@levinhornischer.bsky.social
Assistant professor at LMU Munich, MCMP (Munich Center for Mathematical Philosophy). He/him. Working on: foundations of AI, logic, dynamical systems, semantics, epistemology. https://levinhornischer.github.io/
New preprint: "Universal Analog Computation: Fraïssé limits of dynamical systems"
➡️Via neural nets, analog computation re-gains prominence.
❓It lacks universal machines like digital computation: Can they exist?
💡Using Fraïssé limits from logic, we build universal systems.
philpapers.org/rec/HORUAC
Thank you so much, Shawn!
06.08.2025 19:23 — 👍 2 🔁 0 💬 0 📌 0
The preferences concerning three alternatives (apple, banana, cherries) of three stylized individuals are fed into a stylized neural network. The network outputs a ranking of the three alternatives as the aggregated preference of the group. It selects the top ranked alternative, in this case the apple. In the bottom right, there are two stylized scientists wondering if this network is 'anonymous', 'biased', and 'cycle-free' in its preference aggregation.
New paper in JAIR, with Zoi Terzopoulou: 'Learning How to Vote with Principles: Axiomatic Insights Into the Collective Decisions of Neural Networks'
❓Can neural nets find new voting rules to aggregate preferences?
💡Yes, by optimizing for axioms!
jair.org/index.php/ja...
philpapers.org/rec/HORLHT
Very happy to have co-organized our summer school with an amazing team 🥳 Thank you to the speakers and participants alike for making this such a nice event!
01.08.2025 21:58 — 👍 3 🔁 1 💬 0 📌 0
Take that, Alan!
21.07.2025 13:18 — 👍 4 🔁 1 💬 0 📌 0
So currently our paper is the 2nd most read in Mind. This'd be all good and well, if we hadn't been beaten by... Some bloke's 75 year old stuff. 😎
academic.oup.com/mind/advance...
@levinhornischer.bsky.social @standrewsphil.bsky.social @oupphilosophy.bsky.social
'The Logic of Dynamical Systems Is Relevant' is out!
(Or, How I Stopped Worrying and Learned to Love Relevant Logic Again.)
Download here, Open Access of course:
academic.oup.com/mind/advance...
@levinhornischer.bsky.social @standrewsphil.bsky.social
Thousands of small dots in 10 different colors on a white background. Dots with the same color form clusters. A dot represents an input-label pair ('possible world'). Close-by dots are possible worlds that are similar according to the neural network's reasons structure ('internally similar'). The fact that they form monochromatic clusters means that internally similar worlds typically are also externally similar, i.e., have the same label. In this case, there are 10 labels represented by the 10 colors. So the neural network's reasons structure matches that of the world.
New preprint, with Hannes Leitgeb @lmu-mcmp.bsky.social: "Explaining Neural Networks with Reasons".
➡️We propose a new faithful and scalable interpretability method for neural networks.
💡Based on a novel mathematico-philosophical theory of reasons.
arxiv.org/abs/2505.14424
philpapers.org/rec/HORENN
The algebra of truth values obtained after iterating 'both' and 'neither' two times. It consists of 16 truth values shown as black dots on a white background. Some are connected by solid lines, which indicates that, in the algebra, one is less-or-equal to the other. There is a small text next to each node describing the truth-value. For example, the node closest to the bottom left corner says { {0,1}_n, {0} }_n. This is the following truth value: Neither 'neither true nor false' nor 'false'. The other nodes are variations thereof.
New paper in Notre Dame J. Formal Logic: 'Iterating Both and Neither: With Applications to the Paradoxes'
❓What if we keep on adding new truth-values 'neither a nor b' and 'both a and b'?
➡️Fun math and fresh ideas for paradoxes!
Paper: doi.org/10.1215/0029...
Preprint: philpapers.org/rec/HORIBA
It's been great fun working on this with @franzberto.bsky.social! Read on if you like dynamical systems and/or logic 🙂
❓What's the logic of perturbation conditionals:
➡️ If we perturb the system into a state where A, it will evolve into a state where B.
💡Surprisingly, it's relevant logic!
