• Re: Solving the Gettier cases

    From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math.symbolic,comp.ai.philosophy on Tue Jun 23 09:26:03 2026
    From Newsgroup: comp.ai.philosophy

    On 6/23/2026 12:32 AM, Mikko wrote:
    On 22/06/2026 17:45, olcott wrote:
    On 6/22/2026 2:30 AM, Mikko wrote:
    On 22/06/2026 02:47, olcott wrote:
    On 6/21/2026 5:37 AM, Mikko wrote:
    On 21/06/2026 03:41, olcott wrote:
    Knowledge is not merely a justified true belief.

    Knowledge is a sufficiently justified true belief such
    that the justification is sufficient reason to conclude
    that the belief is true. Copyright PL Olcott 2026

    The problem is what justification is sufficient to call the conclusion >>>>> "knowledge". That problem is a consequence to some peoples desire to >>>>> have a word for a concept that is hard to define and hard to use
    without
    mistakes.

    When we use the court's "reasonable person"
    standard we know that no reasonable person
    would ever construe number of coins in the
    pocket as having anything at all to do with
    getting the job. (the first Gettier case)

    https://iep.utm.edu/gettier/

    On the other hand the company president's opinion
    about who would be hired might be construed as a
    sufficiently justified belief.

    It is hard to construct a rule that simulates a "reasonable person".
    And also hard to test how well some proposed rule achieves that.

    None-the-less the Gettier cases are conquered.

    Merely ad hoc solutions, no computable method.


    I am not aware of any alternative solution to Gettier
    where the judgement of human minds is involved that is
    better than mine.

    My augmentations to PTS approximate on infallibility
    within the atomic base.
    --
    Copyright 2026 Olcott

    My 28 year goal has been to make
    "true on the basis of meaning expressed in language"
    reliably computable for the entire body of knowledge.
    The complete structure of this system is now defined.

    The entire body of knowledge expressed in language is
    comprised of two types of relations between finite strings:
    (a) *Axioms* Expressions of language that are stipulated to be true.

    My system bridges the analytic/synthetic distinction by
    expressly encoding all empirical "atomic facts" in a formal
    language such as CycL of the Cyc project.

    (b) *Inference Rules* Expressions of language that are semantically
    entailed syntactically from (a) and/or (b).
    --- Synchronet 3.22a-Linux NewsLink 1.2
  • From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,sci.math.symbolic,comp.ai.philosophy on Wed Jun 24 11:08:31 2026
    From Newsgroup: comp.ai.philosophy

    On 23/06/2026 17:26, olcott wrote:
    On 6/23/2026 12:32 AM, Mikko wrote:
    On 22/06/2026 17:45, olcott wrote:
    On 6/22/2026 2:30 AM, Mikko wrote:
    On 22/06/2026 02:47, olcott wrote:
    On 6/21/2026 5:37 AM, Mikko wrote:
    On 21/06/2026 03:41, olcott wrote:
    Knowledge is not merely a justified true belief.

    Knowledge is a sufficiently justified true belief such
    that the justification is sufficient reason to conclude
    that the belief is true. Copyright PL Olcott 2026

    The problem is what justification is sufficient to call the
    conclusion
    "knowledge". That problem is a consequence to some peoples desire to >>>>>> have a word for a concept that is hard to define and hard to use
    without
    mistakes.

    When we use the court's "reasonable person"
    standard we know that no reasonable person
    would ever construe number of coins in the
    pocket as having anything at all to do with
    getting the job. (the first Gettier case)

    https://iep.utm.edu/gettier/

    On the other hand the company president's opinion
    about who would be hired might be construed as a
    sufficiently justified belief.

    It is hard to construct a rule that simulates a "reasonable person".
    And also hard to test how well some proposed rule achieves that.

    None-the-less the Gettier cases are conquered.

    Merely ad hoc solutions, no computable method.

    I am not aware of any alternative solution to Gettier
    where the judgement of human minds is involved that is
    better than mine.

    Gettier is fairly unimportant. THe important problem is fo find an
    algrithm to simulate a "reaonable person" as clisely as possibly.

