{"id":"W2123497262","doi":"10.1007/978-94-007-0431-2_9","title":"Reflections on the Categorical Foundations of Mathematics","year":2011,"lang":"en","type":"book-chapter","venue":"The Western Ontario series in philosophy of science","topic":"Logic, programming, and type systems","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Ottawa; McGill University","funders":"","keywords":"Peano axioms; Axiom; Type theory; Foundations of mathematics; Calculus (dental); Naturalness; Set theory; Relation (database); Mathematics; Subject (documents); Type (biology); Order (exchange); Categorical variable; Axiom of choice; Epistemology; Set (abstract data type); Computer science; Algebra over a field; Philosophy; Pure mathematics; Discrete mathematics; Programming language","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003156706,0.000292855,0.0005466606,0.001578159,0.004304621,0.006190405,0.001321453,0.002393146,0.01792069],"category_scores_gemma":[0.006417145,0.000539176,0.0003197323,0.001874161,0.02616076,0.01096099,0.002664366,0.008089111,0.001910655],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.02115071,"about_ca_system_score_gemma":0.008616994,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.1672311,"about_ca_topic_score_gemma":0.2343768,"domain_scores_codex":[0.9981878,0.0006948316,0.00004826036,0.0001547746,0.0007098541,0.0002044235],"domain_scores_gemma":[0.9941031,0.003633513,0.0001928385,0.0004537936,0.001216889,0.0003997895],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000004626776,0.000002434896,0.00003730944,0.00001477755,6.330881e-7,0.000006941547,0.0004753038,0.00005743837,0.00002601642,0.9861157,0.0114636,0.001795243],"study_design_scores_gemma":[0.000007946705,0.000003184782,0.0002580331,0.00008165208,0.000001445845,0.00001935785,0.0006608851,0.0001859802,0.0000676315,0.7192495,0.2794567,0.000007651891],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.009934234,0.04593654,0.01662159,0.3719957,0.003924117,0.00001759405,0.0003275019,0.0001168659,0.5511259],"genre_scores_gemma":[0.5656092,0.05596582,0.01449854,0.03311712,0.008567174,0.0001351135,0.0002679141,0.0003588682,0.3214804],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.1672311,"threshold_uncertainty_score":0.3325155,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1056505991953984,"score_gpt":0.2946283798812661,"score_spread":0.1889777806858677,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}