Conditional Arguments (cont.), Confirmation and Falsification. Phil 12: Logic and Decision Making Winter 2010 UC San Diego 1/13/2010

Transcription

1 Conditional Arguments (cont.), Confirmation and Falsification Phil 12: Logic and Decision Making Winter 2010 UC San Diego 1/13/2010

2 Review: Conditional Arguments Valid argument forms using conditionals: If A, then B!!!! If A, then B A!!!!! Not B!B!!!!!!Not A Modus ponens!!! Modus tollens

3 Invalid conditional arguments Not all arguments starting with conditional statements are valid Consider the following: XIf A, then B Denying the Antecedent Not A!! Not B INVALID Remember, to be valid, argument must be such that if the premises were true, the conclusion would also have to be true Suppose the premises are true. Must the conclusion be true? No. Both B and not B are compatible with the premises There is no valid argument here!

4 Invalid conditional arguments What about this: If XA, then B B!! A Affirming the Consequent INVALID If the premises are true, must the conclusion be true in this case? No. Both A and Not A are compatible with these premises There is no valid argument here either!

5 Review: Conditional Arguments Valid argument forms: If A, then B!!!! If A, then B A!!!!! Not B!B!!!!!!Not A Modus ponens!!! Modus tollens Invalid argument forms: If A, then B!!!! If A, then B Not A!!!! B!!Not B!!!!!!A Denying the antecedent! Affirming the consequent

6 Clicker question 1 What form does this argument have? I know I passed since I took the test, and if I took the test, I passed. A. Modus ponens B. Affirming the consequent C. Modus tollens D. Denying the antecedent

7 Clicker question 2 What form does this argument have? When it rains in San Diego, it snows in Julian. It is snowing in Julian, so it is raining in San Diego. A. Modus ponens B. Affirming the consequent C. Modus tollens D. Denying the antecedent

8 Clicker question 3 What form does this argument have? The color will not turn blue because the temperature did not rise and we know that if the color turns blue, the temperature rises. A. Modus ponens B. Affirming the consequent C. Modus tollens D. Denying the antecedent

9 Reasoning with AND, OR, and NOT A very commonly used valid argument form is the following: Either A or B Not A! [or Not B]! B! [or A]! Alternative Syllogism VALID A common reasoning strategy: start with an exhaustive set of alternatives eliminate all but one conclude that the remaining one is true

10 Representing confirmation and falsification A key feature of scientific reasoning is to confirm or falsify a hypothesis based on the truth or falsity of a prediction We re going to explore how to best characterize the reasoning involved in: falsification (today) confirmation (on Friday) Each seems straightforward, but there are hidden complexities to both

11 The apparent simplicity of showing a hypothesis to be false The initial intuition: a hypothesis is false if a prediction derived from it is false: If the hypothesis is true, then the prediction is true The prediction is not true! The hypothesis is not true Apply this to Halley: Conditional premise: If Halley s comet hypothesis is correct, his comet will reappear in December, 1758 Had his comet not appeared, people would have concluded that his hypothesis was wrong. Argument form: Modus tollens. So it is valid The question is whether the premises are true

12 A compelling simple example of falsification Where do plants get their body mass from? Natural assumption: from the soil In 1649 Jan Baptista van Helmont grew a willow tree for five years in a measured amount of soil, adding only water. The tree increased in weight by 164 pounds The soil diminished by only two ounces. If soil is the source of the mass of trees, then the weight of the soil should diminish as the tree grows. The weight of the soil does not diminish as the tree.!the soil is not the source of the mass of trees.

13 Galen (2nd C): Two bloods According to Galenic physiology, arteries and veins each carried different types of blood away from the heart Venous blood carries nutrients from the liver through the right side of the heart to the body Arterial blood is vivified by the lungs and carried from the left side of the heart to the body Slight seepage from right to left Heart operates to suck blood in from the veins (and ultimately from the liver) Both types of blood are consumed by the body s tissues

14 William Harvey s ( ) evidence against Galen Determined that the valves in the veins would only permit flow into the heart, not out But the Galenic theory predicted that blood could flow away from the heart in the veins If the Galenic theory were right, valves should permit outward flow from the heart into the veins Valves do not permit outward flow from the heart!the Galenic theory is wrong

15 William Harvey s evidence against Galen 2 An assumption of the Galenic theory is that all the contents of arterial and venous blood originate in food and is dispersed Prediction: the mass of food and drink must equal the mass of the material in the arterial and venous blood Harvey measured the amount of blood in the heart at a time (approx. 2 ounces) and multiplied by number of heart beats an hour (2,000), estimated that 40 pounds of blood sent out per hour This exceeded the amount of food and liquid a person consumes and where does it all go? If Galenic theory is true, people need to replenish the stuff of blood from food and drink People do not eat or drink enough to replenish the stuff of blood! Galenic theory is false

16 Holding on to hypotheses despite falsification It is infrequent that a scientist will give up a hypothesis as soon as a prediction fails. Why? An accepted hypothesis often has lots of evidence it its favor things it explains Even a flawed hypothesis is better than no hypothesis Without an alternative theory, stay with what has worked so far There are also other factors involved in deriving a prediction from a hypothesis that can be blamed for a failed prediction...

17 The gap between hypothesis and prediction Few interesting hypotheses lead to predictions all on their own. Other factors involved in deriving a prediction from a hypothesis: Auxiliary assumptions/hypotheses that are assumed to be true and required to make the prediction Features of the observational or experimental design that affect the prediction

18 Blaming auxiliary hypotheses Newton s theory of motion predicted a certain orbit for Uranus, which was discovered in 1781 Auxiliary hypothesis: there were no other massive objects interfering with Uranus Observation: Uranus didn t move as predicted. Two ways of handling this evidence: Blame the main hypothesis: Newton s theory was mistaken Blame the auxiliary hypothesis: there was another massive object perturbing the orbit this turned out to be the planet Neptune, discovered September 1846

19 Case of parallax Copernicus heliocentric theory of the solar system predicts we should observe parallax at different times of year a planet ought to appear at a different position against the fixed stars But parallax was not observed up through early 19th C If the earth is revolving around the sun and if all other auxiliary assumptions are true, then parallax should be observed. Parallax is not observed.! Either the earth is not revolving around the sun or one of the other assumptions is false.

20 Case of parallax Auxiliary assumption: distance to the planets is relatively short If planets are further away than expected, parallax will be very small perhaps undetectable given current experimental procedures parallax finally detected in 1838 If the earth is revolving around the sun and if all other auxiliary assumptions are true and the experimental procedure is adequate, then parallax should be observed. Parallax is not observed.! Either the earth is not revolving around the sun or one of the other assumptions is false or the experimental procedure is inadequate.

21 How to handle false predictions If the hypothesis is true AND all auxiliary hypotheses needed to make the prediction are true AND the experimental setup is adequate, then the prediction will be true The prediction is not true!!!! Either the hypothesis is false, or an auxiliary hypothesis is false, or the experimental setup is not adequate. Challenge: When to reject one of the auxiliary hypotheses or the experiment, and when to reject the main hypothesis?