When Neo-Kantian Met Vienna: A Philosophical Convergence on Quantum Weirdness

Alright, let’s dive into a fascinating little corner of intellectual history. Imagine a philosophical scene in the early 20th century, buzzing with new ideas from physics. You’ve got these sharp minds grappling with the weirdness of quantum mechanics, and how it shakes up our fundamental understanding of reality. What I find particularly intriguing is this unexpected connection, almost a secret handshake, between a figure from the old-school neo-Kantian tradition, Ernst Cassirer, and a rather distinct group I’ve come to know as the ‘Vienna indeterminists’. It’s a story of shared tools but wildly different destinations.

The Vienna Crew and Their Indeterminism

So, who are these Vienna indeterminists? Think of them as a philosophical lineage rooted in Vienna, with physicist Franz Serafin Exner acting as the key link. They trace their intellectual roots back to folks like Ernst Mach and Ludwig Boltzmann, and their ideas flow forward to later thinkers like Richard von Mises and Philipp Frank. What really defined this group, especially as quantum mechanics burst onto the scene, was a few core beliefs:

• Statistical laws aren’t just approximations; they might be fundamental. Forget the old dream of everything being perfectly predictable by deterministic laws.
• Probability is all about frequency. None of that subjective ‘degree of belief’ stuff. It’s about how often something happens in a large series of events.
• The uncertainty relations? They’re statistical. Heisenberg’s famous relations aren’t about messing up a single particle’s measurement; they’re about the spread of results across a whole bunch of identical experiments.

For the Viennese, quantum mechanics felt like the final nail in the coffin for the classical idea of causality. They saw it as proof that the universe, at its most basic level, just isn’t strictly determined in the old-fashioned way.

Enter Cassirer, Stage Left

Now, Cassirer. He’s coming from a different place entirely – the Marburg school of neo-Kantianism. This tradition is all about the structures of knowledge, how our minds shape our understanding of the world, often rooted in Kant’s ideas about a priori principles. You wouldn’t necessarily expect him to cozy up to the more empiricist, positivist vibe of the Viennese. But then comes his 1936 book, Determinismus und Indeterminismus, and suddenly, there’s this undeniable convergence.

Cassirer, surprisingly, seems to embrace those very same tenets championed by the Vienna indeterminists:

• He takes seriously Exner’s idea that fundamental laws could be statistical.
• He adopts von Mises’s frequentist interpretation of probability.
• He aligns with Frank and von Mises on the statistical interpretation of the uncertainty relations.

It’s like they’re all picking up the same cutting-edge tools from the physics workshop. But here’s where the plot thickens, and where the ‘parallel’ part of the ‘parallel convergence’ comes in.

Same Tools, Different Jobs

While the Viennese saw quantum mechanics, armed with these statistical tools, as delivering a fatal blow to the notion of causality, Cassirer had a different target in mind. For him, the real challenge wasn’t to causality (at least, not the right kind of causality), but to the classical notion of substantiality. He was interested in how quantum mechanics challenged the very idea of ‘particles’ as individual, persistent ‘things’ or ‘substances’ that carry properties around.

So, they agreed on the tools and how to interpret certain physical results, but they used that agreement to tackle fundamentally different philosophical problems. It’s a bit like two engineers agreeing on using the same type of wrench, but one is using it to build a bridge and the other to dismantle an old engine.

The Ghost of Laplace

One of the key moves Cassirer makes, which helps him pivot away from the causality debate, is his critique of the famous Laplace demon. You know, that hypothetical super-intelligence that knows the exact state of the universe at one moment and can predict everything forever? That’s often held up as the poster child for classical determinism and causality.

Cassirer argues that this image, particularly as popularized by Emil Du Bois-Reymond, actually distorts the concept of causality. It confuses determinism (things following laws) with fatalism (things being inevitable regardless of conditions). The Laplace demon, if it truly had ‘intuitive’ knowledge, wouldn’t need laws; it would just ‘see’ the whole history of the universe at once. If it relied on empirical knowledge, it would be bound by measurement limitations anyway.

Instead, Cassirer prefers a different understanding of causality, one he finds in Hermann von Helmholtz: causality as the requirement of lawlikeness, the imperative to keep searching for increasingly general laws. This isn’t a statement about the ultimate nature of reality (metaphysical determinism); it’s a statement about the structure of scientific inquiry (critical determinism). For Cassirer, this Helmholtzian view is a regulative principle – it guides our search for knowledge – rather than a constitutive principle that dictates the specific form laws must take.

Probability and the Collective

This is where the embrace of von Mises’s frequency interpretation of probability becomes crucial for Cassirer. Von Mises defined probability based on ‘collectives’ – large sequences of events where the relative frequency of a property tends towards a limit. Cassirer sees these collectives not just as empirical data sets, but as idealized concepts, much like the ‘ideal gas’ or ‘rigid body’ in classical physics.

