So, What Do We Know?

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.

Why worry about knowledge?  This woman is a witch.  Swans are white.  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.

Escaping our prejudices  The danger of bad theories is that they reject counter-evidence.  (E.g., the Freudian will maintain that lack of evidence of sexual desire is repression of the desire.)  But if we are willing to give up any belief, then we will not be permanently trapped (“fallibilism”).

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.

Falsificationism’s flaws Recall the criticisms of falsificationism: 1) It offers no confirmation that theories are true. 2) 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.

But where’s the knowledge? 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?

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 predict in a more formal way, models are theories.

Maps as models

Theory confirmation  We use theories to make predictions. When predictions are true, it confirms (to some degree) a theory. This just means the theory is applicable to (parts of) the world.  A theory should also explain why its predictions are true. It should give a model or mechanism to explain its predictions, which can be observed or used to make further predictions.

Theory revision and rejection  Sometimes falsifying 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 ignored. We say the theory is applicable in some cases, but not in others.  If it is not applicable, makes claims unsupported by experience, and other theories make better predictions, the theory will be rejected as false.

Modifying and rejecting theories  We theorize by abstracting from experience.  True predictions confirm a theory’s range of application.  False predictions lead us to:  Revise the theory to fit experience (add to the map)  Limit the range of application (differences don’t matter)  Explain the apparent falsity as due to a limit of human perception  False predictions that can’t be so explained and aren’t supported by experience, imply the theory is false, even as an abstraction.

Two models of the solar system Ptolemy’s model accounts for the moving planets, sun, and stars by saying they revolve around the Earth every 24 hours. Copernicus’s model accounts for this by saying the Earth rotates every 24 hours.

Good theories hint at truth  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 know we have to reject or change them, or keep searching.  Science is based on experience, and is frequently reliable, which is unlikely if it wasn’t true in some ways.

So what is math?  Conventionalism: mathematical truths are consequences of human agreements.  Mathematical Realism: mathematical truths are objective; they do not depend on human conventions.

Mathematical Realism The mathematical realist 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 by direct intellectual intuition.

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.).

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

The causal argument vs. realism  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.

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.

Solution: math is a theory, too  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.

Mathematics as a model  Euclidean geometry is a model of points, lines and space that is clearly 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 mostly flat surfaces.  So it’s not surprising that math is objective and often true about the world: it is a simplification of the world. We don’t need to posit a metaphysical Platonist heaven to explain math’s universal applicability.

So, what do we know?  So let’s return to the original problem: how do we know that there is an external world, or other minds? All the rest of our knowledge depends on basic beliefs like those.  And how should we define knowledge?

Skepticism as a theory  We could 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 External World Hypothesis (EWH).  Which is the better theory?

BIVH vs. EWH  Consider a simple datum to explain: you see a ball rolling.  The EWH 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.)

BIVH vs. EWH  The BIVH explains: something we never see (the Demon, or the extraterrestrial virtual 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 model of the experience “I see a ball rolling”?

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

The superiority of the EWH  But the EWH stands up to whatever tests we propose.  The BIVH, by contrast, explains nothing about our observations, and makes no predictions other than what the EWH predicts. It also postulates something in addition to experience, that we have no evidence of (the Vat).  So we can regard the external world and other minds as an extremely coherent, useful, and unfalsified theory, even if we can’t prove it.

Realism as the Background  We may go further and suggest that the EWH 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.

Realism as our most basic theory  Giving up external realism would disrupt all our beliefs about the world.  This is not to say that the external world is proven. It is a basic metaphysical assumption. If we “woke up” and saw the Vat, and experienced further falsifying experiences, we would eventually reject the external world.  We would need good reason to do so, though. Until that happens, we have no reason to doubt our animal faith in external realism and other minds.

The Causal Theory of Knowledge  An internalist claims knowledge must be justifiable in reasons that the believer is able to be conscious of.  An externalist claims that knowledge depends on having a reliable causal connection to whatever makes a belief true, even if that connection is unknown to the believer (“outside the believer’s mind”).

Externalism (The Causal Theory of Knowledge)  Externalists replace justification (giving reasons) with reliable causation (what happens to make you believe it).  A “reliable cause” would be one that almost always causes true beliefs.  The believer doesn’t have to understand how knowing causes true beliefs. Example: you may recognize a musical key without being able to explain it, or distinguishing twins.

A challenge for the externalist  While externalism promisingly solves regress and Gettier problems, it raises a puzzle of its own: what if a person doubts their own reliably caused beliefs?  Suppose a doctor has a real causal ability to recognize illness. But she dismisses it because she doesn’t want to risk a patient’s life on her hunch. Isn’t knowing supposed to guide action?

A causal theory of knowledge  Knowledge consists of true belief plus a cause-effect connection between the situation in the world that makes it true and the belief (externalism).  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.  I may have false beliefs caused by some stimuli (“illusions”). Those aren’t knowledge.

Naturalized epistemology  Theories of knowledge must fit our best psychological and biological theories about human cognition.  This helps to explain the cause-effect 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).

So what good is skepticism?  It reminds us that the vast majority of belief depends at least partially on theories, and that appeals to facts often hide theories and errors.  Someone without dogmatic beliefs is less likely to do terrible things, and more likely to consider counter-evidence and change their minds.  Lots of important philosophy, math, and science has been developed in response to skeptical challenges.  (82% of philosophers are realists about the external world, 5% skeptics, 4% idealists, 9% “other.”)