Representational and embodied approaches to cognitive science are often presented in opposition to one another, with Merleau-Ponty serving as a historical precursor to embodied approaches. We argue that the two approaches are compatible and complementary, and that both can be used to interpret Merleau-Ponty's (and Husserl's) work. To support our arguments, we describe two forms of representation associated with two distinct processes. Motor intentionality is a process of direct embodied interaction (reflexes, habits, skilled behaviors) which use mediating representations to bind (...) sensory information together and guide behavior. These internal states reliably indicate specific stimuli (even if just during a transient episode), are associated with a determinate phenomenal character (a “typical physiognomy”), and correspond to what Husserl describes as passive synthesis. Higher-level processes like reasoning make use of more explicit representations (what Husserl calls active processes), which are associated with focused attention and “explicated” propositional contents. The two kinds of process can occur independently, but are often fully woven together, as for example when a friend makes explicit suggestions while the two of you cook. We also discuss Merleau-Ponty’s famous Schneider case, which makes vivid what happens when both types of processes (motor intentionality and high-level reasoning; passive and active synthesis) are intact, but when some explicit representations are damaged. A certain stratum of virtual or projected space is lost, and so a certain kind of abstractly guided behavior is unavailable to him. (shrink)

This theorem is revolutionary. Throughout history, many major shifts—from Newton to Einstein, the Industrial Revolution, World War II, regime changes, and revolutions—can ultimately be traced back to failures in either propositions or definitions. And in our daily lives as well: Is it always correct for a parent to scold a child? Is it always incorrect for a child to scold a parent? The same structure applies to the relationships between bosses and subordinates, constitutions and laws, mathematics and axioms. Whenever we (...) equate things without structural justification, refutation becomes harder than proof. Thus, I propose that “A = B” should always be treated as a provisional assumption, not a proof. The Proposition Refutation Theorem is not based on axioms, but is a theorem in its own right. Why not an axiom? Because in mathematics, an axiom must be unique. There must not be many. (shrink)

I show how existing concepts of supervenience relate to two more fundamental ontological relations: determination and dependence. Determination says that the supervenient properties of a thing are a function of its base properties, while dependence says that having a supervenient property implies having a base property. I show that most varieties of supervenience are either determination relations or determination relations conjoined with dependence relations. In the process of unpacking these connections I identify limitations of existing concepts of supervenience and provide (...) ways of overcoming them. What results is a more precise, flexible, and powerful set of tools for relating sets of properties than current concepts of supervenience provide. I apply these tools to a recalcitrant problem in the physicalism literature – the problem of extras. (shrink)

“If you split zero in two, then 1 + 1 = 0.” This paradoxical premise lies at the heart of "Shinichi Mathematics," a symbolic-structural framework grounded in the axiom √1 = 0. By reinterpreting basic numerical identity through ontological compression and emergence, this theory constructs a novel view of existence and observation. It draws from paradoxical symmetry, structural duality (ATEN/KYOTEN), and the Gauge Paradox, offering a post-classical philosophical foundation for mathematical representation and existential logic.

This paper proposes the \"Shinichi Transformation,\" which gives a definable meaning to the previously undefined expression $1 \div 0$, based on the \( \infty\) Definition Method and the \( \infty{-}1 \) Definition Method. We argue that infinity (\( \infty\) ) does not arise ambiguously from arithmetic operations but instead emerges as a definable mathematical object through the structural definition of $1 \div 0$. This theory presents a philosophical shift in mathematics, where the existence of infinity is rooted in definition rather (...) than in computational divergence. (shrink)

Note: The full text is written in Japanese in order to preserve the precise definitions and logical structure specific to the language. -/- DOI: 10.5281/zenodo.17772964 -/- Abstract (English) You may not know what it means to write √0, but you can write it. That is all I intend to present today. -/- This paper explains the concept √1=0 as a conceptual shift: inscription precedes meaning, and number is treated as algebra rather than as a referent. Since Euclid, a linear perception (...) of number has been mainstream; however, pre-Euclidean thought (e.g., Pythagoras) also permits a “potential” or rotational grasp of number. This is my subjective perspective and requires neither validation nor denial. -/- I define mathematics as an academic discipline that gains meaning only when numbers are handled as meaningless algebra. Accordingly, this work reinterprets the language of “linear numbers” visually, symbolically, and sensually as “potential.” -/- This document is not written to alter the perspectives of scholars; it was written to explain these ideas to my child. If the academic community finds utility in it, that is a fortunate outcome. I release it publicly as the culmination of my previous preprints. -/- Supplementary material: dialogue log with the AI “Gemini”. -/- （DOI: 10.5281/zenodo.18264765） -/- アブストラクト -/- √0 と書いても、その意味は分からないだろう。しかし、書くことはできる。 今日、提示したいのはそれだけである。 -/- 本稿は、記号は意味に先立ち、数字は指示対象ではなく代数である、という転回として √1=0 という概念を説明する。ユークリッド以降、数字に対する「直線的」な捉え方が主流となったが、ユークリッド以前（ピタゴラスなど）には「ポテンシャル」（回転的）な捉え方も存在した。これは私の主観であり、他者か らの承認も否定も必要としない。 -/- 私は、数学という学問は、数字を「意味を持たない代数」として扱って初めて意味を成すと定義している。本稿は、「直線的な数字」という言語を、視覚的・記号的・感覚的に「ポテンシャル」として捉え直したものである 。 -/- これは学者に対して意識を変えるよう訴えるものではなく、単に自分の子供にわかるように説明したものである。もし学術界において利用価値が見出されるならば幸いである。過去のプレプリントの集大成として、ここに公 開する。 -/- （注記：発見の経緯としてAI「Gemini」との対話ログを補足資料として添付。） （DOI: 10.5281/zenodo.18264765） -/- . (shrink)

Is mathematics not, at its core, something that should be proven using numbers and calculation? I must say this: If something cannot be proven purely through equations, then it is not mathematics. To say “Explain why 1 + 1 = 2” just because one does not know the answer is misguided. But to insist that “1 + 1 = 2” is true without truly understanding why it is so— is that not the illusion we must now abandon? That kind of (...) reasoning belongs to architecture, physics, or other sciences—not mathematics. Mathematics is simple. Its answers must be singular, universal, and evident to anyone who sees them. This is the essence of mathematics—and the essence of nature. Mathematics is not about “proof” in the conventional sense. It is about whether or not we realize something—just as one realizes that 1 + 1 = 2. This rebuttal is grounded in the principles outlined in the Theorems of Cosmic Deformation– BOX3 (DOI: 10.5281/zenodo.15477698). At its core lies Theorem 1, which represents infinity not as a symbolic picture (∞), but as a tangible phenomenon. Even if we treat Theorem 1 as a hypothetical defi nition of infinity, it logically follows that Theorem 3 emerges from it—a generative principle capable of producing infinite structures: points, circles, surfaces, solids, and beyond. Thus, Theorem 3 provides the structural essence that replaces π in this paper. This is not a symbol, but a law of emergence. It is not enough for mathematicians to observe infinity as a distant abstraction. Our task is to give it form, logic, and structure. That is the true mission of mathematics. And that is the foundation upon which this work stands. (shrink)

