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Science news… A virtual plunge into a black hole

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Science news… A virtual plunge into a black hole

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  1. Science news…A virtual plunge into a black hole

  2. Background to Hempel • Early model in the philosophy of science • Scientific hypotheses are arrived at by induction • Inter-subjective experience • The universality of logic • Their testing involves deductive reasoning • But the problem of induction… • “Rules” guiding inductive reasoning • Many observations • Variety of observations • No exceptions

  3. New approach: Distinguishing between the contexts of discovery and justification • Context of discovery • The reasoning involved in the discovery of hypotheses or theories. • Inductive? Creative? Luck? Synthesis…? • Any such account should be compatible with the history and current practice of science. • Context of justification • The reasoning involved in the testing of hypotheses or theories. • Deductive, inductive, or something else? • Any such account should be compatible with the history and current practice of science.

  4. “Narrow” (or naïve) inductivism Collect facts → Categorize them → Generalize to a hypothesis → Test the hypothesis Hypothesis Induction Deduction Facts Facts

  5. Hempel: The logic of confirmation Ignaz Semmelweis “The savior of mothers” In 1847, identified “putrid” material and bad hygiene on the part of medical practitioners as implicated in childbed fever His findings were rejected by the medical community He suffered a nervous breakdown and was institutionalized Death reported as a suicide; turned out to be murder

  6. Hempel’s inductivism (scientific reasoning is inductive in a “wider sense”) • The identification or recognition of a problem (something to be explained) • Consideration or generation of hypotheses Consideration: are proposed hypotheses compatible with other things we know? Generation: creativity, accidents, luck… NOT induction or any other logical process • Choosing one or more hypotheses to test (figuring out how…) • Tests • Confirmation or falsification

  7. Hempel’s inductivism (scientific reasoning is inductive in a “wider sense”) • The identification or recognition of a problem: Childbed fever Why the rates were much higher in Division One than in Division Two of the same hospital? (In a sense providing a “natural experiment”) • Consideration or generation of hypotheses Telluric influences, crowding, diet, examination techniques, dread caused by the priest, delivery position…?

  8. Hempel’s inductivism • If childbed fever is caused by telluric influences, women in both divisions should contract it at equal rates, as should women who deliver in home or in the street. • Women who deliver in the second division, as well as women who deliver at home and in the street, do not contract childbed fever at the same rate as those in the first division ---------------------------------------------------- So, childbed fever is not caused by telluric influences.

  9. Hempel’s inductivism The diets are the same in the two divisions Midwives in the 2nd division use the same examination techniques as med students in the 1st division It’s not due to overcrowding in the 1st division, as it is the 2nd that is overcrowded

  10. Hempel: The logic of confirmation • If childbed fever is caused by dread brought on by the priest bringing last rites (here the 2 wards differ), then changing the priest’s route so women in the 1st division don’t see him will result in a drop in cases. • The priest’s route is changed. • There is no drop in cases ---------------------------------------------------- Childbed fever is not caused by dread brought on by the priest bringing last rites.

  11. Hempel: The logic of confirmation • If childbed fever is caused by a woman’s position in delivery (here the 2 wards differ), then changing women’s positions in the 1st division should lead to a drop in cases. • Women’s positions in the 1st ward are changed. • There is no drop in cases ---------------------------------------------------- Childbed fever is not caused by delivery position.

  12. Hempel: The logic of confirmation • Semmelweis arrives at his first confirmed hypothesis because of an accident … the poisoning of a surgical colleague whose skin was punctured by a scalpel during an autopsy. • Why think of cadaveric material as a likely cause? • His illness was directly parallel to that of women who died of childbed fever. • More importantly, only women in the first division were examined by medical students directly after the students performed autopsies… and did not wash their hands.

  13. Hempel: The logic of confirmation • If childbed fever is caused by cadaveric material, then if medical students wash their hands in a solution of chlorinated lime, there will be a drop in the number of cases. • Medical students wash their hands in the solution. • There is a drop in cases of childbed fever. ---------------------------------------------------- So, childbed fever is caused by cadaveric material.

  14. Hempel’s initial schema of the logic of confirmation • If H, then I1, I2… and In • I1, I2… and In ----------------------------------- • H Why is this form of argument inductive? • However many confirmations the hypothesis enjoys, these are finite in number, and can only show that some hypothesis – which is a generalization or universal statement – is probable.

  15. Hempel’s first schema of the logic of confirmation • If H, then I1, I2… and In • I1, I2… and In ----------------------------------- • H • Confirmation of cadaveric material… • But it turns out, cadaveric material is not the ultimate cause of childbed fever and Semmelweis’ initial hypothesis is wrong • As Semmelweis and his students discovered through a gruesome “experiment” • Any “putrid” (infectious) material will cause the fever and death.

