Pragmatic Maxims • 3

Re: Peirce List DiscussionJerry Rhee

Inquiry begins in doubt and aims for belief but the rush to get from doubt to belief and achieve mental peace can cause us to short the integrated circuits of inquiry that we need to compute better answers.

For one thing, we sometimes operate under the influence of fixed ideas and hidden assumptions that keep us from seeing the sense of fairly plain advice, and here I would simply recommend reading those versions of the Pragmatic Maxim again and again and trying to triangulate the points to which they point.

For another thing, not everything in logic is an argument.  A well-developed formal system will have:  (1) Primitives, the undefined terms that acquire meaning from their place in the whole system rather than from explicit definitions, (2) Definitions, that connect derived terms to primitives, (3) Axioms, propositions taken to be true for the sake of the theorems that can be derived from them by means of certain (4) Inference Rules.

But that’s just the formal underpinnings — there’s all sorts of informal heuristics, regulative principles, rules of thumb that go toward sustaining any system of significant practical use, and that’s where bits of practical advice like the Maxim in question come into play.

Reference

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One Response to Pragmatic Maxims • 3

  1. Bhupinder Singh Anand says:

    Dear Jon,

    Thanks for drawing attention to three issues that — to a non-professional — seem implicit in Peirce’s pragmatism:  what scientists do, why it is significant, and how they do it.

    Philosophical Inquiry Should Be Pragmatic By Definition

    Let me, for the moment, frame these issues by positing the following, arbitrary, distinction between the three disciplines:

    • Applied science, whose concern is our sensory observations of a ‘common’ external world;
    • Philosophy, whose concern is abstracting a coherent perspective of the external world from our sensory observations; and
    • Mathematics, whose concern is adequately expressing such abstractions in a formal language of unambiguous communication.

    It seems that we could, then, cogently argue that any philosophical inquiry, by definition, should be labelled ‘pragmatic’ in Peirce’s prescient sense.

    Logic Should Play A Pragmatic Role In Philosophical Inquiry

    Moreover, apropos the role of logic and formal systems in any philosophical inquiry that aims at belief based on sound pragmatic considerations, let me further suggest a paradigm shift which — mandated by our development of a mechanical intelligence (probe) that is seeking the existence of an alter ego beyond our solar system which would signify the presence of an advanced extra-terrestrial intelligence in our universe — recognises that:

    1. language precedes logic, which precedes both truth and provability;
    2. a well-defined logic of a pragmatic language is merely a set of deterministic rules that can constructively assign unique, and verifiable, values of objective, evidence-based, truth and provability to the propositions of a language (such as the first order Peano Arithmetic PA) so as to ensure that the language can adequately represent and unambiguously communicate the content for which it is designed (the properties of the natural numbers in the case of PA);
    3. although we can conceptualise freely what there is within individual paradigms, of that which is common to individual paradigms — and of pragmatic value — we can unambiguously communicate only that which we can express in a language with a well-defined logic.

    Although not viewed as such explicitly, the philosophical significance of such a pragmatic perspective is implicit in the following paper, which is due to appear in the December 2016 issue of Cognitive Systems Research:

    • “The Truth Assignments That Differentiate Human Reasoning From Mechanistic Reasoning : The Evidence-Based Argument for Lucas’ Gödelian Thesis”

    Pragmatism Eliminates The Need For Appeal To Platonic Reasoning

    The paper offers a pragmatic, evidence-based, differentiation between human and mechanistic reasoning which exposes the inadequacy — if not the fallacy — of any Platonic (non-pragmatic?) ‘Truth’ that implicitly reflects the — commonly taught as definitive — classical perspective inherited from traditional logicians such as Kurt Gödel (a self-confessed Platonist) and Alfred Tarski.

    Both logicians were apparently predisposed to hold that an objective (pragmatic) ‘Truth’ cannot be evidence-based, but is an ubiquitous attribute of the panpsychistic content (facts) which precedes both the mathematical language that seeks to describe the content and its logic.

    For Gödel the ‘Truth’ of a (mathematical) proposition was essentially a discovery — eerily akin to a revelation — of an objective ‘fact’; for Tarski whilst arithmetical ‘Truth’ was undefinable, the ‘Truth’ of the proposition ‘Snow is white’ was also dependent on whether or not it is an objective ‘fact’ that snow is, indeed, white.

    However, the definitional approach to ‘logic’, and a pragmatic ‘evidence-based truth’, in the CSR paper offers fresh insight into how a human intelligence can consistently assign algorithmically verifiable truth values of True/False to the propositions of a well-defined language, whilst a mechanical intelligence can consistently only assign algorithmically computable truth values of True/False to such propositions.

    The Turing Test Favours Lucas’ Gödelian Hypothesis

    A significant consequence favouring a pragmatic definition of philosophic inquiry is that whereas, in a Turing Test, a mechanical intelligence would conclude that Gödel’s famous ‘undecidable’ arithmetical proposition [(∀x)R(x)] is algorithmically uncomputable as true, hence False, when interpreted over the domain N of the natural numbers, a human intelligence would conclude that the proposition is algorithmically verifiable as true, hence True, when interpreted over N.

    How A Pragmatic Philosophy Can Resolve The EPR And Other Paradoxes

    That such a definitional approach to a pragmatic ‘logic’, based on ‘evidence-based truth’, could also offer fresh insight into, and possible resolution of, some of the philosophically troubling abstractions of the physical sciences is the subject of the following paper, presented in July 2015 at the ‘Workshop on Emergent Logics’ presented at Unilog 2015, 5th World Congress and School on Universal Logic, at the University of Istanbul, Turkey:

    • “Algorithmically Verifiable Logic vis à vis Algorithmically Computable Logic : Could resolving EPR need two complementary Logics?”

    References

    Regards,

    Bhup

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