【読書ノート】 Ludger Honnefelder, Scientia transcendens

以下は，Ludger HonnefelderのScientia transcendens: Die formale Bestimmung der Seiendheit und Realität in der Metaphysik des Mittelalters und der Neuzeit (Duns Scotus - Suarez - Wolff - Kant - Peirce) (1990)のうち，Peirceに関連する箇所（第4部と結論部の一部）の読書ノートである．原文はドイツ語だが，引用にあたって英語に訳出している．

II. THE CONCEPT OF REALITY

3. Reality as the object of the definite opinion

[T]he distinctness of two mutually exclusive formal objects, according to Scotus, can only be of such a kind as to exist ‘prior’ to any act of cognition. What the two concepts grasp is thus something real, insofar as it constitutes its own formal content ‘prior’ to every act of cognition. Yet this real shows itself nowhere other than in cognition, and only in the terminus of cognition does it prove itself to be real. (pp. 392–393)

In Peirce, the criterion by which the reality of the universal concept is shown in each case is determined in a characteristically different way; yet the parallels to Scotus are once again striking. As for Scotus, so too for Peirce the fundamental assumption of real general concepts follows from the nature of our cognition itself. Nominalism is indeed right to assume that cognition is always cognition of a medium in consciousness. But it does not in the least follow from this that the validity of cognition must be restricted to the mere cognition of the medium, that is, to the cognition of representations in the receptaculum of our consciousness (8.16/II 471). Such a conclusion follows only if one begins from the problematic assumption already mentioned, that reality can only be ‘something independent of a representative relation’ (5. 312/II 239f.), and then draws from the indisputable difference between being-represented and being-real the highly questionable conclusion that the object of representation in a medium can never be real (5. 96). (p. 393)

→ Scotusは，形相性（formalitas）という，ens realeとens rationisの中間に位置するような存在論的領域を見出す．形相性は，それを把握する認識においてのみ現れるものでありながら，把握される内容は認識の働きに「先だって」あり，いわば事物の側に基盤を有しているという意味でリアルなものである．つまり，あるものが認識においてのみ存在する，あるいは認識作用の産物であるからといって，それがただちにリアルではないということにはならない．これはまさにPeirceの唯名論批判の要点でもあり，ここにPeirceとScotusの議論に同型性を見出すことができる．

With the reference to the mediated immediacy of our cognition, Peirce secures the fundamental assumption of the reality of its correlate. Yet no criterion has thereby been gained by which it can be decided whether a given concept represents truly, that is, whether it genuinely grasps reality. Unlike Scotus, who holds that a concept represents a reality when it can be shown as the simple result of a simple act of straightforward cognition, Peirce sees in the character of our cognition as an ‘immediate perception’ no sufficient criterion that a given concept is ‘truly representative’, that is, that it grasps reality. The claim to truth must rather be regarded as a hypothesis which itself requires justification (5.288/II 225f.). (p. 394)

→ 認識の「直接知覚」としての性格から，概念が実在を表象しているとするScotusとは対照的に，Peirceは，それだけではある概念が真に実在を捉えていると言うための十分条件ではないと見なす．Peirceにとって実在性を規定するのは，無際限の探究に末にたどり着くはずの理念的な「最終意見」である．

Without doubt, the appeal to the final opinion of the community of inquirers highlights the considerable difference between the path taken by Peirce and the teaching of Scotus. After Hume and Kant, Peirce could no longer fall back, in so immediate a way as Scotus does, on the noetic–noematic parallelism. (p. 395)

→ ScotusとPeirceの見解の相違を，HonnefelderはHumeやKantを経ているかどうかの相違に帰しているが，より根本的には近代科学の成熟が背景にあると考えることもできるだろう．

Nevertheless, the determination of reality carried out with its help is not so far removed from the Scotist approach as it might seem. The central significance that Peirce ascribes to semiotic representation within the category of Thirdness can indeed be understood as a radicalisation of the doctrine advocated by Scotus, namely of the cognition of the pure ad se as a cognition within the medium of a representation. And when Peirce emphasises that the reality of what is known, its objective precedence over thought, shows itself nowhere else than in its result ‘in the long run’ (8.12/II 467ff. and elsewhere), namely in its agreement with the final opinion of the community of inquirers, this too can be read as a radicalisation of the Scotist thesis: that the reality of formal contents, i.e. their precedence over all acts of understanding, manifests itself in no other way than in their result, namely in the conceptus proprii that formal contents are able to ‘bring about’ (terminare) in the act of cognition. (pp. 395–396)

III. The Understanding of ‘Being’

In considering Peirce, one must ask: by what guiding sense of ‘being’ is the explication of the concepts realis and realitas determined, upon which Scotus grounds his interpretation of the reality of the universal? And to what extent does this sense also find expression in Peirce’s reception of the relevant Scotist concepts? That there is a close connection between Scotus’s determination of the reality of the universal, within his doctrine of the natura communis and of the formalitates, and the central doctrine of his metaphysics, namely the doctrine of the concept of ‘being as such’, cannot be doubted. For Scotus, the two doctrines stand in a necessary, reciprocal relation: every attempt to determine the ‘reality’ of the essential determinations and formal structures grasped in our concepts presupposes an answer to the question of what ‘being’ means at all. (p. 396)

→ 「普遍者に関する実在論」の観点からPeirceとScotusの関係や，PeirceがSoctusから受けた影響については多くの研究の蓄積があるが，「実在性」概念のさらに根底にある「存在」（ens）の理解においても，PeirceはScotusの独自の学説を継承しているとHonnefelderは論じていく．

 [A]ccording to Scotus, something is set apart from non-being in the sense of the intrinsically contradictory not first by the fact that it exists outside its cause, but rather because to its content there belongs formaliter ex se (‘formally from itself’) the possibility of being. The content’s own dispositio (intrinsic disposition) grounds that ratitudo (capacity-to-be, ontological aptitude) by which it is distinguished from the nothingness of the self-contradictory chimera, and on account of which it is, positively expressed, not repugnant to existence, and thus can be designated as ‘being’ in the broad sense. (p. 397)

→ Scotusにとって存在は"not repugnant to existence" (non repugnantia ad esse)であることによって規定される．

This ‘beingness’ shows itself as such only in thought, when the relevant content is grasped as that which is non-self-contradictory, as what is logically possible; but it is not constituted by thought. The intellect is only principiative (principle-giving) of the ground of that possibility which distinguishes something from the non-being of the chimera, insofar as—just as Scotus explains with reference to the divine intellect—it is the ‘first external principle’ for the fact that the relevant content is brought forth into being-thought. The possibility as such, however, belongs to the content itself prior to all thought, formaliter ex se. (p. 397)

→ 上記の箇所の続き．

 ‘Being’, as Peirce elsewhere states, encompasses in its broadest sense only the connection of subject and predicate expressed in the is, whether this is has the sense of actuality (‘actually is’) or of possibility (‘would be’) (1.548 / II 49f.). (pp. 398–399)

→ これはPeirceの「新しいカテゴリー表」からの引用．ここでのPeirceのBeingの理解は，Scotusのミニマルな「存在」の捉え方を引き継いでいる．

Even the reality that is recognisable and attested in the ‘final opinion’ is, after all, the reality of a ‘noumenon’ (8.13/II 469f.), and as such of the ‘nature of thought,’ so that the question remains, ‘wherein (ultimately) its reality consists’ (8.153). Is the ‘real’ that whose properties are independent of what anyone may think about them (5.405/III 271), or is the ‘real’ ‘the final objective opinion, which is indeed independent of the thought of any individual, but not in-dependent of thought altogether’ (7.336)? Must ‘reality’ be understood as the product of the act of thinking it, or does it merely find its expression in that act of the intellect? But this amounts to the question of whether intelligibility grounds the status of ‘being’ (in the broad sense described), or whether, conversely, beingness is the ground of intelligibility. But then, how is ‘beingness’ to be determined? (p. 400)

→ Peirceは，1890年代以降に「リアルな可能性」を認めることによってこの問題を解決したとHonnefelderは論じる．ここでも「可能的なもの」としての「存在」という，「存在」のScotus的な捉え方が前提となっている．

Only with this assumption of a ‘real possibility’, which shows itself in cognition but pre-cedes it and thus founds its status as ‘reality’, does Peirce succeed in connecting idealism or phenomenalism with realism in the form of a third path that leaves behind the extreme positions. The ‘scholastic realism’ thus proves to be an indispensable presupposition of the pragmatic realism formulated by Peirce. (p. 401)

With the theorem of the ‘real possibility,’ Peirce is not advocating an ‘extreme scholastic realism’ which—as he thinks against the background of his concept of nominalism—would go beyond Scotus himself (8.208). Rather, as the comparison shows, he is bringing into play precisely that understanding of ‘beingness’ which constitutes the core of Scotus’s metaphysics. (p. 401)

→ Peirceの自己理解では，「リアルな可能性」を認める彼の後期の実念論は，Scotusよりもさらに実念論的な「極端なスコラ実念論」であるが，Scotusの実際の学説と照らし合わせれば，この自己理解は必ずしも適切ではない．

When Peirce writes ‘that the third category—the category of thought, representation, triadic relation, mediation, genuine thirdness, thirdness as such—is an essential ingredient of reality, yet does not by itself constitute reality,’ (5.436), he is thereby attempting to express a relation between thought and reality such as Scotus determines through the connection of the criteria formaliter ex se and principiative per intellectum. (pp. 401–402)

Conclusion

For the question of whether and to what extent the formal determination of reality in Scotus and Kant’s approach can be brought into substantive correlation, Peirce’s solution provides a kind of counter-test. His attempt is explicitly both a “modification of Kantianism” (5.452) and a continuation of Scotist realism. (p. 459)

→ Peirceはどこかで「KantはScotusを読むべきだった」と書いているが，このことから窺えるように，彼の哲学はScotusの立場からKantianismを修正する試みであると言える．

In the second edition of the Critique of Pure Reason, Peirce sees proof that Kant, in developing the problem of idealism and realism beyond the restriction of the objective validity of our concepts to possible experience, and the consequent implication that then only our representations exist, relies on a third moment: “the flat denial that the metaphysical conceptions do not apply to things in themselves.” For Peirce, this third moment in Kant’s thought is “the very sun round which all the rest revolves” (6.95). (p. 460)

→ Peirceの引用は1903 Lowell Lecturesの第6講義より．

【読書ノート】 William Seager, Natural Fabrications: Science, Emergence and Consciousness

"The creation of the magnetic field of a bar of iron by spontaneous symmetry breaking is thus a case of emergence which is unpredictable in principle. Similarly, the ratio of the relative strength of the four forces and the masses of the force carrying particles may not be set by nature but emerge through a random process. No matter how much one knew about the symmetric phase, it would be impossible to predict these values" (p. 23)
→ 強磁性体をCurie温度以上に熱すると強磁性が失われるが，それを徐々に冷却していくと再び強磁性が回復する．磁性体は同時に，特定の（当初とは異なる）磁気モーメントの向きを得るが，この向きを決定する法則はなく，ランダムに決まる．これは自発的対称性の破れの一例．強磁性を回復する前は，磁気モーメントの向きに関してすべての空間方向が対称的だが，強磁性の回復によってこの対称性が自発的に（ランダムに）破れる．初期宇宙において，一つの統一的な力から四つの基本的な力が分れていったのも，同様の過程によると考えられている．いずれの場合においても，対称性が破れる前の状態において，破れた後の状態に関わるパラメータ（強磁性体の場合は磁気モーメントの向き，四つの力の分岐の場合は力の相対的な強さや媒介粒子の質量）は原理的に予測できない．したがってこれは創発（正確には下で触れる通時的創発）の例である．