    My augmentations to PTS approximate on infallibility
    within the atomic base.

    No reason to think in does.
    --
    Mikko
    --- Synchronet 3.22a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,comp.ai.philosophy,sci.math.symbolic on Wed Jun 24 14:31:06 2026
    From Newsgroup: comp.ai.philosophy

    On 6/24/2026 3:08 AM, Mikko wrote:
    On 23/06/2026 17:26, olcott wrote:
    On 6/23/2026 12:32 AM, Mikko wrote:
    On 22/06/2026 17:45, olcott wrote:
    On 6/22/2026 2:30 AM, Mikko wrote:
    On 22/06/2026 02:47, olcott wrote:
    On 6/21/2026 5:37 AM, Mikko wrote:
    On 21/06/2026 03:41, olcott wrote:
    Knowledge is not merely a justified true belief.

    Knowledge is a sufficiently justified true belief such
    that the justification is sufficient reason to conclude
    that the belief is true. Copyright PL Olcott 2026

    The problem is what justification is sufficient to call the
    conclusion
    "knowledge". That problem is a consequence to some peoples desire to >>>>>>> have a word for a concept that is hard to define and hard to use >>>>>>> without
    mistakes.

    When we use the court's "reasonable person"
    standard we know that no reasonable person
    would ever construe number of coins in the
    pocket as having anything at all to do with
    getting the job. (the first Gettier case)

    https://iep.utm.edu/gettier/

    On the other hand the company president's opinion
    about who would be hired might be construed as a
    sufficiently justified belief.

    It is hard to construct a rule that simulates a "reasonable person". >>>>> And also hard to test how well some proposed rule achieves that.

    None-the-less the Gettier cases are conquered.

    Merely ad hoc solutions, no computable method.

    I am not aware of any alternative solution to Gettier
    where the judgement of human minds is involved that is
    better than mine.

    Gettier is fairly unimportant. THe important problem is fo find an
    algrithm to simulate a "reaonable person" as clisely as possibly.

    My augmentations to PTS approximate on infallibility
    within the atomic base.

    No reason to think in does.


    Only because you don't even understand how PTS
    differs from TCS.

    In proof‑theoretic semantics an expression has
    semantic meaning only if there is a chain of
    canonical inference steps from some atomic base
    to that expression. If no such chain exists,
    the expression does not inherit meaning from the base.
    --
    Copyright 2026 Olcott

    My 28 year goal has been to make
    "true on the basis of meaning expressed in language"
    reliably computable for the entire body of knowledge.
    The complete structure of this system is now defined.

    The entire body of knowledge expressed in language is
    comprised of two types of relations between finite strings:
    (a) *Axioms* Expressions of language that are stipulated to be true.

    My system bridges the analytic/synthetic distinction by
    expressly encoding all empirical "atomic facts" in a formal
    language such as CycL of the Cyc project.

    (b) *Inference Rules* Expressions of language that are semantically
    entailed syntactically from (a) and/or (b).
    --- Synchronet 3.22a-Linux NewsLink 1.2
  • From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,comp.ai.philosophy,sci.math.symbolic on Thu Jun 25 10:43:10 2026
    From Newsgroup: comp.ai.philosophy

    On 24/06/2026 22:31, olcott wrote:
    On 6/24/2026 3:08 AM, Mikko wrote:
    On 23/06/2026 17:26, olcott wrote:
    On 6/23/2026 12:32 AM, Mikko wrote:
    On 22/06/2026 17:45, olcott wrote:
    On 6/22/2026 2:30 AM, Mikko wrote:
    On 22/06/2026 02:47, olcott wrote:
    On 6/21/2026 5:37 AM, Mikko wrote:
    On 21/06/2026 03:41, olcott wrote:
    Knowledge is not merely a justified true belief.

    Knowledge is a sufficiently justified true belief such
    that the justification is sufficient reason to conclude
    that the belief is true. Copyright PL Olcott 2026

    The problem is what justification is sufficient to call the
    conclusion
    "knowledge". That problem is a consequence to some peoples
    desire to
    have a word for a concept that is hard to define and hard to use >>>>>>>> without
    mistakes.

