Sumários
The Problem of Induction - 7
5 Abril 2022, 09:30 • António José Teiga Zilhão
The Deductivist Attempt at Solving the Problem of Induction
1. The notion of a Confirmation Theory. How the problem of erecting a viable theory of confirmation is connected to the problem of induction. Logical Theories of Confirmation (e.g., Hempel's theory): survey of their basic principles.
2. The paradoxes logical theories of confirmation originate.
2.1. The Paradox of the Ravens.
2.2. The Paradox of Tacking by Conjunction.
2.3. The difficulties afflicting different attempts at solving these paradoxes from within logical theories of confirmation.
3. Popper's deductivist attempt at solving the problem of induction.
3.1. Popper's radical diagnosis of the problem afflicting logical theories of confirmation: they fall prey to the same error as any attempts at vindicating inductive reasoning - they try to determine how a general empirical hypothesis may be proven to be true, given the evidence available; but this is impossible, as Hume has convincingly shown.
3.2. Popper's own falsificationist approach: scientific reasoning does not aim at producing true hypotheses; it aims at rejecting false hypotheses. Neither induction nor logical confirmation are needed for that; false hypotheses are rejected through a deductive process (Modus Tollens). Hypotheses are tested against one another. Those that are better at withstanding empirical testing survive; the others are eliminated.
4. Some criticisms to Popper's falsificationism.
4.1. It does not seem to square well with the facts described in the History of Science.
4.2. It is unable to provide any reason why we should trust our everyday beliefs about the world.
4.3. It does not seem to have the means to discriminate against the multiple "Goodmanian" versions of any hypothesis that has withstood testing.
The Problem of Induction - 6
29 Março 2022, 09:30 • António José Teiga Zilhão
The Pragmatic Attempt at solving the Problem of Induction
1. Pascal's wager - it is impossible to know the truth value of a proposition stating God's existence; we must wager one way or other; so the best we can do is to wager in such a way that we choose the dominant option, given the payoffs involved.
2. Reichenbach's pragmatic attempt at justifying induction is structurally similar to Pascal's wager - it is an argument the purpose of which is to justify not the belief in a proposition but the choice of a wager. Thus, instead of trying to justify the belief in the Principle of Uniformity of Nature, his pragmatic approach tries to justify our following the strict rule of induction as a wager: by behaving in that way we are choosing the dominant option, given the cognitive payoffs involved.
3. Reichenbach's frequentist approach to probability and his endorsement of the law of large numbers; Reichenbach's view of the strict rule of induction as a means to ascertaining probability on the basis of evidence; Reichenbach's view of the conclusion of an induction as a posit concerning the value of a probability.
5. Analysis of the structure of Reichenbach's pragmatic argument. Reaching a decision concerning its soundness depends upon the justification given for the payoffs associated with each wager and the way the world might be. There is a case that reveals itself to be problematic: the ascription of a negative payoff to the option of following any kind of inductive method of inference under the supposition that Nature is not uniform. Reichenbach's argument for justifying such an ascription.
6. Criticism of Reichenbach's argument for justifying the ascription above: it fails to establish the conclusion it purports to establish.
7. Criticism of Reichenbach's pragmatic solution to the problem of induction: it is based on our accepting as adequate the ascription of a negative payoff to one of the possible options; but the adequacy of such an ascription was not properly established; thus, the structure of the payoffs defining the wager cannot be accepted to be appropriate.
The problem of Induction - 5
22 Março 2022, 09:30 • António José Teiga Zilhão
Inductivist Attempts at Solving the Problem of Induction - 2.
C. The Proposal of the Reliabilists
1. Distinction between different types of circularity: premise circularity vs. rule circularity.
2. Arguments falling prey to premise circularity are invalid (e.g., petitio principii); arguments falling prey to rule circularity needn't be. The inductivist argument justifying induction exhibits rule circularity but not premise circularity.
3. Examples of valid arguments involving rule circularity and of invalid arguments involving rule circularity; what distinguishes them is the validity or invalidity of the rule being used in the inference. Rule circular arguments containing valid rules of inference are valid; rule circular arguments containing invalid rules of inference are invalid.
4. Therefore, if the Rule of Inductive Inference (RII) is a valid rule of inference, then the inductivist argument justifying induction is a valid argument. Thus, if there is an external justification for RII, the validity of the inductivist argument for induction will be vindicated.