定義存在学を説明する前に以下の文章を読んでもらいたい。 「風も光も存在しない」「我々は“そう呼んでいる”」 この文章を誤解なく読むことができるだろうか? これを哲学と呼ぶなら物理学に未来はないと言い切れる。 まず、物理学の定義をしなければならない。 物理学とは、風の力を数量化・光の速度を数量化など、その他にも、あらゆるエネ ルギーと言う抽象的な感覚(哲学)を1つずつ数量化して記述し、人間の認知範囲に おける現象を記憶として補完する行為である。 つまり、物理学は【人間の集合知の記憶】と記述することができる。 逆に言えば、未来を測定しているようで、未来は測定できない事を証明する行為で もある。 筆者は物理学や、あらゆる学問に対して否定的ではなく、偉大な先人たちの叡智の 結晶であり、先人の叡智がなければ、『風も光も存在しない』などとは記述しないだ ろう。 では、本論文での物理学の定義をする。 物理学とは『エネルギーと言う抽象的な定義を基軸にした学問である。』 エネルギーがなぜ抽象的なのか? 風が吹くのは温度差があるからであり、風力をエネルギーと抽象化する事にある。 もっと細分化すると温度と言うのは存在と存在の時間のズレからであり、温度を エネルギーと抽象化する事で数量化を試みている。 何故、温度があるのか? 何故、時間がたつと温度は一定になるのか? それは存在と存在の時間のズレを温度として抽象化している。 (抽象化すると言うのは、『温度』具現化する行為ともとれるが、この場合の抽象化と は存在と存在の時間のズレと言うのをどのように人間が感じるかという事を抽象的 に捉えないと温度と言う具象化が生まれないからである。) この表現は非常に誤解を生む表現だが、風を感じると言うのはそもそもの原因は温 度変化なのだが、その根本的な状態を具体性を持って突き詰めていくと温度変化が 問題ではなくて、存在と存在の間による時間が発生している事が原因になっている。 つまり、抽象的記述が個人(個存在)の感覚であり、具象的記述が人間(集合存在) の感覚となるからである。 しかし、物理学ではこれが逆転する。 人間(集合存在)が風を感じる(感覚)のは、具象的記述が原因であると定義する からである。 個人(個存在)の感覚は抽象的記述であるため、物理学としてはズレが記述されて いることになる。 個人(個存在)の再現性を人間(集合存在)で記述する際には、人間(集合存在) を個存在として定義しなければ再現性は得られないのである。 なぜならば、集合存在は個存在として同一ではない。 であるならば同一的感覚を記述するためには集合存在を個存在と定義する力学が記 述される。 この原理が物理学であり、同一化と集合のズレによる記述なのである。 例えば月と地球の意識について記述してみよう。 月は地球を感じ、地球は月を感じている。 だから地球は月とぶつからない。 だから月は地球の周りを回っている。 地球が月を同一ではないと定義しているし月が地球を同一ではないと定義してい る。 地球も月も意識と認識と記述をしている事になる。 しかし、地球も月も集合体であると個存在として定義をしている。 コレらは全ての存在においての力学である。 存在の同一化が定義と結果による力学を記述して存在を生成しているように定義 している。 この全ての存在による同一化の定義こそが時間となる。 よって時間の総量を1または0と記述する事ができる。 なぜなら、0 は集合であり、1は同一性である。 この記述のズレが力学となる基準を定義存在学と名付ける。 定義存在学では物理学で量化されているエネルギーの抽象概念を一つにまとめる ことができる。 つまり、物理的に現象化された認識のズレを時間として量化する計算を定義圧と 名付ける。 定義圧は時間であるため英語で記述されるTIMEとは同一化できない。 何故ならTIME は人間の定義に内包されている定義であるため存在の集合におけ る力学では差が生まれるため同一化の保存では計算できない。 時間は日本語で記述される言語であり本論文では英語で TIME と訳す事も出 来る。 しかし、本論文では日本語の数学的集合を利用し時間を JIKAN と定義し記述 する。 それでは風の簡易思考実験をすると、扇風機はどうなるという科学者がいるだ ろう。 扇風機とは温度差から生まれる風と定義された現象を再現した記述である。温度 性を重力性に変換した記述となる。 つまり、これが物理学であり、物理学の限界でもある。 何故なら風の再現に温度性を無視し重力性のみを記述している。 温度とは重力とは何かを哲学的に計算し記述していない。 (...) つまり、定義存在学とはエネルギーの抽象化による再現性の担保こそが物理学の 最大の利点なのである。. (shrink)

Fermat’s Last Theorem — A Trilogy of Conversations in Mathematical Language フェルマーの最終定理ー数学言語での会話3部作 -/- Note: The full text is written in Japanese in order to preserve the precise definitions and logical structure specific to the language. DOI: 10.5281/zenodo.17772964 -/- --- 【1】Fermat’s Last Theorem via Fermat’s Proof (Paper 1) フェルマーの証明によるフェルマーの最終定理（論文.1） -/- Abstract (English) This paper reinterprets Fermat’s Last Theorem (FLT) not as the claim that integer solutions do not exist, but as a matter of computational dynamics: for (n \ge 3), one cannot (...) construct both an integer-solution equation and a function-generating equation within the same decomposition. To this end, I propose the FLT Decomposition Method, which treats an equation not as a mere numerical relation but as a structural decomposition starting from (Z). I show that function generation holds for (n=1), whereas for (n \ge 3) the decomposed terms fail to preserve the integer equation and the function-generating structure. In conclusion, I argue that the core issue is not the existence of solutions, but that the equation “collapses” (i.e., the number fails to be well-formed). -/- アブストラクト 本稿はフェルマーの最終定理を「整数解がない」という主張ではなく、n≥3 において整数解方程式と関数生成方程式が構成できないという“計算の力学”として再解釈する。その方法として、等式を単なる数値関係ではなく、Zを起点とした構造分解として扱う FLT分解法を提案し、n=1では関数生成が成立する一方、n=3では分解項が整数方程式／関数生成を保持できない点を示す。結論として、問題は解の有無ではなく「方程式が破綻する（数が成立しない）」ことにある と主張する。 -/- --- -/- 【2】Fermat's Little Theorem is the Conjecture of Fermat's Last Theorem (Paper.2) フェルマーの小定理はフェルマーの最終定理予想である（論文.2） -/- Abstract (English) This paper repositions Fermat’s Little Theorem not as a result to be memorized (e.g., (a^{p-1}\equiv 1 \pmod p) for prime (p)), but as a conjecture-generating device connected to Fermat’s Last Theorem, shifting the focus to why its structure becomes inevitable—for example, through decomposition patterns such as ((n^2-1)=(n-1)(n+1)). It also specifies description rules, including fixed IDs and a separation of roles between uppercase and lowercase symbols, and develops the argument within a framework that does not confuse the conditions for the establishment of numbers (structure) with numerical substitution (value). -/- アブストラクト 本稿は、フェルマーの小定理を「素数から1を引いた数の冪が素数の倍数を生む」という結果の暗記ではなく、なぜその構造が必然となるか（例：((n^2-1)=(n-1)(n+1)) の分解構造）へ焦点を移し、フェルマーの最終定理へ連結する“予想装置”として再定位する。記述ルールとして固定IDと大文字／小文字の役割分離を明示し、数の成立条件（構造）と数値代入（値）を混同しない枠組み で議論を行う。 -/- --- Fermat's Testament: The FLT Decomposition Method is Fermat's Proof (Paper.3) フェルマーの遺言 FLT分解法はフェルマーの証明（論文.3） -/- Abstract (English) This paper argues that the standard mathematical reading in terms of *element-wise condition equations* shifts the point at issue by retranslating Fermat’s original claim not as “integer solutions do not exist,” but as “numbers do not exist (i.e., the equation collapses / fails to be well-formed)” for (n \ge 2). By separating the natural-language argument of the original text into uppercase (the establishment of numbers permitted by the system) and lowercase (variables within the permitted system), it presents the “true translation” that (Z^n = X^n + Y^n) means that numbers do not exist for (n \ge 2). In conclusion, it positions the FLT Decomposition Method as isomorphic to Fermat’s proof. -/- アブストラクト 本稿は、フェルマー原文の主張を「整数解が存在しない」ではなく、「n≥2では“数が存在しない”（方程式が破綻する）」という論点として翻訳し直すことで、現代数学が採用してきた要素条件方程式の読みが論点をす り替えていると主張する。原文の自然言語的主張を、大文字（体系が許可する数の成立）と小文字（許可された体系内の変数）に分離し、Z^n = X^n + Y^n は n≥2では数が存在しないという“本当の翻訳”を提示する。結論として、FLT分解法がフェルマーの証明と同型であると位置づける。 -/- . (shrink)

