Download Logical Testing of Cause and Effect in Macroeconomics: Necessity and Sufficiency - Prof. L and more Exams Introduction to Macroeconomics in PDF only on Docsity! EC132 Macroeconomic Principles Woods College of Advancing Studies, Boston College 1.09a Mechanics of “Truth:” Logical Negation and Logical Affirmation Professor Ware Page 12 Draft: 6-Sep-04 Printed: 15-Sep-04 EC132 Handout 1a 1.09a Cause and Effect: EC132 Handout 1.09 outlines three Methods of Science by which ordinary mortals can discover, explain, and verify real world relations between things claimed as an Antecedent Cause (of sorts) and things claimed as a Consequent Effect. Relations between Cause and Effect can be expressed efficiently in the form of a Hypothetical (If- Then) Syllogism, as shown in (1) below. As an example, Syllogism (2) identifies a Necessary Condition (Only If) and a Sufficient Condition (If) under which an antecedent common cold virus, CCVirus, is linked to a consequent common cold, CommonCold: SUFFICIENT NECESSARY Empirical Probability 0 < P( ) < 1 CONDITION CONDITION ↓ ↓ Antecedent → → → → Consequent (1) If and Only If Cause Then Effect (2) If and Only If CCVirus Then CommonCold Logical Negation: The “truth” of the relation claimed in syllogism (2) is tested in two ways: First, Logical Negation tests the claim of the Necessary Condition -- that only if a CCVirus enters the body will a CommonCold result. This is summarized in experiment (3) below where CCVirus is actually kept outside the body (antecedent denied) and research shows that a CommonCold never occurs (consequent false). This result is taken as “proof” that CCVirus is necessary to a CommonCold (a triumph for scientific research!). On the other hand, as summarized in (4), if CCVirus is actually kept outside the body (antecedent denied), but a CommonCold happens anyway (consequent true), then CCVirus cannot claim to be necessary for a CommonCold (another triumph for scientific research!) NECESSITY Test NECESSITY: Deny Antecedent, Observe Consequent ↓ Antecedent → → → → Consequent Relation is: Only If CCVirus» Then CommonCold (3) Denied and Actually False → Necessary P( ) = 1 (4) Denied and Actually True → → NOT Necessary Logical Affirmation: The second test involves an Affirmation of the Sufficient Condition claimed in (2) above -- that if a CCVirus enters the body, then a CommonCold will result. This test is summarized in (5) and (6) where a CCVirus actually enters the body (antecedent affirmed). Suppose, as a result, a CommonCold results (consequent true). Then CCVirus can rightly claim to be sufficient for a CommonCold. This can be taken as “proof” -- at some probability, 0 < P( ) ≤ 1 -- that CCVirus is a “cause” of a CommonCold (science triumphs again!). If a CommonCold does not result (consequent false), then CCVirus cannot claim to be sufficient to “cause” a CommonCold: SUFFICIENCY Test SUFFICIENCY: Affirm Antecedent, Observe Consequent ↓ Antecedent → → → → Consequent Relation is: If CCVirus Then CommonCold (5) Affirmed and Actually True → Sufficient 0 < P( ) ≤ 1 (6) Affirmed and Actually False → NOT Sufficient Logical Nonsense: Note that only the antecedent of a hypothetical syllogism is subject to a process of negation or affirmation. The consequent is simply dragged along for the empirical ride. This is consistent with the underlying scientific claim expressed by the syllogism -- that antecedent cause somehow produces consequent effect, not the other way around. Attempting the opposite -- affirming the truth of the consequent and claiming that this proves the truth of the antecedent -- leads only to indiscriminate nonsense, since this approach permits anything to be claimed (and, therefore, anything to be proven to be) necessary and/or sufficient to any other empirical event or datum in the real world.
