I begin with a typology of reasoning and cross it with types of processes. I demonstrate that the thrust of Plato’s Republic is theory-building. This involves the critical and dialectic processes which are paradigms of Platonic methodology. Book I displays abductive analogical reasoning joined by an induction that is embedded in a deduction; hence there is a deduction–induction–abduction chain. In Book VI, Plato constructs a visual model of the divided line, which also displays model-based and abductive hypothesis generation that is (...) essential to theory building. Book VII provides an abductive metaphor model of the allegory of the cave. Both models depict degrees of reality and the ascendency of knowledge. The multimodal model-based allegory has far reaching applications from criminal justice to information systems. I conclude by capturing the narrative of the Republic as a critical and dialectic process of theory building using deductive–inductive–abductive chains, an abductive visual model and an abductive metaphor model. Hence, the Republic is simultaneously a masterpiece of deductive reasoning and a marvel of complex model-based abduction, involving visual models, analogies and metaphors. (shrink)

Abduction* is the genus with deduction and induction as species. Modus tollens is backward reasoning as an unknown proposition is inferred from a known proposition. Reductio ad absurdum is abductive because the conclusion is inferred by deriving a contradiction from an assumption. Inductive reasoning from effect to cause is also backward reasoning. But abduction* consists of forward reasoning as well. The generic structure of abductive* argumentation is universal among all cultures, occupations and disciplines.

First, ‘Is Justified True Belief Knowledge’ is imprecise but Gettier is explicit that ‘know’ is analysed as the definiendum is ‘S knows that P’. Second, Gettier does not misrepresent as Plato’s definition as the expressions used are ‘Plato considers’ and ‘seems to accept’. Third, Gettier is not mistaken to apply Plato’s definition to propositions since propositional knowledge is a species of Plato’s definition. Fourth, for Plato true belief temporally precedes an account. ‘Jones owns a Ford’ is never a true opinion, (...) hence no account for it can be given. The counterexample is reconstructed with temporality built into it. Fifth, Gettier does not fail to establish the equivalence of ‘believe’, ‘accepts’ and ‘sure’ in the three versions as this is implicitly established in the shifts made in the paper. Sixth, ‘entails’ logically is used only when the entailing proposition is true, but in the counterexamples a false proposition is taken to imply a true one. ‘Entail’ is to be taken in the ordinary sense of implies. Seventh, in Case I, the implication is preserved with the proper representation: → [Gy ↔ ], which implies { → [Gy ↔ ]}’. Eighth, the counterexample is reworked to avoid the objection that justification for p and justification for q may not be sufficient justification for ‘p & q’. (shrink)

I argue for the possibility of knowledge by invention whch is neither á priori nor á posteriori. My conception of knowledge by invention evolves from Poincaré’s conventionalism, but unlike Poincaré’s conventions, propositions known by invention have a truth value. An individuating criteria for this type of knowledge is conjectured. The proposition known through invention is: gounded historically in the discipline to which it belongs; a result of the careful, sincere and objective quest and effort of the knower; chosen freely by (...) the inventer or knower; and, private in its invention but public once invented. I extend knowledge by invention to include the knowledge of the invented proposition by those who do not invent it but accept it as a convention for good reasons. Finally, knowledge by invention combined with a revisionist, Platonist definition of knowledge as actively justified true belief provides a pedagogical model reviving the proactive spirit of the Socratic method with an emphasis on invention and activity and a de-emphasis on information gathering and passivity. (shrink)

The inclusion of the truth condition in the definition of knowledge has been responsible for a number of paradoxes. Some epistemologists claim that in the case of knowledge justification entails truth or that belief implies truth as there is a causal relation between truth and belief. Truth hence becomes redundant in the definition of knowledge. I do not drop the truth condition for this reason because this denies the autonomy of the distinct conditions for knowledge. I argue that truth and (...) knowledge are inseparable. However. “that p is true” should not be a necessary condition in the definiens of the definiendum “S knows that p is true.” Whereas the quest of truth is a necessary condition for knowledge. While I drop the truth condition from the definition of knowing that p is true, I do not dropthe condition that p is false from the definition of knowing that p is false. This means that though I may know something that is not true, I cannot know something that is false. This is a compromised revision of the long standing intuition of epistemologists that if I know something then I cannot be wrong. Linda Zagzebski defines knowledge as: “Knowledge is a state of true belief arising out of acts of intellectual virtue.” (Zagzebski, 1996, 271). She has hence dropped the truth condition. Intellectual virtues direct us towards truth but they do not guarantee truth. In the ideal case whatever I know will be true, but in most cases it will be true to the best of my knowledge. (shrink)

In a Realist ontology relations are subsisting or existing entities distinct from ordinary things. Idealists claim that the notion of relations is subject to a vicious infinite regress. Nominalists claim that relations are particularized instances. In an attempt to search for the roots of a Realist conception of relations and to meet these challenges I investigate Plato's conception of relations in the Phaedo. ;Against the current of a majority of Plato scholars, Castaneda finds evidence for a distinction between relations and (...) properties at Phaedo 102 b-d. I enter the debate on Castaneda's side and find support for his interpretation of the passage in the context of the dialogue as a whole. The relation--quality distinction resolves the paradox of Simmias being both taller than Socrates and shorter than Phaedo at the same time, since Plato possesses relational characteristics of tallness and shortness, which are not contraries unlike the the contrary properties of hot and cold which could not coexist in an individual. Gallop offers the alternative essence--accident distinction which also resolves the paradox since tallness and shortness as accidents may coexist. The latter distinction however Aristotelianizes Plato. I have shown how the essence--accident distinction is incompatible with Plato's theory of Forms, as it leads to such odd conclusions as the admittance of accidental Forms. ;Castaneda claims that Plato reduces relations to Form-chains in which individuals participate in pairs. I offer the alternative of Plato's positing of relational Forms as distinct from monadic Forms. I survey the corpus of Platonic dialogues in search of support for the distinction between relations and properties. I find that in the Statesman there is a distinction between two types of Forms which generates the distinction between monadic Forms and relational Forms. ;I conclude that there is ample evidence in Plato's dialogues and in Aristotle's assessment of Plato to ascribe this distinction to Plato. Plato's explanation of relations in terms of Forms, which have the highest grade of reality for him, sets up the basis for any Realist theory of relations--for reductionist theories reducing relations to relational properties or some other subsisting entities, as well as for the irreducible concept of relations as abstract subsisting entities. (shrink)