"Picture then the state of the universe when approximately 1 s old. Is there anything missing from our cosmological picture? Considered from the standpoint of the recognized scientific disciplines, almost everything. There is no chemistry (organic or even inorganic), no biology, no psychology and no sociology. Is this surprising? From a purely physical point of view, not at all. Conditions of the universe at this time are, by Earthly standards, very extreme. The temperature was something like one billion degrees and it was quite impossible for atoms to form. The formation of stable atomic nuclei was just becoming possible as the temperature dropped below 1 billion. There was then a small window of opportunity where density and temperature permitted the synthesis of hydrogen and helium nuclei (as described above). Thus it is a natural fact that the only science which applies to the universe at the age of 1 s is physics. As we move back in time closer to the big bang itself, we encounter more exotic, eventually frankly speculative, physics, but it’s physics all the way back. However, as we pursue time away from the big bang towards the present, we obviously enter the domain of application of all the other sciences. Thus, for example, chemical and biological entities and processes (such as molecules, bonding, living organisms and natural selection) must be in some sense emergent phenomena. A little more precisely, any phenomenon which appears in a system which heretofore did not exhibit it can be labeled diachronically emergent. The cosmological tale as we now conceive it must be a tale of diachronic emergence" (p. 23)
→ ビッグバンから1秒後の宇宙には当然，生物学や社会学の研究対象となるようなものはなく，すべて物理学の研究対象となるものである．つまり初期宇宙に適用可能な科学は物理学だけである．そこから時間が経つにつれて，化学や生物学といった他の科学が研究するような対象が徐々に生まれてくる．これも通時的創発である．通時的創発と対比される創発の形態として，共時的創発(synchronic emergence)も考えられる．上で触れたような宇宙の発展は，通時的創発だけでなく共時的創発も示している．というのも，初期宇宙に存在していた対象は，生物学的な性質（例えば自然選択によって進化するといった性質）を持っていなかったと考えられるが，120億年後には，そのような性質を持った対象が存在することが知られているから．

"The weird behavior of some quantum systems called entanglement, in which two systems that have interacted maintain a mysterious kind of connection across any distance so that interaction with one will instantaneously affect the state of the other, might appear to contradict the adjacency requirement of cellular automata. But, again, it is far from clear that this is a real problem for digital physics and for the same reason. The spatial distance separating the ‘parts’ of an entangled system which makes entanglement seem ‘weird’ need not be reflected in the underlying workings of our hypothetical universal CA. In fact, could it be that the phenomenon of quantum entanglement is trying to tell us that what we call spatial separation is not necessarily a ‘real’ separation at the fundamental level of interaction?" (p. 70)

"When we burn books, it looks as though we are destroying information, but of course the information about the letters remains encoded in the correlations between the particles of smoke that remains; it’s just hard to read a book from its smoke. The smoke otherwise looks universal much like the thermal radiation of a black hole. But we know that if we look at the situation in detail, using the full many-body Schrödinger equation, the state of the electrons evolves unitarily" (Luboš Motl, "Hawking and Unitarity").

"Although both the weather and the Solar System are chaotic dynamic systems, the timescale on which chaos reveals itself in the latter case is so long that we can preserve the illusion that the Solar System is easily predictable. The same would be true of the weather if we wished to use our models to make predictions for the next five minutes (though of course it will take longer than five minutes to get any ‘predictions’ out of our weather models). Predictability is a relative notion: relative to the timescales natural to human observers, relative the natural timescales of chaos of the systems in which we are interested and relative to the time it takes for our models to generate their predictions" (p. 104)

自然の階層構造

自然が階層構造を成していることは自明であるという前提でSeagerは議論を進めている："If anything about the structure of nature seems obvious and irrefutable it is that nature possesses a hierarchical structure within which ‘higher level’ entities have properties lacked by ‘lower level’ entities" (p. 65). しかしこれは決して自明ではない．実際，自然が階層構造を成していることを否定する論者もいる （James Ladyman & Don Ross, Every Thing Must Go）．ここでは「自然が階層構造を成している」という描像がどの程度の妥当性を持つか考えてみる．

私たちが「階層」と呼んでいるのは現象のパターンであり，自然をどのように階層に切り分けるかは，どのパターンに注目するかという観測者の視点から切り離せないように思われる．ただ，四つの基本的な力の到達距離と強さの違いが，観測者の視点に依存しない自然な階層を作っているのは事実である．例えば強い力の到達距離は10 ^-15 [m] くらいなので，それよりも大きいスケールではその影響を無視できる．また重力に比べて電磁気力の方が圧倒的に強いが，大きい物体では電磁気力は打ち消し合う傾向にあるので，天体のスケールまで行くと重力の影響だけを考えることになる．このように，原子核のスケール，電磁気力支配のスケール，そして重力支配のスケールという三つの自然な階層を区別できる（ただし電磁気力支配から重力支配への移行は滑らかである）．

しかし私たちはスケールだけで自然を階層に切り分けているわけではない．例えば生物個体や生物集団に固有のスケールは存在しない．私たちが生物個体の階層を階層として同定するのは，生物に特有の振る舞いのパターン（自己増殖，エネルギー変換，恒常性維持など）に注目することによってである．また生物個体の階層が決まれば，生物集団の階層がそれに相対的に決まる．一般に，自然の中のどのパターンに注目するかという観測者の視点から独立に自然の階層構造が厳然と決まっているわけではないと思われる．この点を念頭に置く限り，「下位」レベルからの「上位」レベルの創発を考えることに特に問題はないだろう．

Conservative and radical emergence

Seagerは（通時的・共時的創発の区別とは別に），下位レベルの法則によって上位レベルの性質をすべて「原理的に」記述できるかどうかによって，創発を"conservative emergence" (CE)と"radical emergence" (RE)の二種類に分けている．記述できるのがCEで，記述できないのがREである．問題は，この世界にREが存在するかどうかだが，SeagerはREの存在を否定し，CEだけが存在するという立場を取っている．そして究極的には，世界のすべての現象は「原理的には」基礎物理学の法則によって記述できるという（「原理的には」って便利の良い言葉だなと思う．原理的に記述できるかどうかって一体どうやって判定するんだ？）

しかし私はSeagerの立場に懐疑的で，「原理的にも」（それがどういう意味であれ）基礎物理学によって記述できないような現象があるのではないかと考えている（そもそもSeager自身が取り上げている上記の対称性の自発的破れはREの例ではないのか？）．Seagerを含む分析系の哲学者には，上位レベルの現象のモデルは，下位レベルのモデルの単なる「圧縮」だと考えている人が多い印象がある．つまり彼らは，上位レベルのモデルが，予測にとって実際的には有用だったり不可欠だったりするとしても，下位レベルのモデルから情報の一部を削ぎ落としただけのものだと考えている．因果構造の情報論的な分析から，実はそうではないと論じる面白い研究がある：Erik P. Hoel (2017) "When the Map is Better Than the Territory”（テクニカルでない解説としては，同著者の"Agent Above, Atom Below: How Agents Causally Emerge from Their Underlying Microphysics"を参照）．それぞれのレベルにおける現象のモデルの因果構造を情報伝送路に見立てると，誤り訂正符号が情報伝送を効率化するのと同じ原理で，上位レベルのモデルは下位レベルのモデルを効率化するらしい．その結果，上位レベルのモデルが下位レベルのモデルよりも大きな情報量を持ち得る．これはとりもなおさず，下位レベルのモデルでは見えないような因果構造が，上位レベルのモデルに現われているということである．これはもちろん，下位レベルの法則によって記述できないような性質が上位レベルにあるということなので，REに相当する．ここで思い出すのが，「考え深い読者よ，政治的党派心のバイアスのかかったオッカム的な先入観——思考においても，存在においても，発展過程においても，不確定なものは，完全な確定性という原初的状態からの退化に由来する，という先入観を取り払いなさい」というPeirceの言葉である．上位レベルのパターンが下位レベルのパターンの単なる「圧縮」だというのは，Peirceの言うところのオッカム的な先入観なのではないだろうか．

下方因果

自己組織化や創発の議論でよく話題になるのが，いわゆる「下方因果」(downward causation / top-down causation)である．しかし，Seagerの本に触発されて下方因果についての研究をいくつか読んでみたところ，用語の使い方が曖昧で，議論が酷く混乱している印象を受ける．Menno Hulswitが指摘するように（"How Causal is Downward Causation?"），原因と結果それぞれの存在様式（一般的な法則なのか，個別的な出来事なのか，何らかの実体なのか）にほとんど注意が払われていないことが，混乱を生み出す要因の一つになっているように思われる．また「下方因果」というときの因果性が，作用因なのか，それとも形相因・目的因的なものなのか，判然としないことが多い．

下方因果の捉え方として有望だと思われるものが二つある．一つは，下方因果の「原因」に相当するのは，下位レベルの法則に付加される「境界条件」だというMichael Polanyiの理論である（例えばKnowing and Being: Essays by Michael Polanyi, pp. 233–34）．例えばある言語で発話される文章をいくつかの階層に分けるとすると，最下位には音韻があり，次に語彙があり，その次に文法規則があり，その次に文章作成のスタイルがある，といった具合である．音韻は，与えられた言語で許される音の組み合わせを規定するが，でたらめに音を並べただけでは単語にならないので，さらにその言語の語彙を指定する必要がある．語彙は音韻の規則を破ることなく，許される音の組み合わせを制限する．同様に，でたらめに単語を繋ぎ合わせただけでは文にならないので，単語の組み合わせ方に制限を加える文法規則がさらに必要である．このように上位レベルの規則は，下位レベルの規則を破ることなくそれに対して制限を加える「境界条件」になっているというのがPolanyiの理論である．生命の階層と，物理的・化学的な法則によって支配される非生命的物質の階層の間にも同様の関係があると彼は言う．この理論では，下方因果の「原因」に相当するのは，下位レベルの法則に付加される一般的な法則だということになる．しかし，こうした境界条件がどのように生じるのかはあまり明らかでない．

もう一つの捉え方は，下方因果は形相因・目的因的なもので，「原因」に相当するのは一般的な法則だというもの．Peirceの立場がこれに該当すると思われる．例えばスポーツ観戦で熱狂する群衆を考えると，群衆の一人一人のメンバーの振る舞いは，群衆全体の雰囲気の影響を受けるが，この影響は，「一般的な法則ないし習慣が個々の出来事を，共通のパターンに従うように方向付ける」という意味で目的論的な影響である．このような影響が可能であるためには，（単なる無知の表れではないという意味で）客観的な偶然が必要である．というのも，もし各要素の振る舞いがすべて決定論的に決まっているとすれば，目的論的な法則がそれを「方向付ける」余地はなくなってしまうから．目的論的な法則は，そこからの逸脱の可能性があって初めて成立する．

【メモ】 Vincenzo De Risi / Geometry and Monadology: Leibniz's Analysis Situs and Philosophy of Space

Preface

That space is actually constituted by points, though here abstractly meant as terms of situational relations, is perhaps the highest result of Leibniz’s geometrical investigation and, at the same time, it also marks the core of Leibniz’s theory of phenomenal expression. It shows in fact that a set of non-spatial relations (such as those occurring between monads) can be isomorphic to (“expressed by”) a set of situational relations that per se suffice to produce phenomenal extension and thus, ultimately, faithfully represent the supersensible through the sensible. (p. xii)

