Necessary, Transcendental, and Universal Truth

A simple puzzle leads Fine to conclude that we should distinguish between worldly sentences like “Socrates exists,” whose truth values depend on circumstances and unworldly ones like “Socrates is human,” which are true or false independently of circumstances. The former, if true in every circumstance, express necessary propositions. The latter, if true, express transcendental propositions, which, for theoretical convenience, we regard as necessary in an extended sense. Here it is argued that this understanding is backwards. Transcendental truths and sentences true in every circumstance (here labeled universal truths) are both species of necessary truth. The revised understanding is clarified by a simple formal system with distinct operators for necessary, transcendental, and universal truth. The system is axiomatized. Its universal-truth fragment coincides with something that Arthur Prior once proposed as System A. The ideas of necessary, transcendental truth are further clarified by considering their interaction with actual truth. Adding an operator for actually true to the formal system produces a system closely related to one of Crossley and Humberstone.

Comments on Joseph Almog’s “One Absolutely Infinite Universe to Rule Them All: Reverse Reflection, Reverse Metaphysics”

Joseph Almog’s chapter is a daring and dazzling investigation into the nature of the universe, situated within the grand tradition of absolutist metaphysics, but motivated more by the comparison of the absolute with the set-theoretic universe than with God. It is impossible for me to deal adequately with the deep and difficult issues which his chapter raises and so I hope I may be forgiven if I focus on a few remarks he makes in his Appendix on “the Nature versus Concept/Essence of BO and {BO}.” Some of my comments are relatively minor and serve simply to clear up possible misunderstandings of my position, but others raise substantive and neglected issues concerning the possible “absolutist” source of necessary truth....

Reply to Boghossian on the A Priori and the Analytic1

This chapter replies to Boghossian’s defence of the a priori–a posteriori distinction against the arguments for its shallowness in?The Philosophy of Philosophy. In particular, it shows how to understand the example of an unorthodox thinker who is linguistically competent with conjunction but refuses to treat the rule of conjunction elimination as logically valid. It also rebuts Boghossian’s charge of circularity against the account of knowledge of metaphysical modality in terms of the cognitive capacities required to assess ordinary counterfactual conditionals. For the explanation of knowledge of logic and mathematics, the key significance is emphasized of the distinction between knowing the truth of what is in fact a necessary truth and knowing that it is necessary.

Problems of using computer control of vermicular graphite in the microstructure of cast iron

In recent decades, there has been an increase in industrial interest in compacted graphite iron, which has a very wide range of properties more depended on the graphite form. The same time, to date, there are no methods for controlling graphite in the microstructure of CGI necessary truth. In the present work, the automatic calculation error of the fraction of vermicular graphite is estimated, which is associated with the automatic identification error of the type of graphite inclusion. It is shown that automatic calculation without the metallographist increases accuracy in comparison with GOST 3443-87, but its error remains not acceptably high for materials science tasks and requires further improvement.

The Rejection of Modality

This chapter examines how Russell came to reject modality on the basis of his rejection of idealism. Russell’s anti-modal views rest on the Moore-Russell theory of propositions, not on Russell’s attack on internal relations. This theory derives from Moore’s criticisms of Bradley’s theory of judgment. Unlike most readers of Moore, who find these criticisms mostly unpersuasive, I show that, in fact, they present a substantial challenge to Bradley. Moore uses the theory of propositions that he adopts to remedy the defects of Bradley’s theory of judgment to argue, against Kant, that all true propositions are necessarily true. For Russell, Moore’s argument demonstrates that there is no distinction between truth and necessary truth, nor between truth and possible truth, which is to say, amodalism.

Enigma

The history of scurvy is heavily marked by the conflict of interests between those who dwell inside the drama and those who don't. The biochemical breakthrough that isolated ascorbic acid and explained its physiological and neurological importance to the human organism was never aligned with the history of empirical knowledge of the disease. That is to say, biochemistry and naval medicine never shared an inevitable and common destination, although there were many occasions when a coalition of the two was accidentally and briefly achieved. This chapter shows that it is difficult for anyone outside the disorganized and passionate situation of scurvy itself not to consider its history as anything but periodic fits of willful ignorance that blinded the world to a necessary truth and an obvious cure: a dismal record then of lost opportunities and culpable amnesias.

Radical Contingentism, or; Why Not Even Numbers Exist Necessarily

Bob Hale championed the view that some objects exist of necessity, most prominently, mathematical objects like numbers. In contrast, this chapter upholds radical contingentism, the view that no object exists necessarily, and seeks to undermine the idea that the best possible candidates for necessary existence, the natural numbers, exist necessarily, despite there being in fact many contingent objects. Even the best neo-Fregean arguments for the existence of natural numbers depend on assumptions a nominalist may reject. A positive account of cardinalities as belonging to multitudes shows that every finite cardinality is exemplified only if there are two or more individuals, but that there are at least two individuals is not a necessary truth. Hence, even if numbers were admitted to abstract existence contingently upon their being exemplified—which the chapter denies—they would not exist necessarily.

Norris, John (1657–1711)

John Norris was a philosopher in the Platonic tradition of the seventeenth century. His philosophy combines elements from both the French and English aspects of that tradition: he was an admirer of Henry More and was the leading English disciple of Malebranche, whose philosophy he did much to popularize in England. A churchman by profession, much of his writing is concerned with the practical application of divinity. Central to Norris’ thought is his theory that the proper and immediate object of both human knowledge and human love is God, who is identified with truth. Thus necessary truths are known directly in God and, conversely, to know eternal and necessary truth is to know God.