By adopting this view, Cassirer can argue that statistical laws, which describe the behavior of these collectives, are just as ‘strict’ and legitimate as dynamical laws, which describe the behavior of individual systems (ideally, dispersion-free ones). Dynamical laws become a special, limiting case of statistical laws where the dispersion is zero. This dissolves the paradox of a ‘statistical law’ and gives statistical laws the same ‘dignity’ as dynamical ones. This move is quite counter-intuitive for a neo-Kantian, siding with the empiricist von Mises against figures like Schlick who clung to more Kantian-rooted probability theories.

Quantum Weirdness and What It Really Means

Now, apply this to quantum mechanics. The uncertainty relations (Heisenberg’s principle) are a prime example. Cassirer, following the Viennese lead (Frank, von Mises), insists on the statistical interpretation. This isn’t about a measurement disturbing a single particle; it’s about the inherent spread (dispersion) in the results when you measure position and momentum across a collective of identically prepared systems. Quantum mechanics says you simply cannot prepare a collective where both position and momentum have zero dispersion simultaneously.

Classical physics assumed you *could*, in principle, prepare a dispersion-free collective, even if you couldn’t do it in practice. Quantum mechanics declares it impossible in principle. For the Viennese, this impossibility was the final nail in causality’s coffin. But Cassirer spins it differently. He argues this doesn’t mean laws are ‘sloppy’ or causality is dead. Quantum mechanics still provides ‘strict laws’ – they just govern the behavior of collectives (the evolution of the wave function) rather than individual particles with sharp properties. The ‘causal principle,’ understood as the search for lawlikeness, is still alive and well.

Particles Losing Their “Stuff”

So, if quantum mechanics doesn’t kill causality (in the Helmholtzian sense), what *does* it challenge? Cassirer argues it challenges substantiality, specifically the idea of particles as individual substances that retain their identity over time, independent of their properties. The inability to have dispersion-free collectives of position and momentum means the classical notion of a well-defined trajectory for a particle becomes meaningless. And without a trajectory, how do you track the identity of a particle over time? How do you say ‘this electron now is the same electron as that one a moment ago’?

Cassirer traces this back through the history of physics, arguing that even in classical physics, the idea of an individual, identifiable ‘material point’ was more of a useful conceptual tool than an empirical fact. Quantum mechanics, with the indistinguishability of identical particles (like electrons), pushes this much further. Particles of the same kind aren’t just qualitatively identical; they can’t even be treated as distinct individuals that you can label and follow. The statistics used in quantum mechanics (Fermi-Dirac, Bose-Einstein) reflect this lack of individuality, unlike classical Maxwell-Boltzmann statistics where permuting identical particles counts as a different state.

This, for Cassirer, is the real ‘epistemological rupture’ – not the abandonment of causality, but the challenge to the substance-concept in favor of the function-concept. Quantum mechanics provides functional relations (laws) for how the state of a collective evolves, but that ‘state’ no longer refers to individual, identifiable substances with sharp properties like position and momentum.

The Aftermath: Praise and “Decomposition”

How was this ‘parallel convergence’ received? Interestingly, some of the Viennese, like von Mises and Frank, recognized the agreement on key points. Frank even wrote a review acknowledging Cassirer’s closeness to a ‘purely positivistic conception’ by reducing causality to legality and questioning the material point concept. However, Frank’s praise was double-edged. He saw Cassirer’s work as a prime example of the ‘decomposition process’ of traditional philosophy when confronted with modern science.

Frank felt Cassirer didn’t go far enough. By holding onto causality as an a priori, regulative principle – the maxim to always search for laws, even a final unified system – Cassirer retained a ‘dark background,’ a ‘remnant of metaphysical idealism’ or ‘Kantianism’ that a true positivist would shed. For Frank, the principle of causality, if not a mere convention, was at best a vague, non-empty statement about seeking ‘simple’ laws.

But I think Frank missed Cassirer’s deeper motivation. In the turbulent 1930s, amidst rising anti-intellectualism, Cassirer wasn’t just doing abstract philosophy. He was defending the very value of the scientific endeavor. That ‘remnant’ of an a priori principle, the unwavering commitment to the search for lawlikeness, was, for Cassirer, the essential core of scientific rationality, a beacon against the storm of irrationalism. It wasn’t stubborn adherence to tradition; it was a defense of the scientific spirit itself.

So, there you have it. A fascinating case of intellectual cross-pollination. Cassirer, the neo-Kantian, and the Vienna indeterminists, the empiricist-positivists, finding common ground on the technical interpretation of quantum mechanics, only to use that ground to launch attacks on different philosophical fortresses: causality for the Viennese, substantiality for Cassirer. A true ‘parallel convergence’ indeed.

Source: Springer