  16. Hempel on the problems of confirmation • Yes, confirmation can only demonstrate the probability of a hypothesis But every positive test is one which opened the possibility that the hypothesis would be falsified. The more confirmations a hypothesis enjoys, the more warranted we are in (provisionally) accepting it as the basis for further research. • Moreover deductive logic has its limits as well… Even in mathematics or formal logic, deductively valid arguments or “proofs” do not themselves dictate any specific conclusion: indeed, an infinite number of results will follow logically.

  17. Hempel on the problems of confirmation • Moreover deductive logic has its limits as well… Even in mathematics or formal logic, deductively valid arguments or “proofs” do not themselves dictate any specific conclusion: indeed, an infinite number of results will follow logically. In logic, for example, we can prove the following: P --- P or Q (‘or’ is inclusive in logic – at least one is true) And from ‘P or Q’, we can prove ‘P or Q or R’…

  18. Hempel on the problems of confirmation • Moreover deductive logic has its limits as well… Consider the deductively valid argument form of the logic of falsification (Modus Tollens) If P, then Q or If H, then I Not Q Not I --------------- -------------- Not P Not H

  19. Hempel on the problems of confirmation Imagine that the experiment went differently: • If childbed fever is caused by cadaveric material, then if medical students wash their hands in a solution of chlorinated lime, there will be a drop in the number of cases. • There is not a drop. ---------------------------------------------------- • Childbed fever is not caused by cadaveric material … but should we conclude that? After all, there were good reasons to believe it was.

  20. The logic of falsification • If childbed fever is caused by cadaveric material, then if medical students wash their hands in a solution of chlorinated lime, there will be a drop in the number of cases. • What might we ask? • Did the medical students wash their hands? • Did they wash their hands after examining each patient? • Was the solution strong enough? • Does chlorinated lime kill whatever it is that cadaveric material contains and causes childbed fever?

  21. Hempel: Getting a better understanding of the logic of testing • It is never just H that yields the prediction I • Auxiliary assumptions such as • Ceteris paribus (all things being equal) • I’ve identified all the variables that might affect the outcome of the experiment • Lime solution can kill the infectious agents that cause childbed fever… Students washed their hands… • [If (H & A1) &(A2… and An)] then I. • Not I --------------------------------------------- Not (H & A1) &(A2… and An)

  22. Complications in the logic of testing • It is never just H that yields the prediction I • A historical case. • Tycho Brahe reasoned: • If the Copernican hypothesis is true, then we should observe stellar parallax (a change in the angle of a given star to an observer as the earth moves). • We do not observe stellar parallax. ------------------------------------------------------ So, the Copernican hypothesis is false.

  23. Complications in the logic of testing • If the Copernican hypothesis is true, then we should observe stellar parallax (a change in the angle of a given star to an observer as the earth moves). A The stars are close enough that stellar parallax would be seen by the naked eye. • We do not observe stellar parallax. ------------------------------------------------------ So, not (H and A)!

  24. Getting a better understanding of the logic of testing • It’s also not just H and auxiliary assumptions that are at work • We must also assume “initial conditions” • I is really shorthand for “If C, then E” where ‘C’ symbolizes ‘initial conditions’ and ‘E’ symbolizes an event or outcome. If H & [(A1& A2)… and An], then [If C, then E] Not E --------------------------------------------- Not [(H & A1) & …] OR Not C. Not C: the medical students did not wash their hands…

  25. Back to the “logic” of discovery Hempel cites examples, such as Kekule’s discovery of the structure of the Benzene molecule, as evidence that there is no logic to discovery (nor given testing need we worry about that) Other examples that support him: Alfred Wallace, who also came up with natural selection as a mechanism that allows evolution, arrived at the hypothesis during a fever induced by Malaria… And then, there’s Kepler…

  26. Back to the “logic” of discovery And then, there’s “poor Kepler”… Johannes Kepler (1571-1630) Who wrote in his notebook: “I have seen Mars and it is square and brightly colored”

  27. Revisiting discovery • Wasn’t there a logic to Semmelweis’ reasoning? • Problem → Consider hypotheses → Reject those incompatible with other things we know → Devise tests of those that survive the first round → Accept or reject on the basis of success or failure of predictions → Revise or abandon hypotheses earlier confirmed if new evidence warrants it… • Sometimes, “accidents” only lead a well prepared mind to a hypothesis…

  28. Popper: the logic of falsification • There is no “principle of induction” that will justify induction or an inductivist account of scientific method/reasoning • Like Hempel, Popper emphasizes that there is no logic of discovery, but only a logic of justification (testing) • But, unlike Hempel, Popper argues that the important logic involved in justification or testing is deductive and, specifically, the logic of falsification (Modus Tollens).