Chapter I. Historical Survey

"Having thoroughly inquired, I have found that two things are perfectly similar when they cannot be discerned other than by compresence, for example, two unequal circles of the same matter could not be discerned other than by seeing them together, for in this way we can well see that the one is bigger than the other. You may object: I shall measure the one today, the other tomorrow, and thus I will discern them even without seeing the two of them together. But I say that this still is a way of discerning them not by memory, but by compresence: because the measure of the first one is not stored in your memory, for magnitudes cannot be retained by memory, but in a material measure marked off on a ruler or some other thing. In fact, if all of the things in the world affecting us were diminished by one and the same proportion, it is evident that nobody could make out the change." (Letter to Jean Gallois, September 1677; GM I.180, A III.ii.227-28, A II.i.380) (pp. 58-59)

Chapter II. Geometry

He [Leibniz] says that two figures are congruent not only provided they are only distinguishable through the simultaneous perception of them (which would be the similarity definition), but also provided such a perception requires the presence of a third object (which was not a condition for similarity). For example, two spheres are similar, for you can distinguish them only by seeing them both simultaneously (otherwise, seen one at a time, they prove totally indiscernible). Furthermore, if they are also congruent, you can distinguish them only through their reciprocal situation (one being on the right, the other on the left), which calls in the use of a reference element external to the two spheres such as, for instance, a third object that fixes right and left, or proximity and distance, or an ideal object such as given set of coordinates (Specimen Geometriae luciferae, GM VII.275) (p. 143)

On the notion of homogony and in general on the importance of motion in the foundation of the continuum, Cassirer has forcefully insisted in his Leibniz' System: «Man begreift jedoch, dass es für Leibniz schwierig sein musste, die reine Auffassung der Kontinuität, die er zunächst am Problem der Veränderung gewonnen hatte, auch dann festzuhalten, wenn er für die Definition vom Sein der Ausdehnung ausging. Denn gerade dies erwies sich als das Originale von Leibniz' Gedanken, dass er die Unmöglichkeit zeigt, die Stetigkeit als Eigenschaft an einem gegebenen Sein erschöpfend zu bestimmen. Erst aus dem Gesetz des Werdens verstehen wir das Kontinuum. Die Unbestimmtheit, die wir auch in Kants Definition noch fanden, lässt sich gleichfalls darauf zurückführen, dass Kant die Kontinuität hier noch als Eigenschaft der Grösse, nicht als Prinzip ihrer Entstehung sucht.» [It is understood, however, that it would be difficult for Leibniz to maintain the pure notion of continuity, which he had first gained from the problem of change, even if he had assumed the definition of being as extension. For precisely this proved to be the originality of Leibniz's thinking: that he showed the impossibility of exhaustively determining continuity as a property of a given being. Only from the law of Becoming can we understand the continuum. The indeterminacy which we have also found in Kant's definition can also be attributed to the fact that Kant seeks continuity here as a property of magnitude rather than a principle of its origin.] (Werke, vol. 1, p. 167). Here we need however to remark that, no matter how much you look into kinematics, never will you extract from it nor from its metaphysical foundation even the least proof that it should be continuous. Nor let us be deceived by the fact that Leibniz has assumed it to be true since his young years for definition purposes («motus est mutatio situs continua»), as he should then demonstrate (and he does not) that a continuous change of situation is also possible, which is untrue if one assumes space to be discontinuous. The answer Cassirer seems to suggest to such a puzzle is that continuity of motion is however dynamically founded, i.e. founded on the continuity of force, which in turn may be founded on the continuity of monadic activity. Yet, it is precisely in this way that one goes out of kinematics and thus geometry, so that all objections about using motion in geometry present themselves again—in fact motion cannot be used in geometry because the continuity of changes of a monad is (perhaps) only a contingent one. Hence, it is not motion in itself, let alone the motion generated by the system of forces, that can guarantee continuity of space, but rather, as already suggested, some transcendental operation of production of space. (pp. 184-85n)

Chapter III. Phenomenology

"That is said to express a thing in which there are relations [habitudines] which correspond to the relations of the thing expressed. But there are various kinds of expression; for example, the model of a machine expresses the machine itself, the projective delineation on a plane expresses a solid, speech expresses thoughts and truths, characters express numbers, and an algebraic equation expresses a circle or some other figure. What is common to all these expressions is that we can pass from a consideration of the relations in the expression to a knowledge of the corresponding properties of the thing expressed. Hence it is clearly not necessary for that which expresses to be similar to the thing expressed, if only a certain analogy is maintained between the relations." (G VII: 263–64) (p. 298)

What most matters here about the relational character of the distinctive properties of monads is that an isomorphism which fully or partly expresses intermonadic relations as relations occurring between representational elements whatsoever is clearly a faithful isomorphism, in the sense that beyond such relations there is nothing else that may further characterize monads. In other words, saying that a perceptual isomorphism expresses the relations between monads is equivalent to saying that it expresses monads themselves, because monads consist in those relations or, at least, are perfectly individuated by them. Leibniz's substance, as it were, ends up as a function. (p. 323)

As however supersensible and phenomenal elements, at least in their distinctive features, are reducible to two sets of relations, an isomorphism for which all relations between monads are preserved would only express the logical identity between the noumenal world and the phenomenal one—hence, it would radically deny any phenomenalism. As we can see, some relations must exist that are not preserved by the situational isomorphism or at least (distributive) by the totality of homomorphisms. (p. 326)

[M]ost divergences between Critical Idealism and Leibnizean Phenomenalism can be reduced to the following. In Leibniz, the relation between phenomena and noumena is regulated by a structural morphism, whereas in Kant by a simply functional relation (not a determination, but only the ground of it, the Bestimmungsgrund). Thus, for example, no real intentionality can be recognized in Berkeley's idealism, because here, owing to the lack of any partial isomorphism, the noumenal world is simply overruled (i.e., identified with the phenomenal one): «But, say you, though the ideas themselves do not exist without the mind, yet there may be things like them, whereof they are copies or resemblances, which things exist without the mind in an unthinking substance. I answer, an idea can be like nothing but an idea; a colour or figure can be like nothing but another colour or figure.» (Treatise, §8). It is evident that here Berkeley deals with similarity in a most ingenious way and without having the notion of a structural identity that can be preserved beyond material distinctions of genus between phenomena and noumena. What he misses is the very concept of expression. Relevantly, even though no morphism is involved in Kantian philosophy, some functional relationship however subsists there linking a phenomenon to the thing-in-itself. (p. 327)

[T]he limited expressivity of the perceptual isomorphism—which is required in order to establish a distance between phenomena and noumena—finds its further specifications in certain limits of aesthetic comprehension. Furthermore, as it is the only representational content distinguishing monads from one another, only the limitedness of aesthetic comprehension guarantees the possibility for a plurality of substances to be determined, which substances at this point can be distinguished through the different limits of their aesthetic comprehension. In effect, since monads also express such a difference phenomenally through each one's different situs, the most accurate specification of the limits of their finite aesthetic comprehension is to be found in the situation of the phenomenon that expresses the representing monad. Clearly, a monad superordinated to another one will have a broader aesthetic comprehension. We have arrived thus at Leibniz's well-known simile of a town multiplied perspectively. ... [E]ach sight sees the whole town (however variously deformed according to different points of view)—which means that it is not different isomorphisms we are dealing with here, but just one isomorphism variously specified into different homomorphisms. (p. 334)

[I]n order for the various (real) homomorphisms to be determined as genuinely expressive, i.e., referred to a unique intentional object (the noumenal world as a given set of relations), or also, say, as harmoniously perceptual homomorphisms, the ideal isomorphism needs to be determined as a regulative limit of the set of such homomorphisms. It plays actually no other role, in Leibniz's system, than that of an indispensable ideal unity that makes universal harmony possible. (pp. 339-40)

"In fact, even though a circle of a foot [pedalis], one of half a foot [semipedalis], etc., all are different between them, no definition of a foot can nevertheless be given, but there must be some fixed and permanent sample; this is why usually measures are made of a long-lasting material, and it has even been suggested that the Egypt Pyramids, which have lasted for many centuries and presumably will still last for a very long time, be employed for this purpose. Thus, as long as we assume that neither the globe of the Earth nor the motions of stars are significantly to change, our descendants will be able to recognize the same quantity of the Earth's degrees as we have. And if any forms keep their sizes throughout the world and the centuries, as is the case, according to many, with the cells of a honeycomb, these may also provide a constant measure. And as long as we assume that nothing is going significantly to change in the causes of gravity and the motions of the stars, our descendants will be able to learn about our measures through a pendulum. If on the contrary, as I have already said elsewhere, God changed everything and yet preserved the proportions, every measure would fail us, nor could we ever know exactly how much things have changed, because measure cannot by any means be defined, nor can it be kept by memory: and its real preservation is necessary. From this argument, I think, the difference between size and form, or between quantity and quality, appears most clearly." (Specimen Geometriae luciferae, GM VII.276) (pp. 356-57)

"If we conceive of two points existing together, and wonder why we say that they exist together, we will think that this is so either because they are perceived together or because it is just possible to perceive them together. When we perceive an object as existent, for this reason we perceive it in space, that is, we perceive that an indefinite number of other objects absolutely indiscernible from it can exist. Or, still in other words: we perceive that such an object can move, and thus come to be either in one place or in another one; but, since it cannot exist in a plurality of places at the same time, nor can it move in just one instant, this is why we perceive this place as continuous." (Characteristica geomterica §108) (p. 412)
→ もし運動がなければ空間もない（？）

"There is, moreover, a definite order in the transition of our perceptions when we pass from one to the other through intervening ones. This order, too, we can call a path. But since it can vary in infinite ways, we must necessarily conceive of one that is most simple, in which the order of proceeding through determinate intermediate states follows from the nature of the thing itself, that is, the intermediate stages are related in the simplest way to both extremes. If this were not the case, there would be no order and no reason for distinguishing among coexisting things, since one could pass from one given thing to another by any path whatever. It is this minimal path from one thing to another whose magnitude is called distance."(Initia rerum mathematicarum metaphysica, GM VII.25) (p. 423)
→ 二点間の移行のしやすさの度合いを「距離」と呼ぶ。

Chapter IV. Metaphysics

In many places we read that the possible must possess an internal tendency to existence, without which nothing would ever exist (De rerum Originatione radicali G VII.303) (p.440)

【メモ】 Lawrence Sklar (1982) "Saving the Noumena"

以下、頁番号はすべてThe Philosophy of Science (Oxford Readings in Philosophy)のもの。

二つの理論があって、経験的帰結だけではどちらの理論が正しいかを決定できないとき、実証主義者はこう考える：同じ経験的帰結をもたらす二つの理論は等価である。（これを実証主義の等価原理と呼ぶ）

この考えは一見説得的だが、Sklarによると、理論的対象（原理的に観測不可能な対象）に対する反実在論的な態度を伴う。例えば電子に対して存在論的にコミットする理論と、単に道具主義的に扱う理論とが、「現象を救う」限りにおいて等価になってしまう。実在論者としては、これを回避したいが、そのためには実証主義の等価原理よりも強い何らかの理論の等価性の条件を案出しなければならない。

【構造的同型性】

Sklarが提案するのは、二つの理論の間に構造的な同型性があること。

Two theories might have all the same observational predictions but be so radically different in their structure at the theoretical level that one ought to take them as attributing (realistically) quite different explanatory structures to the world. (p.67)

Together, these two features of the theory, commonality of observational consequences and the existence of the appropriate structural mapping at the theoretical level, are taken to be enough to establish theoretical equivalence. (p.66)

しかし、この条件には難点があるとSklarは言う。デカルト流の、欺く悪霊の想定や、水槽の脳のような想定が、通常の実在論的な記述と等価になってしまうという点である。これだと実証主義に接近し過ぎだとSklarは指摘する。

For if the brain-in-a-vat account of the world is really equivalent to the ordinary material object world account, so long as the brain-in-a-vat account is suitably formally structured, then have we really gotten very far from merely saving the phenomena as sufficient for theoretical equivalence? (p.70)

