[Peirce] claims that a sensation of tone, for example, can be seen as a kind of hypothetic inference; the idea is that through unconscious inference, a sequence of distinct vibrations of the eardrum are unified into a single experience, the sensation unifying a manifold of vibrations just as a hypothesis unifies a variety of data. This suggestion that we think of sensations as analogous to predicates is supported by rejecting the nominalist assumption that sensations are wholly singular representations. If an image or representation is wholly singular, Peirce believes that for any property p, the situation represented would either be represented as one in which p was realized or as one in which it was not. The state of affairs would be determinate. The 'generality' of sensory images is revealed in their vagueness: for example, we can see a speckled surface without seeing it as having a definite number of speckles; our sensation is applicable to a variety of distinct states of affairs so is implicitly general. (pp.34-35)
"And what do we mean by the real? It is a conception which we must first have had when we discovered that there was an unreal, an illusion; that is, when we first corrected ourselves. Now the distinction for which alone this fact logically called, was between an ens relative to private inward determinations, to the negations belonging to idiosyncrasy, and an ens such as would stand in the long run. The real, then, is that which, sooner or later, information and reasoning would finally result in, and which is therefore independent of the vagaries of me and you. Thus, the very origin of the conception of reality shows that this conception essentially involves the notion of a COMMUNITY, without definite limits, and capable of a definite increase of knowledge." (C. S. Peirce, "Some Consequences of Four Incapacities," Collected Papers 5.311)
Adoption of any method of fixing belief presupposes that one finds it unsatisfactory that one's beliefs are inconsistent: if the predictions based upon my theories clash with experience, I am prompted to reassess my theories. One explanation of why we find inconsistent beliefs unsatisfactory is that they cannot all be true; 'but here already is a vague concession that there is some one thing to which a proposition should conform'. Unless I accept the realist hypothesis, it is unclear what motivation I have for removing inconsistencies or doubting what clashes with experience. (...) The general strategy, I hope, is clear: starting from a characterization of the aim of inquiry as the settlement or fixation of belief, Peirce hopes to derive a statement of the 'propositions of the logical question' from a consideration of how certain methods of inquiry simply cannot be adopted. Simply asking 'How should I conduct my inquiries?' reveals my acceptance of propositions which help me to answer the question. (p.49)
Peirce distinguishes the acritical elements of our practice - those which cannot be subjected to logical criticism - from those which are subject to logical criticism. The importance of these acritical elements becomes clear when we notice that a rough paraphrase of Peirce's theory of truth would be that a statement is true if and only if none of its perceptual consequences clash with experience. The notions of 'consequence' and 'clash with experience' seem to be used in formulating the doctrine. If consequence is to be explained in terms of the preservation of truth [演繹的推論の帰結のこと] and if a statement clashes with experience if its known to be perceptually false, then the presence of these notions in the definition introduces circularity. The circularity seems particularly acute when we note that Peirce allows that our perceptual beliefs are fallible, and may be corrected in light of subsequent experience. (...) However, we should note here that he claims that both perceptual judgements and deductive reasoning are acritical, i.e. we cannot control the ways that we conduct them. Our logical self-control is restricted to assessing our practices of ampliative reasoning - induction and abduction. Thus, in controlling our practice of reasoning, we employ rules that attempt to find hypotheses which make coherent sense of our experience, while respecting the criteria of coherence embodied in our practice of deductive reasoning. (p.71)
