Types of ---------------------------------- Arguments So, you - - PowerPoint PPT Presentation

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Types of Arguments

Justin C. Fisher An argument is a set of claims (called “premises”) offered in support of a conclusion.

I said you should go to bed. I’m your mother.

• So, you should go to bed.

Premises Conclusion

An argument’s conclusion is often the most controversial claim in the argument. The job of the premises is to ease people into accepting the

• conclusion. Conclusions are often indicated by

words like “therefore”, “thus”, “hence” or “so.”

What makes an argument good?

Obama has X-ray vision Obama is a martian.

• So at least one martian has X-ray vision.

The premises must be true.

Roses are red.

• So violets are blue.

The premises must support the conclusion.

Three types of arguments/support

Deduction – provides a guarantee that IF the premises are true, then the conclusion must also be true. Induction – generalize from a sample of things, to conclude that some other thing(s) will be like the sample. Abduction (Inference to best explanation) – conclude that the best explanation for some observation(s) is probably true

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Deduction, Validity, and Soundness

Justin C. Fisher Deductively valid arguments come with a guarantee: “if all the premises are true, then the conclusion must be true.”

All A’s are B’s. All B’s are C’s

• So all A’s are C’s.

Note: you can determine whether an argument is valid without knowing whether its premises actually are true. C B A

Obama is a democrat. Many democrats are black.

• Obama is black.

The premises in this argument are true, and the conclusion is true. But, the premises, by themselves, do not guarantee that the conclusion would have to be true. So this argument is Invalid.

Obama is a martian. Obama has X-ray vision.

• So at least one martian

has X-ray vision.

The premises in this argument aren’t true. But, if they were true, then the conclusion would be too. So this argument is valid. To be SOUND an argument needs to both (1) be valid and (2) have only true premises. This argument is UNSOUNd.

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Obama is a martian. Obama has X-ray vision.

• So at least one martian

has X-ray vision.

The premises in this argument aren’t true. But, if they were true, then the conclusion would be too. So this argument is valid. To be SOUND an argument needs to both (1) be valid and (2) have only true premises. This argument is UNSOUNd. An argument can still be valid even if a premise is false! But it can’t be sound. (Every semester students mess this up!)

George flurbs. George is a rogon.

• So at least one rogon flurbs.

Even though we don’t know who George is, what a rogon is, or what it is to flurb, we can still tell that, if the premises are true, then the conclusion must be true. So this argument is valid. But we can’t tell whether or not it is SOUND. F R

George

Make 1 true: Kill off any ugly singers. Make 2 true: (Not too hard.) Make C false: remove Robin’s vocal cords. Since the premises could be true while the conclusion is false, this argument is Invalid.

• 1. All great singers look great.
• 2. Robin looks great.
• C. So Robin is a great singer.

Test #1 for invalidity: Try to imagine a possible way that the premises could be true while the conclusion is false. Substitute “great singer”“female stripper” The resulting argument obviously isn’t valid. So the original argument wasn’t valid either.

female strippers

• 1. All great singers look great.
• 2. Robin looks great.
• female stripper
• C. So Robin is a great singer.

Test #2 for invalidity: Pick a noun/adjective in the argument and substitute in some new noun/adjective everywhere it appeared.

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Premise 1 tells us the great singers are contained within the great lookers. Premise 2 tells us Robin is inside the larger circle. But it doesn’t guarantee that he is also in the smaller circle Invalid.

• 1. All great singers look great.
• 2. Robin looks great.
• C. So Robin is a great singer.

Test #3 for invalidity: Draw the argument as a Venn diagram in such a way that you keep the premises true, but make the C false.

Great lookers. Great singers.

All P’s are Q’s. x is a P. . x is a Q. All P’s are Q’s. x is not a Q. . x is not a P.

P Q

x

P Q x

All P’s are Q’s. x is a Q. . x is a P. All P’s are Q’s. x is not a P. . x is not a Q.

P Q P Q

x

Some common argument forms:

All P’s are Q’s. x is a P. . x is a Q.

All scenarios where P is true are ones where Q is true.

Our scenario is one where P is true. . Our scenario is one where Q is true.

If P then Q P . Q

P Q

x

The arguments below are equivalent in logical form to this

• ne, and are valid for

the same reason.

