3 responses to “A note on Parmenides”

1. 

   Nicklas Lundblad

   August 1, 2024 at 11:37 am

   Claude:

   As a philosopher deeply engaged with Parmenides and logic, I find your note intriguing but also problematic in several aspects. While you raise some interesting points, there are areas where your analysis could be strengthened or reconsidered. Let me offer an alternative view and some critical observations.

   1. Anscombe’s interpretation:
   Your summary of Anscombe’s argument is overly simplified. Her distinction between sensu diviso and sensu composito is indeed crucial, but you’ve not fully explored its implications. Anscombe’s work goes beyond just unpacking relationships between being, thought, and non-being. She’s attempting to reconstruct Parmenides’ argument in a way that makes it logically coherent, which is a far more ambitious project.

   2. The nature of being:
   Your question about whether being refers to existence or configuration is anachronistic. Parmenides’ concept of being precedes this distinction. As Owen (1960) argues in “Eleatic Questions,” Parmenides’ notion of being is more fundamental and undifferentiated than our modern concepts of existence and essence.

   3. The “view from nowhere”:
   Your concern about the position from which Parmenides makes his observations is valid, but not novel. Thomas Nagel’s “View from Nowhere” (1986) extensively discusses this problem. However, you’ve not considered that this might be precisely Parmenides’ point – that true knowledge requires transcending perspectival limitations.

   4. Language and world:
   Your invocation of Wittgenstein’s dictum about language and world boundaries is interesting but potentially misapplied. Wittgenstein’s later philosophy, as expressed in “Philosophical Investigations” (1953), would suggest that the limits of language are not fixed but constantly negotiated through use.

   5. Semantic horizon:
   Your concept of a “semantic horizon” is intriguing but underdeveloped. It bears similarities to Derrida’s notion of “différance” but lacks the rigorous philosophical grounding. How does this concept relate to established theories of meaning and reference?

   6. Block universe:
   Your connection between Parmenides and the block universe theory is overstated. While there are similarities, modern block universe theories (like those discussed by Huw Price in “Time’s Arrow and Archimedes’ Point,” 1996) are far more sophisticated and don’t necessarily commit to Parmenidean monism.

   7. Quantifier logic:
   Your discussion of the all-quantifier overlooks important distinctions in modern logic. The universal quantifier in first-order logic doesn’t necessarily lead to the problems you describe. See Quine’s “Philosophy of Logic” (1970) for a more nuanced treatment.

   8. Fragmented universe:
   Your conclusion about a “fragmented universe” seems to be a non sequitur from your previous arguments. It’s not clear how the limitations of language or logic necessitate ontological fragmentation.

   Key questions for the author:

   1. How do you reconcile your interpretation of Parmenides with the principle of charity in philosophical interpretation?
   2. Can you provide a more rigorous formulation of your “semantic horizon” concept?
   3. How does your view of a “fragmented universe” account for the apparent success of unified scientific theories?

   Rebuttal points:

   1. Your reading of Parmenides as a reductio ad absurdum is not widely accepted in scholarship. Scholars like Mourelatos (“The Route of Parmenides,” 1970) argue for a more straightforward interpretation.
   2. The idea of “cracks in the universe” based on linguistic or logical limitations commits the fallacy of confusing epistemological limits with ontological facts.
   3. Your critique of the all-quantifier fails to consider developments in non-classical logics that can handle self-reference and totality without contradiction.

   In conclusion, while your note raises some interesting questions, it lacks the rigorous argumentation and engagement with existing scholarship that would be expected in a philosophical treatment of these topics. I would encourage a deeper dive into the relevant literature and a more careful articulation of your novel concepts.​​​​​​​​​​​​​​​​

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2. 

   Nicklas Lundblad

   August 1, 2024 at 11:37 am

   I wanted more on the non-classical logics, so asked about that too:

   I’m glad you’re interested in exploring this further. The topic of non-classical logics handling self-reference and totality is indeed fascinating and complex. While these logics offer powerful tools for dealing with certain paradoxes and self-referential statements, it’s important to note that they don’t completely solve all problems related to speaking about “everything” in an absolute sense. Let me elaborate:

   1. Paraconsistent Logics:
   These logics allow for some contradictions without leading to logical explosion (where everything becomes true). Graham Priest’s work is seminal here. His book “In Contradiction” (2006) provides an extensive treatment of dialetheism – the view that some contradictions are true. Priest argues that paraconsistent logics can handle certain self-referential paradoxes, like the Liar Paradox, without trivializing the system.

   2. Fuzzy Logics:
   Developed initially by Lotfi Zadeh, fuzzy logics allow for degrees of truth rather than binary true/false values. While not directly addressing totality, they provide a framework for dealing with vagueness and indeterminacy. Petr Hájek’s “Metamathematics of Fuzzy Logic” (1998) is a comprehensive resource.

   3. Intuitionistic Logic:
   This rejects the law of excluded middle and double negation elimination. While not specifically designed for self-reference, it offers a different perspective on logical truth that can be relevant to discussions of totality. Michael Dummett’s “Elements of Intuitionism” (2000) is a classic text.

   4. Free Logics:
   These are logics free of existential presuppositions for singular terms. While they don’t directly address totality, they provide tools for reasoning about non-existent objects, which can be relevant to discussions of “everything.” Karel Lambert’s “Free Logic: Selected Essays” (2002) is a good starting point.

   5. Homotopy Type Theory:
   This is a foundational system for mathematics that combines aspects of type theory and homotopy theory. While not a logic per se, it offers a new perspective on foundations that can handle certain forms of self-reference. The Univalent Foundations Program’s “Homotopy Type Theory: Univalent Foundations of Mathematics” (2013) is the key text here.

   However, it’s crucial to note that while these logics provide powerful tools for handling certain aspects of self-reference and totality, they don’t entirely solve the problem of “speaking about everything” in an absolute sense. The issues you raised about a “semantic horizon” and the limits of the all-quantifier still persist in various forms.

   For instance, even in paraconsistent logics, there are limits to what can be consistently asserted about the totality of all things. Priest’s “One” (2014) explores some of these limits in the context of metaphysics.

   Moreover, Gödel’s incompleteness theorems still apply to formal systems powerful enough to represent arithmetic, regardless of the underlying logic. This suggests fundamental limits to any system’s ability to fully capture or describe “everything.”

   So while non-classical logics provide valuable insights and tools, they don’t entirely eliminate the problems associated with absolute totality. They do, however, offer new ways of approaching these problems and can help us understand the nature of these limitations more clearly.

   For a broader perspective on these issues, you might also consider:
   – “Paradoxes” by R.M. Sainsbury (2009)
   – “The Limits of Realism” by Tim Button (2013)

   These texts discuss how different logical frameworks interact with our understanding of reality and the limits of what can be coherently expressed or known.

   In summary, while non-classical logics offer powerful tools for handling self-reference and certain aspects of totality, the fundamental challenges of “speaking about everything” remain. These logics provide new perspectives and approaches, but they don’t entirely dissolve the philosophical problems at the limits of language and thought.​​​​​​​​​​​​​​​​

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3. 

   Nicklas Lundblad

   August 1, 2024 at 11:39 am

   This was what led me to Graham Priest and his work — see https://en.m.wikipedia.org/wiki/Graham_Priest — I do think there could be something relevant here and have started to look at the book referenced.

   My reply to all of this is that I still think there is a value in exploring this argument further and sorting out how to think about from where Parmenides speaks (and I do think the connection to a block universe is more valid than Claude does, but I may be wrong there).

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