→ もし真理が、経験との衝突がないことよって定式化され、また、知覚経験が真であったり偽であったりするならば、循環定義になってしまう。なぜなら、「真の知覚経験から導かれる言明は真である」、「偽の知覚経験から導かれる言明は偽である」といったような定式化は、真偽の概念を予め導入してしまっているからである。この困難は、パースにおいては、知覚経験（知覚判断）をacriticalとすることによって回避されている。知覚経験（知覚判断）は前批判的であり、真であったり偽であったりしない。ただし、acriticalだからといって、incorrigibleではない。これはabuductionと同様である。パースにとって、acriticalな判断と統御可能な判断の差はグラデーションをなしており、我々が統御できるのは、reasoningの意識的な部分のみである。
【パースの"remarkable theorem"】
The best known systems of modern quantificational logic provide counterexamples tp Peirce's '[remarkable] thoerem'. Within these logics, we can define triadic predicates in terms of dyadic ones using axioms of the form
(Rxyz≡(x)(y)(z)(Ew)(Txw & Syw & Uzw))
For example, we might define a relation R which a bears to b and c just in case there is someone of a is the aunt, b is the brother and c is the father. (p.98)
→ しかしイギリスの論理学者A. D. Kempeなどの研究を通して、パースはこのような困難の存在を知っていった。パースは、このような困難が生じるような形式的言語の採用を峻拒する。
Peirce insists that 'the combination of concepts is always two at a time' (CP 1.294). He does not permit triple bonding. (p.99)
If we form a complex conception out of two conceptions of valencies μ and ν, by linking λ bonds of one with bonds of the other, the number of unsaturated bonds in the resulting complex conception is given by
(μ + ν - 2λ) (CP 3.484)
(...) The formula has its highest value when λ=1, and it is a simple matter to verify that
(μ + ν - 2)
can equal three or more only when either μ or ν is equal to at least three. Hence, so long as all our devices for forming complex conceptions fit this rule, it is not possible to reduce triadic relations to dyadic ones. However, tetradic relations can be reduced to complexes of triadic ones, for
(3 + 3 - 2) = 4. [右辺が左辺に還元される]
And in fact, all tetradic relations can be represented as constructed in this manner. (pp.99-100)
Now we have two options. We can dismiss Peirce's result as a quirky feature of an eccentric logic which has no philosophical interest, or we can accept that the restrictions that he places upon acceptable definitions are natural and well motivated, in which case the familiar counter-examples to his theorem can be discounted. (p.100)
→ 後者の選択肢を取るとして、パースがその使用を擁護するような言語に着目の対象を限定する十分な根拠を提示するには、どうすればいいか。
One possibility would be to argue that the reduction of triadic predicates to dyadic ones effected by using triple bonding is not genuine. If it could be shown that we could reduce a triadic predicate to a combination of dyadic ones by using a conception which had to be thought of as triadic, or even tetradic, the reduction would be of little interest. For example when we define the triadic relation R in terms of the three dyadic relations T, S, and U, we have to think of R as standing in the tetradic relation of 'resulting-by-triple-bonding' from T, U, and S. Hence, the definitional procedure does not show that tetradic [or triadic] relations are dispensible. On the other hand, if we think of a relation resulting by double bonding from two other relations we only have to use a triadic relation: the concepts we use in effecting the reduction are not at odds with the reductive claims that are made. Thus, the Peircean logic employs only those definitional resources that can be used in a genuine reduction of the valency of relations. This thought has some intuitive appeal, but it is difficult to find a clear sense in which (for example) a triadic or tetradic conception is exercised in the use of a statement like our axiom for the triadic relation R in the notation of familiar first order logic. (p.100)
→ もう一つの可能性は、認知の理論に訴えることである。例えば、ある二項関係Rを表象する記号Sがあるとすると、ここでの関係の結合は、必ずdouble bondingになる。これが、知覚活動を扱う限りにおいて、概念の結合をdouble bondingに限定する根拠になりうる。しかしこの場合、パースの定理の普遍性が損なわれるように思われる。
【カテゴリー論】
