FOM Digest, Vol 234, Issue 36
Mark Lance
lancem at georgetown.edu
Sun Jun 26 08:16:35 EDT 2022
"Vuillemin gave a seminal classification of *genuine* philosophical
systems that is to say systems that are based on only one or two basic
assertions. ... Another important point is that every genuine philosophical
theory *is* a foundation"
Yes, if you build into the definition that the system is based on one or
two assertions, then - depending on (or perhaps ignoring) details of "based
on" and "foundation," it is hardly surprising that you get the conclusion
that the theory has a foundation.
No true scotsman.
Mark Lance (they/them)
professor of philosophy
professor of justice and peace
Co-director, program on justice and peace
Georgetown University
On Sat, Jun 25, 2022 at 8:24 PM <fom-request at cs.nyu.edu> wrote:
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> Today's Topics:
>
> 1. Re: Fwd: Foundations and Foundationalism (Joseph Vidal-Rosset)
> 2. Re: Shannon's information theory and foundations of
> mathematics (Ellerman, David)
> 3. disinformation in a formal system as exploitation of the
> undecidability and proof complexity (Jos? Manuel Rodr?guez Caballero)
>
>
>
> ---------- Forwarded message ----------
> From: Joseph Vidal-Rosset <joseph at vidal-rosset.net>
> To: fom at cs.nyu.edu
> Cc: Harvey Friedman <hmflogic at gmail.com>, tchow at alum.mit.edu
> Bcc:
> Date: Sat, 25 Jun 2022 08:36:13 +0000
> Subject: Re: Fwd: Foundations and Foundationalism
>
> Hello everyone,
>
> About philosophical disagreements, I do not know better and deepest
> books than Jules Vuillemin's book, I mean "What are philosophical systems?"
>
>
> https://www.cambridge.org/core/books/what-are-philosophical-systems/12CC0EEF3C4372B0740E0A1BA74C13B9
>
> @book{vuillemin_1986, place={Cambridge}, title={What Are Philosophical
> Systems?}, DOI={10.1017/CBO9780511753336}, publisher={Cambridge
> University Press}, author={Vuillemin, Jules}, year={1986}}
>
> And also his book about Diodorus's Master Argument
>
> https://press.uchicago.edu/ucp/books/book/distributed/N/bo3616790.html
>
> @book{vuillemin1996a,
> title = {Necessity or {{Contingency}}: {{The Master Argument}}},
> author = {Vuillemin, Jules},
> year = {1996},
> series = {Center for the {{Study}} of {{Language}} and
> {{Information}} - {{CSLI Lecture Notes}} 56},
> publisher = {{CSLI Publications}},
> isbn = {978-1-881526-85-8 1-881526-85-2 1-881526-86-0}
> }
>
> Vuillemin gave a seminal classification of *genuine* philosophical
> systems that is to say systems that are based on only one or two basic
> assertions. It is an axiomatic theory of philosophical systems (similar
> to Russell's analysis of Leibniz's philosophy) that should interest many
> readers of the FOM list.
>
> One of Vuillemin's points is that philosophical theories are essentially
> *polemical*, by contrast with scientific theories. Another important
> point is that every genuine philosophical theory *is* a foundation:
> Realism (i.e. Platonism for Vuillemin), Conceptualism (for example
> Aristotle's philosophy), Nominalism, Intuitionism and Skepticism are the
> five classes of genuine philosophical systems and are all foundations of
> knowledge (even Skepticism, in a destructive way).
>
> I do not know what exactly "Foundationalism" means in mathematics, if no
> distinction is made between classical mathematics and intuitionistic
> mathematics for example, because these foundations are different.
> Logical criteria draw distinctions between a classical (i.e.
> non-constructive) proof and an intuitionistic one, but the decision to
> reject or to accept the validity of the former is purely philosophical.
> Philosophy is both a free and a rational decision, according to
> Vuillemin's theory.
>
> Good discovery!
>
> All the best,
>
> Jo.
>
>
>
>
>
> ---------- Forwarded message ----------
> From: "Ellerman, David" <david at ellerman.org>
> To: Vaughan Pratt <pratt at cs.stanford.edu>
> Cc: fom at cs.nyu.edu
> Bcc:
> Date: Sat, 25 Jun 2022 11:47:08 +0200
> Subject: Re: Shannon's information theory and foundations of mathematics
> Disinformation! Shannon's theory gives a negative mutual information for
> certain sets of three random variables, e.g., in the standard example that
> pairwise independence for three variables is not the same as joint
> independence. The joke is: "We didn't know what "negative information" was
> until Trump got elected."
> That is why Shannon himself never defined mutual information for three or
> more variables. But all of Shannon's compound notions of joint,
> conditional, and mutual information satisfy the usual Venn diagrams as if
> the Shannon formula was a measure on a set (which it is not). But the usual
> inclusion-exclusion principle shows how Shannon information can be extended
> to many-variable Venn diagrams where the negative mutual information pops
> up. In the best book on the Shannon theory by Cover and Thomas, they have
> the surprisingly casual statement "There isn’t really a notion of mutual
> information common to three random variables." [p. 49] without any
> further explanation or analysis.
