Philosophy of science

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Depiction of Copernicus

This page started as a collaborative study resource for a philosophy of science course (see the discussion page). This is now a content development project where Wikiversity participants can organize and develop learning resources about philosophy of science.

Course: Introduction to Philosophy of science[edit]


Questions and Answers[edit]

1. Was Copernicus using what Bacon calls the method of anticipation of nature, or the method of interpretation of nature, or something else? Justify your answer by explaining the method Copernicus used and how it differs from the other method(s).

Copernicus was using a different method to Bacon's. Copernicus' method is as follows:
  1. Start from a hypothesis and from that make a deduction.
  2. Make suitable observations to test the deduction.
  3. If the phenomena observed fits the deduction then this gives reason to believe the hypothesis. If the phenomena does not support the deduction then one should doubt the hypothesis.
This method differs from Bacon's because:
  1. The hypothesis does not have to be (but can be) arrived at by induction; and
  2. The hypothesis is not taken as fixed (as a general axiom is) - if there is evidence to show it is incorrect, then reject it.

2. What does Bacon say needs to be done to determine whether it is the earth or the heavens that rotates once per day? Did Copernicus do this?

Bacon said that you needed to show that the earth or heavens has the form/nature of spontaneous rotation, using tables to find them. Copernicus didn't do this (i.e. he didn't use tables) so could not discover this form.

3. What did Bacon propose as a crucial instance for determining whether it is the earth or the heavens that rotates once per day? Is this really a crucial instance? Could Bacon reasonably have thought that observation might give the result he says would prove the earth is stationary? Explain.

Bacon purposes that if we observe simlilar east to west motion in the heavens as we observe in the sea such that the nearer the planet is to the earth the slower the motion and further away the faster the motion. The fastest of all being the starry sphere. If all this is observed than we should accept the earth as fixed and take the heavens as moving.
Not a real crucial instance because the movement observed is relative to the earth.
Bacon could not reasonably have thought this because his crucial instance would be impossible to observe (i.e. Venus and Mercury appear to orbit the earth in the same period as the sun even thought they are different distances from the earth.)

4. (a) What does Descartes (in the first page of his "Letter from the author") say is needed for knowledge to be perfected? (b) What is this first condition he says principles must satisfy? (c) How does what Descartes says here differ from Aristotle?

(a) Knowledge must be deduced from principles.
(b) The principles must be so clear and evident that they can't be doubted when attentively considered.
(c) Aristotle used induction and dialectic whereas Descartes didn't. Induction and dialectic are doubtable so Aristotle's principles don't meet the first condition that Descartes says principles must satisfy (i.e. that they must be so clear and evident that they can't be doubted when attentively considered.

5. What is the first principle of Descartes' philosophy? What is his argument for it?

First principle is existence of his own mind. Argument: because if you try to doubt it (i.e. attentively consider it) then you must have a mind because you are able to doubt it.

6. What is the argument that Descartes gives for the existence of a perfect being? Is the argument valid? Explain.

P: The idea of a perfect being includes existence
C: So a perfect being exists
Not deductively valid. Since what really follows from P is that if a perfect being exists then it exists.

7. Having established (a) the existence of a perfect being, Descartes argues that it follows that (b) we cannot be mistaken about the things of which our mind has a very clear and distinct perception. Explain fully Descartes' argument that (b) follows from (a).

Because perfect being created my mind, he would be a deceiver if what I clearly and distinctly perceive could be false. The perfect being is not a deceiver (since he is a perfect being)
Therefore, we cannot be mistaken about things our mind perceives.

8. Descartes said that his theory of vortices, and his theories about the invisible parts of bodies, could be false. Would he say that if he had got them by following the methodology that, at the beginning of Principles of Philosophy, he said should be followed? Explain.

No, the methodology should be to start from undoubtable principles and deduce things that must be true. For Descartes' to say that these theories may not be true, must mean that he didn't follow this methodology.

9. What is an argument that Descartes gives for saying that his theories about the invisible parts of bodies could be false?

If you consider two clocks from the outside that appear the same, they could be very different on the inside (i.e. a different mechanism). God could make the world in more than one way that appear to be the same to us

10. Descartes claimed that his theories about the invisible parts of bodies were "morally certain". What does this mean? How did Descartes argue for this claim?

