Click here and press the right key for the next slide (or swipe left)
(This may not work on mobile or ipad. You can try using chrome or firefox, but even that may fail. Sorry.)
(If the slides don’t work, you can still use any direct links to recordings.)
also ...
Press the left key to go backwards (or swipe right)
Press n to toggle whether notes are shown (or add '?notes' to the url before the #)
Press m or double tap to slide thumbnails (menu)
Press ? at any time to show the keyboard shortcuts
Lecture 15:
Mind & Reality
\def \ititle {Lecture 15}
\def \isubtitle {Mind & Reality}
\begin{center}
{\Large
\textbf{\ititle}: \isubtitle
}
\iemail %
\end{center}
\section{Three Kinds of Inference}
\emph{Reading:} §Chapter 3 of Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press, 2003., §Douven, Igor. ‘Abduction’. In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, Summer 2017. Metaphysics Research Lab, Stanford University, 2017. https://plato.stanford.edu/archives/sum2017/entries/abduction/., §Hume, D. (1739). A Treatise of Human Nature. Oxford University Press, Oxford.
‘What connection between an observation and a theory makes that observation evidence for the theory?
In some ways, this has been the fundamental problem in the last hundred years of philosophy of science.’
Godfrey-Smith, 2003 p. 39
Three kinds of inference
- deductive(logically valid)
- inductive(not logically valid)
- abductive (inference to the best explanation)(not logically valid)
1. All chocolate is good
2. This is chocolate
Therefore:
3. This is good
1. Every type of chocolate in my randomly selected sample (of 316) is good
Therefore:
2. All types of chocolate are good
1. My chocolate is gone
Therefore:
2. Someone stole it
So how should we distinguish these?
Have a think about how to distinguishes the two
The key is to think about the two sample arguments.
What distinguishes them?
‘I will use the term “induction” only for inferences from particular observations in support of generalizations.’
Godfrey-Smith, 2003 p. 39
‘Inductive inferences [...] may be characterized as those inferences that are based purely on statistical data’
Douven, 2017
‘What connection between an observation and a theory makes that observation evidence for the theory?
In some ways, this has been the fundamental problem in the last hundred years of philosophy of science.’
Godfrey-Smith, 2003 p. 39
Ans.1: The observation features in an abductive (or inductive) argument for the conclusion that the theory is true.
Philosophers have mostly focussed on inductive arguments
But inductive arguments are comparatively rare in science.
(E.g. \citet{fitts:1954_information}, which introduces Fitts’s Law,
is clearly abductive because it starts with some speculations about the motor
system’s information capacities and offers the law as the best explanation of the
observations.)
Also, ‘Gilbert Harman argued [plausibly] in 1965 that
inductions are justified only when they are explanatory inferences in disguise’
\citep[p.~43]{godfrey-smith:2003_theory}
Perhaps another way of formulating the question, which makes it seem more tractable.
Q.2: What is the relation between the premises of an
abductive (or inductive) argument and its conclusion?
https://www.pexels.com/video/a-street-in-london-on-a-rainy-night-3037295/
worse argument
1. I have run numerous traffic lights without accident
Therefore:
2. I can run these traffic lights without accident
What is wrong with this argument? (Give them a moment).
Premise is not a random sample (data collection would be ended by the
first accident).
better argument
3. I have never seen Ayesha stop for a red light
Therefore:
4. Ayesha will not stop for this red light
brace for the crash position
in conclusion ...
‘What connection between an observation and a theory makes that observation evidence for the theory?
In some ways, this has been the fundamental problem in the last hundred years of philosophy of science.’
Godfrey-Smith, 2003 p. 39
Ans.1: The observation features in an abductive (or inductive) argument for the conclusion that the theory is true.
Q.2: What is the relation between the premises of an
abductive (or inductive) argument and its conclusion?
‘’tis impossible for us to satisfy ourselves by our reason, why we shou’d extend that experience beyond those particular instances, which have fallen under our observation.’
Hume, 1739 1.3.6.11/91–2
Hume wanted justification ...
in conclusion ...
‘What connection between an observation and a theory makes that observation evidence for the theory?
In some ways, this has been the fundamental problem in the last hundred years of philosophy of science.’
Godfrey-Smith, 2003 p. 39
Ans.1: The observation features in an abductive (or inductive) argument for the conclusion that the theory is true.
Q.2: What is the relation between the premises of an abductive (or inductive) argument and its conclusion?
We’ve actually taken a step backwards since Hume.
Hume thought he understood the connection between observations and theories.
We want to understand that connection.
\section{What Is a ‘Purely Formal’ Theory?}
\emph{Reading:} §Chapter 3 of Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press, 2003.
first idea
Arguments have forms.
recall this inference ...
1. All chocolates are good
2. This is a chocolate
Therefore:
3. This is good
second idea
deductive validity
recall this inference ...
1. All chocolates are good
2. This is a chocolate
Therefore:
3. This is good
1. All Fs are G
2. This is a F
Therefore:
3. This is G
An argument is deductively valid just if there is no possible situation in which its premises are true and its conclusion false.
All arguments of this form are deductively valid.
In case you fell asleep ...
The predicate variables are just holes. You can put anything in them you like as
long as (a) it’s a predicate, and (b) where the holes are marked with the same
letter or colour, you put the same predicate in there.
third idea (just seen)
Some argument forms
guarantee deductive validity
in this sense:
any argument of that form is deductive valid.