For the Wittgensteinian, our ability to speak for all [i.e., in a 'universal voice'] in mapping the grammar of our language is something we cannot justify, it marks a point where rational justification has come to an end. Yet, as Cavell notes [in "Aesthetic Problems in Modern Philosophy"], our ability to speak for all in this way is a necessary condition of our being able to speak at all. Similarly, for Peirce, we demand the right to go by what we find ourselves wanting to say in phenomenological inquiry; we cannot justify our claim that our 'intuitions' have universal validity. But unless they could do so, common language and the rational control of deliberation would not be possible at all. (p.110)
"In point of fact, a syllogism in Barbara virtually takes place when we irritate the foot of a decapitated frog. The connection between the afferent and efferent nerve, whatever it may be, constitutes a nervous habit, a rule of action, which is the physiological analogue of the major premiss. The disturbance of the ganglionic equilibrium, owing to the irritation, is the physiological form of that which, psychologically considered, is a sensation; and, logically considered, is the occurrence of a case. The explosion through the efferent nerve is the physiological form of that which psychologically is a volition, and logically the inference of a result." (CP 2.711)
【知覚論】
Central to Peirce's response to these difficulties [上記の真理の定義の循環性のこと] is the claim that the fundamental form of reference to existing objects involves the use of demonstrative expressions, indicies, in perceptual judgments. Subsequent inquiry may lead us to revise our conception of the object of a given perceptual judgment, but this subsequent inquiry is still anchored to reality through that perception. (p.154) → 指示対象の保存。バスカーの言う知識のintransitive dimensionに対応？
"Abductive inference shades into perceptual judgment without any sharp line of demarcation between them; or, in other words, our first premises, the perceptual judgments, are to be regarded as an extreme case of abductive inferences, from which they differ in being absolutely beyond criticism. The abductive suggestion comes to us like a flash. It is an act of insight, although extremely fallible insight. It is true that the different elements of the hypothesis were in our minds before; but it is the idea of putting together what we had never before dreamed of putting together which flashes the new suggestion before our contemplation." (CP 5.181)
"When you look at it you seem to be looking at the stairs from above. You cannot conceive it otherwise. Continue to gaze at it, and after two or three minutes the back wall of the stairs will jump forward and you will now be looking at the under side of them from below, and again cannot see the figure otherwise. After a shorter interval, the upper wall, which is now nearer to you, will spring back, and you will again be looking from above. These changes will take place more and more rapidly, the aspect from above always lasting longer, until at length, you will find you can at will make it look either way." (CP 7.647)
"The perceptive judgment, and the percept itself, seems to keep shifting from one general aspect to the other and back again" (CP 5.183). These phenomena, Peirce claims, function as the "true connecting links between abductions and perceptions" (CP 5.183). → かくしてパースは知覚と知覚判断の二元論を解消する。一般的なアスペクトを切り換えるごとに、階段の「見た目」が変わるということは、一般性が知覚そのものに潜んでおり、知覚判断だけが変わっているわけではないことを示している。知覚にも解釈が常に混入しており、abductionと同様incorrigibleではない。しかし同時に、知覚（知覚判断）はacriticalである。知覚のこのacriticalな部分を指してパースはpercipuumと呼ぶ： "The percipuum, then, is what forces itself upon your acknowledgment, without any why or wherefore, so that if anybody asks you why you should regard it as appearing so and so, all you can say is, 'I can't help it. That is how I see it.'" (CP 7.643) percipuumを捉えることはacritical abductionである。パースは、acriticalとcontrollableの間のケースを例示することによって、その差がグラデーションをなしていることを論証している。そして、知覚のacriticalな部分（percipuum）とclashしないように信念体系を調整するのが科学的推論の役割ということになる。したがって、clash with experienceに訴える真理定義は、循環を含まない。また、そもそも信念を改訂することができるのは、indexが個物を指示しており、指示対象は信念改訂の前後を通して保存されているため。