Something morally certain, is something that could be wrong, but practically certain to be right. It's something that we can rely on, but we don't know to be true, such as the claim that the building we are in is going to still be standing in the next 5 minutes. Descartes argues that it explains so many things that it would be amazing if 1 hypothesis to explain so many things turned out to be wrong (he used the example of the coded letter during class).

11. Descartes gives an argument that his theory of vortices, and his theories about the invisible parts of bodies, are absolutely certain; but in each case he soon backs away from the argument. What is the argument? Is the argument a good one? Explain.

He says that these theories are hypotheses that could be wrong. However he says they are morally certain (i.e. sufficiently certain to be relied on for practical purposes). He then moves on to say that they are absolutely certain because they seem more than morally certain and God is not a deceiver. Descartes backs away from the argument. The arguement is not a good one as Descartes used the method of hypothesis instead of deducing from first principles. The method of hypothesis is fallible since if we reached conclusions from that method God would not be deceiving us.

12. In each of the following pairs, explain the difference between the relative and absolute concepts. Support your explanation with an example. (a) Relative and absolute time (b) Relative and absolute space (c) Relative and absolute motion

(a) Relative time is time measured relative to perceptible motion. Absolute time flows at the same constant rate. Relative time could be that measured by a clock. No example of absolute time.
(b) Relative space is space defined relative to perceptible objects. Absolute space is fixed and not perceptible. Relative space example could be the space four walls of a room. Absolute space is imperceptible so there's no example.
(c) Relative motion is motion with respect to relative space. Absolute motion is motion with respect to absolute space. Relative motion example could be someone walking who is moving with respect to someone sitting down. That person sitting down is experiencing absolute motion.

13. A stone is thrown horizontally and eventually falls to the ground. Explain how Newton's laws of motion imply that there is a force acting on the stone after it has been thrown, and the direction of this force. (Assume that the earth is at rest.)

Isaac Newton (1643-1727
The stone is not exhibiting uniform motion which implies by the first law that there's a force acting upon it. That change of motion is in the direction of the force applied to it (by the second law) which is towards the centre of the earth.

14. A magnet and a piece of iron are floating in separate dishes in a basis of water. The magnet is twice as heavy as the iron. The iron has acceleration a towards the magnet. Use Newton's laws of motion to determine the acceleration of the magnet; indicate which laws you are using and where they are used.

Acceleration of the magnet is half that of the iron. From the second law that states F=ma, and the third law that says the forces acting are equal and opposite, we can calculate the acceleration of the magnet. Let a= acceleration of magnet, m = mass of magnet, b = acceleration of iron, n = mass of iron. So F = b2m and F = ma. Solving gives 2b=a, so b=0.5(a)

15. According to Newton, what is the direction of the force that keeps the moon in its orbit? From what does Newton deduce this?

The direction of the force is towards the centre of the earth. Explanation: the moon traces out an equal area of its orbit in equal period of time (phenomenon 6).

16. According to Newton, how is the force on the moon related to the moon's distance from the earth? From what does Newton deduce this?

Force on the moon is proportional to 1 / (distance)^2 . This is derived from the assumption that the apogee is stationary.

17. Explain how, after establishing the properties of the force that keeps the moon in its orbit, Newton goes on to argue that this force is gravity. Say where Newton's rules of reasoning are used in this argument.

Using that force is proportional to 1 over the distance squared, Newton compares the acceleration of moon at the earths surface to the acceleration of the moon at its usual distance. We observe then that: a_s/a=d^2/d_s^2. Thus, we see that the acceleration of the moon at the earth's surface is the same as another falling body on the earth's surface. Using the first and second rules of reasoning there is then no reason to assign any new causes to the observed phenomenom. Thus, Newton draws the conclusion that the force that keeps the moon in orbit is gravity.

18. Explain how, after arguing that the moon is kept in its orbit by gravity, Newton goes on to argue that all planets have gravity. Say where Newton's rules of reasoning are used in this argument.

We observe that the moons of other planets behave similarly to the moon of Earth. By Newton's second rule of reasoning we should assign the cause of such behavior to these planets having gravity. The planets Mercury and Venus have no moons but are similar to the bodies of other planets. Therefore, by Newton's third rule of reasoning all planets have gravity.