> The connection to logic and foundations requires a little background.
> Normally "logic" is identified as reasoning about propositions. But the
> mathematical logic underlying propositional logic is the Boolean logic of
> subsets of which propositional logic is the special case where the
> universet set has one element. And mathematically (category theory), the
> notion of subsets is dual to the notion of partitions (or equivalence
> relations or quotient sets). Hence there is a dual mathematical logic, the
> logic of partitions, that is equally basic from that mathematical viewpoint
> as the logic of subsets. Each logic has a quantitative version. The
> quantitative version of the Boolean logic of subsets was also developed by
> Boole, namely finite probability theory. The quantitative version of the
> logic of partitions is the theory of logical entropy which was recently
> covered in a Special Issue of the open-access journal 4Open here
> <https://www.4open-sciences.org/component/toc/?task=topic&id=1575>.
> Logical entropy is a measure in the sense of measure theory so it naturally
> has all the Venn diagram notions of simple, joint, conditional, and mutual
> logical information. Moreover, all those compound notions of Shannon
> entropy are the result of a non-linear dit-bit transform that transforms
> logical entropy into Shannon entropy, and that transform preserves Venn
> diagrams--which accounts for Shannon entropy satisfying those diagrams when
> it is not a measure in the sense of measure theory. But the dit-bit
> transform does not preserve non-negativity of the logical entropy
> measure--which allows the negative mutual Shannon information.
> Best,
> David Ellerman
> www.ellerman.org
>
>
> On Sat, Jun 25, 2022 at 12:41 AM Vaughan Pratt <pratt at cs.stanford.edu>
> wrote:
>
>> Recently Rohit Parikh suggested to me that disinformation was not
>> information. As I've always considered disinformation about any given
>> proposition to be less likely that the conventional wisdom about it, it
>> seemed to me that with Shannon's information theory, a less likely message
>> contains more information than a more likely one. Hence in particular
>> disinformation should convey more information than the conventional wisdom.
>>
>> Is there a foundational way of approaching these seemingly conflicting
>> notions of information that isn't too wildly ad hoc?
>>
>> Vaughan Pratt
>>
>
>
> --
> __________________
> David Ellerman
>
> Email: david at ellerman.org
>
> View and/or download my publications at my webpage: www.ellerman.org
>
>
>
>
> ---------- Forwarded message ----------
> From: "José Manuel Rodríguez Caballero" <josephcmac at gmail.com>
> To: Foundations of Mathematics <fom at cs.nyu.edu>
> Cc: Vaughan Pratt <pratt at cs.stanford.edu>
> Bcc:
> Date: Sat, 25 Jun 2022 13:45:46 -0400
> Subject: disinformation in a formal system as exploitation of the
> undecidability and proof complexity
> Vaughan Pratt wrote:
>
>> Recently Rohit Parikh suggested to me that disinformation was not
>> information. As I've always considered disinformation about any given
>> proposition to be less likely that the conventional wisdom about it, it
>> seemed to me that with Shannon's information theory, a less likely message
>> contains more information than a more likely one. Hence in particular
>> disinformation should convey more information than the conventional
>> wisdom.
>
> and asked:
>
>> Is there a foundational way of approaching these seemingly conflicting
>> notions of information that isn't too wildly ad hoc?
>
>
> There are conceptual distinctions among disinformation, misinformation,
> and malinformation:
>
>> Misinformation refers to false information that is not intended to cause
>> harm.
>> Disinformation refers to false information that is intended to
>> manipulate, cause damage, or guide people, organizations, and countries in
>> the wrong direction.
>> Malinformation refers to information that stems from the truth but is
>> often exaggerated in a way that misleads and causes potential harm.