-/- The Ruin Equation: Shinichi Matter（√1=0）ー破滅方程式 シンイチ物質（√1=0）ー -/- Note: The full text is written in Japanese in order to preserve the precise definitions and logical structure specific to the language. -/- DOI: 10.5281/zenodo.17772964 -/- Abstract (English) This paper proposes the "Ruin (Breakdown) Computation" method (Hatan Keisan-ho), a way to continue computation even when the equality relation is structurally broken (i.e., contradictory), without requiring an axiomatic rescue. The central claim is that if computation can be carried out starting from a broken (...) equation such as sqrt(1)=0, then an axiomatic system can be built around that computation, and dismissing it merely because it "breaks standard axioms" misses the point. -/- To make this explicit, the paper introduces fixed concept IDs and a deliberate distinction between uppercase symbols (system-level structures) and lowercase/numerical symbols (dynamic substitution processes), separating mathematical proof as a static result from causal proof as a process. It also formalizes a "true/false pseudo-axiom method" and a time-lag-preserving view of computation, using the symbol Xi to mark causal equivalence distinct from ordinary "=". -/- As an application, the paper connects this framework to the FLT Decomposition Method, which reinterprets Fermat's Last Theorem not as the "non-existence of integer solutions," but as a computational dynamic in which, for n>=3, an integer-solution equation and a function-generating equation cannot be jointly constructed within the same decomposition. Consequently, the core issue is framed not as the absence of solutions, but as "equation failure"—a collapse in which numbers themselves fail to be well-formed; we refer to this state as "Shinichi Matter." -/- アブストラクト -/- 本稿は、等号関係が構造的に破綻(矛盾)している状況でも、公理による救済を前提とせずに計算を継続する方法「破綻計算法」を提案する。中核の主張は、sqrt(1)=0 のような破綻した等式を起点としても計算が遂行できるなら、その計算を基礎として公理体系を構成しうるのであり、「標準的公理に反するから無意味だ」と退けるのは論点の取り違えである、という点にある。 -/- この目的のために、本稿は固定IDによる概念管理と、大文字(体系・構造)/小文字・数(置換を含む動的プロセス)の役割分離を導入し、「結果としての数学的証明」と「プロセスとしての原因証明」を分離する。さら に「真偽仮公理法」と命題時間差を保存する計算観を与え、通常の "=" とは異なる原因的同値を表す記号として Xi を定義する。 -/- 適用例として、本稿はFLT分解法と接続し、フェルマーの最終定理を「整数解が存在しない」という存在命題ではなく、n>=3 において「整数解方程式」と「関数生成方程式」を同一の分解内で同時に構成できないという計算の力学として再解釈する。等式を単なる数値関係ではなくZを起点とする構造分解として扱うことで、n=1では関数生成が 成立する一方、n=3では分解項が整数方程式/関数生成の保持に失敗することを示す。結論として、問題は解の有無ではなく、「方程式の破綻(数そのものが成立しない)」という現象として捉え直される。 -/- . (shrink)

The author outlines a provisional phenomenology of problem solving. He begins by reviewing the history of problem-solving psychology, focusing on the Gestalt approach, which emphasizes the influence of prior knowledge and the occurrence of sudden insights. He then describes problem solving as a process unfolding in a field of consciousness against a background of unconscious knowledge, which encodes action patterns, schemata, and affordances. A global feeling of wrongness or tension is resolved by a series of field transitions, which are guided (...) by peripheral experiences of coherence or “rightness.” The author treats the distinction between reproductive thought and productive thought as a difference in field structure. With reproductive thoughts and actions we perform operations to solve a problem in a semi-automatic sequence. In productive thought, by contrast, a kind of parallel search occurs. This may explain the otherwise obscure phenomenology of struggling to break an impasse. (shrink)

This paper introduces the Infinity Definition Method a foundational redefinition of structure in mathematics. By adopting the symbolic identities \[ \frac{1}{\infty} = 0 \quad \text{and} \quad \frac{1}{0} = \infty \] as axiomatic, the method reconceptualizes arithmetic, limits, and equality. We examine the latent role of \( \frac{1}{\infty} = 0 \) in convergent series and unveil the hidden symmetry in limit operations where \(\sqrt{1}= 0 \) is implied structurally.

This paper presents a novel resolution to the P vs NP problem within the framework of Shinichi Mathematics, founded on the Ramanujan Resonance Theorem. This theorem demonstrates that solutions emerge naturally from the structural properties of the problem itself, effectively dissolving the conventional distinction between P and NP when viewed from the Shinichi paradigm. Related Works: Shinichi Mathematics: DOI: 10.5281/zenodo.15362210 Theorems of Cosmic Deformation-BOX3: DOI: 10.5281/zenodo.15477698.

