Lecture 6

1.1. Mental gymnastics to prepare to tackle HumeMental gymnastics to prepare to tackle Hume2.2. The Problem of Induction as Hume argues for itThe Problem of Induction as Hume argues for it

1.1. His questionHis question2.2. His possible solutionsHis possible solutions3.3. His conclusionHis conclusion

3.3. Salmon’s illustration of the problemSalmon’s illustration of the problem(By the way, do current evolutionary theory and (By the way, do current evolutionary theory and cognitive science “solve” the problem?)cognitive science “solve” the problem?)

4.4. Anticipating the reading by Carl HempelAnticipating the reading by Carl Hempel

Logic puzzlesLogic puzzles

Background: Of the majors that score Background: Of the majors that score highest on the LSATs and GREs, highest on the LSATs and GREs, Philosophy majors and double majors in Philosophy majors and double majors in Philosophy and a science are consistently Philosophy and a science are consistently in the highest group (or are the highest in the highest group (or are the highest ranking group)ranking group)

Explanation: the particular emphasis Explanation: the particular emphasis Philosophy places on logical reasoning and Philosophy places on logical reasoning and arguments.arguments.

Logic puzzlesLogic puzzles

Guidelines for solving logic puzzles:Guidelines for solving logic puzzles:1.1. Take the information given as if Take the information given as if written in stonewritten in stone..2.2. Pay attention to Pay attention to thethe question asked. question asked.3.3. Find the beginning of a thread: Find the beginning of a thread: one thing you can one thing you can

be sure ofbe sure of; this is enables you to unravel the rest.; this is enables you to unravel the rest.4.4. In general, proceed from the first piece of In general, proceed from the first piece of

information provided to the next…information provided to the next…5.5. Assume there Assume there isis a correct answer and that it can be a correct answer and that it can be

reached given the information provided.reached given the information provided.

A logic puzzleA logic puzzle

In a mythical (?) community, politicians always lie and non-In a mythical (?) community, politicians always lie and non-politicians always tell the truth.politicians always tell the truth.

An anthropologist meets 3 natives of the community. She An anthropologist meets 3 natives of the community. She asks the first native if she is a politician.asks the first native if she is a politician.The first native answers.The first native answers.The second native reports that the first native denied The second native reports that the first native denied being a politician.being a politician.The third native states that the first native is a politician.The third native states that the first native is a politician.

How many of these natives are politicians?How many of these natives are politicians?

A logic puzzleA logic puzzle

Ground rule: politicians always lie and non-politicians Ground rule: politicians always lie and non-politicians always tell the truth.always tell the truth.

The anthropologist asks the first native “Are you a The anthropologist asks the first native “Are you a politician?”politician?”

Can we know what she answered, without relying on Can we know what she answered, without relying on what the 2what the 2ndnd and 3 and 3rdrd natives say? natives say?

What do we know about the 2What do we know about the 2ndnd native given what she native given what she said? said?

And does she help us to figure out what the 1And does she help us to figure out what the 1stst native native is?is?

A logic puzzleA logic puzzle

What can we know given the third native’s What can we know given the third native’s claim about whether claim about whether

What can we know about the first native or What can we know about the first native or the third the third isis a politician? a politician?

Recall the questionRecall the question Can we answer it?Can we answer it?

A logic puzzleA logic puzzle

Yes. The first native, whether a politician or a non-Yes. The first native, whether a politician or a non-politician, had to deny being one. We don’t know politician, had to deny being one. We don’t know what she is.what she is.

We know that the second native is a non-politician We know that the second native is a non-politician because she reported the truth about what the first because she reported the truth about what the first native said (and had to say).native said (and had to say).

If the 3If the 3rdrd native is a politician, the first native is not. If native is a politician, the first native is not. If the 3the 3rdrd native is a non-politician, the first native is a native is a non-politician, the first native is a politician.politician.

So there is one and only one politician.So there is one and only one politician.

Part IIPart II

Hume on theHume on the

““Problem of Induction”Problem of Induction”

Inductive reasoningInductive reasoning For empiricists such as Hume, all the evidence For empiricists such as Hume, all the evidence

there is for empirical knowledge (i.e., knowledge there is for empirical knowledge (i.e., knowledge concerning “matters of fact,” including scientific concerning “matters of fact,” including scientific knowledge), is sensory experience. knowledge), is sensory experience.

For Hume, we achieve empirical knowledge by For Hume, we achieve empirical knowledge by reasoning from individual experiences/singular reasoning from individual experiences/singular statements to generalizations/universal statements to generalizations/universal statements using induction (and we certainly do statements using induction (and we certainly do this a lot).this a lot).

