Position:

Logicist epistemology has a position in the Factasia utopian vision. It underpins the implementation and exploitation of the analytic aspect of the global superbrain.

The Global SuperBrain provides a perspective on the future which recognises the pervasive impact of information technology and global networks. The Factasian conception of the global superbrain is presented in two complementary aspects, each of which can be related to an aspect of epistemology in Factasia.

The Holistic aspect of the Global SuperBrain involves the globe as an intellectual and cultural community mediated by global computing and telecommunications infrastructure. It concerns the way in which this community develops its vision of the future of the world, and how that vision is realised. Factastic epistemology concerns the kind of knowledge involved in chosing a future and making it happen.

The Analytic aspect of the Global SuperBrain is concerned with the automation of reasoning and with the development and exploitation of analytic truths. This is technical infrastructure for a wide range of model based problem solving capabilities. Logicist epistemology provides philosophical rationale and foundations to underpin the analytic SuperBrain, and a broad conception of the scope of applicability of analytic modelling.

The FAn Oracle Hypothesis The "Global Superbrain" discussion can be made into a precise philosophical thought experiment via the FAn Oracle hypothesis. A FAn Oracle is an oracle which can decide the truth of analytic conjectures, or solve problems whose solution is analytic (i.e. provide a witness for an analytically true existential claim over suitable domains).

Humean Forks:

Parallels and contrasts are drawn with Hume's epistemology.

The Fundamental Dichotomy

Drawing Lines Central to Hume's skeptical epistemology is the distinction which he draws most clearly in his enquiry (ECHU Section IV Part 1) between "Relations of Ideas, and Matters of Fact" recognising that the former can be proven with great certainty but that the latter cannot. Logicist Epistemology also affirms the fundamental triple dichotomy. Hume's denial that an ought can be derived from an is introduces a third category of value judgements giving us Two epistemological triads and Three kinds of judgement.

Sheep from Goats Having established the essential difference, Hume then goes on to separate the sheep from the goats, enumerating many different kinds of proposition which, because they concern matters of fact, are not susceptible of demonstrative proof and cannot therefore be known with certainty. The goats include all empirical generalisations and inductive inference, even to probabilistic conclusions. Science and morality transcend logic and lack its certainty.

AI and Trust Hume's ideas are not only applicable to curbing the excesses of rationalist philosphers. They are applicable to more modern problems, telling us limits on what can reliably be established by artificial intelligence, however far our technology may progress. Hume's skepticism is a precursor to the exploitation thread of Logicist Epistemology, which concerns the scope of applicability of deductive reason.

Skepticism about Reason

Doubting a Proof Though in the most prominent parts of his philosophy, particularly in his Enquiries Hume affirms the certainty attained by demonstrative proof, he does pause to doubt even this. In "A Treatise on Human Nature", Book 1, Part IV, Section 1, he still affirms that a demonstrative proof confers certainty, but admits that one can be mistaken about whether he is in posession of such a proof.

Doubting a Proof Checker Just as people can be mistaken about the correctness of a proof, so can machines be. Proper care should therefore be taken in building an analytic superbrain that it does not make such mistakes. Since the checking of proofs is mechanical this comes to the correctness of the algorithms fulfilling this purpose in the superbrain. The epistemic status of a claim to correctness for such a system is just one of many epistemological problems associated with engineering an analytic superbrain.

Doubting a Logic Though Hume did not himself doubt that a proof conferred certainty, we can and should. Advances in modern logic have taught us that we can be mistaken not only about whether our proof is correct, but also about whether our logic is sound. The implementation aspect of logicist epistemology is concerned with this kind of foundational problem.

Rationality and Deduction

Hume and Rationality Hume had a very black and white attitude to the relevance of demonstrative reasoning to establishing a conclusion. Since matters of fact are not susceptible of demonstrative proof, and even statements of probability about such facts cannot be proven demonstratively, demonstrative reasoning must be wholly irrelevant to establishing them. Importantly, he took this to mean that belief in matters of fact cannot be rationally supported. He seemed to believe that for a belief to be rational it must be demonstrable.

Against Hume At this point Logicist Epistemology parts company with Hume. Drawing a distinction related to Popper's distinction between verifiability and falsifiability. Even for kinds of proposition which cannot be logically demonstrated, rationality remains a relevant requirement, and can be connected with a requirement for logical consistency. Thus an empirical generalisation, though not deducible from particular observations on which it is based, should nevertheless be logically consistent with them. Kant's Categorical Imperative is an example of the relevance of rationality to moral judgements. Even though logical judgements are not analytic, there are considerations of consistency in moral judgement which are reducible to matters of logic.

Consistency, Models, Rationality Rationality, we hold, encompasses not only those domains such as mathematics in which results are established by deduction, but also all other sphere's where factual or evaluative judgements may be expected to be consistent. Ideally consistency may be established using formal models. Foundationally, epistemologically, we may ask whether there are any aspects of rationality which are not thus reducible to logic, and whether we may therefore claim that the relevance of a FAn oracle or the Analytic Superbrain is to the whole of rational discourse.

