The Age of the Universe and its Measurement

Current wisdom in cosmology has it that the Universe is about 13.8 billions year old. Statements about the age of the Universe are not just difficult to confirm, but also carry a lot of presuppositions. The aim of this talk is to make explicit these presuppositions, to discuss their significance and to trace the implications for an emipirical investigation of the age of the Universe.

Computable Diagonalizations and Turing’s Cardinality Paradox

A. N. Turing’s 1936 concept of computability, computing machines, and computable binary digital sequences, is subject to Turing’s Cardinality Paradox. The paradox conjoins two opposed but comparably powerful lines of argument, supporting the propositions that the cardinality of dedicated Turing machines outputting all and only the computable binary digital sequences can only be denumerable, and yet must also be nondenumerable. Turing’s objections to a similar kind of diagonalization are answered, and the implications of the paradox for the concept of a Turing machine, computability, computable sequences, and Turing’s effort to prove the unsolvability of the Entscheidungsproblem, are explained in light of the paradox. A solution to Turing’s Cardinality Paradox is proposed, positing a higher geometrical dimensionality of machine symbol-editing information processing and storage media than is available to canonical Turing machine tapes. The suggestion is to add volume to Turing’s discrete two-dimensional machine tape squares, considering them instead as similarly ideally connected massive three-dimensional machine information cells. Three-dimensional computing machine symbol-editing information processing cells, as opposed to Turing’s two-dimensional machine tape squares, can take advantage of a denumerably infinite potential for parallel digital sequence computing, by which to accommodate denumerably infinitely many computable diagonalizations. A three-dimensional model of machine information storage and processing cells is recommended on independent grounds as better representing the biological realities of digital information processing isomorphisms in the three-dimensional neural networks of living computers.

Newton’s Metaphysics of Space as God’s Emanative Effect

In several of his writings, Isaac Newton proposed that physical space is God’s “emanative effect” or “sensorium,” revealing something interesting about the metaphysics underlying his mathematical physics. Newton’s conjectures depart from Plato and Aristotle’s metaphysics of space and from classical and Cambridge Neoplatonism. Present-day philosophical concepts of supervenience clarify Newton’s ideas about space and offer a portrait of Newton not only as a mathematical physicist but an independent-minded rationalist philosopher.

Wissen wir, was wir nicht wissen können?

«Was kann ich wissen?» – Für Immanuel Kant ist das eine der Grundfragen der Philosophie. Wie können wir sie heute beantworten? Und warum ist sie wichtig?

Intentionality in Reference and Action

This essay asks whether there is a relation between action-serving and meaning-serving intentions. The idea that the intentions involved in meaning and action are nominally designated alike as intentionalities does not guarantee any special logical or conceptual connections between the intentionality of referential thoughts and thought-expressive speech acts with the intentionality of doing. The latter category is typified by overt physical actions in order to communicate by engaging in speech acts, but also includes at the origin of all artistic and symbolic expression such cerebral and linguistic doings as thinking propositional thoughts. There are exactly four possibilities by which meaning and action intentionalities might be related to be systematically investigated. Meaning-serving and action-serving intentionalities, topologically speaking, might exclude one another, partially overlap with one another, or subsume one in the other or the other in the one. The theoretical separation of the two ostensible categories of intendings is criticized, as is their partial overlap, in light of the proposal that thinking and artistic and symbolic expression are activities that favor the inclusion of paradigm meaning-serving intentions as among a larger domain of action-serving intentions. The only remaining alternative is then developed, of including action-serving intentions reductively in meaning-serving intentions, and is defended as offering in an unexpected way the most cogent universal reductive ontology in which the intentionality of doing generally relates to the specific intentionality of referring in thought to the objects of predications, and of its artistic and symbolic expression.