Inductive reasoningInductive reasoning Empirical generalizations (an argument form or type):Empirical generalizations (an argument form or type):

1.1. On day DOn day D11, at time T, at time T11, a black raven was observed., a black raven was observed.2.2. On day DOn day D22, at time T, at time T22, another black raven was , another black raven was

observed.observed.....n.n. On day DOn day Dnn, at time T, at time Tnn, yet anotherblack raven was , yet anotherblack raven was

observed.observed.++ A non-black raven has never been observed.A non-black raven has never been observed.----------------------------------------------------------------------------------------------------------------------------------------------All ravens are blackAll ravens are black

For some empiricists – including Hume – the only For some empiricists – including Hume – the only other (respectable) kind of reasoning is deductiveother (respectable) kind of reasoning is deductive And it involves what Hume calls “relations of ideas”And it involves what Hume calls “relations of ideas” The intuition here is that some sentences (such as ‘2 + The intuition here is that some sentences (such as ‘2 +

2 = 4’) are true by definition (if we know what ‘2’ and 2 = 4’) are true by definition (if we know what ‘2’ and ‘4’ mean, as well as what ‘+’ and ‘=‘ mean, then we ‘4’ mean, as well as what ‘+’ and ‘=‘ mean, then we know the sentence is true) or by form (such as ‘A rose know the sentence is true) or by form (such as ‘A rose is a rose’).is a rose’).

And if a sentence is the conclusion of an argument And if a sentence is the conclusion of an argument that is deductively valid and has all true premises, we that is deductively valid and has all true premises, we know its conclusion is true as well (a sound argument). know its conclusion is true as well (a sound argument). Mathematical theorems, as derived from axioms, are Mathematical theorems, as derived from axioms, are examples.examples.

Hume calls knowledge arrived at in this way Hume calls knowledge arrived at in this way “demonstrative knowledge”“demonstrative knowledge”

Hume’s questionHume’s question What What justifiesjustifies our use of induction? our use of induction? Recall that for Hume, there are two places to look Recall that for Hume, there are two places to look

for a source of such justification:for a source of such justification: Experience Experience Reason Reason

So he proposes we explore each to see if we can So he proposes we explore each to see if we can discover what justifies inductive reasoning…discover what justifies inductive reasoning…

Experience?Experience?

1.1. Millions of ravens have been observed and all are black.Millions of ravens have been observed and all are black.2.2. A non-black raven has never been observed.A non-black raven has never been observed.------------------------------------------------------------------------------------------------------------------3.3. All ravens are blackAll ravens are black Empirical generalizations, like other forms of inductive Empirical generalizations, like other forms of inductive

arguments, are arguments, are ampliative ampliative – the conclusion goes beyond – the conclusion goes beyond the premises. So, the truth of the premises the premises. So, the truth of the premises does not does not guaranteeguarantee the truth of the conclusion. There is a gap. the truth of the conclusion. There is a gap.

Can we not say, though, that “induction has worked in the Can we not say, though, that “induction has worked in the past and currently works – so it is justified”?past and currently works – so it is justified”?

Hume’s questionHume’s question

Can Can experience experience justify our use of induction?justify our use of induction?Say, we argue:Say, we argue:

Induction has worked in the past and present to Induction has worked in the past and present to allow us to predict events/phenomena.allow us to predict events/phenomena.------------------------------------------------------------------------------------------------------------------------------------So, induction will work in the future to allow us to So, induction will work in the future to allow us to predict events/phenomena and, thus, is justified.predict events/phenomena and, thus, is justified.

If this reasoning doesn’t justify induction, why If this reasoning doesn’t justify induction, why doesn’t it?doesn’t it?

Hume’s questionHume’s questionCan Can reasonreason (demonstrative knowledge) provide the (demonstrative knowledge) provide the

justification?justification?No.No.Because:Because:There is no There is no necessary connectionnecessary connection (as there is in ‘2 + (as there is in ‘2 +

2= 4) between2= 4) between““I’ve always (and so has everyone else) I’ve always (and so has everyone else) experienced that X causes Y”experienced that X causes Y”andand““The next X I encounter will cause Y”The next X I encounter will cause Y”

Hume’s questionHume’s question

Can Can experience experience justify our use of induction?justify our use of induction?Maybe if we add a premise:Maybe if we add a premise:Say, we argue:Say, we argue:

Induction has worked in the past and present to allow us Induction has worked in the past and present to allow us to predict events/phenomena.to predict events/phenomena.Nature is uniform.Nature is uniform.----------------------------------------------------------------------------------------------------------------------------------------------------So, induction will work in the future to allow us to So, induction will work in the future to allow us to predict events/phenomena.predict events/phenomena.