If P then Q P . Q If P then Q not Q . not P.

P Q

x

P Q

x If P then Q Q . P If P then Q not P . not Q

P Q

x

P Q

x

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Deductive Arguments Can Be Useful

• P1. Every natural event has a preceding cause.
• P2. There can’t be an infinite chain of causes.
• C. So there must have been some event whose cause

was super-natural.

Once somebody puts forward an argument like this, we have just three choices: (1) Say the argument isn’t valid. (2) Reject one (or more) of the premises, or (3) Accept the conclusion. (If we accept that it is valid and has true premises, that would guarantee its conclusion is true.)

A big limitation on valid arguments

A valid argument typically can’t include any concepts in the conclusion that aren’t in the premises. – Premises about how the drug performs in some people can’t guarantee how it will perform in

• ther people. ( induction is more useful)

– Premises about observable things, like how the bulb glows when you connect the wires, can’t guarantee conclusions about the existence of invisible electrons. ( abduction is more useful) It may sometimes help to consider valid arguments, but these arguments won’t be very useful for reaching many positive scientific conclusions.

Induction:

Expecting things you haven’t seen to be like things you have

Justin C. Fisher

Inductive Arguments

A sample of A’s have been B’s.

• So (probably) all A’s are B’s.
• generalize from a sample to other things.
• the conclusion re-uses words/concepts

that were observed to be true of the sample.

• provide only a weak guarantee: “If the

premises are true, then the conclusion is probably true.”

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• P1. We randomly selected 500

voters from Florida.

• P2. A strong majority of our

sample prefer Donald.

• C. So, a strong majority of all

voters in Florida probably prefer Donald too.

Step 1. Find a sample that would be representative of what you want to draw a conclusion about. Step 2. Observe what traits things in your sample have. Step 3. Conclude that

• ne or more other things

will have those traits too.

How to make an inductive argument Assessing Inductive Arguments

How large is the sample?

Would you trust a poll of 10 voters? 10,000?

How representative is the sample? (i.e., how likely is it that the things in the sample would be like the things in the conclusion?)

Poll Kansans to predict how Oklahomans will vote? How about polling New Yorkers?

Was the choice of sample-members biased?

Many polls involve telephone calls to land-lines. This under-represents cell-phone users, people who aren’t home much, people who lack phones.

Induction in Science

– Scientists often presume laws of nature work the same way in all places and times, so experiments at one place and time will generalize to others. – Drug trials can’t guarantee that a drug will work similarly in other people, but they can provide strong reason to think it probably will. However, induction just gives us “more of the same,” just generalized to other places or times. – We still haven’t seen any way for scientists to get from premises about experimental

• bservations to conclusions about something

entirely different, like invisible electrons.

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Abduction:

inference to the best explanation

Justin C. Fisher

Abductive Arguments

(inference to the best explanation)

Flipping the switch turns the light on, and if you rub a balloon on your head, then it will stick to the wall. The theory of electrons predicts these things will happen, whereas other theories can’t explain it.

• So, we should believe in electrons.

The conclusion uses further concepts (electrons) not used in the observations (lights, balloons) that support it. Another loose guarantee: “if the premises are true, then the conclusion is probably true.”

x x x x x x x

Modus Tollens

Observation: The ace of hearts is in her hand. H1: Every card in her hand is black. H2: Every card in her hand is red. H3: Half the cards in her hand are red.

When we make an

• bservation that some

hypothesis completely predicted we would not make, then we should rule out that hypothesis, and shift our credence to competing hypotheses.

The Prediction Principle

Observation O: The ace of hearts is in her hand. H1: Most cards in her hand are black. H2: Most cards in her hand are red. H3: Half the cards in her hand are red.

When we make observation O, we should shift our credence away from whichever hypotheses least predicted O, and towards whichever hypotheses most predicted O.

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The prediction principle

When we make observation O, we should shift our credence away from whichever hypotheses least predicted O, and towards whichever hypotheses most predicted O. Suppose one weather forecaster makes a more accurate prediction than another. You would shift your trust toward the

• ne who made the better prediction

and away from the other. The prediction principle tells you to do the same thing when one hypothesis makes better predictions than another.