"Objects are not moving." It is only that there exists an entity which recognizes something as moving; in truth, nothing is actually moving. What if such a situation were real? -/- First, physics is a discipline that uses mathematics as a tool, within a philosophical framework, to organize the phenomena of the real world into formulas and ensure repro ducibility. Mathematics is a tool for describing all phenomena of human existence in terms of “numbers,” while philosophy is a tool for (...) describing those same phenomena in terms of “language” (concepts). When abstracted, unresolved human problems can be divided into two categories: “con sciousness” and “the universe.” Consciousness lies within the brain; the universe lies outside the brain. The investigation of these two domains requires both mathematics and philoso phy. Although this paper is written as a work of physics, the definition of what physics is must first be clarified for the argument to be properly understood. For this reason, the above conceptual clarification is placed at the outset. The author has constructed a new mathematical tool, “Shinichi Mathematics,” which is not based on the conventional standard 1 +1 =2 but rather on 1+1 ̸ = 2. In this framework, 1+1 = 0 is taken as a foundational standard, and the definition √1 = 0 is introduced, allowing a mathematical system to be constructed from an “absolute zero” that possesses neither time nor space. Within this framework, 1 = √N expresses that the entity “1” is divisible into N parts. This is discussed in detail in the separate paper The Shinichi Transformation and forms the computational foundation of the Gauge Paradox Theory in physics. This paper builds upon the definitions of Shinichi Mathematics, incorporating the con cepts of gauge redundancy and phase–geometric structure, to classify physical phenomena into “emergent” and “non-emergent” categories in a geometric manner. To engage with the discussion beyond the conventional frameworks of physics and mathematics, the reader is invited to set aside previous assumptions and approach the subject from the starting point of zero. We present a geometry-first formulation of the Gauge Paradox Theory grounded in Shinichi Mathematics (SM). The central declaration is the SM identification 1 ≡S √N: “the unit” is read as a resolvable mode √N. Signs are redundant and are absorbed into a phase shift by π (Sign-as-Phase), so only correlation/phase and the radius √N matter. Emergence is defined relationally by comparing a world N against a baseline N′: N < N′ ⇒ Plus (emergent), N ≥ N′ ⇒Minus(non-emergent). We keep the coordinate convention X = time, Y = space, and emphasize a purely geometric statement: once a single point on the phase circle is fixed, a four-point set is determined by symmetry; this is the visual content behind gauge redundancy. This paper is conceptual; operational protocols (e.g., ε-LCM cells, four-phenomena maps) are detailed in the attached references. (shrink)

This paper introduces the Expansion Theorem of Shinichi Mathematics, a novel mathematical framework that begins with the axiomatic structure √1 = 0 and redefines foundational concepts such as number, ratio, and emergence. The paper formalizes a series of laws including: the Infinite Ratio Transformation Law, the Root-N Conversion Method, the Root-N Dynamic Method, the Squared Total Ratio Transformation Law, and the Shinichi Theorem — all of which describe how the entity "1" can be structurally decomposed and recomposed through abstract combinatorial (...) and geometric relationships. These theorems present a new view of unity and structure beyond conventional mathematical systems. (shrink)

Note: The full text is written in Japanese in order to preserve the precise definitions and logical structure specific to the language. -/- DOI: 10.5281/zenodo.17772964 -/- 【1】 Equation Mathematics Foundations 方程式数学基礎 -/- Abstract (English) -/- Mathematics proves nothing. -/- This paper presents the foundations of Equation Mathematics, an axiomatic framework that treats computation as the primary axiom, where computation is defined as transformation by definition. In this framework, “proof” is defined as a computational result that transforms an expression into a (...) symbol, characterized by reproducibility: a specified operation yields the same result. “State” is defined as the intermediate phase of computing an expression or a symbol relative to a unit. Using equality, elementhood, a redefinition of unit, and Peano-style generation via a constant “+1” as materials, the paper provides a base in which intermediate steps remain available and computation stays thinkable. The aim is not to produce a prescriptive specification, but to preserve a system in which definitional change and its limits can be repeatedly explored. -/- アブストラクト 本論文は、数学を「証明の体系」としてではなく、「定義によって変化させる方法」としての計算を公理に置く体系（方程式数学）の基礎を提示する。ここで証明は、式を記号へ変形する計算の結果として定義され、特定の 操作が必ず同じ結果を与える再現性として扱われる。状態は、式または記号を単位として計算する途中である。等号（=）と要素関係（∈）に対応する枠組み、単位の再定義、そして +1（定数）による生成を素材として配置し、読者が「途中」を保持したまま計算を継続できるための母体を与える。本論文の狙いは、決められたとおりに実行する仕様書を作ることではなく、計算が成立しにくい箇所をあ えて露出させ、定義と変化の関係を反復可能な素材として残す点にある。 -/- ================================ -/- 【2】If Einstein was mistaken in thinking that light travels in a straight line, then humanity is likely making the same mistake. アインシュタインは光が直線で進んでいると勘違いしていたなら、人類も同じように勘違いしている。 -/- Abstract (English) Building on Equation Mathematics Foundations, this paper recasts hierarchical structure in society and cognition as an order formed through unreflective use of equality (“=”). It defines light not as a constant but as a relational structure arising between two substances X and Y, using the form X + Y = Z as its description. Space is defined as the “one-second-prior space” recognized by C in A + B = C, so that the same additive form splits into (i) an inter-material structure and (ii) a form of recognition. Einstein is referenced as a symbolic figure associated with invariance and constants; the aim is not criticism but to provide materials for comparing how the desire “light = constant” can arise and how similar misreadings may be repeated in general human cognition. By treating thought experiments as computation and defining “being alive” as mutual recognition, the paper repositions science as a process through which shared recognition is generated. -/- アブストラクト 本論文は、方程式数学基礎に準拠しつつ、社会や認識に現れるヒエラルキー構造を、無自覚な等号（=）の使用によって形成される秩序として捉え直す。さらに、光を定数としてではなく、二つの物質 X, Y の間を結ぶ関係性によって生じる構造として定義し、式 X + Y = Z をその記述形式として採用する。空間は、A + B = C において C が認識する「1秒前の空間」として定義され、同じ加法形式が「物質間の構造」と「認識の形」に分岐する。アインシュタインは光速度不変（定数）を提唱した象徴として参照されるが、本論文は批判を目的とせず、「光 = 定数」という願望がどのように成立しうるか、またその誤認が人類一般の認識にも反復されうることを比較可能にするための素材を提示する。思考実験を計算として扱い、「生きている」を相互認識として定義することで、 科学を共通認識の生成過程として再配置する。 . (shrink)

Both right angles and straight lines are at rest. -/- This paper presents an AI-assisted analytic reconstruction of a geometric thesis that deliberately eliminates time-parameterized kinematics (velocity and acceleration), replacing them with a purely spatial framework based on arc length, curvature, observation scale L, and observational resolution ε. We redefine “straightness” not as an ontic reality but as an identification label assigned when curvature is operationally undetectable (the ≪Straight-Line Illusion≫). Concretely, for curvature κ observed over scale L, the sagitta deviation (...) satisfies δ ≈ κL^2/8, and whenever δ < ε the segment is identified as κ=0 (straight) despite κ>0. Conversely, a “right angle” is re-interpreted not as a natural shape but as a singularity induced by representational compression: when a smooth trajectory is approximated by a polyline under sparse sampling, a vertex can appear where tangency is undefined. This vertex is defined as ≪Right Angle≫ and is synonymous with ≪Rest≫. -/- Within this framework, Aristotle’s Wheel paradox is resolved as the geometric impossibility of satisfying simultaneous no-slip correspondence conditions for concentric circles of different radii: if the outer rim satisfies S=Rθ, then an inner rim rigidly sharing the same rotation angle θ cannot simultaneously satisfy S=rθ when R≠r. -/- Furthermore, this paper provides the solution to the fundamental proposition presented in the appended paper “If Einstein Misunderstood That Light Travels in a Straight Line, Then Humanity Is Misunderstanding It Too,” within Equation Mathematics Foundations (DOI: 10.5281/zenodo.18102417): -/- [Quoted Proposition] [1] Proposition to Einstein All existence cannot turn at a right angle. It must necessarily come to rest. If so, it cannot proceed in a straight line either. Because it would mean using a 90-degree angle relative to existence. -/- The solution proposed herein is that light and motion are not “travel” but “spatial relationships (structures).” Light is not treated as a projectile moving from X to Y, but as the establishment of a relational constraint—schematically, X+Y=Z—where the primitive content is structural rather than time-indexed. Since “travel” is not taken as a primitive in this definition-based ontology, “moving in a straight line” is deconstructed as an identification regime (≪Straight-Line Illusion≫), integrating physics into a time-free, definition-first ontology. ================================================================ -/- Reference: Equation Mathematics Foundations (DOI: 10.5281/zenodo.18102417) -/- 【AI Models Used】 -/- The analysis and reconstruction in this work utilized the following AI models: -/- * ChatGPT 5.2 (Reasoning Model) -/- * Gemini 3.0 Pro -/- * Grok (Auto Mode) -/- . (shrink)