What is a purely formal theory of a kind of reasoning (deductive, abductive or inductive)?
It is a theory according to which
the form of an argument is
what determines whether it is valid.
worse argument
1. All chocolates are good
2. This is good
Therefore:
3. This is chocolate
better argument
1. All chocolates are good
2. This is a chocolate
Therefore:
3. This is good
Can we show that all deductive arguments are valid in virtue of their form?
No! But this isn’t our concern on Mind & Reality (see Logic III).
1. I have run numerous traffic lights without accident
Therefore:
2. I can run these traffic lights without accident
3. I have never seen Ayesha stop for a red light
Therefore:
4. Ayesha will not stop for this red light
Can we show that all inductive arguments are valid in virtue of their form?
What form does this argument have?
Are all arguments of that form inductively valid?
relate back to overall question
‘What connection between an observation and a theory makes that observation evidence for the theory?
In some ways, this has been the fundamental problem in the last hundred years of philosophy of science.’
Godfrey-Smith, 2003 p. 39
Ans.1: The observation features in an abductive (or inductive) argument for the conclusion that the theory is true.
Q.2: What is the relation between the premises of an
abductive (or inductive) argument and its conclusion?
\section{Hempel’s Ravens}
\emph{Reading:} §Chapter 3 of Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press, 2003., §Hempel, Carl G. ‘Studies in the Logic of Confirmation (I.)’. Mind 54, no. 213 (1945): 1–26., §Hempel, Carl G. ‘The White Shoe: No Red Herring’. The British Journal for the Philosophy of Science 18, no. 3 (1967): 239–40. https://doi.org/10.1093/bjps/18.3.239.
1. I have never seen Ayesha stop for a red light
Therefore:
2. Ayesha will not stop for any red light
Which observations count as evidence for this?
Candidate answer: Those where the light is red and Ayesha does not stop.
conclusion about a particular
3. I have never seen Ayesha stop for a red light
Therefore:
4. Ayesha will not stop for this red light
In general, an observation of an F which is G is evidence for All Fs are G.
1. Any observation of an instance is evidence for the generalisation.
The light is red and Ayesha does not stop. [This F is G]
Ayesha will not stop for any red light. [All Fs are G]
2. Any evidence that confirms a generalisation also confirms any logically equivalent generalisation.
Two generalisations are logically equivalent if there is no possible situation in which one is true and the other false.
Generalisation 1: Ayesha will not stop for any red light.
Generalisation 2: Anything Ayesha will stop for is not a red light.
Observation: Ayesha stops for a pedestrian to cross.
Observation: Ayesha stops for an ambulance to overtake.
1. I have never seen Ayesha stop for a red light
Therefore:
2. Ayesha will not stop for any red light
Which observations count as evidence for this?
Candidate answer: Those where the light is red and Ayesha does not stop.
3. I have often seen Ayesha stop for things other than red lights
Therefore:
4. Ayesha will not stop for any red light
We cannot accept all three. At least one must be false. (I do like a good inconsistent triad.)
1. Any observation of an instance is evidence for the generalisation.
The light is red and Ayesha does not stop. [This F is G]
Ayesha will not stop for any red light. [All Fs are G]
2. Any evidence that confirms a generalisation also confirms any logically equivalent generalisation.
Two generalisations are logically equivalent if there is no possible situation in which one is true and the other false.
3. ‘I have often seen Ayesha stop for things other than red lights; therefore Ayesha will not stop for any red light’ is a bad argument.
Which one should we give up?
Could get there by using the first argument and deduction to the logically equivalent conclusion anyway.
relate back to overall question
‘What connection between an observation and a theory makes that observation evidence for the theory?
In some ways, this has been the fundamental problem in the last hundred years of philosophy of science.’
Godfrey-Smith, 2003 p. 39
Ans.1: The observation features in an abductive (or inductive) argument for the conclusion that the theory is true.
Q.2: What is the relation between the premises of an
abductive (or inductive) argument and its conclusion?
\section{Hempel’s Ravens (Fast & Formal Version)}
\emph{Reading:} §Chapter 3 of Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press, 2003., §Hempel, Carl G. ‘Studies in the Logic of Confirmation (I.)’. Mind 54, no. 213 (1945): 1–26., §Hempel, Carl G. ‘The White Shoe: No Red Herring’. The British Journal for the Philosophy of Science 18, no. 3 (1967): 239–40. https://doi.org/10.1093/bjps/18.3.239.
1. Any observation of an instance is evidence for the generalisation.
2. Any evidence that confirms a generalisation also confirms any logically equivalent generalisation.
Everything which is F is G
Everything which is not-G is not-F
Observation: This is F and G
Observation: This is not-F and not-G
Inconsisten Triad:
1. Any observation of an instance is evidence for the generalisation.
2. Any evidence that confirms a generalisation also confirms any logically equivalent generalisation.
3. Not any obseration of a non-G which is non-F counts as evidence for the generalisation all Fs are Gs.
relate back to overall question
‘What connection between an observation and a theory makes that observation evidence for the theory?
In some ways, this has been the fundamental problem in the last hundred years of philosophy of science.’
Godfrey-Smith, 2003 p. 39
Ans.1: The observation features in an abductive (or inductive) argument for the conclusion that the theory is true.
Q.2: What is the relation between the premises of an
abductive (or inductive) argument and its conclusion?