19. How did Newton argue that the center of gravity of the solar system is at rest? How does it follow from this that the earth moves?

Hypothesis 1: The centre of the solar system does not move. If the centre of gravity of the solar system moved, then it would move in a straight line at constant velocity. If the centre of gravity moves in a straight line at constant velocity, then the center of the system moves (by any reasonable definition of centre). Since the centre does not move (hyp 1), the centre of gravity of the system does not move (prop 11)
The earth moves: the centre of gravity of the ss is at rest (prop 11), and the sun is always close to that (prop 12), so it is nearly true that the sun is at rest. The earth moves a lot relative to the sun, so therefore the earth really moves.

20. (a) When Newton said that "hypotheses... have no place in experimental philosophy", did he mean that hypotheses should not be stated? Justify your answer with at least one reference to Newton's writings. (b) Did Newton accept the method of hypothesis? What was his reason?

(a) No he didn't mean that they should never be stated since he stated hypotheses. E.g. hypothesis 1. He must mean that he isn't making a hypothesis about the cause of gravity.
(b) He rejects the method of hypothesis because he thinks that for every phenomenon there are multiple hypothesis to explain it.

21. According to Newton, what is the right way to establish causes and general laws in science? Did Newton follow this method when he argued that the moon is held in its orbit by gravity? Justify your answer to the latter question.

According to Newton the right way to establish causes and general laws in science is to start from phenomenon and from this infer through induction causes and then the most general causes. Newton did not follow this method. In phenomenon 6 accounts for the inconsistency of what is observed by applying what he sought to prove (i.e. that the moons motion is affected by the sun).

22. Why does Hume think that any justification for belief in unobserved matters of fact must assume the future will resemble the past? Your answer should state the other kinds of justification that Hume recognizes and explain why they are not possible in this case; it should also explain how belief in a matter of fact that has not been observed could be justified by assuming the future will resemble the past.

An unobserved matter of fact cannot be based on intuition, demonstration, or perception. They (intuituion, demonstration, perception) are not possible because they are logically necessary, whereas a matter of fact is not. We must base our beliefs about the future on our past experience.

23. State Hume's argument for his claim that our beliefs about unobserved matters of fact are unjustified.

Matters of fact aren't known by perception. Experience and future will resemble the past. So circular argument and unjustified.

24. What is Hume's skeptical claim about matters of fact that we have not observed? Did Hume think it is sensible to take past experience as a guide to the future? Justify your answer to the latter question.

Skeptical claim: matters of fact that we have not observed are not justfied. Hume would say that it is sensible to take past experience as a guide to the future. Justification: Hume says: "And no none but a fool or a madman will ever pretend to dispute the authority of experience..." pg 36 book. NQ 183

25. According to Hume, what causes us to have the beliefs we do about matters of fact that we have not observed? Give an example that illustrates how this cause operates.

Custom or habit makes us have the beliefs we do about matters of fact. For example, the fact that the sun rises everyday gives us confidence that the sun will rise and we fall into the habit of anticipating that it will.

26. Hume's investigation of the concept of causation involves looking for where we could get an impression of necessary connection. (a) Why is necessary connection relevant to causation? (b) Why does Hume think we must have an impression of it? (c) What does he hope to achieve by finding that impression?

(a) because it is usually thought that if C causes E then there is a necessary connection between C and E.
(b) assumes necessary connection is a simple idea. And simple ideas are copies of impressions.
(c) if you can find that impression, Hume hopes it will be possible to clarify and make less obscure the simple ideas.

27. What is the impression that gives rise to our idea of necessary connection, according to Hume? What causes us to have this impression?

It's an impression of reflection that when we see A we expect B which is our idea of necessary connection. This impression is caused by repetition of the same things observed.

28. Does Hume think it is true that if C causes E then there is a necessary connection between C and E? Explain.

No he doesn't think there's a necessary connection. Because it's an idea in the mind.

29. What is probability, according to Laplace? Is the probability of an event the same for everyone? Why, or why not?

Probability of an event = (number of favorable cases) / (number of possible cases) where the cases are all equally possible.
Not the same for everyone because if you know that there are fewer possible cases, then the probability of an event is higher.