    When we use the court's "reasonable person"
    standard we know that no reasonable person
    would ever construe number of coins in the
    pocket as having anything at all to do with
    getting the job. (the first Gettier case)

    https://iep.utm.edu/gettier/

    On the other hand the company president's opinion
    about who would be hired might be construed as a
    sufficiently justified belief.

    It is hard to construct a rule that simulates a "reasonable person". >>>>>> And also hard to test how well some proposed rule achieves that.

    None-the-less the Gettier cases are conquered.

    Merely ad hoc solutions, no computable method.

    I am not aware of any alternative solution to Gettier
    where the judgement of human minds is involved that is
    better than mine.

    Gettier is fairly unimportant. THe important problem is fo find an
    algrithm to simulate a "reaonable person" as clisely as possibly.

    My augmentations to PTS approximate on infallibility
    within the atomic base.

    No reason to think in does.

    Only because you don't even understand how PTS
    differs from TCS.

    Irrelevant. Apparently you don't know how PTS differs from useful.

    In proof‑theoretic semantics an expression has
    semantic meaning only if there is a chain of
    canonical inference steps from some atomic base
    to that expression. If no such chain exists,
    the expression does not inherit meaning from the base.
    A consequnce of that restriction is that it often excludes what
    is actually needed for solving some problem. For example, consider
    the calssical prblem of trisecting an angle. How does PTS help
    with that?
    --
    Mikko
    --- Synchronet 3.22a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to sci.logic,sci.math,sci.math,comp.theory,comp.ai.philosophy on Thu Jun 25 11:23:36 2026
    From Newsgroup: comp.ai.philosophy

    On 6/25/2026 2:43 AM, Mikko wrote:
    On 24/06/2026 22:31, olcott wrote:
    On 6/24/2026 3:08 AM, Mikko wrote:
    On 23/06/2026 17:26, olcott wrote:
    On 6/23/2026 12:32 AM, Mikko wrote:
    On 22/06/2026 17:45, olcott wrote:
    On 6/22/2026 2:30 AM, Mikko wrote:
    On 22/06/2026 02:47, olcott wrote:
    On 6/21/2026 5:37 AM, Mikko wrote:
    On 21/06/2026 03:41, olcott wrote:
    Knowledge is not merely a justified true belief.

    Knowledge is a sufficiently justified true belief such
    that the justification is sufficient reason to conclude
    that the belief is true. Copyright PL Olcott 2026

    The problem is what justification is sufficient to call the >>>>>>>>> conclusion
    "knowledge". That problem is a consequence to some peoples
    desire to
    have a word for a concept that is hard to define and hard to >>>>>>>>> use without
    mistakes.

    When we use the court's "reasonable person"
    standard we know that no reasonable person
    would ever construe number of coins in the
    pocket as having anything at all to do with
    getting the job. (the first Gettier case)

    https://iep.utm.edu/gettier/

    On the other hand the company president's opinion
    about who would be hired might be construed as a
    sufficiently justified belief.

    It is hard to construct a rule that simulates a "reasonable person". >>>>>>> And also hard to test how well some proposed rule achieves that.

    None-the-less the Gettier cases are conquered.

    Merely ad hoc solutions, no computable method.

    I am not aware of any alternative solution to Gettier
    where the judgement of human minds is involved that is
    better than mine.

    Gettier is fairly unimportant. THe important problem is fo find an
    algrithm to simulate a "reaonable person" as clisely as possibly.

    My augmentations to PTS approximate on infallibility
    within the atomic base.

    No reason to think in does.

    Only because you don't even understand how PTS
    differs from TCS.

    Irrelevant. Apparently you don't know how PTS differs from useful.