This paper reconstructs the structural basis of prime number distribution by defining $\infty - 1$ as either a prime or composite number. We introduce the concept of "definition pressure"—a principle whereby structural constraints are imposed through mathematical definitions—and explore the consequences for infinite constructs in mathematics.

Where there is mathematics, there are numbers. Where there are numbers, there is life. Thus, I have proven that the universe is alive. Because when you see a box called 1 = N, you feel compelled to put a number into it. The box we call the universe is not the same size for you and me. Yet we have mistaken it as the same. This is where it all begins. Thus, a + b = c tells us nothing, because (...) it assumes a and b come from the same space — but that assumption is the first illusion. I expressed this as: 1 = √N, because the universe began not with 1, but with √1 = 0. This leads to Theorem 3: Let Y = 1, or multiply both sides by 1/Y. Either way, we reveal the structure that makes everything appear as 1 — when it never truly was. That false “1” is where the universe begins to breathe. Because Theorem 1 cannot prove the collapse of the ABC Conjecture. (shrink)

本稿は数学と哲学の根本的な結合ではなく、数学と哲学の根源的な主題である『認 識』と『意識』を文法的枠組みで細分化して問い直す。 本研究の主張は、数学的認知と哲学的(語学)認知のズレによる本質的な問題につい て説明する。これは、証明ではなく説明である。 数学・哲学とは記述であり、記述する対象を『1』としたときに『1』をどのように 記述するかの違いに着目していた事を説明する。 『This one』と『That one』の関係性のズレにこそメカニズムがあり、その力学を新 しく『定義存在学』と名付け活用されたい。 定義存在学の論文を作る前段として利用してもらいたいのが、この数学文法認知哲 学である。この数学文法認知哲学を踏まえ数学理想主義と合わせると定義存在学が フレームが見えてくる。 そして、この定義存在学こそがシンイチ数学を哲学的に解説した物であり、全ては一 つの完成された体系のように見えてくるだろうが、これは、筆者が作った体系ではな く宇宙と意識を説明しただけである。 宇宙人を見たことがないから信じないという論理があるが、1+1=2と言う概念は 見た物しか信じないという論理思考である。 なぜ、筆者が宇宙と意識の関係性を説明できるのかは感じたからである。感じる事と 見る事の違いは何かと説明できないのは証明と言う価値を捨て、定義に基づく解を 許容することである。.

存在とは認識であり、認識されないものは存在しない。では、「存在しないもの」 を認識することは、そもそも可能なのか。 本稿では、言語を「存在を認識した結果としての形状」と捉え、言語の構造そのも のが「存在の認識の形」を決定するという立場をとる。 言語の特性は大きく二種類に分類できる。 (1)自分(主観)が存在することを前提に構築された言語/(2)自分が存在しない ことを前提に構築された言語。 この差異が、認識におけるズレを生む。 自分が存在しないと認識できる言語は「物が存在しない」という結論を受け入れる 構造を持つ一方で、自分も物も存在すると前提する言語は「存在の不在」そのものを 扱うことができない。 重要なのは、われわれが本当に存在するか否かという事実ではない。そうではなく、 「存在している/していない」と認識させる言語特性そのものが存在するという 事実である。 本論文は、英語では“Pen is this”が真にならず、日本語では“Pen is”が真と して成立するその理由を、「認識の言語構造」から導き、定義存在学(Definitional Ontology)は英語では証明され得ないことを示す。.

The core question of the Collatz Conjecture is deceptively simple: Why does any non-negative integer eventually reach 1 through repeated application of the Collatz process? The answer lies in the transformation rules: even numbers are divided by 2. This means that once a value reaches a power of two, it naturally collapses down to 1 through successive halving. Therefore, the true object of proof is not the even numbers — their behavior is predictable and mechanically reducible. The real challenge is (...) to understand why and how odd numbers inevitably lead into a power-of-two structure. If this mechanism can be structurally shown, the conjecture as a whole is proven. For every odd integer (X > 0), the following relation: 3X + 1 = 2Z is shown to structurally lead to convergence to 1. (shrink)

This record provides a public summary of an operational program to test the Gauge Paradox Theory inside Shinichi Mathematics (SM). The approach treats numbers as a language and studies emergence as a relational, gauge-aware effect between channels (e.g., heat → light). We present the conceptual building blocks—state space D=[0,∞)×S1\mathcal{D}=[0,\infty)\times S^1D=[0,∞)×S1, a Z2\mathbb{Z}_2Z2 gauge (Sign-as-Phase), and a radius invariant A2=NA^2=NA2=N—and describe, at a high level, how a “native influence region” would be identified in experimental maps. -/- What this is not. This (...) is not an attempt to overthrow existing scholarship; it is a conceptual and ethical invitation to test specific qualitative predictions. To avoid premature or unsafe deployment, implementation-critical details (exact thresholds, decision inequalities, morphology parameters, and reduction pipelines) are withheld here. -/- Qualitative predictions. (1) A constructive band that drifts monotonically with frequency; (2) monotone temperature scaling of a native influence measure; (3) systematic material dependence (spatial slope / temporal lag); (4) gauge redundancy: absolute sign is unobservable, only relative π\piπ-phase flips matter. -/- Access to methods (on request). Complete preregistered protocols and analysis assets are available to qualified laboratories upon request under an ethical-use agreement. Interested groups are invited to contact the author. -/- Ethical Use Notice. Use is prohibited for weapons development, surveillance targeting, psychological manipulation, coercive control, or discriminatory purposes. Requests will be screened case-by-case with human-rights and privacy considerations. (shrink)