30. Suppose A, B, and C are three urns of which one contains only black balls and the other two contain only white balls. What is the probability that a ball drawn from urn C will be black (a) for a person who has only the information stated? (b) for a person who also knows that A contains only white balls? (c) for a person who also knows that A and B contain only white balls?

(a) 3 equally probable cases. 1 favorable case.
probability = 1/3 (show the formula)
(b) With the knowledge that A contains only white balls that means there are only 2 possible cases where the outcome is unknown. So prob. = 1 / 2
(c) After eliminating non favorable cases, left with 1 possible and 1 favorable case. so probability = 1 / 1 = 1

31. Suppose that the possible causes of effect E are C1,...,Cn. State a formula for the probability of C1 given E; do not assume that the causes are equally probable a priori.

see notes.

32. State the law of likelihood and give a proof of it.

see notes.

33. Did the evidence available to Ptolemy and Copernicus support Copernicus' claim that the planets orbit the sun over Ptolemy's claim that they orbit the earth? Justify your answer by applying the law of likelihood to at least two specific pieces of evidence.

E = the observed planetary motion
P = Ptolemy's claim that sun & planets orbit the earth
C = Copernicus' claim that earth and other planets orbit the sun
Facts about E -
1. Mercury and Venus never get far from the sun. This must be true given C. It doesn't have to be true given T.
2. Superior planets are closest to the earth when in opposition to the sun. This must be true given C. It doesn't have to be true given T.
So P(E|C) is greater than P(E|T) , so E supports C over T

34. State Laplace's rule for the probability that a future event F will occur, given that event E has been observed.

If C1.... Cn are the causes that might be operating, and if we have observed event E the probability of some future event F is
P(F|E) = P(F|C1)P(C1|E) + ... P(F|Cn)P(Cn|E)

35. What is Laplace's rule of succession? What does Laplace assume in order to derive this rule?

If you know nothing about the chance of an event happening except that so far it has occurred n times in a row, the probability it will happen next time is (n+1)/(n+2)
To derive this rule, Laplace assumes (1) the event has some chance of happening between 0 and 1. (2) All possible values of this chance from 0 to 1 are equally probable a priori. (3) the 6th and 7th principles of probability.

36. Hume said that our conclusions about unobserved matters of facet "suppose, as their foundation, that the future will resemble the past." Does Laplace's use of probability theory support or contradict this claim of Hume's? Explain.

Laplace's theory contradicts Hume's claim as Laplace makes no assumption that the future resembles the past, like Hume says you would have to do to make conclusions about unobserved matters of fact. In fact, Laplace says that it's possible the future doesn't resemble the past.

37. One of Darwin's arguments that species have been produced by natural selection is based on the experience of breeders. Explain the argument.

Artificial selection has produced large changes in species (he refers to selective breeding in England). There is a comparable process of natural selection. So, we should expect species to be modified by natural selection.
Contrary to what people thought at the time, artificial selection does not seem to be limited in what it can do. Since natural selection can work more effectively and over a much larger period of time than artificial selection, it is probable that the modifications produced would eventually be so great that we would call the result a new species.
Darwin in 1842 with his eldest son, William Erasmus Darwin

38. Darwin argues that there is no sharp distinction betwen species and varieties. Supposing this is correct, does it support natural selection over independent creation as the origin of species? Justify your answer using the law of likelihood.

E = no sharp distinction between species and varieties.
N = species arose by natural selection
C = species were independently created
P(E|N) is high. This is because there is a divergence from 1 species into varieties and then species. This is a gradual process between species and varieties so there exists no sharp distinction. This must be be the case with natural selection.
P(E|C) is low. There is no reason why E has to be true.
So by the law of likelihood, E supports N over C.

39. What does it mean for parts of organisms to be homologous? Give an example of parts of different species that are homologous with one another.

Homologous means that the parts of the organisms have the same structure. Example: bone structure of the arm of a man, and leg of a horse are similar and therefore homologous.

40. Do the observed homologies between different species support natural selection over independent creation as the origin of species? Justify your answer using the law of likelihood.

