So I've been taking my sweet time to respond to some longstanding arguments w.r.t. some previous work and I finally have a bit of free time to sit down and do just that
To be sure, I still have a lot to learn and there may be some difficulties that remain but I do think these provide a solid basis upon which to proceed with those particular works
For brevity, I won't canvass the particular debates in much detail (you can read the works yourself - at the very least they provide a solid overview)
For privacy reasons, I'll also summarize the core objections and won't, for example, simply post the emails here
Regarding The Liar Paradox
Objection from Solomon Feferman: the FOLT-Scheme as you have articulated it is not what we normally would call an axiom (otherwise it's a really cool paper).
Summary: an axiom, formally understood, is taken to comprise two components: (1) its being tautological and (2) its being true. (1) entails (2), (2) does not entail (1).
Reply: the T-Scheme as it is normally articulated (e.g. - Tf(s) iff s where T is the truth-predicate [understood as a meta-linguistic predicate] and f is a mapping between a sentence or proposition and its name - what we attach predicates to) is not what we would call an axiom either. Why? Because the Liar Paradox emerges simply by adding the normal alethic machinery (T-Scheme and F-Scheme) to classical first-order logic revealing the inconsistency or incoherence of T-Scheme. This is hardly a sufficient reply by itself as it's an argument tout cort. What it does demonstrate is that the desiderata regarding evaluations of alethic theories should not require our alethic inferences themselves to be tautological though they should be nevertheless true. FOLT-Scheme satisfies that condition. T-Scheme doesn't.
Objection from Graham Priest: you still generate revenge: if s =df ~Tf(s) and s is grounded then s results in revenge. Cool paper!
Summary: Doesn't the Liar sentence result in revenge?
Reply: the Liar sentence cannot be grounded by the procedure defined. Consistency proof added. Hence, revenge does not emerge from it.
Comments: the system I developed suggests that we simply shouldn't apply alethic reasoning to Liar-Like sentences. Truth Grounding is probably a poor choice for terming or labeling the core group of sentences from which we can build out a non-contradictory remainder - this evokes Kripke-esque terminology (I like Kripke but the terms, though similar, are not particularly similar w.r.t. the specific concepts that they are handles for). To my knowledge, this is the only solution to Yablo's paradox.
See also: Logical Pluralism
Also: Propositional Stability
Regarding Billy Collin's Aristotle (The Poem)
I love that poem. Here's my unpublished "reply":
Regarding The MUH
Comments: Max Tegmark's Mathematical Universe Hypothesis has been very influential - heck, it's a cool theory! Over 259 citations in the Physics and Philosophy of Science community and has spawned quite a bit of interest over at FQXI (lots of physicists and philosophers - see: this for context).
The paper of mine above was a very simple early attempt (back in undergrad) to assess the veracity of the position. Basically, Tegmark's obviously a super smart guy and the idea is probably one of the most evocative and compelling ideas around. My position about theories like this has many facets at least one of which is that while they may incomplete, slightly off, whatever... they nevertheless inspire a whole body of future research - I know it did for me!
Philosophers often don't know much about modern physics (it gets weird as hell down at the Quantum "level" - subatomic if you prefer - and at relativistic speeds) but physicists don't know much about modern philosophy. The cool thing is that papers like Tegmark's have fostered much closer cooperation between these two disciplines! That being said, there are some fundamental assumptions he implicitly endorses that we can knock out or have strong grounds to not think are true.
For starters, I think metaphysics (which is often just called ontology though some people use the terms slightly differently) as a discipline is important (namely because the concepts like object, relation, function, etc. are highly useful for data modeling, database design, mathematical theory creation, programming, or general theory design - called ontological engineering) - but drawing conclusions about scientific theories - namely that they ultimately are descriptive and not merely predictive relies on an inference called the no-miracles argument - really a philosophical assessment.
Even if we were to just accept scientific realism (which I have a hard time doing) over say instrumentalism or anti-realism (which are different but often poorly distinguished), there's a lot of assumptions about mathematical structures (what the hell are we describing or doing in math, huh?) and how representation works (how exactly do our theories, true statements, and models mirror the world?) that are highly questionable.
Regarding Ontic Structural Realism
Comments: This has been a long time in the works and has undergone enormous modification over the years. Basically, the objective is to just show that all the arguments for Ontic Structural Realism as well as all the arguments against it (at least those that stem from what really amounts to arguments from ignorance or lack of creativity) are just wrong.
I laid out what is really akin to the general concept of a set and not say ZFC Set Theory and recovered the ordinals. I think there are some pretty cray cray flipping consequences for programming - namely what I'm inclined to call definitional compression - something like getting hypercomputation out of language... Furthermore, I think a reorganization of our ontological concepts like abstract and concrete require refinement!
Please pardon how Ontic.be renders in the iframe - it uses dynamically generated logic to determine sizing and positioning which breaks here (yikes!)
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