→　これに対しては、次のように答えることができる。もし存在論的なコミットメントに関して異なる二つの理論が構造的に同型であるならば、その二つの理論は等価である。構造を離れた何らかの存在者を想定する必要はない、と。「欺く悪霊」の理論は、我々の通常の世界記述を、ミスリーディングな言い回しで言い換えたものに過ぎないのではないか。

【理論の決定】

経験的なレベルにおける等価性よりも強い等価性の条件を主張すると、理論選択の合理化の問題が再浮上する。

Taking equivalence to demand more than commonality of observational consequences, the realist is faced with the threat of skepticism which arises when he tolerates inequivalent theories having all their observational consequences in common. (p.73)

例えば理論の単純性や、過去の理論との連続性といった基準が考えられるが、実在論者は、その基準が合理的である理由を説明する必要がある。

→　思うに、この点が問題になるのは、観察可能／観察不可能という区分を、Sklarが真に受け過ぎているから。彼は、観察可能性と検証可能性とを混同している。前者は後者を含意しない。というのも、観察不可能だが間接的に検証可能な事例は数多く存在するから。例えば、電場。電場は直接観察不可能だが、真空中の荷電粒子が加速されるのを観察できれば、荷電粒子に力を及ぼす空間の性質が存在すると結論できる。これを我々は電場と呼んでいるわけだ。要は、検証可能性は観察可能性よりも広い概念だということ。そして、Sklarの想定する実在論者に反して、この広い意味の検証によっても区別できない二つの理論があれば、その二つの理論は等価であると主張しても良いのではないか。今の私に擁護できるテーゼではないが、次のように主張したい：同じ経験的帰結を含意する二つの理論は、構造的にも同型である。つまり、構造が異なれば、その違いは必ず（間接的にであれ）検出可能だということ。

【説明】

理論の決定問題は、データから理論へ向かう「上向き」の問題であった。次は理論からデータへ「下向き」へ向かう説明の問題を考える。ある理論のCraigian還元、つまりその理論の観察可能な帰結をすべて述べる文への還元を考える。実在論者は、Craigian還元が、元の理論と等価、あるいは元の理論よりも単純で優れた定式化であるという結論を回避したい。そのために、実在論者は、Craigian還元には説明力がないと主張する。

Theoretical postulation, we are told, does not merely summarize observational generality nor accommodate it in a compact syntactical form. Theoretical postulation is taken to explain the observational generality. Hence the mere statement of that generality is, in a fundamental sense, totally devoid of any real explanatory power. (p.76)

しかし、「説明力」とは何であろうか。少なくとも、（経験的等価性に加えて）構造の同型性を理論の等価性の十分な条件と見なすような実在論者にとっては、このような観察可能な事実を超えた「説明力」の概念は収まりが悪い。

I want to argue that there is a fundamental tension between the realist's desire to posit a notion of explanation over and above that adopted by the positivist, and his desire to maintain a theory of the meaning of theoretical terms which allows for the notion of theoretical equivalence we have been discussing. (p.77)

理論的な対象や性質を措定することによって、現象に一体何が加わるのか？という問いに対する答えの一つの候補は、「統一」である。例えば、慣性運動が特権的な運動状態として観察されることから、時空構造そのものを、運動する物体から独立の実体として措定するケースを考える。物理的系と、その背後にあるこの時空構造との関係によって、慣性運動と非慣性運動の力学的・光学的な差異が説明される。実在論者によれば、かくして多様な現象が、一つの形式の元に統一される。

これに対する実証主義者の反論：
The appearance of additional explanatory value in the substantivalist spacetime account, over the purely relationist theory, is due to the fact that while the reference to spacetime itself is really introduced only in the holistic-place-in-the-theory manner of the realist we have been emphasizing, the naive picture of spacetime as a kind of "ghostly" substance, sort of like a thin "rigid" extended material thing, gives us the impression that we are getting an explanation like that which the other kind of realist would offer. (p.78)

これは全くその通りと思われる。結局、

[T]his notion of theoretical meaning [as holistic place in the theory] and of theoretical equivalence [as observational equivalence + structural isomorphism] ... suffers also from the difficulty of making it hard for us to see just what it is that is explanatory in a theory, or in any of its equivalents, which is not already there in the allegedly nonequivalent and non-explanatory Craigian reduction of the theory so beloved of positivists. (p.79)

Craigian還元でもなく、理論外からの意味の輸入に依存するような説明でもない、二つの極端の間を行く何らかの「統一」の概念が必要と考えられる。

感覚の秩序と物理的世界の秩序

感覚の秩序：
事物は、それらが生体に対して及ぼす効果に応じて分類され、感覚の秩序へ組み込まれる。ある事物がこの秩序内に占める位置は、生体に対してその事物が及ぼす効果を表現している。

物理的世界の秩序：
事物は、それらが互いに及ぼす効果に応じて分類され、物理的世界の秩序へ組み込まれる。事物がこの秩序内に占める位置は、それが他の諸事物と取り結ぶ相互的な関係を表現している。

科学の過程は、前者の感覚秩序による事物の分類を、徐々に、後者の物理的秩序による事物の分類に置き換えて行く過程と見なすことができる。これはすなわち、事物が生体に対して及ぼす効果を度外視していく過程に他ならない。

例えば、水と塩酸は、見た目は同じであるから、（少なくとも視覚刺激に限定すれば）感覚秩序においては同じ事物として分類される。しかし、水は鉄と反応しないが、塩酸は鉄を溶かす、という風に、他の事物との相互関係に基づいて、我々は水と塩酸を別の事物として分類できる。これはごく素朴な例であるが、感覚秩序を徐々に物理的秩序に置き換えて行く過程のエッセンスを捉えていると思われる。

ここで重要なのは、物理的世界の秩序はあくまで関係の秩序である、という点。物理的な事物は、物理的構造の中のノードとしてしか意味を持たず、その構造と無関係であるような如何なる性質も持たない。「塩酸」という概念の意味は、それが他の概念と取り結ぶ関係によって尽くされており、それを超えた「塩酸そのもの性」のようなものはない。

物理的構造の実在性

『実体概念と関数概念』においてCassirerは、変換に対する頑強性を以て構造の客観性（実在性）を定義した。しかし、これだけでは、少なくとも物理的構造の場合、客観性の基準として十分でないように思われる。というのも、同じデータを説明できる構造が、一意的に決まるとは限らないからである。変換に対する頑強性という客観性の捉え方の不十分さは、経験との結び付きが欠けていることに起因している。経験を考慮するには、ある構造の予測能力が、変換によってどの程度影響を蒙るかを考察する必要がある。

【メモ】 Christopher Hookway / The Pragmatic Maxim: Essays on Peirce and Pragmatism

Introduction

"there is no need to justify current beliefs, only changes in belief" (Isaac Levi, "Pragmatism and Change of View" p.179)

Chapter 1: Peirce and Scepticism

[In the nominalist conception of reality] we know about external things through the mediation of what seem to be intuitions, singular representations ("sensations") which are determined by ("directly influenced by") the transcendental object and which provide the sole basis for our thoughts. (...) This view assigns a fundamental role to intuitions: they are our point of contact with (and only source of information about) reality. The method of doubt can then be seen as a device for identifying what is really given to us in intuition; it helps us to free ourselves from those aspects of our perceptual beliefs that are determined by background substantive assumptions rather than being determined by the transcendental object. (p.31)

"This final opinion, then, is independent, not indeed of thought in general, but of all that is arbitrary and individual in thought; is quite independent of how you, or I, or any number of men think." (CP 8.12)

Chapter 3: Truth, Reality, and Convergence

When a proposition is true, "anyone who investigates" is fated to arrive at belief in it. Now "investigates" is a transitive verb. So, anyone who investigates what? When this is spelled out, a variety of distinct theses emerge.

1. If a proposition is true, then anyone who inquires "into the nature of reality" (well enough and long enough) is fated to believe it.

2. If a proposition is true, then anyone who investigates some question to which that proposition provides the answer is fated to believe it.

The "traditional" reading of Peirce, the reading that leads to claim that he is committed to an absolute conception of reality, suggests that he accepts (1): any truth is, in principle, accessible to any inquirer. Position (2) need not lead to such an interpretation of his views. It is compatible with the recognition that a particular inquirer might be fated never to confront a question to which some true proposition provides the answer, perhaps even with the admission that some inquirer could never even understand such a question. (p.56)

Chapter 5: Normative Logic and Psychology

Suppose that I am justified in believing that someone is an extremely successful poker player. When I learn that they make use of a particular strategy of reasoning in the course of their play, then, we might suppose, I have good, albeit defeasible, reason for thinking that the kinds of reasoning they employ are indeed good ones. I would not have an explanation of what their goodness consists in. But I do have strong inductive evidence that the inferences they use can be trusted. It is important that this depends upon the normative premiss that the poker player is successful. The target of Peirce's criticisms is a position where no such normative information is already available. A similar phenomenon occurs when philosophers of science attempt to construct an account of the scientific method through detailed historical studies of scientific practice. We identify norms for scientific practice through (psychological?) descriptions of how science has actually proceeded. Paul Thagard observed that this is not strictly a case of using descriptions of scientific practice in order to determine how scientific inquiry ought to be. The whole inquiry depends upon the selection of examples of good science as subjects of historical inquiry. A crucial normative judgement is already made at the very beginning. (pp.95-96)
→　「しかし、ある科学がgoodかbadかの判断は、それがevidenceに合致しているかどうかという事実によって決まるのではないか」という疑問に対しては、科学は「evidenceに従うべき」という規範にやはり従っている、と答えることができる。

Chapter 6: "The Form of a Relation"

The major difficulty for the ante rem [structuralist] position is that it needs to explain what the reality of the required structures consists in when there are no systems that exemplify them. (p.125)

Chapter 9: The Principle of Pragmatism

"Pragmatism is the principle that every theoretical judgment expressible in a sentence in the indicative mood is a confused form of thought whose only meaning, if it has any, lies in its tendency to enforce a corresponding practical maxim expressible as a conditional sentence having its apodosis in the imperative mood." (EP 2: pp.134-135)
→　条件付きでない確率はconfusedであるという論点との繋がり。「確率とは、ある行為（推論の条件）に対して、ある事象（推論の帰結）が成立する相対頻度である」という定式化は、確率概念のpragmatic clarificationに相当すると言える（？）

プラグマティズムの格率の二つの定式化：

(i) If the circumstances are C and you have desires D, then (you ought to) perform an action of type A.

(ii) In circumstances C, if you were to do A, then you would experience E.

次の補助命題によって、(ii)から(i)を導出できる：

(iii) If you desire to experience E, then you can do so by doing A.