Existence is recognition; what is not recognized does not exist. But then, is it even possible to “recognize what does not exist”? -/- In this paper, I treat language as “the form that appears as the result of recognizing existence,” and I adopt the view that the very structure of a language determines the form of recognizing existence. -/- Linguistic systems can, in broad terms, be classified into two types: -/- Languages constructed on the premise that the self (subjectivity) exists. (...) -/- Languages constructed on the premise that the self does not necessarily exist. -/- This difference generates a structural gap (zure) in recognition. -/- A language that can recognize “a self that may not exist” has a structure that can accept the conclusion that “things do not exist.” By contrast, a language that presupposes the existence of both the self and things cannot even handle the notion of “the absence of existence”. -/- What matters here is not the metaphysical fact of whether we truly exist or not. Rather, it is the following: -/- There exist linguistic structures that themselves make us recognize “existing / not existing.” -/- This paper shows that, in English, the sentence “Pen is this” cannot be true, whereas in Japanese, “Pen is” can be accepted as true. From this difference, I derive the reason why Definitional Ontology cannot be proven in English, by analyzing the linguistic structure of recognition. -/- This paper is not a translation of the Japanese original, but a simplified English edition designed to convey its core ideas within the structural limits of the English language. The author wishes that readers ultimately refer to the original Japanese paper, where the full theoretical structure is presented. (shrink)

本稿は、「1+1=2」という算術の最も基本的な命題を手掛かりに、数学における 「イコール」の意味を問い直す。本研究の主張は、イコールとは現実において完全に 成立するものではなく、理想世界においてのみ成立する近似値的概念であるという 点にある。すなわち、数学は現実を完全に写し取る体系ではなく、同一性をズレを通 じて規定し、そのズレを集合として再現可能にするための記号的装置である。この視 座から、数学を「理想の近似値」として位置づけ、現実世界におけるズレで成立する 人間的営みとしての数学を再定義する。.

Note: The full text is written in Japanese in order to preserve the precise definitions and logical structure specific to the language. -/- DOI: 10.5281/zenodo.17772964 -/- What Is a Scholar? —学者とは— -/- Abstract (English) -/- This paper argues that the concept of “the scholar” should not be treated as a single, homogeneous category. Instead, it proposes a fundamental distinction between two types: explorers of knowledge, who engage directly in the act of discovery, and interpreters of exploration, who explain, systematize, and (...) circulate those discoveries within institutional frameworks. -/- Using autobiographical experience and metaphorical analysis, the paper clarifies this distinction through the analogy between “searching for food” and “eating food.” Both are essential, but they are not interchangeable. Figures such as Darwin, Fermat, and Van Gogh are discussed as historical examples of knowledge explorers whose work was initially marginal yet later transformative. -/- The paper does not argue for the superiority of either type. Rather, it claims that intellectual integrity requires scholars to clearly state whether they speak as explorers or interpreters, since the nature of definition and evaluation changes accordingly. -/- アブストラクト 本論文は、「学者」という概念が単一の役割として扱われてきたことに疑問を呈し、学者を探学者（知の探検者）と解学者（探検の解説者）という二つの異なる類型に分けて捉える必要性を提案する。前者は未知を直接探究 する者であり、後者はその成果を説明・整理・流通させる制度的役割を担う。 -/- この差異は、「食べ物を探すこと」と「食べること」という比喩によって明確化される。両者はいずれも不可欠であるが、同一視することはできない。ダーウィン、フェルマー、ゴッホといった人物は、当初は理解されなか った探学者の典型例として位置づけられる。 -/- 本論文の目的は、どちらが正しいかを論じることではなく、学術的対話における最低限のマナーとして、自らが探学者か解学者かを表明することの重要性を示す点にある。. (shrink)

Note: The full text is written in Japanese in order to preserve the precise definitions and logical structure specific to the language. -/- DOI: 10.5281/zenodo.17772964 -/- The Axiom of Ignorance: Equation Mathematics 無知公理—方程式数学— -/- Abstract(English) Mathematics is meaningless. This is the Axiom of Ignorance. -/- This paper does not present a system of calculation or proof, but instead proposes a framework for generating an axiomatic space prior to such systems, focusing on the selection of definitions and rules of identification that (...) make mathematics possible. By relativizing the act of definition implicitly assumed in set theory and the Peano axioms, this study introduces the Axiom of Ignorance as a foundational principle that connects problems and solutions. -/- The Axiom of Ignorance formalizes the set of definitions that are necessarily excluded when a single solution is selected. Through this axiom, mathematical concepts such as equations, order, sets, and algebraic expressions can be treated at a stage prior to their conventional formalization. The framework is organized as Equation-Based Mathematics, in which the symbolic order expression x = y ∈ z functions as a foundational schema aligning axioms, problems, and solutions without directional bias. -/- Rather than proposing new computational techniques, this paper redefines, at the axiomatic level, what it means for a solution to be valid as a solution within mathematics itself. -/- アブストラクト -/- 数学とは意味がない。これが無知公理である。 -/- 本論文は、計算や証明を行う数学体系そのものではなく、それらが成立する以前の段階における「定義の選択」と「同一視規則」に着目し、公理空間を生成する枠組みを提示するものである。本研究では、既存の集合論やペ アノ公理において暗黙に前提とされている定義行為そのものを相対化し、≪無知公理≫を導入することで、問題と解が結び付く条件を記述する。 -/- ≪無知公理≫とは、解を一つ選択することによって同時に排除される定義の集合を明示的に公理化するものであり、これにより数式・方程式・順番・集合といった数学的概念が成立する以前の状態を形式的に扱うことが可能 となる。本論文では、この枠組みを≪方程式数学≫として整理し、x=y∈z という記号順序式を基準に、公理・問題・解の方向性が揃う条件を示す。 -/- 本研究の目的は、新たな計算手法を提示することではなく、数学において「解が解として成立するとは何か」という基礎的問題を、公理レベルで再定義する点にある。 . (shrink)

Note: The full text is written in Japanese in order to preserve the precise definitions and logical structure specific to the language. -/- DOI: 10.5281/zenodo.17772964 -/- Euler–Einstein Transformation—オイラー＝アインシュタイン変換— -/- Abstract (English) This paper introduces the Euler–Einstein Transformation, defined as an operation that normalizes an equation L = R by mapping it to the form L/R = 1, or equivalently to a zero-shift form. Rather than treating algebraic manipulation as logical inference, the transformations presented here are regarded as manufacturing rules for (...) constructing difference equations. -/- By adopting cubic structures x^3 as the generative core and applying a sequence of model selections, the formulation converges to the difference equation -/- A^2 = B r^3 e^{i3θ}. -/- This process demonstrates how heterogeneous algebraic forms can be unified through normalization and structural aggregation, without relying on conventional axiomatic derivations. -/- アブストラクト 本稿は、等式 L = R を L/R = 1 の形へ正規化する操作、すなわちゼロ移動形式への写像として定義されるオイラー＝アインシュタイン変換を導入する。本研究では、代数的変形を論理的推論としてではなく、差分方程式を構成するための製造規則として扱 う。 -/- 立方構造 x^3 を生成核としてモデル選択を行うことで、最終的に -/- A^2 = B r^3 e^{i3θ} -/- という差分方程式へと収束する過程を示す。本製造過程は、従来の公理的導出に依存することなく、正規化と構造集約によって異質な代数形式を統一できることを示している。 . (shrink)

