Logic in Philosophy of Science: Classical vs. Contemporary Approaches - Prof. William Mich, Study notes of Philosophy of Science

Download Logic in Philosophy of Science: Classical vs. Contemporary Approaches - Prof. William Mich and more Study notes Philosophy of Science in PDF only on Docsity! 1 PHIL250 Kallfelz Lecture2 Page 1 9/4/2007 Argument Forms Relevant to Scientific Reasoning: The Role of Logic in the Philosophy of Science PHILOSOPHY OF SCIENCE’S CHIEF AIMS AND PREOCCUPATIONS (“Classical” 1 ) (“Contemporary” 2 ) Rational Reconstruction Methods, Justification, Of Scientific Theories Reliability of scientific Practice (theoretical, experimental, and all aspects between these “extremes.” • As the terms “rational reconstruction” suggest, “Classical” Philosophy of Science distinguished itself, by and large, as a “Normative” enterprise, i.e. preoccupied primarily with questions concerning what criteria an ideal scientific theory should conform to, as well as the criteria associated with scientific reasoning (suitably idealized). (E.g., Hans Reichenbach (1938 3 ): Philosophers of Science deals with science’s context of justification, not science’s context of discovery.) • Moreover, in its attempt to focus on “rational reconstructions” of domains of science, “classical” philosophers of science tended to strictly demarcate the process versus the products of science. The processes were relegated as part of the (“uninteresting”) context of discovery, which included all steps of scientific procedure prior to the completion of a “textbook-ready” fully developed scientific theory. Conversely, the final products of worthy of study for philosophers of science were the fully-developed (“textbook-ready”) scientific theories. 1 Ca. before the 1980s 2 Ca. 1980 to present 3 Experience and Prediction (Chicago: University of Chicago Press, 1938) 2 IGNORE: FOCUS ON: The “Classical” Conception • Conversely, contemporary Philosophy of Science distinguishes itself (from “Classical”) as being more of a descriptive enterprise, focusing, for instance, on questions concerning the methods, reliability, justification of actual procedures employed by practicing scientists. • This naturally leads contemporary philosophers of science to blur the distinctions between process and product, and resist the division of the philosophical study of science into contexts of discovery versus contexts of justification. This lends itself to a more inclusive picture: contemporary philosophers of science see their field as both a “normative” as well as a “descriptive” enterprise. FOCUS ON: The “Contemporary” Conception LOGIC plays an essential role in the Philosophy of Science (both Classical and Contemporary) “Logic is the science of pure idea, i.e. the idea in the abstract element of reasoning.” -G. W. F. Hegel 4 (1930: p20) 4 Encyclopëdie d. philosophische Wissenschaften im Grundrisse. Zum Gebrauch seiner Vorlesungen (Dritte Ausgabe Oss wald’scher Verlag: Heidelberg, 1830), p.20 Context of discovery: Experimentation, analysis, hypothesis-generation & testing Context of justification’s: “Data” should be final textbook- ready theories Context of “justification’”: Rational reconstruction final textbook- ready theories f discovery: Experimentation, analysis, hypothesis-generation & testing 5 • Note1: Conditional statements (P→Q) play a central role in deductive reasoning. (Note all the different ways a)-e) used to express the same thing…that should tell you its importance!) P (what lies to the left of →) is the antecedent. Q(what lies to the right of →) is the consequent. • Note 2: One speaks of two (or more) propositions as logically equivalent (denoted by the biconditional ↔ or by ≡ in the case of a definition, and expressed as “if and only if” ) when the two (or more) statements are true and false in exactly the same set of conditions. Logical equivalence is constructed from implication and conjunction: P ↔ Q ≡ (P→Q) ∧ (Q→P) • Note 3: It’s wrong to assume logical connectives mean exactly the same thing as their associated ordinary language counterparts “not, or, and,…” (For instance, recall the note above regarding disjunction being inclusive). Another counter- example: In ordinary language we often specify “and” in terms of a specific order, i.e. “Put on your shirt and your sweater” whereas disjunction is commutative (independent of order, i.e. P∧Q ↔ Q∧P. ) Quantifier Symbol Example Existential ∃ x ∈ {cats} M : “meows” ∃x:Mx : a) “Some cats meow” b) “There exists11 a cat that meows” c) “ A cat meows” d) “There is12 a cat that meows” Universal ∀ ∀x:Mx : a) “All cats meow” e) “Any cat meows” c) “ Every cat meows” • Note 4: In the above table, the examples can be expressed more formally by not restricting the (logical) variable x initially to the set of cats, but rather define the predicate C as “being a cat”. Then the first example (“some cats meow,” etc) can be re-written as: ∃x:Cx ∧ Mx , (“There exists an x such that x is a cat and x meows”). The second example can be re-written as a universal conditional: ∀x:(Cx → Mx). In other words, “all cats meow” is logically equivalent to the universal conditional: “For all x, if x is a cat, then x meows.” 