"The occasion of such action would be some sensible perception, the motive of it to produce some sensible result." (W3: pp.256-266)
→　行為の目的とは常に、何らかの感覚可能な結果をもたらすことである。

概念の使用は常に、（たとえ潜在的であれ）その概念に対する何らかの働きかけ（行為）を伴うとすれば、概念使用がpractical bearingsを持たねばならない理由が分かる。(p.177)

"[The end of an explanatory hypothesis] is, through subjection to the test of experiment, to lead to the avoidance of all surprise and to the establishment of a habit of positive expectation that shall not be disappointed." (EP 2: p.235)

[W]hat is required of pragmatic clarifications is that they can be interpreted in this way [in the form of conditional resolutions]; it is not required that they explicitly take this form. (p.180)
→　実際、定式化(i)を実際のclarificationで適用するのは、想定可能な場面や欲求が多すぎて実質的に不可能。

One of Peirce's strategies for proving pragmatism, was to argue that the pragmatic clarification of a proposition (or concept) would constitute its "ultimate" or "final" logical interpretant. Even if such an interpretant is not useful to us, is not easy to formulate or apply in practice, the fact that the final logical interpretant takes this form is the key to the correctness of pragmatism. So perhaps the final logical interpretant can take the form of a huge set of conditional resolutions, even if our everyday pragmatic clarifications cannot do so. (p.180)

[James's definition of pragmatism] differs from mine only in that he does not restrict the "meaning," as I do, to a habit, but allows percepts, that is, complex feelings endowed with compulsiveness to be such. If he is willing to do this, I do not quite see how he need give any room at all to habit. (CP 5.494)
→　habitでなければindividual reactionsになってしまい、一般的なパターンを確立できない。

Chapter 11: How Peirce Argued for His Pragmatic Maxim

Peirce talks of the logic of judgement and assertion, and compares this with a psychology of belief. We understand judgement as a practice of belief formation which is governed by logical norms; in making a judgement, I commit myself to the correctness of doing so. (p.204)

The mathematician's notations will typically instantiate the abstract structure that she studies. We obtain knowledge of abstract structures by experimenting upon their instantiations. Thus our knowledge of mathematics doesn't provide counterexamples to the pragmatic maxim. (p.218)

"I will say that a sign is anything, of whatsoever mode of being, which mediates between an object and an interpretant; since it is both determined by the object relatively to the interpretant, and determining the interpretant with reference to the object, in such wise as to cause the interpretant to be determined by the object through the mediation of this 'sign'." (EP 2: p.410)

The two italicized phrases can be best understood as follows: the rash is a sign of measles because it has the power to be understood or interpreted in that way; and the sign can be understood as an indication of measles because the object (the measles) has produced the sign. (p.222)

[O]nly a habit can serve as the ultimate interpretant of an intellectual concept. (p.228)

"It can be proved that the only mental effect that can be so produced and that is not a sign but is of a general application is a habit change; meaning by habit change a modification of a person's tendencies toward action, resulting from previous experiences or from previous exertions of his will or acts, or from a complexus of both kinds of cause." (CP 5.475)

"[E]very man exercises more or less control over himself by means of modifying his own habits; and the way in which he goes to work to bring this effect about in those cases in which circumstances will not permit him to practice reiterations of the desired kind of conduct in the outer world shows that he is virtually well-acquainted with the important principle that reiterations in the inner world—fancied reiterations—if well-intensified by direct effort, produce habits, just as do reiterations in the outer world; and these habits will have power to influence actual behaviour in the outer world; especially, if each reiteration be accompanied by a peculiar strong effort that is usually likened to issuing a command to one's future self." (EP 2: p.413)
→　これはnormativityの自然的説明たりうるのではないか。ただし、実際の場面でnormativityを自然的な記述に還元できる、という意味ではない。

【メモ】 Stewart Shapiro / Thinking About Mathematics: The Philosophy of Mathematics

【論理主義】 

一つ前の記事参照。

【直観主義】

・直観主義は排中律の拒否に尽きるわけではない。直観主義の根本にあるのは「数学は心的に構成される」という哲学であって、排中律の拒否はその一つの帰結に過ぎない。その他にも例えば、被定義項を含む集合への言及を含む非可述的定義の拒否がある。直観主義の理解では、言及される集合は構成に先立って存在するわけではないから、こうした非可述的定義は循環していることになる。これは排中律の拒否とは論理的に独立。また、可能無限の立場も排中律の拒否だけからは出てこない。確かに ¬∀xPx ⇒ ¬¬∃x¬Px ⇒ ∃x¬Px という推論は排中律の拒否によってブロックされるが、これが直ちに可能無限の立場を意味するわけではない。

・まだちゃんと考えたわけではないものの、直観主義論理と古典論理のどちらが「正しい」かという問いには答えがない気がする。現象論のレベルでは古典論理が有用だけれど量子のレベルでは分配律が破れるのと同様、記述対象に応じた使い分けの問題なのかもしれない。 例えば宇宙の状態は一意的に確定できないというRovelli流のRQMには直観主義論理が適しているように見える。

・Dummetの直観主義は謎。

【プラトニズム】

"But, despite their remoteness from sense experience, we do have something like a perception of the objects of set theory, as is seen from the fact that the axioms force themselves upon us as being true. I don't see any reason why we should have any less confidence in this kind of perception, i.e., in mathematical intuition, than in sense perception, which induces us to build up physical theories and to expect that future sense perceptions will agree with them." (Kurt Gödel, "What is Cantor's Continuum Problem")

[F]or Gödel, the independence of CH from ZFC shows that "these axioms do not contain a complete description of reality." (p.210)
→　ゆえにCHの真偽を確定するためには、ZFCを超出しなければならない。不完全性定理の証明において、算術体系の命題を決定するために算術体系を超出したのと同様に。

the "notion of analyticity ... just subsides into the humbler domain where its supporting intuitions hold sway: the domain of language learning and empirical semantics." (W. V. O. Quine, "Reply to Geoffrey Hellman")

To echo Mill, we know by experience that [mathematical] intuition is reliable. (p.224)

【虚構主義】

Arithmetic and real analysis can be simulated in space-time, using certain space-time points and regions as surrogates for numbers. One can also formulate a version of the continuum hypothesis in Field's synthetic physics. (p.232)
→　しかしこれは構造が等価と言ってるだけで、CHは構造そのものだとすれば、結局Fieldは数学をやっていることになるのでは、ってツッコミながら読んでたら、後でShapiroが同じこと言ってた。

Let P be a scientific statement that makes reference to say, real numbers, and let P' be a nominalistic reconstrual of P. The hermeneutic nominalist claims that P and P' have the same meaning, and so despite appearances, P does not really make any reference to real numbers. Burgess and Rosen point out that if P and P' do have the same meaning, then one is justified in the opposite conclusion: despite appearances, P' does make reference to real numbers, since it has the same meaning as P. After all, synonymy is a symmetric relation ... (p.248)

EddingtonとStrawsonの汎心論についてのメモ

自分の研究計画の中からボツった一節をとりあえず上げておきます。

Dr. Galen Strawson's argument is based on the idea of the physicist Arthur Eddington, that since science reveals only the structural form of things and not their intrinsic nature, there is nothing that prevents us from ascribing to these things the stuff of consciousness; and that it is in fact silly not to, for we have a direct insight into the intrinsic nature (or in Eddington's words, the "background") of a certain small part of the universe, namely, the consciousness nature of our brain, and it would be pointless to introduce some other nature inconsistent with consciousness, and then wonder where the latter comes from. The natural inference is that it is consciousness all the way down.

課題：Strawsonは論文"Realistic Monism"の中で上記のEddingtonの論法に依拠して汎心論を唱えているが、この論法は彼の別の論文"Panpsychism?"の中で粗描されているミニマルな実体概念（性質によって尽くされてしまうような）と果たして整合するか。

【メモ】 リバタリアニズムの人間観―ヴィルヘルム・フォン・フンボルトに見るドイツ的教養の法哲学的展開 （吉永圭）

【序章　 法哲学の厳密性を確保する法思想史方法論と現代福祉国家の問題】

「リバタリアンは人間の完全性への憧憬を持ち合わせていないため、近代法がただ強い個人を想定しているのとは異なり人間は不完全なものであり理性には限界があるということを強く意識するがゆえにあえて無色透明な人間像を採用しているのではないだろうか。つまり、リバタリアンが経済力・交渉力の格差を考慮に入れない無色透明な人間像を前提とするのは、法が法主体の多様性を把握することは不可能だという一種の諦観に基づいているからだと思われる」（橋本祐子「リバタリアニズムの法理論」p.67）
→　こうしたリバタリアニズムを「確固たる人間観なきリバタリアニズム」と呼ぶことにする

人間をあるがままの自然状態の中に放置すると想定する。すると、人間はハートが指摘したような弱さ故、自然と強制力を持った装置を熱望するのではないか。……リバタリアニズムが個人の生活への国家介入を拒否するならば、そこには何等かの目的意識から構成された人間観が必要なのではないか。あるいは確固たる人間観なきリバタリアニズムは、自らは人間のあり方から不自然でない形で最小国家論を導いたかのように装うが、実はある一定の人間観を密輸入して自己の理論を組み立てているのではないか。(p.33)

【第一章　一八世紀後半ドイツの状況】

カントにとって重要なのは立法権と行政権の分離であり、行政権は元首に委ねられる。この元首とは、カントの時代においては国王である。立法においては代議制のみが採り得る道としながらも、執行権を掌握するという形で国王の君臨を許すことから、カントが少なくとも現代的な意味での民主制を支持しなかったと結論して良い。(p.99)

「民主主義のために戦ったのちの自由主義的教義とは異なり、初期の自由主義は通常、統治の最善の形式に関して慎重に言明を避け続けた。万民の最大限の自由を保障する政体である限りは、君主制でも、貴族政でも、民主制でも良かったのである。」(Frederick C. Beiser, The Early Political Writings of the German Romantics p.xxiii)

【第三章　フンボルトの前期思想】

「人間の真の目的は、——変わりやすい傾向ではなく、いつまでも変わらない理性によって示されるものであるが——人間の持つ諸力を最高にしかも最も調和のとれた一つの全体へと陶冶すること（Bildung）である。この陶冶の為に自由は、第一の不可欠な条件である」（『国家活動の限界を決定するための試論』）

「彼［フンボルト］の自由の概念は彼の文化の概念と密接に繋がっている。彼にとって自由とは、人間の諸力の発展と、それゆえ文化の発展の不可欠の基礎を形成する、不定で多様な活動の可能性を意味する」（Reinhold Aris, History of Political Thought in Germany from 1789 to 1815 p.147）。つまり、フンボルトの自由はそれ自体が価値を持つのではなく、最終的に己の諸力を文化形成に資するように導くための概念なのである。ここに政治参加への自由、といった積極的自由の概念は見られない。フンボルトの自由は、消極的自由の範囲を出ない。(p.142)

「われわれの存在に関する究極課題とは、次のようなものである。われわれの人格の中に、われわれの生前と死後を問わず、われわれが後に残す生き生きとした活動の痕跡によって、人間性（Menschheit）の概念に対して出来るだけ多くの内容を与えることである。このような課題を解決するためには、われわれの自我を世界と結び付けて、最も普遍的で、最も活発な、最も自由な相互作用を保つほかになす術はない。このことだけが、人間の認識のあらゆる部門の取り扱いを評価するための、真の尺度とならなければならない」 （『人間形成と言語』pp.68-69）

シュプランガーによる、フンボルトの人間性理念の説明：「個性」（Individualität）が諸力の「全面性」（Allseitigkeit）・「普遍性」（Universalität）を通じて自らを「全体性」（Totalität）へと形成していく。

ここで注意すべきは、フンボルトが社会集団あるいは社会関係というものを想定していたとしても、それは専ら個人という存在に対する影響に関する限りで彼の関心を引いたということだ。我々は社会集団（共同体）がフンボルトによって言及されているからといって、そこに政治的組織といった含意を読み取ることはできないのである。(pp.145-146)

フンボルトの哲学にはライプニッツの予定調和的世界観がある（個人に可能な限り自由を認めることが全体にとっても良い）。しかし社会における全体の秩序は個人の完成への努力に比べてあくまで副次的な問題。(p.147)

「後の自由主義とは異なり、彼［フンボルト］は民主制の擁護者ではなかった。彼の視野においては、容易く下層民の暴走に転じ得る民主制よりも独裁制や貴族政の方が自由を保障し得る。」
Frederick C. Beiser, Enlightenment, Revolution, and Romanticism p.111)
→　モンテスキュー、ルソー、ヴィーラント、そしてカントも、小さな共同体以外で民主制が現実になることを疑っている。