Note: The full text is written in Japanese in order to preserve the precise definitions and logical structure specific to the language. -/- DOI: 10.5281/zenodo.17772964 -/- The Axiom of Ignorance: Definition Ontology 無知公理—定義存在学— -/- Abstract(English) Language is alive. This is the Axiom of Ignorance. -/- This paper presents a framework of Definition Ontology grounded in the Axiom of Ignorance, reconstructing the relationships among existence, cognition, consciousness, and definition. In this context, the Axiom of Ignorance denotes the act by which selecting (...) a single solution necessarily excludes alternative possibilities, and is positioned as an indispensable axiom for the formation of problems and solutions. -/- The study distinguishes definitions whose subject is cognition from those whose subject is consciousness, clarifying how these processes manifest as abstraction and concept, respectively. Furthermore, when the Axiom of Ignorance itself becomes a fixed subject, the resulting structure is defined as a Hierarchy Layer, through which the conditions for problem formation, refutation, and solution emergence are systematically described. -/- Rather than addressing correctness or provability, this paper aims to define the preconditions under which problems and solutions become describable at all. In doing so, it proposes an axiomatic description of a foundational structure shared across mathematics, logic, and language. -/- アブストラクト 言葉は生きている。これが無知公理である。 -/- 本論文は、≪無知公理≫を基礎として、存在・認識・意識・定義の関係を再構成する定義存在学的枠組みを提示するものである。本研究において≪無知公理≫とは、解を一つ選択することによって同時に選ばれなかった他の 可能性を排除する作用そのものを指し、問題と解が成立するために不可避な公理として位置付けられる。 -/- 本論文では、認識を主体とする定義と、意識を主体とする定義を区別し、それぞれが抽象および概念として現象化する過程を整理する。さらに、≪無知公理≫が主体として固定された場合に生じる構造を≪ヒエラルキー階層 ≫として定義し、問題設定・反証・解の成立条件を統一的に記述する。 -/- 本研究の目的は、正誤や証明可能性を論じることではなく、問題が問題として成立し、解が解として記述される以前の条件を明示的に定義することである。これにより、数学・論理・言語に共通する基礎構造を、公理的に記 述する可能性を示す。 -/- . (shrink)

This chapter is devoted to criticisms of the views of propositions defended by my co-authors, Jeff King and Scott Soames. The focus is on criticism of their attempts to explain the representational properties of propositions. The criticisms are varied, but one theme is a tension between their view that our actions can explain the representational properties of propositions and their commitment to the idea that propositions have their representational properties essentially.

REVIEW (1): "Jeff Kochan’s book offers both an original reading of Martin Heidegger’s early writings on science and a powerful defense of the sociology of scientific knowledge (SSK) research program. Science as Social Existence weaves together a compelling argument for the thesis that SSK and Heidegger’s existential phenomenology should be thought of as mutually supporting research programs." (Julian Kiverstein, in Isis) ---- REVIEW (2): "I cannot in the space of this review do justice to the richness and range of (...) Kochan's discussion [...]. There is a great deal in this foundational portion of Kochan's discussion that I find tremendously interesting and engaging [...]." (David R. Cerbone, in Studies in History and Philosophy of Science) ---- REVIEW (3): "Science as Social Existence will be of interest not only to Heidegger scholars but to anyone engaged in science and technology studies. [...] This is an informative and original book. Kochan should be praised for his clear, pleasant-to-read prose." (Michael Butler, in CHOICE). (shrink)

This paper defends “moral individualism” against various arguments that have been intended to show that membership in the human species or participation in our distinctively human form of life is a sufficient basis for a moral status higher than that of any animal. Among the arguments criticized are the “nature-of-the-kind argument,” which claims that it is the nature of all human beings to have certain higher psychological capacities, even if, contingently, some human beings lack them, and various versions of the (...) idea that there is a special form of life that all human beings share but of which no animal can be a full participant. The paper concludes that none of these arguments succeeds in demonstrating that there are moral reasons to permit animals to be treated less well than members of our own species whose psychological capacities and potential are no higher than those of the animals. (shrink)

Herman Cappelen and Josh Dever (C&D) have recently argued that the ideal/non-ideal distinction is ‘useless’ in philosophy of language. This paper responds to C&D’s argument, develops an account of the distinction, and applies it to philosophy of language. Section 1 summarizes C&D’s argument against Charles Mills’s version of the distinction. Section 2 develops an account of the distinction that’s inspired by Mills’s work but that differs from what C&D take Mills’s view to be. Section 3 shows that, pace C&D, this (...) distinction picks out interesting subsets of work in philosophy of language. We say that ideal theories adopt models of the social world that fail to recognize systemic oppression and are therefore systematically inaccurate. Nonideal theories correct these inaccuracies. (shrink)

I discuss and defend two arguments against semantic theories which wish to avoid commitment to propositions. The first holds that on the most plausible semantics of a class of natural language sentences, the truth of sentences in that class requires the existence of propositions; and some sentences in that class are true. The second holds that, on the best understanding of the form of a semantic theory, the truth of a semantic theory itself entails the existence of propositions. Much of (...) the discussion engages Davidsonian alternatives to a propositionalist semantic theory. (shrink)

Historians have claimed that the two closely related concepts of animism and natural teleology were both decisively rejected in the Scientific Revolution. They tout Robert Boyle as an early modern warden against pre-modern animism. Discussing Avicenna, Aquinas, and Buridan, as well as Renaissance psychology, I instead suggest that teleology went through a slow and uneven process of rationalization. As Neoplatonic theology gained influence over Aristotelian natural philosophy, the meaning of animism likewise grew obscure. Boyle, as some historians have shown, exemplifies (...) this uneven process. There is an unresolved tension between his religious convictions and the implicit animism of his empirical practice. (shrink)

Author's response to: Raphael Sassower, 'Heidegger and the Sociologists: A Forced Marriage?,' Social Epistemology Review and Reply Collective 7, no. 5 (2018): 30-32. -- Part of a book-review symposium on: Jeff Kochan (2017), Science as Social Existence: Heidegger and the Sociology of Scientific Knowledge (Cambridge UK: Open Book Publishers).

This paper exposes a common mistake concerning the division of linguistic labor. I characterize the mistake as an overgeneralization from natural kind terms; this misleads philosophers about which terms are subject to the division of linguistic labor, what linguistic labor is, how linguistic labor is divided, and how the extensions of non-natural kind terms subject to the division of linguistic labor are determined. I illustrate these points by considering Sally Haslanger’s account of the division of linguistic labor for social kind (...) terms and raising an objection to it. Then, I draw on Tyler Burge’s work to characterize a conception of the division of linguistic labor that avoids the mistaken overgeneralization and grounds 1–4 above in social norms and practices. (shrink)

I reply to criticisms from King and Soames and critically examine two aspects of current orthodoxy about propositions: that they are representational and that they are structured. I argue that (especially once one gives up on intrinsically representational propositions) there is no good reason to think that propositions have representational properties, and distinguish a few different senses in which propositions might be structured, expressing some skepticism about the more ambitious ones.

