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Bibliografiset tiedot
Päätekijä:	Yeon, Jeong Min
Aineistotyyppi:	Recurso digital
Kieli:	englanti
Julkaistu:	Zenodo 2026
Aiheet:	Philosophy Mathematical logic
Linkit:	https://doi.org/10.5281/zenodo.20069437
Tagit:	Lisää tagi Ei tageja, Lisää ensimmäinen tagi!

Sisällysluettelo:

This work develops an operational account of objecthood. Instead of treating an object merely as an element of a category, it asks when a candidate can be formed and preserved as one re-identifiable object under multiple descriptions, operations, and categorical transitions. The central claim is that objecthood has two layers. First, an object is formed through separable sharing. Its descriptive axes must remain separately operable while jointly referring to the same candidate. Categorically, if A1,…,AnA_1,\dots,A_nA1,…,An are attribute or operand categories and each projects to a common reference category BBB, then the object-level category is not the unrestricted product A1×⋯×AnA_1\times\cdots\times A_nA1×⋯×An, but the pullback-like compatibility locus Aobj=A1×BA2×B⋯×BAn.A_{\mathrm{obj}} = A_1\times_B A_2\times_B\cdots\times_B A_n.Aobj=A1×BA2×B⋯×BAn. Thus an object is not a mere tuple of independent attributes. It is a compatible family of readings that share one reference. Second, once formed, the object must be preserved under admissible operations and categorical transitions. An operational categorical system is written as Ci=(Ai,Oi),\mathcal C_i=(\mathcal A_i,\mathcal O_i),Ci=(Ai,Oi), where Ai\mathcal A_iAi is a category of operands and Oi&sube;End⁡(Ai)\mathcal O_i\subseteq \operatorname{End}(\mathcal A_i)Oi&sube;End(Ai) is a chosen category of admissible endofunctors. For two such systems, an operand transition Tij:Ai→AjT_{ij}:\mathcal A_i\to\mathcal A_jTij:Ai→Aj and an operator transition Φij:Oi→Oj\Phi_{ij}:\mathcal O_i\to\mathcal O_jΦij:Oi→Oj preserve objecthood when, for every admissible operator O∈OiO\in\mathcal O_iO∈Oi, there is a natural isomorphism ηO:Tij∘O⇒&sim;Φij(O)∘Tij.\eta_O: T_{ij}\circ O \xRightarrow{\sim} \Phi_{ij}(O)\circ T_{ij}.ηO:Tij∘O&sim;Φij(O)∘Tij. This condition says that acting first and transferring later agrees, up to natural isomorphism, with transferring first and acting by the transferred operator. The paper interprets familiar categorical structures—pullbacks, naturality, functoriality, and action preservation—as criteria for operational objecthood. Examples include ordinary objects such as coins, physical mixtures such as saltwater, Euler’s formula as a compatibility relation preserving unit rotation, and object detection in artificial intelligence, where pixels, labels, bounding boxes, and latent features count as one object only when they jointly stabilize the same candidate. The final thesis is: objecthood=separable sharing+stable re-identification.\boxed{ \text{objecthood} = \text{separable sharing} + \text{stable re-identification}. }objecthood=separable sharing+stable re-identification. In ordinary language, a thing becomes an object when its many distinguishable ways of being read still point back to one same candidate, and its admissible ways of being acted upon continue to preserve that candidate.

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