フンボルトにとって民主制採用を阻む障害は「無教養な民衆」である。この層が政治を掌握すれば、暴発し、専制あるいは無秩序になるという懸念があったのだろう。これは、フランス革命直後のパリを視察したフンボルト自身の経験が教えるところであったと推測される。(p.161)
→　教養を身に付けていない者が政治に口を出せば、己の利益のために政治を利用し、他者（および自身）の陶冶を妨げることになる。

フンボルトには政治的討議で自己を練磨していくという発想は見られない。(p.162)

【第四章　フンボルト国家論における人間観の問題】

フンボルトの教育論にデヴィッド・ソーキンは、新人文主義と啓蒙主義の和解を見る。即ち、啓蒙主義、特に統治者側からの啓蒙的理念において陶冶概念は国家に有益なものであった。しかしフンボルトは陶冶を単なる道具的概念とすることを認めたくなかった。そこで、啓蒙の諸目的は間接的に、陶冶の意図されたしかし付随的な帰結として実現されるべきである。フンボルトは自由な個人になるように教育された人間の方が、市民になるように教育された人間よりも、究極的にはより良き市民となる、と主張した。「道徳的人間あるいは良き市民」の状態を作り出し国家に奉仕することが国家の究極の目的である。しかしカリキュラム上は直接そのことを目指すのではない。国家目的は、個人を無益な職業訓練に従事させることではなく、個人独自の性格を発展させるように教育することによって、最も良く達成される。(p.193)

フンボルトの作品の随所で登場する「（諸）力」の概念は、ライプニッツの「力」概念の継承。フンボルト自身の受けた教育の中で特に影響力が強かったのはライプニッツであった（ライプニッツはフンボルトにとって最初の哲学的支柱であった）。(p.208)

【第五章　フンボルトの限界とその克服の試み】

「社会の全員が常に社会的意識を持て」と命令することはリバタリアンには許されていない。我々はただ、確固たる人間観なきリバタリアニズムの議論より「緩やかな程度の政治志向性」の方が、社会的意識を有した人間が多く登場すると言い得るのみである。(p.255)

「国家の配慮というものは、全ての者が何を学ぶかではなく、全ての者が学ぶということにある」(Hans Maier, Staat, Kirche, Bildung p.72)

【終章　現代正義論へ向けて】

個々人の善の領域における幸福追求 も、その周囲を囲む領域の安定が前提となっている。秩序安定のために様々な制度（例えば、国家）が考案されるのであるが、この秩序維持に最も重要な要素はやはり人間ではないか。いくら機能的な制度を秩序維持のために導入しても、運用・利用する人間がそれに適合的な資質を持たなかったら、当該制度は秩序の維持に失敗するか、あるいは一部の人間が秩序維持目的の制度を独断的に利用し、他の人々の善を破壊するほどに暴走する恐れがある。(pp.280-281)

【メモ】 Ernst Cassirer: The Last Philosopher of Culture (Edward Skidelsky)

【第二章　マールブルク学派】

Natorp and the young Cassirer both rebelled against this [Cohen's] mathematical dogmatism; both tried, as we shall see in the next chapter, to extend the critical method to nonscientific experience. But they nonetheless viewed such experience as a mere "first stage" in the process of objectivization, culminating eventually in physics. Their sights remained fixed on the universal, intersubjective realm of science. The Marburg school thus never fully overcame what we identified in the last chapter as the alienation of scientific reason. Although it struggled mightily against the detachment of science from morality, it could not solve—indeed, it could hardly acknowledge—the more fundamental problem of its divorce from what Husserl was later to call the Lebenswelt—the world of life. (p.45)

Radicalism—as the career of Heidegger amply illustrates—is an ambiguous virtue. Revolutions in thought have an unhappy tendency to be realized in action. Cassirer's refusal, as he put it, to hurl his ideas into empty space, his effort to relate them to those of his Kantian precursors, was fundamentally an attempt to preserve a link with the civilization that his more original contemporaries were busily dismantling. (pp.48-49)

【第三章　新しい論理学】

"The analytic function of thought, with which all these logicians appear to be exclusively concerned, has indeed a good logical claim and practical significance. But we hold fast to the conviction to which Kant has given almost classic expression: 'Where the understanding has not previously united, it cannot dissolve.' Thus ... it is synthesis that is necessarily primary for the logical understanding of knowledge, and the analysis of meaning is required only as its pure corollary." (Paul Natorp, Die logischen Grundlagen der exakten Wissenschaften p.9)

Cassirer rejected both attitudes outlined above. He did not share Carnap's view of logic as the framework of all meaningful discourse. Neither did he view it [as Heidegger did] as something to be dissolved "in the turbulence of a more original questioning." His position represents a characteristic refusal to take sides in the debate between a narrow, scientistic rationalism and a virulent irrationalism. By recasting the new logic as transcendental logic, Cassirer was able to register both its achievement and limitation. (p.56)

The historical Kant regarded the concepts of Aristotelian formal logic as constituting an independent "form of thought" which must be "schematised in intuition" in order to yield the categories of transcendental logic. In the Marburg interpretation, this relationship is reversed. Kant may have used formal logic as a "clue" to transcendental logic, explains Cassirer, but this was done not "with the aim of basing the transcendental concepts on the formal ones, but conversely, with the aim of basing the latter on the former, and in that way yielding a more profound understanding of the ultimate ground of their validity." (Kant's Life and Thought p.173) In other words, formal logic is just an abstraction from transcendental logic, with no independent philosophical significance. This revision reflects what I described in the last chapter as the Marburg school's historicization of the transcedental subject. Kant's timeless "form of thought" is dissolved into the ongoing movement of scientific objectivization, which casts off, like dead skins, the structures of pure mathematics and logic. Cassirer's logic of objective knowledge is not to be regarded as founded on symbolic logic, then, but as revealing its true foundation. (p.58)

Science is always looking forward to future consummation; it is, to borrow Cassirer's favorite phrase from Leibniz, gros de l'avenir—pregnant with the future. We must therefore reject the binary view of scientific theories as either true or false. The movement of science is not from false to true but from less comprehensive to more comprehensive. (p.62)

From the standpoint of conventional formal logic, according to which all propositions are either true or false, they [Cassirer's passages] are almost unintelligible. But from Cassirer's standpoint, it is formal logic that ultimately renders unintelligible the dynamic process of scientific discovery. (pp.62-63)

His real objection is to Cohen's more fundamental philosophical claim that the relation "is a category only insofar as it is a function [関数]." And here Russell's calculus of relations comes to his assistance. It enables Cassirer to transfer priority from the specifically mathematical notion of function to the general logical notion of relation. The former now appears as a special case of the latter, with no uniquely "categorical" significance. The possibility of categorical yet nonetheless nonmathematical relations—and thus of nonmathematical objectivization—is opened up. (p.65)

【第四章　イロニーと悲劇の間で】

"for the genius one case counts for a thousand" (Goethe)

Particularly interesting, from our point of view, is a 1932 essay by the art historian Edgar Wind, a former doctoral student of Cassirer and a member of his intellectual circle. Although personally on good terms with Cassirer, Wind was critical, from an empiricist standpoint, of his philosophy of symbolic forms. His portrait of Goethe throws some light on their differences. Wind looks askance at the very thing Cassirer so admired in the poet—namely, his irony, his capacity to treat every interpretation of reality symbolically. Where Cassirer sees only breadth and flexibility of mind, Wind discerns a subtle form of evasion. "Goethe said of himself that he viewed everything symbolically. This is an admission that in his case imagination served to transform things into images, to divest them of their substantiality, enabling him to escape the claims they might have had on him as things." It was only by renouncing reality, with its harsh, conflicting demands, that Goethe was able to achieve his celebrated inner harmony. His entire career can be seen as "a flight from life to image." It is possible that Wind formulated these remarks with his former teacher in mind. They certainly apply as well to Cassirer as they do to Goethe. (p.86)

One of the very few persons who read it [Habilitationsschrift, Experiment and Metaphysics] was the late Ernst Cassirer, and I am sorry to say it made that amiable man extremely angry. In honour of his memory I must protest against the suggestion that we held the same view about the nature of symbols. My thesis was that symbols are "real" only to the extent in which they can be embodied in an experimentum crucis whose outcome is directly observable—in his view a deplorable lapse into "empiricism." (Edgar Wind, letter to the Times Literary Supplement)

Opposition to the positivist instrumentalization of science was, as we have seen, a central part of the program of Marburg neo-Kantianism and Substance and Function. But it was only later that Cassirer began to attack positivism and instrumentalism not simply as theories in the philosophy of science but as cultural and political phenomena. Like Warburg, he viewed them as expressions of the hubris of a civilization that has forgotten or suppressed its own mythical origins, thereby opening the door to their revival. Cassirer cites as an example the degeneration of Comtean positivism into a pseudoreligion, complete with priests and temples of science. And in The Myth of the State he shows how the instrumentalization of political reason, initially undertaken in a spirit of enlightenment, eventually gives rise to the myths of modern totalitarianism. Cassirer explicitly conceived his own philosophy as an antidote to the "forgetfulness" of positivism. Like the Warburg Library, it is an attempt on the part of reason at mnemosyne or recollection. It is based on the conviction that reason can understand and feel "at home" with itself only when it has succeeded in reconstructing its own ascent from the sphere of myth. (p.98)

【第五章　象徴形式の哲学】

For all his phenomenological flirtations, Cassirer remained faithful to Cohen and Natorp's conception of philosophy as "bound to the fact of science as this constitutes itself, and therewith to the whole of human culture." Philosophy has no empire of its own; it can do no more than clarify and draw together the tendencies implicit in the arts and sciences. It is, so to speak, the self-consciousness of culture. (p.102)

[Ernst's wife] Toni Cassirer's memoir contains the following revealing story. When Cassirer's son Heinz expressed a wish to study philosophy directly after leaving school, Cassirer demurred. "It was Ernst's unshakable opinion," adds Toni, "that philosophy should never stand isolated but should rather spring spontaneously from the study of other sciences." (Toni Cassirer, Mein Leben mit Ernst Cassirer p.134)

The mythical origins of human culture cannot be eliminated altogether, but they can be confined to what Warburg called "the distant shadowy realm of the explicit metaphor." The myths we need are the spiritualized ones of religion and the playful ones of art. These absorb, discipline, and refine the energies that would otherwise find expression in the brutally literal myths of totalitarian politics. (p.109)

Expressive phenomena are not to be viewed, insists Cassirer, as a "projection" of inner states onto a neutral physical substratum. On the contrary, it is this "neutral substratum" that is itself derivative, a product of scientific analysis. "We arrive at the data of mere sensation—such as light or dark, warm or cold, rough or smooth—only by setting away a fundamental stratum of perception, by doing away with it, so to speak, for a definite theoretical purpose. (...) This disregard is perfectly justified from the point of view of the purely theoretical intention, the intention of building an objective order of nature and apprehending its laws; but it cannot do away with the world of expressive phenomena as such." (The Philosophy of Symbolic Forms 3.37). Myth is therefore not, as commonly presented, a spiritualization of a neutral physical reality but a state prior to the very distinction between the spiritual and the physical. (...) All nature is imbued with spirit, yet spirit, by the same token, belongs entirely to nature. (p.116)

【第六章　論理実証主義】

 "I would allow as 'a priori' in the strict sense, really only the thought of the 'unity of nature,' that is to say the lawfulness of experience in general (...): but how this thought is made specific in particular principles and presuppositions—this comes to light only in the progress of scientific experience." (Ernst Cassirer, letter to Schlick)