H = different species have homologous parts that are used for very different purposes.
N = species arose by natural selection
C = species were independently created
P(H|C) is low. There is no reason why organs should be homologous. Surely if species were created, they would be better (e.g. a horse's leg that doesn't break).
P(H|N) is high. You would expect to see this if all species developed from a common ancestor with parts adapted over time.
So by the law of likelihood, H supports N over C.

41. Does the similarity of embryos of different species support natural selection over independent creation as the origin of species? Justify your answer using the law of likelihood.

E = embryo's of different species are similar in structure.
P(E|C) is low. No reason to expect this - why would embryos have 'gills' which are not required.
P(E|N) is high. Organism adapts in later states of life, so it doesn't matter than an embryo has 'gills' so the embryo can be unchanged.
So by the law of likelihood, E supports N over C.

42. Does the existence of rudimentary organs support natural selection over independent creation as the origin of species? Justify your answer using the law of likelihood.

R = many species have rudimentary organs.
P(E|C) is low. Since there's no reason to expect this phenomenon. Why create beetles with wings that don't work.
P(E|N) is high. Since changes are small you would expect to find rudimentary organs since ancestors have the same organs.
So, by the law of likelihood, R supports N over C.

Questions and Answers part 2[edit]

J S Mill (1806-1873)

1. According to Mill, what is the meaning of "law" and "law of nature"? Give an example that illustrates the difference.

A law is a general regularity. Laws of nature of the simplest regularities from which all others are deduced.
Example:
  1. Suppose A is always accompanied by D
  2. Suppose B is always accompanied by E
  3. It follows that AB is always accompanied by DE
All are laws but only 1. and 2. are laws of nature.

2. According to Mill, what does it mean for A to be the cause of B? Does it follow from Mill's definition that night is the cause of day? Explain.

"A is the cause of B" means that when A happens B invariably and unconditionally follows
It does not follow from this definition that night is the cause of day because that would be conditional (i.e. not unconditional) and hence does not satisfy Mill's definition.

3 Does our everyday use of the terms 'cause' and 'effect' agree with Mill's definitions? Explain and give an example.

Our everyday use does not always agree with Mill's definitions, since we often don't talk about an exhaustive list of causes. For example, we might say that the cause of a man dying was the food he ate at a restaurant. This would not be the cause under Mill's definition, as there was no mention of things like the biological makeup of the man, the reasons the meal poisoned him etc..

4. What is the nature of the necessary connection between causes and effects, according to Mill? How does Mill's account of this differ from Hume's?

The necessary connection between causes and effects according to Mill consists in B following A unconditionally. For Mill, necessary connection is in the world, whereas Hume thinks that necessary connection is in the mind.

5. Does Mill think induction by simple enumeration is always reliable, usually reliable, usually unreliable, or never reliable? Why does Mill take the position he does?

Usually unreliable. As you often don't have reason to believe that you know there are no instances to the contrary.

6. What is the law of causation? What is Mill's justification for this law?

Every fact which has a beginning has a cause. Because knowledge of this is such that we would know of instances to the contrary.

7. What is the method of agreement? What is Mill's justification for this method?

If two or more situations agree in A but nothing else, and in every case a results, then A is the cause of a. Justification: By the law of causation, a has some cause. Mill assumes that a has only one cause. Hence the cause of a is something common to all the situations. So since A is the only common factor, A is the cause.

8. What is the method of difference? What is Mill's justification for this method?

If a results when A is present, and a doesn't result when A is absent but the antecedents are otherwise the same, then A is the cause of a or a necessary part of the cause. Justification: by the law of causation, a has some cause. The cause of a can't be any of things present when a is absent (by the definition of cause). Therefore, A is either the cause or a necessary part of the cause.

9. Why is it sometimes not possible to find causes by (a) the method of agreement, or (b) the method of difference?

(a) the method of agreement
  1. Different situations always have more than 1 thing in common
  2. We can discount circumstances we already have good reason to think are irrelevant
  3. But still there are so many circumstances in any situation, not all of them visible to us, that often we can't be sure there isn't some other relevant circumstance common to different situations.
(b) the method of difference
  1. Typical way to apply this is to do an experiment in which we change A and keep the other circumstances the same.
  2. However, it isn't always possible to do this
  3. Example of double refraction

10. What is the joint method of agreement and difference? Under what circumstances is it appropriate to use this method rather than the method of agreement or the method of difference?

