So, What Do We Know?

1. So, What Do We Know?

2. The skeptical worry • We might worry that our most central beliefs are false. • Because the false beliefs are central, many of our other beliefs will depend on them and may also be false. • Worse, because of their centrality, we will dismiss counter-evidence. • We will have many false beliefs and will never realize we are wrong.

3. Why worry about knowledge? • This woman is a witch. • Bleeding cures fevers. • The earth does not move. Or more generally: • People waste money on scams • People buy quack cures • People stubbornly stick to being wrong • People are biased, prejudiced, etc.

4. Falsification strategy • So when should we accept beliefs? • If they explain our experience, and • If they withstand vigorous attempts to find evidence against those beliefs. • We should reject beliefs that fail the test of experience.

5. Escaping our prejudices • The danger of bad theories is that they reject counter-evidence. • (E.g., the believer in Sathya Sai Baba will say that his powers are beyond science.) • But if we are willing to give up any belief, then we will not be permanently trapped.

6. Fallibilism Fallibilismis the view that any belief couldbe false, even those supported by seemingly good reasons. (Charles S. Peirce: 1839-1914)

7. Fallibilism vs. skepticism • By admitting that we could be wrong, the fallibilist hopes to avoid both dogmatism and skepticism. • Dogmatism is avoided, since any belief could be false. • Skepticism is avoided, as the fallibilist is willing to bet on claims being true. But the fallibilist is never certain.

8. Example: Cartesian Doubt • A fallibilistcould be wrong about there being a world. We could all be in a demon’s delusion, or a Matrix-like computer simulation. Call this the Brain-in-a-Vat Hypothesis (BIVH). • Call the common sense alternative, the Real World Hypothesis (RWH). • Which is the better theory?

9. BIVH vs. RWH • Consider a simple datum to explain: you see a ball rolling. • The RWH explains: it’s a round solid object, and such things roll over flat solid surfaces. (If we wanted, we could be a lot more precise, in terms of physics.)

10. BIVH vs. RWH • The BIVH explains: something we never see (the Demon, or the extraterrestrial artificial reality) makes illusions (that look like round solid objects) do something (that looks like rolling) with other illusions (that look like flat solid surfaces). • Is this a better explanation of the experience “I see a ball rolling”?

11. BIVH vs. RWH • The BIVH explains nothing more than the RWH does. Since it doesn’t explain why the Matrix-World operates in the same way that the Real World does, it fails as a theory. • (Why do illusory balls illusion-roll on illusory flat surfaces?) • There’s no gain to believing BIVH.

12. The superiority of the RWH • But the RWH stands up to whatever tests we propose. • The BIVH, by contrast, explains nothing about our observations, and makes no predictions other than what the RWH predicts, so it is unfalsifiable. • So the fallibilist bets on the real world existing, even if we can’t give reasons for it and so don’t know it.

13. Realism as the Background • We may go further and suggest that the RWH isn’t a hypothesis so much as it is a framework for hypotheses. • That is, to form a hypothesis, you assume there is a way things are. • You can’t “debate” an external world without presupposing there is an external world. • It is not a belief, but the basis for all other beliefs: the Background.

14. Realism • Giving up external realism would disrupt all our beliefs about the world. • Which is not to say that the external world is indubitably true. If we “woke up” or kept seeing the Vat, we would eventually reject our Background. • We would need good reason to do so, though. Until that happens, we have no reason to doubt external realism.

15. Hidden assumptions • We need to be cautious since sometimes our background beliefs lead us to deny counter-evidence. • For example, the doctors in Vienna dismissed Semmelweis’s germ theory because of background beliefs (“invisible things can’t make you sick”).

16. Hidden assumptions • Or we might discount evidence that a family member committed a crime because of a strong background belief (“he wouldn’t do that; he’s my brother”). • By contrast, a stranger (like a juror) looking at the same evidence might think the evidence strong.

17. Hidden assumptions • To counter our biases, we must test our background beliefs. • The effectiveness of antiseptic washing at reducing puerperal fever changed the background belief that invisible things couldn’t cause diseases. • We can counter optical illusions.

19. Changing background beliefs • By discovering a genetic or neurological basis for alcoholism or mental illness, we can change our background belief that the alcoholic chooses to be an addict, or that the insane choose to be crazy. • Or we can discover background beliefs with experiments.

20. David Williams’s pain studies • A person’s perception of pain doesn’t necessarily depend on the intensity of the stimulus. • The 40 people who were tested waited longer to say “stop” when a woman was causing the pain than when a man was.

21. David Williams’s pain studies … he measured a subject’s pain threshold.  Then he told the subject that there was no need to say “stop” because he already knew exactly how much the subject could take.  When people were denied control, they felt the hurt as more intense.

22. But where’s the knowledge? This fallibilist model of knowledge still doesn’t give us much confidence about knowing anything. Given how strongly our theories can influence us, how do we know what we call “false” isn’t the result of (other) hidden assumptions or false biases? Scientific theories have changed over time. Why think science gives truth?