5. Van Cleve: Such an external justification exists - it is the contingent way the world is, and the fact that we are adapted to it, that makes it the case that RII is destined to be a successful rule of inference. Thus, the inductivist argument justifying induction is a valid argument, even though it is not a proper means to justify induction; however, it plays an important epistemic role: it helps enhancing the confidence epistemic agents have in a rule of inference which is destined to be successful. Therefore, it is a good argument.
6. Goldman: Such an external justification exists - given the fact that RII leads us reliably from true premises to true conclusions, it is one of the rules that were selected to be part of the canon of rules of inference that our community of reasoners adopted as the outcome of a process of reflective equilibrium (see John Rawls). Thus, the inductivist argument justifying induction is both a valid argument and a good argument. The rule circularity it involves is moreover not particularly damaging - no non circular process of justifying deductive rules of inference exists, and nobody is bothered by that.
D - Howson's criticism to the reliabilist solution to the problem of induction
1. Goldman's argument has the form of a tu quoque argument; but tu quoque arguments are notoriously fallacious.
2. In fact, it is a failed tu quoque argument: any rule of deductive inference admits being justified by a deductive procedure that does not involve it; it is true that the justification of deduction in general involves a holist or coherentist circularity; but this is a sort of circularity distinct from (and much less damaging than) the rule circularity involved in the inductivist attempt at justifying induction .
3. Any reliabilist attempt at justifying induction is still vulnerable to Goodman-type arguments (e.g., the case involving the classifications 'right', 'wrong', and 'ring').
Assessment - I
15 Março 2022, 09:30 • António José Teiga Zilhão
Definition of the topics and titles of the essays. Some methodological considerations regarding writing. Setting of a deadline for handing in the essays.
The Problem of Induction - 4
8 Março 2022, 09:30 • António José Teiga Zilhão
I. Inductivist Attempts at Solving the Problem of Induction.
A. Max Black's Proposal
1. Tarski's stratified solution to the Liar Paradox.2. Black's adoption of a similarly stratified approach as a means to justify inductive reasoning. Examples of level 1 inductive arguments and level 1 inductive rules; level 2 inductive arguments (having as their object level 1 inductive arguments and rules) and level 2 inductive rules; level 3 inductive arguments (having as their object level 2 inductive arguments and rules) and level 3 inductive rules, etc.3. Black's inductive solution to the problem of justifying induction: the inductive rules at any level k are to be justified by inductive arguments and rules of level k+1; the latter are in turn to be justified by inductive arguments and rules of level k+2, and son on; the stratification has no upper level; thus, no circularity will ever occur.
B. Critical Analysis of Max Black's Proposal
1. Skyrms's criticism: Black's proposal does not justify induction, because any rules of reasoning, no matter how absurd, admit being justified in that very same way.2. Skyrms's proof: counter inductive logic. Counter inductive logic is a patently absurd form of reasoning; however, its stratified structure, similar to the one described by Black, enables us to counter inductively justify its counter inductive rules, without ever falling prey to any sort of circularity.3. Skyrms's conclusions: i) If the following of a specific procedure enables us to justify any rule of reasoning, then the following of such a procedure enables us to justify no rule of reasoning; ii) Not falling prey to circularity is a necessary condition for the acceptance of a justificatory procedure; but it is not a sufficient condition for such an acceptance.
1. Tarski's stratified solution to the Liar Paradox.
2. Black's adoption of a similarly stratified approach as a means to justify inductive reasoning. Examples of level 1 inductive arguments and level 1 inductive rules; level 2 inductive arguments (having as their object level 1 inductive arguments and rules) and level 2 inductive rules; level 3 inductive arguments (having as their object level 2 inductive arguments and rules) and level 3 inductive rules, etc.
3. Black's inductive solution to the problem of justifying induction: the inductive rules at any level k are to be justified by inductive arguments and rules of level k+1; the latter are in turn to be justified by inductive arguments and rules of level k+2, and son on; the stratification has no upper level; thus, no circularity will ever occur.
B. Critical Analysis of Max Black's Proposal
1. Skyrms's criticism: Black's proposal does not justify induction, because any rules of reasoning, no matter how absurd, admit being justified in that very same way.
2. Skyrms's proof: counter inductive logic. Counter inductive logic is a patently absurd form of reasoning; however, its stratified structure, similar to the one described by Black, enables us to counter inductively justify its counter inductive rules, without ever falling prey to any sort of circularity.
3. Skyrms's conclusions: i) If the following of a specific procedure enables us to justify any rule of reasoning, then the following of such a procedure enables us to justify no rule of reasoning; ii) Not falling prey to circularity is a necessary condition for the acceptance of a justificatory procedure; but it is not a sufficient condition for such an acceptance.