"This transition [from one form of physical theory to another] never means that the fundamental form absolutely disappears, and another absolutely new form arises in its place. The new form must contain the answers to questions proposed within the older form; this one feature establishes a logical connection between them, and points to a common forum of judgement to which both are subjected." (Substance and Function p.268)

"For a purely descriptive ethics that remains strictly within its own boundaries, there clearly exists no ground for such a rejection [of fanaticism]. In every age, fanaticism has not merely proved its power in human affairs, it has also been advocated and preached as an ideal; and today it is lauded on many sides almost as 'the' moral ideal per se. A moral philosophy that wishes to be nothing more than a science of factual moral evaluations, in their historical actuality and development, must therefore be content to record this fact alongside other facts." (The Philosophy of Symbolic Forms 3.xv)

"Cassirer trusts religious far more than scientific enlightenment as a counter-force to the violence of political myths—he relies on the confinement of myth within its own proper sphere, which was long ago achieved by monotheism."(Jürgen Habermas, The Liberating Power of Symbols p.26)

If we, the enlightened, are to prevail, we cannot shut ourselves up within the closed circle of reason. The formulas of science and economics are not enough. We must learn the language of unreason, the better to master and subdue it. (p.158)

Ritual denunciations of the "genetic fallacy" will convince only those who have already lost faith in tradition as a source of norms. (p.159)

【第七章　生の哲学】

Symbolism is not a dark glass separating us from reality as it is "in itself"; it is the medium within which any possible reality appears. There is, then, no conceivable extrasymbolic reality in contrast to which it can be denigrated as "artificial." Culture is not a garment thrown over the bareness of nature; it is our nature. The mask is the face, the face the mask. (pp.162-163)

[For Bergson, i]f we want the object itself, in all its concrete glory, we must do away with concepts and adopt the standpoint of pure intuition. This is the method of metaphysics, a science that—in a phrase pinpointing Cassirer's disagreement with Lebensphilosophie—"claims to dispense with symbols." (Henri Bergson, An Introduction to Metaphysics p.24) (p.166)

【第八章　ハイデガー】

Through the efforts of Scheler and and others, motifs from Bergson, Dilthey, and Nietzsche were translated into the rigorously "presuppositionless" idiom of Husserl—a process paralleling the transformation of positivism into logical positivism. Thus was born that strange monster: a rigorous irrationalism, a system against systems. This monster came to maturity in Heidegger's masterpiece, Being and Time. (pp.195-196)

Heidegger's philosophy—and this is of course a serious worry—contains nothing to rule out a fascist interpretation. But neither should it simply be identified with fascism or with any other political stance. Philosophical theories are not just sublimated ideologies; they have a dynamic of their own, cutting across ideological boundaries. (p.197)

The truth of a philosophical proposition is not dependent on its political implications. Whoever has philosophy at heart must treat its problems on their own terms, dealing as best he can, through irony, esotericism, or simple silence, with any unpalatable consequences. What he cannot do is change his metaphysics to suit his politics. I am therefore skeptical of recent attempts to revise the verdict of Davos in line with current political sensibilities. Many scholars, especially in Germany, regard Cassirer's rout and subsequent neglect as an injustice, a national disgrace, for which amends must now be made. "The question remains pertinent, indeed overdue," writes Enno Rudolph, "why so constructive and rigorous an anti-nihilistic critique of European modernity as that developed by Cassirer had to lose out, in German philosophy since Heidegger, to the destructive type of anti-modernism." Cassirer lost out not just in Germany, though, but all over Europe, and for reasons that are not just political but authentically philosophical. As we have seen, his vision of philosophy as the critique of culture gave way to the aprioristic conceptions of Wittgenstein and Husserl—a shift whose ultimate explanation lies in the First World War and the accompanying loss of faith in history. Lost faith is not easily recovered. We cannot just "go back" to Cassirer; we cannot pretend that the twentieth century didn't happen. (pp.218-219)

Analytic philosophy has withstood the influence of Heidegger, but only by transforming itself into a purely technical discipline, indifferent to questions of culture and politics. Russell was a free-thinking progressivist, Frege an anti-Semitic reactionary, yet they could converse with perfect amicability on the subject of symbolic logic. Whether this marks the advent of philosophy as "rigorous science" or its final descent into triviality is another question. Our contemporary situation is, then, a torn one. We are inheritors of two histories—the one political, in which liberalism triumphed over its fascist and communist rivals, the other philosophical, in which it lost out to the Existenzphilosophie of Heidegger and the technicism of the analytic tradition. Cassirer's liberalism was all of a piece; it was at once political, cultural, and philosophical. Such unity of vision is impossible for us. Our political principles find no support in our cultural tastes, religious beliefs, or metaphysical insights. We pay tribute to Cassirer, but Heidegger remains the secret master of our thought. (p.219)

【第九章　政治】

Cassirer's appeal lies in his promise to ground political liberalism in a broader vision of human culture. He epitomizes that attitude of mind—dispassionate, ironic, and optimistic—without which liberalism in the narrow [legal or economic] sense cannot hope to survive. (p.222)

Contemporary liberals are faced, whether they like it or not, with the unpromising task of erecting a philosophy of political hope on a foundation of cultural despair. (p.222)

His criticism of Rousseau is at the same time a criticism of the so-called German concept of freedom through the state. His own preference is for the Anglo-Saxon liberal conception of freedom from the state. Yet he avoids the utilitarianism usually associated with this conception, appealing instead to the idealist notions of "humanity" and "personality." Cassirer has, one might say, married a negative conception of political freedom to a positive conception of spiritual freedom. This union is not original; its prototype can be found in Leibniz, Kant, and Humboldt. But in an era when liberalism of any kind was viewed as an excrescence of the English commercial spirit, as a "philosophy of life from which German youth now turns with nausea, with wrath, with quite peculiar scorn," Cassirer's reminder of a distinctively German form of liberalism was apt and timely. (p.229)

We have inherited liberal political institutions from our past, but not the surrounding climate of ideas that once nourished them. Gone are the certainties of the Christian era; gone, too, the cultural optimism of the eighteenth and nineteenth centuries. Our predecessors believed that political liberty would lead not only to greater material prosperity but also to the spread of knowledge, the weakening of prejudice, and the flowering of the arts. Who would dare to assert that now? (p.236)

Under these conditions, liberalism has become a purely official creed, publicly upheld rather than deeply felt, the province of lawyers and academic specialists. Economists can explain the role of law in stimulating growth, but not the point of growth itself. Political philosophers elaborate theories of justice, yet have nothing to say about their historical or metaphysical foundations. The expansive vision of Humboldt, Tocqueville, and Acton has hardened into a set of peremptory legal claims, advanced in shrill, dogmatic tones or at the point of a gun. No wonder we look back with nostalgia to a liberal such as Cassirer, whose interests were not confined solely, or even principally, to politics but spanned the breadth of human civilization. His was a humane and happy dream, and even if it was only a dream, it casts a reproachful shadow on our present age. (pp.236-237)

【メモ】 The American Pragmatists (Cheryl Misak)

Cheryl Misak (2013) The American Pragmatists, Oxford: Oxford University Press.

【第一章　初期アメリカ思想におけるプラグマティズム的諸テーマ】

The fact that we can be surprised suggests that experience is not illusory and the world is not constructed entirely by us. Although we may color the universe, there is something that we are coloring. (p.12) cf. Ralph Waldo Emerson, Collected Works 3: 48

【第二章　Chauncey Wright】

But whatever be the origin of the theories of science, Whether from a systematic examination of empirical facts by conscious induction, or from the natural biases of the mind, the so-called intuitions of reason, what seems probable without a distinct survey of our experiences—whatever the origin, real or ideal, the value of these theories can only be tested ... by an appeal to sensible experience, by deductions from them of consequences which we can confirm by the undoubted testimony of the senses. (Chauncey Wright, Philosophical Discussions p.46)

This is a signal difference between pragmatism and British empiricism. Pramatism is not primarily a view about the sources or origins of belief, but a view of what tests a belief must pass once we have it. It is a view about what it is for a belief to count as non-spurious, genuine, or legitimate. (pp.17-18)

A belief can have consequences for the believer—it can make me feel better, it can influence my train of thought, I can desire it to be true, etc. But that is not the kind of consequence Wright thinks salient. A belief must have consequences not only for the believer, but for the world. The importance of this distinction will amplify as we march through the history of pragmatism. (pp.24-25)

【第三章　Charles Sanders Peirce】

[W]hen Paul Carus associated him [Peirce] with Hume in an article published in The Monist titled "Mr. Charles S. Peirce's Onslaught on the Doctrine of Necessity," Peirce resisted the comparison (Collected Papers 6.605). It is interesting, though, that it was not the empiricism he objected to. It was the nominalist metaphysical underpinnings of it. (p.28)

He [Peirce] did not want to define truth as that which satisfies our aims in inquiry. A dispute about definition, he says, is usually a "profitless discussion" (CP 8. 100). ... The pragmatist is merely getting one fix on the idea of truth. (p.36)

[For Peirce,] a true belief is such that it would withstand doubt, were we to inquire as far as we fruitfully could into the matter. A true belief is such that, no matter how much further we were to investigate and  debate, that belief would not be overturned by recalcitrant experience and argument. Peirce says: "if Truth consists in satisfaction, it cannot be any actual satisfaction, but must be the satisfaction that would ultimately be found if the inquiry were pushed to its ultimate and indefeasible issue" (Collected Papers 5.569; 6.485). (p.37)

We have in our various inquiries and deliberations a multiplicity of aims—empirical adequacy, coherence with other beliefs, simplicity, explanatory power, getting a reliable guide to action, fruitfulness for other research, greater understanding of others, living peacefully with others, increased maturity, and the like. When we say that we aim at the truth, what we mean is that, were a belief really to satisfy all of our local aims in inquiry, then that belief would be true. There is nothing over and above the fulfillment of those aims, nothing metaphysical, to which we aspire. Truth is not some transcendental, mystical thing and we do not aim at it for its own sake. (p.37)

The emotion of surprise is "merely the instinctive indication of the logical situation. It is evolution (φύσις) that has provided us with the emotion" (CP 7.190) (p.39)
→　パースの言う「経験の強制力」は単なる心理的、情緒的な衝動ではない。後者はあくまで進化の産物。（では一体何か？）

What we can say, he [Peirce] thinks, is that the fact that we have only our interpretations of what we experience does not throw us into a sea of arbitrary interpretations, where there is no connection to what is real. Our perceptual judgments, Peirce argues, are indices of our percepts—of the actual clash between us and the world. (p.40)

Peirce ... thinks that we can know something of the world as it exists independently of us—we can know that it is there and that it constrains us. Peirce turns to the idea that we can be mistaken in order to show that there is an objective truth and that reality that [sic] goes beyond what you or I or any collection of people happen to think: "The experience of ignorance, or of error, which we have, and which we gain by means of correcting our errors, or enlarging our knowledge, does enable us to experience and conceive something which is independent of our own limited views" (CP 7.345). (p.40)

This forceful element [of experiential judgements] is our link with a reality, something that goes beyond us: "Now the 'hardness' of fact lies in the insistency of the percept, its entirely irrational insistency, —the element of Secondness in it. That is a very important factor of reality" (CP 7.659). (p.41)

Peirce thinks that the theory of evolution tells us, indeed, that our capacities have been selected for survival, but that, nonetheless, we aim at getting beliefs not merely with survival benefits, but beliefs that are independent of human capacities and contexts of inquiry. (p.41n)

The seemingly unsolvable problem of induction disintegrates once we acknowledge that regularities abound, but only some of them want explanations. Only unexpected or surprising regularities make a demand on us to make an inference to the best explanation. (p.49)
→　驚きを伴わない規則性は習慣の領域に沈滞している。