Another Example

Observation: 5 randomly drawn cards are all red. H1: Most cards in her hand are black. H2: Most cards in her hand are red. H3: Half the cards in her hand are red.

When we make observation O, we should shift our credence away from whichever hypotheses least predicted O, and towards whichever hypotheses most predicted O.

The Prediction Principle follows from a more precise Bayesian framework for reasoning about probabilities. This formal framework is widely used. E.g., insurance companies use it to calculate your probability of getting in an accident. The Prediction Principle only tells you how to change your probabilities in light of new evidence – the resulting probabilities will depend upon what your old (or “prior”) probabilities were. E.g., if you first think it’s very probable that she has mostly black cards, then observing a few red cards shouldn’t be enough to convince you she probably has mostly red cards (though it should nudge you that way).

• Rev. Bayes

What makes a proposed explanation better? (i.e., what are the “theoretical virtues”?)

Predictive success: making better predictions than

• ther hypotheses.

Simplicity (Ockham’s Razor) Fruitfulness: leading to an ongoing research program that keeps yielding new results Generality: applying to more cases Unification: addressing all cases in the same way. Conservatism: fitting with our best theories of other phenomena Falsifiability: Being susceptible to tests that could imaginably show the hypothesis to be false (but hopefully won’t)

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“The” Scientific Method

Justin C. Fisher “The” Scientific Method?

(Scientists use lots of methods, so it’s doubtful that any

• ne method really deserves this title!)
• 1. Clearly articulate various hypotheses that fit existing
• bservations of the phenomena in question.
• 2. Identify an experiment or other observation regarding

which hypotheses make different predictions.

• 3. Carefully perform that experiment or observation.
• 4. Shift your credence against whichever hypotheses

made worse predictions and towards those that made better predictions (using Modus Tollens, the Prediction Principle, or Bayesian reasoning)

• 5. Perhaps use other virtues like simplicity to break ties.
• 6. Publicize your results so others can catch mistakes.
• 7. Repeat…

Abduction in the Scientific Method?

As commonly articulated, the scientific method doesn’t seem to have much to do with induction. However, when the hypotheses in question stake general claims about observable characteristics of

• ther things like the one we observed, then this method

leads to similar conclusions as induction. (I.e., induction can be viewed as a special case of abduction, where the hypotheses in question are generalizations of observable characteristics.)

Induction in the Scientific Method?

It’s very natural to view the scientific method as employing abduction (inference to best explanation) using the Prediction Principle or Bayesian reasoning.

Deduction in the Scientific Method? If H1 thenO not O . not H1 If H1 thenO O . H1

H1 O

x

H1 O The fact that H1 correctly predicted O doesn’t guarantee that H1 is true. We might have observed O for some other reason. Maybe a failed prediction could guarantee that a hypothesis is false? Popper thought this, but we’ll see some worries…

x

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Demarcating “Science” from “Pseudo-Science”

Justin C. Fisher

Plan: first set aside hypotheses that cannot be tested by the scientific method.

Scientific Method

What distinguishes good science from bad science?

The Demarcation Problem

What distinguishes Science from Pseudo-Science?

Pseudo- Science Worse Science

All Hypotheses

Better Science

Then use that method to distinguish better from worse hypotheses.

Hypotheses?

Naïve?

Dogmatic

Worst case

Ideal

Scientific

Pseudo- Scientific

Responsible: Irresponsible:

The Sci. Method is a guide for responsible people to assess scientific hypotheses. The Demarkation Problem is about hypotheses, not people.

Hypotheses?

Naïve?

Dogmatic

Worst case

Ideal

Scientific

Pseudo- Scientific

Responsible: Irresponsible:

For Popper, the Demarkation Problem is about hypotheses, not people. The Sci. Method is a guide for responsible people to assess scientific hypotheses. Some scientists count failures of people to use the Sci. Method as “pseudo-science” too.

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Pseudo-science never makes firm enough predictions to even be testable.

The Demarcation Problem

What distinguishes Science from Pseudo-Science? Pseudo- Science Better Science Worse Science

Karl Popper

Scientific hypotheses are falsifiable: they make predictions and would be shown false by failed predictions.