    *Proof Theoretic Semantics as a new Foundation*
    *for Mathematics, Logic and the Theory of Computation*

    Truth Conditional Semantics (TCS) <is> incoherent
    compared to Proof Theoretic Semantics (PTS).
    Essentially PTS just coherently connects the
    semantic meanings expressed in language together
    into one coherent body of general knowledge.
    It does this without undecidability or mathematical
    incompleteness.

    https://philpapers.org/archive/OLCPTS-2.pdf

    In proof‑theoretic semantics an expression has
    semantic meaning only if there is a chain of
    canonical inference steps from some atomic base
    to that expression. If no such chain exists,
    the expression does not inherit meaning from the base.
    A consequnce of that restriction is that it often excludes what> is
    actually needed for solving some problem. For example, consider
    the calssical prblem of trisecting an angle. How does PTS help
    with that?

    --
    Copyright 2026 Olcott

    My 28 year goal has been to make
    "true on the basis of meaning expressed in language"
    reliably computable for the entire body of knowledge.
    The complete structure of this system is now defined.

    The entire body of knowledge expressed in language is
    comprised of two types of relations between finite strings:
    (a) *Axioms* Expressions of language that are stipulated to be true.

    My system bridges the analytic/synthetic distinction by
    expressly encoding all empirical "atomic facts" in a formal
    language such as CycL of the Cyc project.

    (b) *Inference Rules* Expressions of language that are semantically
    entailed syntactically from (a) and/or (b).
    --- Synchronet 3.22a-Linux NewsLink 1.2
  • From Mikko@mikko.levanto@iki.fi to sci.logic,sci.math,sci.math,comp.theory,comp.ai.philosophy on Fri Jun 26 09:12:19 2026
    From Newsgroup: comp.ai.philosophy

    On 25/06/2026 19:23, olcott wrote:
    On 6/25/2026 2:43 AM, Mikko wrote:
    On 24/06/2026 22:31, olcott wrote:
    On 6/24/2026 3:08 AM, Mikko wrote:
    On 23/06/2026 17:26, olcott wrote:
    On 6/23/2026 12:32 AM, Mikko wrote:
    On 22/06/2026 17:45, olcott wrote:
    On 6/22/2026 2:30 AM, Mikko wrote:
    On 22/06/2026 02:47, olcott wrote:
    On 6/21/2026 5:37 AM, Mikko wrote:
    On 21/06/2026 03:41, olcott wrote:
    Knowledge is not merely a justified true belief.

    Knowledge is a sufficiently justified true belief such
    that the justification is sufficient reason to conclude
    that the belief is true. Copyright PL Olcott 2026

    The problem is what justification is sufficient to call the >>>>>>>>>> conclusion
    "knowledge". That problem is a consequence to some peoples >>>>>>>>>> desire to
    have a word for a concept that is hard to define and hard to >>>>>>>>>> use without
    mistakes.

    When we use the court's "reasonable person"
    standard we know that no reasonable person
    would ever construe number of coins in the
    pocket as having anything at all to do with
    getting the job. (the first Gettier case)

    https://iep.utm.edu/gettier/

    On the other hand the company president's opinion
    about who would be hired might be construed as a
    sufficiently justified belief.

    It is hard to construct a rule that simulates a "reasonable
    person".
    And also hard to test how well some proposed rule achieves that. >>>>>>>
    None-the-less the Gettier cases are conquered.

    Merely ad hoc solutions, no computable method.

    I am not aware of any alternative solution to Gettier
    where the judgement of human minds is involved that is
    better than mine.

    Gettier is fairly unimportant. THe important problem is fo find an
    algrithm to simulate a "reaonable person" as clisely as possibly.

    My augmentations to PTS approximate on infallibility
    within the atomic base.

    No reason to think in does.

    Only because you don't even understand how PTS
    differs from TCS.

    Irrelevant. Apparently you don't know how PTS differs from useful.

    *Proof Theoretic Semantics as a new Foundation*
    *for Mathematics, Logic and the Theory of Computation*

    Truth Conditional Semantics (TCS) <is> incoherent
    compared to Proof Theoretic Semantics (PTS).
    Essentially PTS just coherently connects the
    semantic meanings expressed in language together
    into one coherent body of general knowledge.
    It does this without undecidability or mathematical
    incompleteness.

    https://philpapers.org/archive/OLCPTS-2.pdf

    No reason to revise any of the above comments.
    --
    Mikko
    --- Synchronet 3.22a-Linux NewsLink 1.2