11 “There exists” doesn’t imply unique existence (i.e., it doesn’t imply there’s only one cat that meows) 12 See note 11. Again, the discrepancy with ordinary language (recall Note 3 ) appears here as well. “There’s a” is often used ostensively in ordinary language, i.e. when indicating a particular cat. While “there is a” here is purely descriptive, i.e. meowing pertain to one or more cats. 6 • Definition: A proposition that is always true is a tautology (denoted by ┬). A proposition that is always false is a contradiction (denoted by ⊥). Arguments in FOPL • Recall Note 1 discussed above. An argument is an extension of a conditional statement (P→Q) in which the antecedent consists of two or more propositions. To distinguish arguments from ordinary conditionals, one speaks of premises in place of antecedents and conclusions in place of consequents. The simplest kind of argument is the syllogism, which has just two premises. Example: “All integers are real numbers, a is an integer, therefore a is a real number.” ..is an example of a syllogism. Using the abbreviations for predicates N, R to denote the integers and real numbers, respectively, the above can be written in FOPL as: ∀x:(Nx → Rx) Na or ( ∀x:(Nx → Rx)) ∧ Na ├ Ra ∴ Ra ..where the therefore is depicted as a logical consequence from the premises either by the symbol ∴ (if the argument is represented in column-form, as on the left had side) or by the symbol ├ (if the argument is represented in row-form, as on the right had side). I will follow the convention used by the authors in the anthology, by depicting arguments in the (more intuitively appealing) column form. • Recall Agazzi’s quotes above. What distinguishes logic from any old rule-based formal system, is that in logic, the rules must be truth-preserving. In the case of FOPL, this translates into (14) rules of inference 13 , i.e. rules for forming valid arguments. A valid argument is one whose truth of its premises guarantee the truth of its conclusion. (If all its premises are true, then its conclusion is true). A sound argument is a valid argument whose premises all happen to be true. • Note5 : Validity is a necessary feature of logical form, i.e. it’s a property of the machinery of the logic’s rules of inference. Soundness is a contingent feature of logical content. For example, the argument: 13 They are subdivided into: 6 rules of introduction of the connectives ¬, ∧, ∨, →, and the quantifiers ∀, ∃, and 6 rules of elimination of the connectives ¬, ∧, ∨, →, and the quantifiers ∀, ∃, and the additional two rules: EFSQ (i.e., any proposition can follow from a premise list containing a contradiction) and the Double negation rule: for any sentence ϕ: ¬¬ϕ├ ϕ. 7 “All dogs are cats, and all cats are alligators, therefore all dogs are alligators” …is valid! It’s an example of the medievals referred to as a “Barbara” (AAA form categorical syllogism) which today we recognize as transitive reasoning (“All A are B, and all B are C, therefore all A are C” or more formally: ( ∀x:(Ax → Bx)) ∧ ( ∀x:(Bx → Cx)) ├ ( ∀x:(Ax → Cx)) which can be proven rigorously as valid in FOPL using its 14 rules of inference) The argument, however, is clearly unsound (since its two premises are false). • Question: Does FOPL adequately characterize scientific reasoning, or arguments typically made by scientists? • Answer: ABSOLUTELY NOT!
Aside from only acting as some constraint in the most abstract normative discussion of what theories ‘should’ look like when rationally reconstructed, FOPL fails for that matter to even capture the reasoning found in ordinary arithmetic! (As discussed by Gottlob Frege in the 1880s). Recall note 9 above. FOPL can’t quantify over predicates ( i.e. you’re note allowed to say things like: “some property P holds) but both mathematicians and scientists (as well as ordinary lay-people) do this all the time! (Unbeknownst to us, in fact, we usually quantify over arbitrarily many levels or orders. For example, when one utters: “Some tastes for some colors for all shirts…” this is a third-order statement (The first “some” modifies the 3-rd level property “taste”, which in turn modifies the 2 nd -level property “color,” quantified by the second “some”, which modifies the objects “shirts” which are quantified by all.) …But there is a far more basic shortcoming. Ordinary logic is deductive; i.e. conclusions (whether general or particular) are derived from closed sets of premises (whether general or particular) based on a finite and closed set of rules of inference. Science, however, naively conceived, is an activity whose aims obviously include increasingly refined knowledge of the world of phenomena. Essential scientific reasoning, then, though it may involve deduction, is obviously not essentially deductive. (If it were, such a science would presume itself “final” and “omniscient”, undercutting its fundamentally empirical nature. In other words, it would no longer be science!)