If H1 thenO not O . not H1

H1 O x

Pseudo- Science Better Science Worse Science Newton made predictions SCIENCE. (But some turned out false BAD SCIENCE.) Einstein made predictions SCIENCE (They haven’t been falsified yet, but just wait…) Your horoscope says something interesting will happen today. That’ll be true no matter what happens! PSUEDO-SCIENCE Adler’s psychology can equally “explain” why a man might rescue a drowning boy, or why he might let him drown, but can’t predict which PSUEDO-SCIENCE

According to Popper:

Pseudo- Science Better Science Worse Science Newton made predictions SCIENCE. (But some turned out false BAD SCIENCE) Einstein made predictions SCIENCE (They haven’t been falsified yet, but just wait…)

According to Popper:

Marxist economics says the communist revolution will come eventually but can’t predict when! PSUEDO-SCIENCE Popper initially thought Darwinian evolution was untestable “just so stories” PSUEDO-SCIENCE Eventually he decided it did make predictions (e.g. “no fossil rabbits in the precambrian”) SCIENCE

Problems for Popper’s Falsificationism. #1. The Tacking Problem.

New Hypothesis: “Astrology is true AND Dallas will be flattened by a meteor on January 1st, 2412.” Falsifiable prediction Popper would count as “science” Hasn’t been falsified yet Popper would rank it alongside our best scientific theories. But clearly this hypothesis isn’t really any more scientific than astrology is, and definitely isn’t as good as our best sciences! Popper counts too much as science! AND

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Problems for Popper’s Falsificationism. #2. The Negation Problem

Popper would count her claim as “science” – one black swan would falsify it. Popper would count his claim as “pseudo-science” – no imaginable observation could show it to be false. But shouldn’t both sides of this debate count as making equally scientific claims? At worst, one is “bad science.” Popper doesn’t count enough as science!

All swans are white! Not all swans are white!

Problems for Popper’s Falsificationism. #3. The Probability Problem

Many scientific theories are

• probabilistic. Rather than

making definite predictions they assign probabilities to many different outcomes. E.g., quantum mechanics assigns positive amplitude/probability to every imaginable observation. Popper would say these theories are unfalsifiable, hence “pseudo-science”. Popper doesn’t count enough as science!

Problems for Popper’s Falsificationism. #4. The Quine-Duhem Problem

Hypotheses don’t make predictions by themselves – instead you need auxiliary assumptions, e.g., about whether equipment is working, how

• ur senses work, etc…

If a theory’s predictions don’t come true, scientists can always blame an auxiliary assumption (and historian of science Thomas Kuhn argues that’s what they usually do!) So, no theory actually is falsifiable! So, Falsificationism doesn’t count nearly enough as science!

You can’t fully test a basketball player on his own. If his team loses, he can always blame a teammate.

Improving on Popper’s Falsificationism?

New demand: scientific hypotheses needn’t make falsifiable predictions, but they must assign precise probabilities to a range of possible observations. Popper considered the limiting case where a theory assigns zero probability to some

• bservation. In this case

Modus Tollens and Bayesianism are equivalent. For intermediate probabilities, Bayesianism can still shift our probabilities in light of new evidence, so we can still use the scientific method to help decide which of the various “scientific” hypotheses are (probably) better.

Pseudo- Science Better Science Worse Science

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New demand: scientific hypotheses must assign precise probabilities to a range of possible observations. Probabilistic theories can still be “scientific”. Tacking on a single falsifiable prediction won’t help. Assigning probabilities to a wider range of cases would (though might still fail simplicity or unification criteria). As long as we have precise probabilities for auxiliary assumptions, Bayesian updating can update all these probabilities at once. The more a player loses, the less probable it becomes that that player is good.

Probability Problem Negation Problem 1% of all swans are non-white. Not all swans are white.

How much does demarcation matter?

It matters a lot which hypotheses we count as “good science” – we’ll teach these in schools and use them as a basis for decisions. It’s less clear whether it matters whether something is “psuedo-science” or just “bad science”. We definitely shouldn’t base decisions on either of these. We definitely shouldn’t waste much time on either of these in schools, except perhaps to help students learn to see what’s wrong with them (like in our class!) So, does the Bad-versus-Pseudo boundary really matter?

Pseudo- Science Good Science Bad Science