>
>
> Reference:
> https://cyber.gc.ca/en/guidance/how-identify-misinformation-disinformation-and-malinformation-itsap00300
>
> Gille Deleuze was a 20th-century French philosopher strongly inspired by
> mathematics. He was criticized because his philosophical version of
> mathematical concepts is not always equivalent to the original mathematical
> formulation and his response was always that it was not necessary: he was
> aware that the mathematically inspired philosophical concepts are not the
> same as mathematical concepts. That said, I will try to answer Pratt's
> question in the framework of Deleuze's course: "Appareils d'État et
> machines de guerre"
>
> audio:
> https://www.youtube.com/playlist?list=PLATazQ-QShe-JfDXbmYOXumDjC4BhlLjM
>
> text:
> https://deleuze.cla.purdue.edu/sites/default/files/pdf/lectures/fr/ATP%20V-13b-StateApp-250380%20Fr.pdf
>
> My starting point to formalize the notion of disinformation is this quote
> from Deleuze's course:
>
>> Troisième rubrique, on a vu : « la question des modèles de réalisation
>> dans une axiomatique », à savoir les modèles de réalisation, dans une
>> axiomatique mondiale du capital, étant les États euxmêmes, d’où la question
>> dans cette troisième rubrique : en quel sens [40 :00] peut-on dire que ces
>> États, que les formes diverses d’État, sont isomorphes ou non par rapport à
>> l’axiomatique, avec dès lors toutes sortes de bipolarité : bipolarité entre
>> les États du centre, seconde bipolarité entre États capitalistes et États
>> socialistes-bureaucratiques, troisième bipolarité entre États du
>> centre-États de la périphérie ? Bon, on en était là
>
>
> My non-literary English translation:
>
>> Third heading, we have seen: "the question of the realization of a model
>> in an axiomatic system", namely the realization of models, in a world
>> axiomatic of capital, being the States themselves, hence the question in
>> this third heading: in what sense [40:00] can we say that these States,
>> that the various forms of State, are isomorphic or not with respect to the
>> axiomatic system, with consequently all sorts of bipolarity: bipolarity
>> between the States of the center, second bipolarity between capitalist
>> states and socialist-bureaucratic states, a third bipolarity between
>> central states and peripheral states? Alright, there we were.
>
>
> For Deleuze, a "kind of state" is determined by an axiomatic system, e.g.,
> capitalist (kind of) states, socialist-bureaucratic (kind of) states. But a
> concrete state is just a model of this axiomatic system, e.g., the US is a
> model of a capitalist state, but it is not necessary the same model as
> France, even if they share the axioms of a capitalist state. Now, the
> notion of disinformation enters: because the typical citizen (Alice) is
> aware of the axioms of the kind of state in which she lives, but may ignore
> the details of the particular realization of this model, a malicious
> disinformation agent (Eve) can try to create a narrative to convince Alice
> that the particular realization of the state in which she lives is not the
> real one. To do so, Eve's narrative will keep the axioms of the kind of
> state in which Alice lives as a requirement to be credible, and will only
> play with the undecidable propositions. Therefore, a measure of
> disinformation could be the rate of undecidable propositions in a given
> narrative. If this rate is high, then the text is more likely to be
> disinformation. The threshold for the rate of undecidability concerning the
> distinction between "information" and "disinformation" in a text should be
> determined empirically via statistics.
>
> The problem is how to detect whether a given proposition in a narrative is
> undecidable with respect to the axiomatic system of a kind of state. To do
> so, the first step is to extract the formal system from the text (data
> cleaning in natural language processing). Now, with the formal system at
> our disposal, the task is to detect which propositions are undescidable. In
> general, this task is uncomputable, but in the particular case of an
> axiomatic system corresponding to a kind of state, this task may be
> decidable. Even if it is undecidable, some heuristic rules could be applied
> to find the undecidable propositions, e.g., try to prove the proposition or
> its negation using an automatic reasoning tool such as SMT (Satisfiability
> Modulo Theories) solvers. If it doesn't work, just declare the proposition
> to be undecidable.
>
> This is just a first-order approximation to the problem of disinformation.
> A more elaborate solution may include detecting false propositions such
> that the length of the proof of their falsehood is so large that the
> typical citizen, who is not capable of following 10 steps of reasoning, one
> after another, perceives it as undecidable. The main hypothesis of
> cognitive warfare is that an overloaded brain, maybe due to mental fatigue
> after working many hours, can only follow short proofs, e.g., up to 3
> steps. Therefore, the notion of proof complexity is fundamental for the
> theory of disinformation in formal systems.
>
> Beyond the Deleuzian framework, here are some references related to
> the exploitation of the human's limited capacity of following many steps in
> reasoning (this is not the only factor used in cognitive warfare, but it is
> one of the most important):
>
> Social Laser:
> - paper:
> https://royalsocietypublishing.org/doi/full/10.1098/rsta.2015.0094
> - book:
> https://www.amazon.com/Social-Laser-Application-Information-Processes/dp/981480083X
> - lectures: https://youtu.be/Hm8fEhqZBdk
>
> Cognitive Warfare (innovation hub):
> - Claverie, Bernard, and François du Cluzel. "The Cognitive Warfare
> Concept."
> https://www.innovationhub-act.org/sites/default/files/2022-02/CW%20article%20Claverie%20du%20Cluzel%20final_0.pdf
> - Open Innovation - Cognitive Warfare use case:
> https://youtu.be/xrnjcCgO19I?t=352
>
> I am personally interested in the subject from the point of view of
> biostatistics. More precisely, I find it interesting to measure the ability
> of a human being to follow a large chain of reasoning in different
> circumstances, e.g., under stress, under mental fatigue, with a fresh mind,
> etc. My inspiration for this research is Gromov's quote:
>
>> what is common between mathematicians and schizophrenics: only these two
>> people may trust a chain of 10 consecutive arguments. In life, one or two
>> is enough, you know, the chain breaks down
>
>
> https://youtu.be/buThBDcUYZI?t=1180
>
> Kind regards,
> Jose M.
>
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