It consists of two applications of the method of agreement:
  • First application
    • We look at a variety of circumstances in which a occurs and find that the only antecedent they have in common, so far as we can tell, is A.
    • The method of agreement suggests A is the cause of a.
    • But it still might be that the situations have something in common other than A which is the real cause, so the conclusion is dubious.
  • Second application
    • We look at a variety of circumstances in which a does not occur and find that they agree in not containing A and nothing else so far as we can see.
    • The method of agreement suggests the absence of A is the cause of the absence of a.
From the two applications together we infer that A is the cause of a or an indispensable part of the cause of a.
The second part makes it stronger than method of agreement
  • The first part leaves open the possibility that the real cause is not A but some factor we've overlooked that is common to the situations.
  • If that were true, a could occur when A is absent
  • But the second application suggests this isn't so
This method can be used in some cases where the methods of agreement and difference are not usable, and to further test the right account.

11. What is the method of residues? What must we know in order to identify a cause using this method?

The method
  • If we subtract from a phenomenon the part that is known to be the effect of certain antecedents, the remainder of the phenomenon is the effect of the remaining antecedents.
Symbolic example
  • If ABC is followed by abc, and the effect of A is a, and the effect of B is b, then the cause of c is C.
  • Knowledge assumed in this example
    • We must have previously determined the effects of A and B by some other method, such as the method of difference.
    • We must here know that there is no antecedent besides A, B, and C that could be relevant to the effect.
Scientific example: Discovery of Neptune

12. What is Mill's method of concomitant variations? Give an example of the use of this method.

If two phenomena always vary together in a particular manner then one is the cause of the other, or at least there is a causal connection between them. Example: high tide always occurs when the moon is closest, so using the method of concomitant variations one can conclude that one is the cause of the other or at least there is a causal relation between them.

13. Could Copernicus have argued that the earth orbits the sun using any of the forms of induction recognized by Mill? Justify your answer by stating Copernicus' hypothesis in cause-effect terms and considering each of the forms of induction recognized by Mill.

No. Hypothesis in cause-effect terms:
Effect (m): Observed motion of the heavenly bodies relative to the earth.
Cause (M): Rotation of earth, and orbit of earth and other planets around the sun.
The method of agreement requires us to observe 2 situations where M occurs, but we can't observe M. Therefore we can't use the method of agreement.
The method of difference requires us to observe 2 situations, the first where M occurs and the second where M doesn't occur, but we can't observe M. Therefore, can't use the method of difference.
Similarly the other three methods Mill describes can't be used as they require us to observe M which we can't do (in fact, we're trying to establish M).

14. Could Darwin have argued that species arose from natural selection using any of the forms of induction recognized by Mill? Justify your answer by stating Darwin's hypothesis in cause-effect terms and considering each of the forms of induction recognized by Mill.

No. Hypothesis in cause-effect terms:
Effect (n): origin of species.
Cause (N): natural selection, operating over a very long time.
Can't use any of Mill's methods because they all require one to observe N which we can't do since that's what we're trying to establish

15. When Newton argued that the moon is kept in its orbit by gravity, did he use any of the forms of induction recognized by Mill? Justify your answer.

Newton argues that the force on the moon is directly towards the earth and varies inversely with the square of the distance. This is inferred from
  1. The line from earth to the moon traces out equal areas in equal times, and
  2. Apogee of the moon's orbit is stationary.
Yet none of these phenomena is really observed since Newton made deductions to adjust the data. So because he didn't just use induction, he didn't really follow Mill's methods.

16. Explain what it means for a statement to be analytic or synthetic and give an example of each kind of statement.

For a statement to be analytic is has to be true due to the meaning of words. An example could be "all bachelor's are married". For a statement to be synthetic it's truth or falsity depends on facts. An example could be "Popper was a bachelor".

17. State Popper's argument that induction is unjustified.

Argument:
  1. To justify induction we must establish a principle of induction.
  2. This principle must be synthetic and universal.
  3. Any attempt to justify the principle of induction would use induction.
  4. So the attempt to justify induction leads to an infinite regress.

