Hans-Hermann Hoppe, Libertarianism and the “Alt-Right” (PFS 2017)

A new victimology has been proclaimed and promoted. Women — and in particular single mothers — blacks, browns, Latinos, homosexuals, lesbians, bi, and transsexuals have been awarded victim status, and accorded legal privileges through nondiscrimination or affirmative action decrees as well. Most recently such privileges have been expanded also to foreign national immigrants, whether legal or illegal, insofar as they fall into one of the just mentioned categories, or are members of non-Christian religions such as Islam for instance.

Hoppe does not identify as alt-right, but runs in the same circles as prominent white nationalists. His popularity among fringe anarcho-capitalists – or ancaps – has resulted in a plethora of memes, sometimes depicting Hoppe as Pepe the Frog, and often bearing the slogan “Hippity Hoppity, Get Off My Property.” One of Hoppe’s proposals – that truly libertarian societies be able to “physically remove” Communists and other undesirables from their ranks – has become a meme on the far-right thanks to the “Crying Nazi” himself, Christopher Cantwell. His online store stocks “I ♥ Physical Removal” stickers, along with a “Right-Wing Death Squad” hat, and Radical Agenda shirts depicting a person being thrown from a helicopter – in honor of Augusto Pinochet….

Hoppe told his audience that “many of the leading lights associated with the alt-right have appeared here at our meetings in the course of the years,” including Paul Gottfried, Peter Brimelow, Richard Lynn, Jared Taylor, John Derbyshire, Steve Sailer, and Richard Spencer. And he boasted that these associations have “earned” him “several honorable mentions” by the SPLC, which he called “America’s most famous smear and defamation league.”

According to Hoppe, “many libertarians” are “plain ignorant of human psychology and sociology” and “devoid of any common sense.” He said this explains their tendency to “blindly accept, against all empirical evidence, an egalitarian, blank slate view of human nature that all people and all societies and all cultures are essentially equal and interchangeable.”

The alt-right, on the other hand, does not labor under such delusions. He described the alt-right as “united” in its “identification and diagnosis of [the West’s] social pathologies.” The alt-right is “against, and indeed it hates with a passion, the elites in control of the State, the mainstream media, and academia” because they promote “egalitarianism, affirmative action or nondiscrimination laws, multiculturalism, and free mass immigration as a means to bring about this multiculturalism.”

 

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Modal Structuralism. Thought of the Day 106.0

Structuralism holds that mathematics is ultimately about the shared structures that may be instantiated by particular systems of objects. Eliminative structuralists, such as Geoffrey Hellman (Mathematics Without Numbers Towards a Modal-Structural Interpretation), try to develop this insight in a way that does not assume the existence of abstract structures over and above any instances. But since not all mathematical theories have concrete instances, this brings a modal element to this kind of structuralist view: mathematical theories are viewed as being concerned with what would be the case in any system of objects satisfying their axioms. In Hellman’s version of the view, this leads to a reinterpretation of ordinary mathematical utterances made within the context of a theory. A mathematical utterance of the sentence S, made against the context of a system of axioms expressed as a conjunction AX, becomes interpreted as the claim that the axioms are logically consistent and that they logically imply S (so that, were we to find an interpretation of those axioms, S would be true in that interpretation). Formally, an utterance of the sentence S becomes interpreted as the claim:

◊ AX & □ (AX ⊃ S)

Here, in order to preserve standard mathematics (and to avoid infinitary conjunctions of axioms), AX is usually a conjunction of second-order axioms for a theory. The operators “◊” and “□” are modal operators on sentences, interpreted as “it is logically consistent that”, and “it is logically necessary that”, respectively.

This view clearly shares aspects of the core of algebraic approaches to mathematics. According to modal structuralism what makes a mathematical theory good is that it is logically consistent. Pure mathematical activity becomes inquiry into the consistency of axioms, and into the consequences of axioms that are taken to be consistent. As a result, we need not view a theory as applying to any particular objects, so certainly not to one particular system of objects. Since mathematical utterances so construed do not refer to any objects, we do not get into difficulties with deciding on the unique referent for apparent singular terms in mathematics. The number 2 in mathematical contexts refers to no object, though if there were a system of objects satisfying the second-order Peano axioms, whatever mathematical theorems we have about the number 2 would apply to whatever the interpretation of 2 is in that system. And since our mathematical utterances are made true by modal facts, about what does and does not follow from consistent axioms, we no longer need to answer Benacerraf’s question of how we can have knowledge of a realm of abstract objects, but must instead consider how we know these (hopefully more accessible) facts about consistency and logical consequence.

Stewart Shapiro’s (Philosophy of Mathematics Structure and Ontology) non-eliminative version of structuralism, by contrast, accepts the existence of structures over and above systems of objects instantiating those structures. Specifically, according to Shapiro’s ante rem view, every logically consistent theory correctly describes a structure. Shapiro uses the terminology “coherent” rather than “logically consistent” in making this claim, as he reserves the term “consistent” for deductively consistent, a notion which, in the case of second-order theories, falls short of coherence (i.e., logical consistency), and wishes also to separate coherence from the model-theoretic notion of satisfiability, which, though plausibly coextensive with the notion of coherence, could not be used in his theory of structure existence on pain of circularity. Like Hellman, Shapiro thinks that many of our most interesting mathematical structures are described by second-order theories (first-order axiomatizations of sufficiently complex theories fail to pin down a unique structure up to isomorphism). Mathematical theories are then interpreted as bodies of truths about structures, which may be instantiated in many different systems of objects. Mathematical singular terms refer to the positions or offices in these structures, positions which may be occupied in instantiations of the structures by many different officeholders.

While this account provides a standard (referential) semantics for mathematical claims, the kinds of objects (offices, rather than officeholders) that mathematical singular terms are held to refer to are quite different from ordinary objects. Indeed, it is usually simply a category mistake to ask of the various possible officeholders that could fill the number 2 position in the natural number structure whether this or that officeholder is the number 2 (i.e., the office). Independent of any particular instantiation of a structure, the referent of the number 2 is the number 2 office or position. And this office/position is completely characterized by the axioms of the theory in question: if the axioms provide no answer to a question about the number 2 office, then within the context of the pure mathematical theory, this question simply has no answer.

Elements of the algebraic approach can be seen here in the emphasis on logical consistency as the criterion for the existence of a structure, and on the identification of the truths about the positions in a structure as being exhausted by what does and does not follow from a theory’s axioms. As such, this version of structuralism can also respond to Benacerraf’s problems. The question of which instantiation of a theoretical structure one is referring to when one utters a sentence in the context of a mathematical theory is dismissed as a category mistake. And, so long as the basic principle of structure-existence, according to which every logically consistent axiomatic theory truly describes a structure, is correct, we can explain our knowledge of mathematical truths simply by appeal to our knowledge of consistency.