Social studies of science have often treated natural field sites as extensions of the laboratory. But this overlooks the unique specificities of field sites. While lab sites are usually private spaces with carefully controlled borders, field sites are more typically public spaces with fluid boundaries and diverse inhabitants. Field scientists must therefore often adapt their work to the demands and interests of local agents. I propose to address the difference between lab and field in sociological terms, as a difference in (...) style. A field style treats epistemic alterity as a resource rather than an obstacle for objective knowledge production. A sociological stylistics of the field should thus explain how objective science can co-exist with radical conceptual difference. I discuss examples from the Canadian North, focussing on collaborations between state wildlife biologists and managers, on the one hand, and local Aboriginal Elders and hunters, on the other. I argue that a sociological stylistics of the field can help us to better understand how radically diverse agents may collaborate across cultures in the successful production of reliable natural knowledge. (shrink)

Tim Ingold draws a sharp line between animism and hylomorphism, that is, between his relational ontology and a rival genealogical ontology. He argues that genealogical hylomorphism collapses under a fallacy of circularity, while his relationism does not. Yet Ingold fails to distinguish between vicious or fallacious circles, on the one hand, and virtuous or hermeneutic circles, on the other. I demonstrate that hylomorphism and Ingold’s relational animism are both virtuously circular. Hence, there is no difference between them on this count. (...) A path thus opens for what I call hylomorphic animism. While Ingold’s relational animism leads into obscurity, hylomorphic animism is able to explain the differences in power between material things. (shrink)

In Felicitous Underspecification, Jeffrey King draws our attention to a rich and underexplored collection of linguistic data. These are uses of context-sensitive expressions which seem perfectly felicitous despite being such that, on plausible assumptions, the context in which they are used falls short of securing for them a unique semantic value. This raises an immediate puzzle: if, as King argues, these uses of expressions really do lack unique semantic values in context, how can they—as they manifestly do—make contributions to the (...) conversations in which they occur? King answers this question with a novel theory of conversational updating. Here I focus less on this theory than on King’s examples, and consider some ways of accommodating them without positing felicitous underspecification. In some cases I give some reasons for thinking that the alternative explanation is superior. But my aim is less to establish this conclusion than to suggest some new options for thinking about these examples, and hopefully by so doing to advance the conversation about the data to which King has drawn our attention. (shrink)

ABSTRACT I focus on two of the challenges Pautz raises for representationalist theories of perception. The first is the challenge of explaining the necessity of certain principles which Pautz calls 'laws of appeaeance.' The second is based on the idea that the most promising versions of representationalism seem to lead to irrealism about the sensible qualities.

This paper explores the central question of why soldiers in democratic societies might decide to fight in wars that they may have reason to believe are objectively or questionably unjust. First, I provide a framework for understanding the dilemma caused by an unjust war and a soldier's competing moral obligations; namely, the obligations to self and state. Next, I address a few traditional key thoughts concerning soldiers and jus ad bellum. This is followed by an exploration of the unique and (...) contradicting moral problems that confront modern soldiers and their officers. I argue that although traditional positions such as invincible ignorance provide a rather dangerous ‘head-in-the-sand’ mentality, soldiers serving a democratic government are nonetheless very limited in their legal and moral ability to interpret what is a justifiable war. However, a very few select senior officers are in positions to make such legal and moral decisions concerning jus ad bellum. (shrink)

A verbal dispute is one in which the disputants agree on all of the facts about the intended subject matter of the dispute and disagree only about how to use certain terms. This paper explores the possibility that the dispute between particularists and generalists about the contents of perceptual experience is a verbal dispute. The aim is less to provide a knockdown argument for the conclusion that this dispute is merely verbal than to show how difficult it is to uncover (...) a substantive dispute between the two sides. A concluding section asks whether the argument generalizes beyond the particularism/generalism dispute to other prominent disputes in contemporary philosophy of mind. (shrink)

Recent empirical and philosophical research challenges the view that reason and emotion necessarily conflict with one another. Philosophers of science have, however, been slow in responding to this research. I argue that they continue to exclude emotion from their models of scientific reasoning because they typically see emotion as belonging to the context of discovery rather than of justification. I suggest, however, that recent work in epistemology challenges the authority usually granted the context distinction, taking reliabilism as my example. Emotion (...) may be seen as playing a reliable role in the formation, which for the reliabilist also means the justification of scientific beliefs. (shrink)

Hermeneutic studies of science locate a circle at the heart of scientific practice: scientists only gain knowledge of what they, in some sense, already know. This may seem to threaten the rational validity of science, but one can argue that this circle is a virtuous rather than a vicious one. A virtuous circle is one in which research conclusions are already present in the premises, but only in an indeterminate and underdeveloped way. In order to defend the validity of science, (...) the hermeneuticist must describe a method by which a vague and confused initial knowledge of nature gets transformed into a clear and determinate knowledge of nature. I consider three such methods. The first is regressus demonstrativa, favoured by the physicians of Padua during the fifteenth and sixteenth centuries. The second is mathēsis, introduced by Martin Heidegger in his discussion of seventeenth-century science. The third is Denkstil, a key concept in Ludwik Fleck’s history of syphilology. I conclude by listing three desiderata for a hermeneutic science studies: that it be anti-metaphysical, historical, and sociological. --- Reprinted in: Erich Otto Graf, Martin Schmid & Johannes Fehr (eds.), Fleck and the Hermeneutics of Science (Collegium Helveticum Heft 14) (Zürich, 2016), pp. 85-93. (shrink)

This article argues that the freedom of voluntary action can be grounded in the contingency of the laws of nature. That is, the possibility of doing otherwise is equivalent to the possibility of the laws being otherwise. This equivalence can be understood in terms of an agent drawing a boundary between self and not-self in the domains of both matter and laws, defining the extent of the body and of voluntary behaviour. In particular, the article proposes that we can think (...) of `will' as naming the component of the laws of nature delimited by this boundary. (shrink)

Tradução do capítulo "Animals" (Capítulo 39, páginas 525 a 536), escrito por Jeff McMahan e publicado no livro "A Companion to Applied Ethics", obra organizada por R.G. Frey e Christopher Heath Wellman.

Bruno Latour claims to have shown that a Kantian model of knowledge, which he describes as seeking to unite a disembodied transcendental subject with an inaccessible thing-in-itself, is dramatically falsified by empirical studies of science in action. Instead, Latour puts central emphasis on scientific practice, and replaces this Kantian model with a model of “circulating reference.” Unfortunately, Latour's alternative schematic leaves out the scientific subject. I repair this oversight through a simple mechanical procedure. By putting a slight spin on Latour's (...) diagrammatic representation of his theory, I discover a new space for a post-Kantian scientific subject, a subject brilliantly described by Ludwik Fleck. The neglected subjectivities and ceaseless practices of science are thus re-united. (shrink)

Final instalment of a book-review symposium on: Jeff Kochan (2017), Science as Social Existence: Heidegger and the Sociology of Scientific Knowledge (Cambridge UK: Open Book Publishers). -- Author's response to: Paolo Palladino (2018), 'Heidegger Today: On Jeff Kochan’s Science and Social Existence,' Social Epistemology Review and Reply Collective 7(8): 41-46; and Adam Riggio (2018), 'The Very Being of a Conceptual Scheme: Disciplinary and Conceptual Critiques,' Social Epistemology Review and Reply Collective 7(11): 53-59.