Implementation:

What are the epistemological problems upon which the rationale, design and implementation of the analytic superbrain depends?

Fundamental Dichotomies The possibility of an "analytic superbrain" is entirely predicated on their being a fundamental dichotomy in the kinds of proposition which can be known, with parallel methodological differences in how these propositions should be established.

The Epistemological Status of Logical Truths The design of the analytic superbrain embodies and is dependent upon a particular view of the epistemological status of logical truths.

Logic and Proof If we know (a) that a logic is sound, and (b) that a conjecture is proven in that logic, then of necessity that conjecture is true. The purpose of a formal logic is to make (b) effectively decidable but this still leaves a hole (for infinite regress) in (a).

Characteristica Analytica We need, for the analytic superbrain, if not Leibniz's characteristica universalis, at least something close to a characteristica analytica in which all analytic truths can be expressed. Is there any hope?

Soundness of Logic Given a characteristica analytica we need a logical system to permit reasoning in the language. The logic must be sound; how can we be assured of this?

Correctness of Proof Given a sound logic, its use involves the checking of proofs. Though the rules are mechanical, the proofs may be enormous, how can we be sure that they are correct.

Calulus Ratiocinator Leibniz envisaged, and the analytic superbrain depends upon, not only mechanical checking, but also mechanical finding of solutions and proofs. Does this raise any special epistemological problems?

Mechanisation We envisage not just that much of logic be mechanical, but that it in fact be done by machine. Can we be assured of the truth of a statement whose proof has only ever been surveyed by the same computer which constructed it? Modern developments in automation of reasoning stretch the notion of proof further yet, where are the limits?

Exploitation:

What are the epistemological issues which affect the exploitation of the analytic superbrain? Should it change the methods of epistemology itself?

The FAn Oracle Hypothesis The epistemological aspects of the exploitation side of logicist epistmology are perhaps best investigated with the aid of the FAn Oracle Hypothesis. We first hypothesise that there is available to us a convenient source of infinite wisdom in relation to analytic propositions, and then consider what kinds of knowledge this encompasses, and how knowledge might contribute to our knowledge of matters of fact and judgements of value.	Engineering The epistemological relevance of logic to engineering is of particular interest. Prior to building a complex artefact intended to fulfill some particular purpose it is necessary to produce an overall architecture and detailed design which prescribes what it is that will be fabricated. Before embarking on the fabrication we wish to know that the prescribed artefact will fullfil the purpose for which it is intended. We therefore have a problem of knowledge which it is now routine to address by the construction and analysis of mathematical models.	Philosophy We identify here for particular future consideration the question of standards of rationality in the conduct of philosophy, particularly of analytic philosophy. Because analytic philosophy is considerably concerned with matters a priori, and frequently presents the appearance of logical argument the matters which concern logicist epistemology have a particular relevance to standards of rationality in philosophy. See also: The Method of Formal Logical Analysis.
Three Kinds of Knowledge A more general approach to the examination of the extent of analytic knowledge and how it contributes to other kinds of knowledge can be made in the first instance though consideration of the general characteristics of three kinds of knowledge which we may call logical, factual and evaluative respectively.

Rationality and Deduction:

A pervasive preoccupation of logicist epistemology is the relationship between rationality and deduction. Do these walk hand in hand, or is rationality all encompassing but deduction myopic?

Hume Hume tells us that demonstrative proof is possible only for claims which express a relationship between ideas (what we might now call analytic or logical truths), and not for any matters of fact or value judgements. In this we concur. He further seems to believe that in other beliefs rationality plays no role, that the we draw conclusions about matters of fact (e.g. general scientific laws) purely from habit. From this we demur. Fork Essential Hume's "fork", the distinction of "relations between ideas" from "matters of fact" is fundamental to and inseparable from rationality. To abandon this distinction is to abandon reason. For more see: The Fundamental Triple Dichotomy.

Consistency Deductive reasoning about the consistency of our views permits rationality to constrain our beliefs about matters of fact and value judgements. Logical analysis of sound arguments should always lead to the isolation of a set of premises from which the conclusion is deducible. The conjunction of these premises defines a collection of models (those satisfying the premises) in which the argument is valid. We have consistency only if the set of models is non-empty. Models An important way of testing rationality is through models. Our fundamental beliefs should be presented as (preferably formal) models so that our particular beliefs can be shown to be consistent with the general principles. Such models permit questions of consistency to be reduced to logic.

Limits of Deduction Are there any elements of rationality which are not in principle reducible to deductive logic? A good question, which we propose to approach through a fuller understanding of how broad a range of rational considerations can be formalised. Foundationalism We seek to rehabilitate forms of foundationalism. Deductive arguments are of necessity well-founded, in the sense that a proof is finite and involves a finite set of premises. When we construct a model we have in mind a general model which encompasses some body of particular (supposed) facts. An important element in the justification for the model is that it does entail those facts (whether or not they are indeed facts).

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© created 1995/10/16 modified 1999/10/22