23. Falsificationism’s flaws Recall the criticisms of falsificationism: • It offers no confirmation that theories are true. • It can’t definitively falsify theories, because an apparently falsifying observation may be due to another hypothesis or assumption, rather than the one being tested.

24. Theory revision and rejection • There are degrees of disconfirmation. • Sometimes disconfirming observations lead to revising a theory. These may be ad hoc revisions (changes that have no application other than to save a theory from falsification). • Sometimes they will be puzzles. • Sometimes they will be ignored. • If there are enough, at some point the theory will lose support and collapse.

25. Theory confirmation • A theory should predict and find observations that would be unlikely, unless the theory is true. • A theory should also understand how and why its predictions are true. It should posit a model or mechanism to explain its predictions. That goes against instrumentalism, and support scientific realism.

26. Progress in science • There is continuity in knowledge: new scientific theories include old theories as special cases. (Einstein’s theory includes Newton’s at low velocities.) • Scientific theories don’t contradict each other. When they do, we reject or change them. • Science is frequently accurate, which is unlikely if it wasn’t broadly true.

27. Theories as models • We take some parts of experience as more important than others, and we reason from those parts as if they were all that mattered. Doing this is abstracting from experience. • When we say that what we’ve ignored doesn’t matter in drawing conclusions, we are reasoning by abstraction. • Models are such abstractions. When we use them to explain or predict, models are theories.

28. Maps as models

29. Theory application • We create theories by abstracting from our experience. • True predictions from a theory confirm a range of application of the theory. • False predictions from a theory lead to: • Modify the theory to fit • Restrict the range of application • Explain the anomaly as due to a limit of human perception • False predictions that can’t fit those lead us to abandon the theory.

30. Two models of the solar system Ptolemy’s system accounted for the motion of the sun, the planets, and the stars by saying they revolved around the Earth every 24 hours. Copernicus’s system accounted for these motions by saying the Earth rotated around its axis every 24 hours.

31. So how do we know math? • Conventionalism: mathematical truths are consequences of human agreements. • Mathematical Realism: mathematical truths are objective; they do not depend on human conventions.

32. Mathematical Realism The mathematical realist (or “Platonist”) claims: • Abstract objects exist (objects that do not change and are not in space or time). • Mathematical truths are true or false depending on these abstract objects. • Mathematical knowledge is knowing these objects and their relations.

33. Why be a Platonist? • Math is objective. • But where are the objects of math? • Platonism explains why mathematical truths never change, are necessary and universal, are not observable, but are not mind-dependent. • It explains how there can be truths about physically impossible objects (infinite sets, complex numbers, etc.).

34. Conventionalism • The conventionalist points out that we do not use observation or experience to do math. On the contrary, that would make math less clear. • Math is not based on experiment, but on reason alone, on a priori knowledge. That is why it is necessary and universal, but also why it doesn’t add to our knowledge.

35. The causal argument • The conventionalist argues that if realism were true, then mathematical knowledge would be mysterious. • If math is independent of experience, then it is a world disconnected from our senses or the physical world. • But then it cannot be known, if knowledge is causal.

36. Mathematical Realism • The realist, however, is happy to reject the causal theory of knowledge. • Realists say intuition or reason has immediate access to the abstract realm of numbers. • Realists point out that conventionalism implies that we could agree on different mathematical truths, which we can’t.

37. Mathematics as a model • Just as scientific theories are models abstracting from experience, math is the most abstract model. • We abstract from the experience of counting discrete objects to make a model called the natural numbers. • Extensions of these numbers to handle points on lines that can’t be measured as ratios = irrational numbers. Etc.

38. Mathematics as a model • Geometry is a model of points and lines and space that is obviously false: a point has no space, a line has no width. But as an abstraction, we can use it where those differences don’t matter, as in relatively flat surfaces. • So it’s not surprising that math is objective and (when used correctly) is true about the world: it is drawn from the world of objects.

39. So, what do we know? • So let’s return to the original problem: what is knowledge? • Here’s a reasonable model.

40. A causal theory of knowledge • (1) Knowledge consists of true belief plus the “appropriate” connection between the truth and the belief, and (2) we need not know that connection (“externalism”). • Typically the appropriate connection will be a causalconnection, e.g., between the chair and my belief that there is a chair. • I may not know the causal workings that lead from the chair to my eye to my beliefs, but I still know that I see a chair.

41. Epistemology naturalized • Naturalized epistemology: theories of knowledge must fit our best psychological and biological theories about human cognition. • This helps to explain the “appropriate connection” between truth and belief. • Knowledge isn’t internal to the mind of any one person, but consists of causal links in the world (the natural relations of humans to their environment).

42. What good is skepticism? • Someone without beliefs is less likely to do terrible things, and more likely to consider counter-evidence and change their minds. • Lots of good philosophy, math, and science has been developed in response to skeptical doubts. • (82% of philosophers are realists about the external world, 5% skeptics, 4% idealists, 9% “other.”)