Frege on what mathematics isn’t

Mathematics is an iceberg on which the Titanic of modern empiricism founders.  It is good now and then to remind ourselves why, and Gottlob Frege’s famous critique of John Stuart Mill in The Foundations of Arithmetic is a useful starting point.  Whether Frege is entirely fair to Mill is a matter of debate.  Still, the fallacies he attributes to Mill are often committed by others.  For example, occasionally a student will suggest that the proposition that 2 + 2 = 4 is really just a generalization from our experience of finding four things present after we put one pair next to another – and that if somehow a fifth thing regularly appeared whenever we did so, then 2 and 2 would make 5.

Just say the damn sentence already

Suppose you are a Catholic who thinks the death penalty ought never to be applied in practice under modern circumstances.  Fine.  You’re within your rights.  Whatever one thinks of the arguments for that position, it is certainly orthodox.  However, that position is very different from saying that capital punishment is always and intrinsically wrong, wrong per se or of its very nature.  That position is not orthodox.  It is manifestly contrary to scripture, the Fathers and Doctors of the Church, and the consistent teaching of the popes up until at least Benedict XVI.  The evidence for this claim is overwhelming, and I have set it out in many places – for example, in this article and in this book co-written with Joe Bessette.  Attempts to refute our work have invariably boiled down to ad hominem attacks, red herrings, question-begging assertions, special pleading, straw man fallacies, or other sophistries and time-wasters.

Links for thinkers

David Oderberg’s article “Death, Unity, and the Brain” appears in Theoretical Medicine and Bioethics.

Nicholas Maxwell at Aeon calls for a revival natural philosophy.  Gee, maybe someone ought to write a book on the subject.

Philosopher Kathleen Stock on gender dysphoria and the reality of sex differences, at Quillette.  At Medium, philosopher Sophie Allen asks: If transwomen are women, what is a woman?

The Onion on liberal self-satisfaction.

The bishops and capital punishment

A group of five prelates comprising Cardinal Raymond Burke, Bishop Athanasius Schneider, Cardinal Janis Pujats, Archbishop Tomash Peta, and Archbishop Jan Pawel Lenga this week issued a “Declaration of the truths relating to some of the most common errors in the life of the Church of our time.”  Among the many perennial Catholic doctrines that are now commonly challenged but are reaffirmed in the document is the following:

In accordance with Holy Scripture and the constant tradition of the ordinary and universal Magisterium, the Church did not err in teaching that the civil power may lawfully exercise capital punishment on malefactors where this is truly necessary to preserve the existence or just order of societies (see Gen 9:6; John 19:11; Rom 13:1-7; Innocent III, Professio fidei Waldensibus praescripta; Roman Catechism of the Council of Trent, p. III, 5, n. 4; Pius XII, Address to Catholic jurists on December 5, 1954).

Augustine on capital punishment

In his book On Augustine: The Two Cities, Alan Ryan says that Augustine’s “understanding of the purpose of punishment made the death penalty simply wrong” (p. 82).  That is a bit of an overstatement.  In The City of God, Augustine writes:

However, there are some exceptions made by the divine authority to its own law, that men may not be put to death.  These exceptions are of two kinds, being justified either by a general law, or by a special commission granted for a time to some individual.  And in this latter case, he to whom authority is delegated, and who is but the sword in the hand of him who uses it, is not himself responsible for the death he deals.  And, accordingly, they who have waged war in obedience to the divine command, or in conformity with His laws, have represented in their persons the public justice or the wisdom of government, and in this capacity have put to death wicked men; such persons have by no means violated the commandment, “You shall not kill.” (Book I, Chapter 21)

A clarification on integralism

Talk of integralism is all the rage in recent weeks, given the dispute between David French and Sohrab Ahmari and Matthew Continetti’s analysis of the state of contemporary conservatism, on which I commented in a recent post.  What is integralism?  Rod Dreher quotes the following definition from the blog The Josias:

Catholic Integralism is a tradition of thought that rejects the liberal separation of politics from concern with the end of human life, holding that political rule must order man to his final goal. Since, however, man has both a temporal and an eternal end, integralism holds that there are two powers that rule him: a temporal power and a spiritual power. And since man’s temporal end is subordinated to his eternal end the temporal power must be subordinated to the spiritual power.

Continetti on post-liberal conservatism

At the Washington Free Beacon, Matthew Continetti proposes a taxonomy of contemporary American conservatism.  Among the groups he identifies are the “post-liberals.”  What he means by liberalism is not twentieth- and twenty-first century Democratic Party liberalism, but rather the broader liberal political and philosophical tradition that extends back to Locke, informed the American founding, and was incorporated into the “fusionist” program of Buckley/Reagan-style conservatism.  The “post-liberals” are conservatives who think that this broader liberal tradition has become irredeemably corrupt and maybe always has been, and thus judge that the fusionist project of marrying a traditionalist view of morality, family, and religion to the liberal political tradition is incoherent and ought to be abandoned.