This is a This is a deductively valid argumentdeductively valid argument, so why can’t it solve the , so why can’t it solve the problem of induction?problem of induction?

Hume’s questionHume’s question

But what is the justification for this premise?But what is the justification for this premise?

Hume’s conclusionsHume’s conclusionsIf it’s not justified, then why do we engage in inductive If it’s not justified, then why do we engage in inductive

reasoning?reasoning?And can we avoid engaging in inductive reasoning if Hume is And can we avoid engaging in inductive reasoning if Hume is

correct about why we do?correct about why we do?His conclusion about induction is a skeptical one: but what is His conclusion about induction is a skeptical one: but what is

the nature of the skepticism?the nature of the skepticism?And what are the implications of the problem of induction And what are the implications of the problem of induction

(which, though many have claimed to “solve it,” has in (which, though many have claimed to “solve it,” has in fact no solution…) for science?fact no solution…) for science?

Part IIIPart III

Salmon’s poor physics studentSalmon’s poor physics student

Salmon’s physics studentSalmon’s physics studentwho is also studying Hume!who is also studying Hume!

So this poor student is learning about some laws So this poor student is learning about some laws of nature , and having them demonstrated to him, of nature , and having them demonstrated to him, in his physics class and labs but alsoin his physics class and labs but also

Learning from his Philosophy Prof and TA that Learning from his Philosophy Prof and TA that these laws (because they are empirical and they these laws (because they are empirical and they are generalizations) not only can’t be proven but are generalizations) not only can’t be proven but it’s irrational (according to Hume) to believe in it’s irrational (according to Hume) to believe in themthem

Salmon’s physics studentSalmon’s physics studentwho is also studying Hume!who is also studying Hume!

Perhaps predictably, the student assumes that Perhaps predictably, the student assumes that Hume’s arguments date to a time when what he Hume’s arguments date to a time when what he (Hume) calls “secret powers” somehow (Hume) calls “secret powers” somehow connecting each event A with an event B were not connecting each event A with an event B were not yet known. So it’s simply a historical piece yet known. So it’s simply a historical piece without current relevance (and so he asks, “Why without current relevance (and so he asks, “Why am I asked to read this at all??)am I asked to read this at all??)

Is he right? Why or why not?Is he right? Why or why not?

Salmon’s physics studentSalmon’s physics studentwho is also studying Hume!who is also studying Hume!

Second hypothesis: Hume’s problem is not any Second hypothesis: Hume’s problem is not any longer a problem because since his time, we have longer a problem because since his time, we have discovered many laws of nature: conservation of discovered many laws of nature: conservation of energy, conservation of momentum, etc. which energy, conservation of momentum, etc. which allow us to predict (correctly) the outcome of any allow us to predict (correctly) the outcome of any and all relevant experiments and occurrences.and all relevant experiments and occurrences.

What does he learn from his professors in each What does he learn from his professors in each discipline about the status of the laws of nature?discipline about the status of the laws of nature?

The physics student’s professorsThe physics student’s professors

His philosophy TA: did your physics professor say His philosophy TA: did your physics professor say that the laws of conservation of energy and that the laws of conservation of energy and momentum are, by their nature, inviolable, or momentum are, by their nature, inviolable, or that there are that there are no known exceptionsno known exceptions? ?

His physics professors to whom he asks “Is it His physics professors to whom he asks “Is it possible that any or all of these laws will possible that any or all of these laws will stop stop holding tomorrow or on some future date?holding tomorrow or on some future date?””

Their answer:Their answer:

Part IVPart IV

Carl Hempel andCarl Hempel andSophisticated InductivismSophisticated Inductivism

What do to with/about the problem of induction What do to with/about the problem of induction in accounts of science?in accounts of science?

Hempel argues against and offers an Hempel argues against and offers an alternative to what he calls “narrow” alternative to what he calls “narrow” inductivism (others of us call this “naïve” inductivism (others of us call this “naïve” inductivism)inductivism)

Uses a case study to illustrate what he thinks Uses a case study to illustrate what he thinks is a model of scientific reasoningis a model of scientific reasoning

What lessons does he draw from the case?What lessons does he draw from the case? And be sure to understand what he means by And be sure to understand what he means by

“narrow” and “sophisticated” inductivism“narrow” and “sophisticated” inductivism