See our H5W. They, instead, simply accepted and took for granted quantum reality is classically mechanical! As we, et al., have accused elsewhere, they, as did Einstein, adhered naïve AKA 'local' realism.
To us, quantum reality is n¤t classically mechanical and thus it is n¤t classically logical. To us, quantum logic is an oxymoron.
Quantonics is a novel emerscenturing quantum~science and ~philosophy which attempts to cure many of these classical ills.
Doug - 10Sep2004
6. - Quantum Logic and Logic
Jammer begins this section, "To analyze the more recent views on the relation between quantum logic and logic in general let us resume the problem, partially discussed earlier, whether quantum logic could ever possibly supplant ordinary logic."
He continues, "It would be inconsistent, it was argued, to claim for quantum mechanics as a theory the validity of some kind of nonstandard logic and, at the same time, to apply to quantum mechanical calculations ordinary mathematics which, as is well known, presupposes standard logic." This quote shows classical thing-king's desperate attempts to retain its legacy hierarchy of logic, mathematics, and then science (based upon former twos' hierarchy).
These conundra appeared to demand a whole novel and presumed formal approach.
We see how entrapped all these folk are in classical thing-king methods (CTMs). They cannot get out! They are stuck! They keep looping on CTMs and endlessly reiterating classical, malputative bilge: scalarbation!
To avoid a new quantum principia of quantum formality, Pascual Jordan "...restricted explicitly the scope of quantum logic to the laws of possible connections of statements about the state of a physical system..." Trouble is, folks, quantum reality is n¤t classically physical, n¤r formal, n¤r has it any classical state-icity.
Prion said, "Let's keep the old classical logic! It works in quantum reality too!" But it does n¤t!
Jammer points out that all logic since Aristotle, follows Aristotle, and folks Jammer, et al., did not grasp this conclusion, but that is our problem! Simply, Aristotle blew it, in spades. He logically damned everyone who followed him and believed in his sand- and toy-box toddling.
One notion that is incredibly important to grasp here is that all 'as practiced' logic and mathematics on Earth today find their bases in Aristotle! Few understand that he was just wrong! To us, that is a major catastrophe for our world. It is the key SOM disabler of nearly all thinking on Earth at Millennium III's emergence. Perhaps even more important: Aristotle infects everyday judgment, society, law, epistemology, ethics, politics, and so on. It is an unmitigated disaster of maltuitive thought. We've lived with it for 2500 years. It is nowings rent and purchase for change.
"According to...David Finkelstein..., there is no such thing as an a priori universally valid logic; logic like geometry, undergoes a process of evolution whose first major revolutionary change or 'fracture,' as he called it, became apparent through the abandonment of distributivity—just as the first fracture in Euclidean geometry appeared with the abandonment of Euclid's fifth postulate." Amen! Finkelstein is one of our heroes. To a large extent, he understands. Essentially, Finkelstein denies Aristotle too. Read pp. 404-405 for detail here.
Section 6 continues rehashing, with other actors, issues already covered above. Let's leave it at that.
If you need medication at this juncture, an antidote to too much classicism, see (Irving) Stein (Concept of Object as Foundation of Physics), plus both Don Howard, and Jon P. Jarrett (Philosophical Consequences of Quantum Theory). For some samples and examples see our Bell Theorem Study.
Doug - 11Sep2004.
7. - Generalizations
Except for one paragraph in section 7 of chapter 8, Jammer generalizes quantum logic back into SOM's box. We quote that paragraph in its entirety, "Just as there are two schools among quantum logicians which differ on the issue of whether to formulate quantum logic bivalently or multivalently, so there are, roughly speaking, two opposing views concerning the role which quantum logic has to play methodologically. According to the more radical school the non-Boolean logic, qua empirical logic, plays the role of an explanatory principle in physics; the ultimate significance of the conceptual revolution brought about by quantum mechanics lies in the 'emancipation' of logic from the status of an a priori and purely formal discipline to that of an empirically significant explicans. It is this idea that Finkelstein and Putnam had in mind when they pointed to the analogous development of geometry which in classical physics had an a priori status and became in general relativity an empirically manifested explanatory principle of large-scale space-time phenomena."
So, we give up distributivity...
But folks, that's not all we have to give up! Let's make another one of Doug's notorious lists:
We have to give up classical notions of,
From what we have read and what we understand and what we believe, whatever system of thought accomplishes giving up those notions and innovating novel quantum supersedents, won't be anything like what we mean when we classically say "logical." Quantum reality simply urges us to give up all that classical embungling bogosity.
Jammer penultimends thus, quoting Finkelstein, "We are in a delicate position, using logic to study the need for changing logic." And, potentially, as we would add, eliminating it... Quantum logic is an oxymoron.
Our situation here is kin our own conundrum of using quantum mechanics to rid our world of classical formal mechanics and replace it with a Bohmian nonmechanics supported by a Bohmian nonmathematics which presupposes a Bohmian quantum nonlogic...perhaps quantum super~holographic empiricism (QsHE) or similar.
Jammer's text is simply delicious reading. Our copy has post-its on nearly every page. Jammer and we should benefit were he to place its text on-line for easy access and reference.
Doug - 30May2004 through 12Sep2004.