"The sole immediate purpose of thinking is to render things intelligible; and to think and yet in that very act to think a thing unintelligible is a self-stultification. It is as though a man furnished with a pistol to defend himself against an enemy were, on finding that enemy very redoubtable, to use his pistol to blow his own brains out to escape being killed by his enemy. Despair is insanity. ... We must therefore be guided by the rule of hope" (CP 1.405)

【第四章　William James】

He [James] notes with approval that Jonathan Edwards thought that it was by the fruits not the roots that we must test our beliefs (The Varieties of Religious Experience p.25). (p.70)

【第五章　Holmes、Royce、Schiller】

[For Holmes, law] is an enterprise of inquiry, or "successive approximation," that starts from precedent and then is driven by experience, conflict, and unanticipated problems. (p.78)

Peirce is adamant, with Royce, that we have to preserve a gap in which error can live. (p.84)
→　パースにおいては、outward clashがこの間隙を保証する。

【第七章　John Dewey】

[For Dewey] A belief has to satisfy the inquirer's needs and it has to satisfy the situation. It is bound to the personal or the psychological but it also has to meet what the situation demands of it. (p.112)

"The way in which men do 'think' denotes ... simply the ways in which men at a given time carry on their inquiries. So far as it is used to register a difference from the ways in which they ought to think, it denotes a difference like that between good and bad farming or good and bad medical practice. Men think in ways they should not when they follow methods of inquiry that experience of past inquiries shows are not competent to reach the intended end of the inquiries in question" (The Later Works 12.107)
 →　パースが規範性を未来の探求に求めるのに対して、デューイは過去にそれを見出す。

It is certainly the case that those pragmatists who want to talk about the world and its constraints need to work hard to show how there is some space between their view and that of their realist opponents. We have seen that Peirce opens us that gap by arguing that we have no cognitive access to the world of independent objects—it is only by abstracting the forceful element from experience that we can get an inkling that the world is there. Dewey, on the other hand, needs to work to say why his view remains suflficiently far away from his idealist opponents who have a hard time making sense of the ideas of improvement, mistakes, and standards. (p.119)

"It is the situation that has these traits [vagueness and confusion]. We are doubtful because the situation is inherently doubtful" (The Later Works 12.109)

"The question naturally arises how Professor Dewey comes to have a metaphysics. How does he know that specificity, interaction, change, characterize all existence, and that these distinctions are not merely logical, made for purposes of getting along in this world, but characters of an independent existence? Why does he impute the features presented in human experience to a nature embracing, but containing more than, that experience?" (Ernest Nagel, "Can Logic be Divorced From Ontology?" p.707)

Nagel thinks that we need to distinguish "symbols from the subject-matter to which they point." We have seen that Peirce agrees, although his way of distinguishing these two things is as minimal as possible—all we can do is point or gesture at the subject matter. (p.121)

"Mr. Russell proceeds first by converting a doubtful situation into a personal doubt, although the difference between the two things is repeatedly pointed out by me. I have even repeatedly stated that a personal doubt is pathological unless it is a reflection of a situation which is problematic. Then by changing doubt into private discomfort, truth is identified with removal of this discomfort. The only desire that enters, according to my view, is desire to resolve as honestly and impartially as possible the problem involved in the situation. 'Satisfaction' is satisfaction of the conditions prescribed by the problem. Personal satisfaction may enter in as it arises when any job is well done according to the requirements of the job itself; but it does not enter in any way into the determination of validity, because, on the contrary, it is determined by that validity" (The Later Works 14.156)

Dewey is set against the "intellectualist" account of truth, on which truth is "antecedent to any process of verification" (The Middle Works 4.76).

Another way of putting this disagreement between Peirce and Dewey is to ask whether truth is a static phenomenon. Both reject the idea that truth is static in the sense that our beliefs either mirror the world of the Absolute (and are hence true) or fail to do so (and are hence false). But Peirce thinks that truth is static in the sense that a belief either would or would not survive the rigors of inquiry. Again, Dewey usually stays away from this thought. His interest ends with beliefs that show themselves to resolve a particular, local problem. (p.127)

 【第八章　Mead、Santayana】

He [Santayana] thinks that "in their hearts and lives," Americans are all pragmatists: "Their real philosophy is the philosophy of enterprise." They are optimists who "turn their scorn of useless thought into a glad denial of its existence" ("Apologia Pro Mente Sua" p.248-249 in Paul Schilpp, The Philosophy of George Santayana). He did not want to be associated with the American "business intellect" way of thinking. He preferred the intellectual company of Spinoza and the ancient Greeks. (p.144)

He alludes to the two shortcomings in Dewey's philosophy—the awkward metaphysics and the inability to adjudicate—in one harsh sentence. Dewey remains an idealist with Emerson, Schelling, and Hegel: "romantic, transcendental, piously receiving as absolute the inspiration dominating moral life in their day and country" ("Dewey's Naturalist Metaphysics" p.680). (pp.144-145)

"Living when human faith is again in a state of dissolution, I have imitated the Greek sceptics in calling doubtful everything that, in spite of common sense, any one can possibly doubt. But since life and even discussion forces me to break away from a complete scepticism, I have determined not to do so surreptitiously nor at random, ignominiously taking cover now behind one prejudice and now behind another. Instead I have frankly taken nature by the hand, accepting as a rule in my farthest speculations the animal faith I live by from day to day." (Scepticism and Animal Faith p.308)

Philosophy must begin in the middle of things. We assume that many of our beliefs are true and we need not be pushed into trying to prove those beliefs or show that they are certainly or infallibly true. We do not need Cartesian requirements for certainty. (p.147)

"I stand in philosophy exactly where I stand in daily life ; I should not be honest otherwise." (Scepticism and Animal Faith p.vi)

"You cannot prove realism to a complete sceptic or idealist; but you can show an honest man that he is not a complete sceptic or idealist, but a realist at heart" ("Three Proofs of Realism" in Essays in Critical Realism p.184)

Santayana and Peirce struggle mightily to articulate the good side of this thought [James's idea of the Will to Believe]. They both argue that we must accept the bulk of our beliefs, but always keep them open to recalcitrant experience and never believe them on grounds extraneous to facts and reasons. This last point is important. Like Peirce, when Santayana uses the word "faith," he does not mean to mark something that is unbacked by reasons. He says that instead of using "so brutal a term as animal faith," he might have used "cognitive instinct, empirical confidence, even practical reason" ("Apologia Pro Mente Sua" p.586). Each of these alternatives makes it clear that there is something normative or non-arbitrary in what we need to assume. (p.148)

"Why does belief that you can jump a ditch help you to jump it? Because it is a symptom of the fact that you could jump it, that your legs were fit and that the ditch was two yards wide and not twenty. A rapid and just appreciation of these facts has iven you your confidence, or at least has made it reasonable, manly, and prophetic; otherwise you would have been a fool and got a ducking for it." ("The Genteel Tradition in American Philosophy" in The Genteel Tradition in American Philosophy and Character and Opinion in the United States p.61)

The encountering of "brute fact" is the "ground" for Santayana's realism ("Apologia Pro Mente Sua"p.504-505). The "experience of shock" "establishes realism"—it establishes "a world of independent existences" (Scepticism and Animal Faith p.142). Santayana does not want to be associated with the pragmatists because he thinks that a pragmatist such as Dewey is "a philosopher of the foreground" ("Dewey's Naturalistic Metaphysics" p.680), too content with the surface of things. (p.148)

【第十章　Clarence Irving Lewis】

With Peirce (and Kant), Lewis takes the given to be that which is not under our control—that which is independent of the mind's constructive activities. (p.183)

[For Lewis] the given is that which impinges upon us or resists our attempts to change it and thus constrains our opinions (this is the set of thoughts he shares with Peirce). There is no need to add that the given is something that has a certain structure or quality. (p.183n)

What Lewis argues is that there must be something constraining the truth and falsity of our statements and beliefs. (p.184)

For Lewis, it is experience—not logic, not conceptual truth—that is brute and compelling. (p.192)
→　ア・プリオリな真理は確かに必然的だが、それのみを受け容れるよう我々を強制するという意味で必然的ではない。そのような意味でbruteなのは経験の抗力。

"What is a priori is necessary truth not because it compels the mind's acceptance, but precisely because it does not. It is given experience, brute fact, the a posteriori element in knowledge which the mind must accept willy-nilly. The a priori represents an attitude in some sense freely taken, a stipulation of the mind itself, and a stipulation which might be made in some other way if it suited our bent or need. Such truth is necessary as opposed to contingent, not as opposed to voluntary. "("A Pragmatic Conception of Truth" p.231)

"we cannot capture the truth of experience if we have no net to catch it in" (The Mind and the World Order p.271) →　この網がア・プリオリな概念やカテゴリー。それは経験のあり方を規定するから経験から独立なのではなく、経験を規定しない（経験のbrtueな抗力に任せる）からこそ独立。また、この網は一つとは限らず、プラグマティックに選択され得る。Lewisの言葉を使えば、それは"uncompelled initiative of human thought"である。

Lewis rejects the idea, again sometimes found in James, that "new truth" replaces "old truth." When a new belief replaces an overturned belief, that should suggest that the old belief was false, not an old truth. ... An assertion always "outruns" our current evidence and best thinking. It reaches into the future and makes a prediction that the evidence and best thinking will continue to support the assertion. This, of course, is the Peircean conception of truth. (p.194)

【第十一章　Willard van Orman Quine】

[T]he insight of disquotationalism is precisely the insight of pragmatism. Both hold that when we assert that p is true, what we are doing is asserting p. The Peircean pragmatist modifies this shared thought slightly, not wanting to limp around with warranted belief. When we assert that p is true, what we are doing is asserting p and asserting that p would remain assertible. ... Both pragmatism and disquotationalism, that is, keep us focused on first-order inquiry. (p.206)

【第十三章　Richard Rorty】

Calling for a dissolution of a dualism, such as that between relativism and absolutism, does not guarantee that one succeeds in escaping the pitfalls of one or the other of the two positions. And it does not guarantee that one will not end up shuttling between the two disliked positions, depending on the particular critique to which one is responding. That is, after the call for the abandonment of a way of looking at things, one must replace the problematic mode of thinking with a new way that really does undercut the problems endemic in the old way of seeing the issue. One must replace the old dichotomy of "objective standards or no standards at all" with low-profile, non-absolutist conceptions of truth and objectivity which can guide us in our inquiries and deliberations. The pragmatist must replace the old dichotomy with distinctly pragmatist accounts of truth, objectivity, and normativity. (p.231)

Frank Ramsey also held that the pragmatist need not take "p is true" to be identified with "p is useful." For the belief p will be useful only if p. See his "Facts and Propositions." (p.232n)

As [Huw] Price puts it, pragmatists start not by asking what the analytic definition of truth is, but rather, why speakers have the notion of truth they have. They should see, he thinks, that our notion of truth does not line up neatly with warrant asertiblity, nor with disquotation. We need a stronger notion of truth than is provided by either of those notions (Naturalism Without Mirrors p.16). (p.233)

To do without truth is to silence our conversations—both our conversations with others and our internal conversations. For the very essence of the norm of truth is to give disagreement its immediate normative character. It is to make disagreement matter. Without the grit provided by the concept of truth, the wheels of argument do not engage; disagreements slide past one another. (p.234)

【第十四章　Hilary Putnam】

[For Putnam] One cannot dodge the problem of saying what truth is by replacing truth with assertibility and then not saying what assertibility is. And once one says what assertibility is, one is taken to a substantial view of truth. (p.242)