Socrates on the Moral Mischief of Misology

In Plato’s dialogues, the Phaedo, Laches, and Republic, Socrates warns his interlocutors about the dangers of misology. Misology is explained by analogy with misanthropy, not as the hatred of other human beings, but as the hatred of the logos or reasonable discourse. According to Socrates, misology arises when a person alternates between believing an argument to be correct, and then refuting it as false. If Socrates is right, then misanthropy is sometimes instilled when a person goes from trusting people to learning that others sometimes betray our reliance and expectations, and finally not to placing any confidence whatsoever in other people, or, in the case of misology, in the correctness or trustworthiness of arguments. A cynical indifference to the soundness of arguments generally is sometimes associated with Socrates’ polemical targets, the Sophists, at least as Plato represents Socrates’ reaction to these itinerant teachers of rhetoric, public speaking and the fashioning of arguments suitable to any occasion. Socrates’ injunctions against misology are largely moral, pronouncing it ‘shameful’ and ‘very wicked’, and something that without further justification we must ‘guard against’, maintaining that we will be less excellent persons if we come to despise argument as lacking the potential of leading to the truth. I examine Socrates’ moral objections to misology which I show to be inconclusive. I consider instead the problem of logical coherence in the motivations supposedly underlying misology, and conclude that misology as Socrates intends the concept is an emotional reaction to argumentation on the part of persons who have not acquired the logical dialectical skills or will to sort out good from bad arguments. We cannot dismiss argument as directed toward the truth unless we have a strong reason for doing so, and any such argument must itself presuppose that at least some reasoning can be justified in discovering and justifying belief in interesting truths. The relevant passages from Socrates’ discussion of the soul’s immortality in the Phaedo are discussed in detail, and set in scholarly background against Socrates’ philosophy more generally, as represented by Plato’s dialogues. I conclude by offering a suggestive list of practical remedies to avoid the alienation from argument in dialectic with which Socrates is concerned.

Against Logically Possible World-Relativized Existence

The thesis that entities exist in, at, or in relation to logically possible worlds is criticized. The suggestion that actually nonexistent fictional characters might nevertheless exist in nonactual merely logically possible worlds runs afoul of the most general transworld identity requirements. An influential philosophical argument for the concept of world-relativized existence is examined in Alvin Plantinga’s formal development and explanation of modal semantic relations. Despite proposing an attractive unified semantics of alethic modality, Plantinga’s argument is rejected on formal grounds as supporting materially false actual existence assertions in the case of actually nonexistent objects in the framework of Plantinga’s own underlying classical predicate-quantificational logic.

Collingwood on religious atonement

R. G. Collingwood’s philosophical analysis of religious atonement as a dialectical process of mortal repentance and divine forgiveness is explained and criticized. Collingwood’s Christian concept of atonement, in which Christ TeX the Atonement (and also TeX the Incarnation), is subject in turn to another kind of dialectic, in which some of Collingwood’s leading ideas are first surveyed, and then tested against objections in a philosophical evaluation of their virtues and defects, strengths and weaknesses. Collingwood’s efforts to synthesize objective and subjective aspects of atonement, and his proposal to solve the soteriological problem as to why God becomes flesh, as a dogma of some Christian belief systems, is finally exposed in adversarial exposition as inadequately supported by one of his main arguments, designated here as Collingwood’s Dilemma. The dilemma is that sin is either forgiven or unforgiven by God. If God forgives sin, then God’s justice is lax, whereas if God does not forgive sin, then, also contrary to divine nature, God lacks perfect loving compassion. The dilemma is supposed to drive philosophy toward a concept of atonement in which the sacrifice of Christ is required in order to absolve God of the lax judgment objection. God forgives sin only when the price of sin is paid, in this case, by the suffering and crucifixion of God’s avatar. The dilemma can be resolved in another way than Collingwood considers, undermining his motivation for synthesizing objective and subjective facets of the concept of atonement for the sake of avoiding inconsistency. Collingwood is philosophically important because he asks all the right questions about religious atonement, and points toward reasonable answers, even if he does not always deliver original philosophically satisfactory solutions.

Algebra of Classical Theoretical Term Reductions in the Sciences

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of K-O comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type.

Collective Referential Intentionality in the Semantics of Dialogue

The concept of a dialogue is considered in general terms from the standpoint of its referential presuppositions. The semantics of dialogue implies that dialogue participants must generally have a collective intentionality of agreed-upon references that is minimally sufficient for them to be able to disagree about other things, and ideally for outstanding disagreements to become clearer at successive stages of the dialogue. These points are detailed and illustrated in a fictional dialogue, in which precisely these kinds of referential confusions impede progress in shared understanding. It is only through a continuous exchange of question and answer in this dialogue case study that the meanings of key terms and anaphorical references are disambiguated, and a relevantly complete collective intentionality of shared meaning between dialogue participants is achieved. The importance of a minimally shared referential semantics for the terms entering into reasoning and argument in dialogue contexts broadly construed cannot be over-estimated. Where to draw the line between referential agreement and disagreement within any chosen dialogue, as participants work toward better mutual understanding in clearing up referential incongruities, is sometimes among the dialogue’s main points of dispute.