Talk of the percipuum - fusing the percept and perceptual judgement into a whole - is an attempt, I suggest, to prevent those problems [もし知覚判断には一般性が関わっており、知覚そのものには一般性が含まれていないのだとしたら、我々がただ好き勝手に実在に対して一般的概念を宛がっているという唯名論が帰結してしまう、という問題。この場合、三性は実在ではなく我々の認知活動に属することになる] arising by rejecting an oversimple dichotomy of cognitive processes. If we can prescind the firstness of our perceptual experience from the rest (or prescind its secondness), it does not follow that we can find distinct cognitive processes: the percept-perceptual judgement distinction reflects imposing a crude cognitive model on the phenomenologically rich complex of the sensory and the conceptual which is the 'given' of perceptual experience. Thirdness is given in the percipuum, it is perceptually experienced. Our acritical judgements report what we see; they involve general classifications; and our reports of shifts in general aspect show that there are sensory manifestations of thirdness in the percipuum. (p.166)
"being at all is being in general." (CP 5.349; 3.93n)
if the specimens form a kind or natural class, they will vary continuously along some dimension. (p.175)
→ 普遍者（一般的なクラス）と連続性との関連。よく分からない。
【帰納とアブダクション】
"By saying that we draw the inference provisionally, I mean that we do not hold that we have reached any assigned degree of approximation as yet, but only hold that if our experience be indefinitely extended, and if every fact of whatever nature, as fast as it presents itself, be duly applied, according to the inductive method, in correcting the inferred ratio, then our approximation will become indefinitely close in the long run; that is to say, close to the experience to come (not merely close by the exhaustion of a finite collection)" (CP 6.40) → 宇宙の片隅のunrepresentativeなサンプルであっても、その外側の（潜在的）宇宙に触れることさえできれば、推論は訂正されるし、触れなければ、それは十分長期ではない、ということになる。
"The procedure described may be called the method of anticipation; in choosing h(n) as our posit, we anticipate the case where n is the "place of convergence." It may be that by this anticipation we obtain a false value; we know, however, that a continued anticipation must lead to the true value, if there is a limit at all." (Hans Reichenbach, Experience and Prediction p.353)
→ n個の集団の中からある性質Aを持った個体がm個観測されたとする。このとき、性質Aを持った個体の比率を表すためにm/n = h(n)と置く。ライヘンバッハの言う"principle of induction"によれば、母集団の個体数をnからsに増やしたとすれば、h(s)はh(n)近傍の小さな領域に収まることを我々は期待するはずである。もし大きく外れれば、今後h(s)の近傍に収まることを期待する（信念改訂）。あるfrequencyが常に維持されるという、確実な根拠はもちろんない（ライヘンバッハはこれを"blind posit"と呼んでいる）。しかし、確率の頻度説の性質より、もしm/nが性質Aを持った個体全体の割合を表しているならば、取る母集団のサイズを大きくすればするほど、任意のεに対して、観測されるA個体の割合とm/nの差がε以下に収まるような、母集団の選択sequenceが必ず存在する（sequenceが収束する）。この原理が成り立つためにはもちろん、統計的極限が予め存在していなければならない。
"the instances excluded from being subjects of reasoning would not be experienced in the full sense of the word, but would be among these latent individuals of which our conclusion does not pretend to speak." (CP 6.42)
"man has a certain Insight, not strong enough to be oftener right than wrong, but strong enough not to be overwhelmingly more often wrong than right, into the Thirdnesses, the general elements, of Nature. An Insight, I call it, because it is to be referred to the same general class of operations to which Perceptive Judgments belong. This Faculty is at the same time of the general nature of Instinct," (CP 5.173)
【プラグマティズム】
However, the interest of the [pragmatic] principle does not hinge upon a concern with useful methodological advice. Rather, the fact that this is good advice - if Peirce is correct - reveals important truths about meaning and reality. (p.235)
That there are truths about the actual world which will never be discovered [カエサルがルビコン川を渡るとき何回くしゃみしたかとか] need not conflict with Peirce's claim that rational inquirers are fated to reach a stable consensus on all questions about the nature of reality. Reality is the mode of being of laws and general principles. Peirce makes no corresponding claim about existence, which is the mode of being of individuals and states of affairs that involve them. (p.291n)