18. State one similarity and two differences between Popper and Hume on induction.

They are similar in that they both argue that induction is unjustified.
They are different in that:
  1. Hume says we should still use induction whereas Popper says we should not, and
  2. Hume argued that to use induction we must assume that the future resembles that past. Popper says that we must assume something, but not necessarily that the future resembles the past. (So Popper's criticism of induction could be used against Laplace's theory of succession but Hume's criticism could not.)


19. Compare and contrast Popper's view of scientific method with the method of hypothesis (as advocated, for example, by Descartes).

His method is like the method of hypothesis because it begins with a hypothesis from which testable predictions are deduced and then are tested, but it differs in its verification. In the method of hypothesis, if the tested hypotheses are shown to verify the theory, the theory is taken as likely to be true, but Popper says that positive results don't give us any more information or more reason to believe the theory is true.

His method results on the resistance to falsification.

20. What are Popper's requirements for an acceptable theory in empirical science? Explain what each requirement means.

His requirements are that it must be:
  1. Synthetic: relies on facts to say whether it is true or false
  2. Falsifiable: inconsistent observation
  3. Corroborated: the theory has been tested and has passed the tests.

21. What is Popper's reason why only tested theories are acceptable in science? Is this consistent with other things popper says? Explain.

Otherwise one would not know if the theories corresponded to the facts of the world. No this is not consistent with other things he says since passing a test doesn't add anything to a theory because multiple verification don't compile since he doesn't accept induction.

22. What is the methodological rule that Popper uses to ensure that theories can be falsified? Why is a methodological rule needed?

We only modify a hypothesis if the modified hypothesis creates new and testable predictions. Needed because deductive logic is not sufficient because it only shows whether one auxiliary hypothesis is wrong.

23. Can Popper's scientific method ever require a true theory to be regarded as false? Explain.

Yes it can. If counterevidence seems to falsify a hypothesis and an auxiliary hypothesis is regarded as untestable, then Popper's method falsifies they hypothesis.

24. On Popper's theory of science, is science any better than reading tea leaves as a way to find the truth? Explain.

No it's not. For Popper verification doesn't show confirmation of give any indication of probability. Theories also cannot be falsified or even probably doubtable.

25. State a similarity and a difference between the following statements: (a) e logically implies h (b) The degree to which e confirms h is r

Each of the statements is actually a logical statement, which means that applicability of the statement does not depend on empirical data. These statements differ in that in part a) e logically implies h, meaning it is logically impossible for h not to be true; in part b) there is confirmation of h only to a certain degree, thus it is logically possible for h not to hold.

26. What does Carnap mean by 'probability1' and 'probability2'? Are propositions involving these concepts analytic or synthetic, according to Carnap? What kind of things are related by these two kinds of probability?

Carnap believes that there are two types of probability: probability1 and probability2. probability1 is conceptualized as a logical concept that relates propositions or sentences, and is concerned with degree of confirmation. Probability2 is a factual concept that relates classes of things. Probability2 also concerns relative frequency in the long run.

Though I don't have notes on the matter, conceptually probability1 seems to be analytic whereas probability2 seems synthetic. The distinction between 'logical' and 'factual' seems to coincide with the very distinction between analytic and synthetic. Please correct me if I am wrong.

27. Give an example in which the probability1 of a coin landing heads, given the available evidence, is different to the probability2 of the same coin landing heads.

Consider a 2-sided trick coin, that is such that it has two identical faces. Here, probability2 is either 1 or zero depending on the face that is represented on this coin. Probability1 is ½, since it is know that this coin has two sides with the same face, but it is not know what face that is.

28. Was Laplace talking about probability1 or probability2? Justify your answer with reference to Laplace's principle of indifference and his statement that probability is relative to our knowledge.

Laplace was tallking about probability1. Because the principle of indifference says that when we have no reason to believe one alternative over the other then those alternatives are equally probable. If they're equally probable given our evidence (probability1), then that's plausible. But if these alternatives happen equally often in the long run relative to what we know (probability2) then that's crazy.
Saying that probability given our evidence (probability1) is relative to our knowledge makes sense. Saying that things happen equally often in the long run (probability2) relative to our knowledge is crazy.

29. What is deductive logic about, according to Carnap? What is inductive logic about?

Deductive logic studies logical implication. Inductive logic studies degree of confirmation (which is probability). They are both logical relations, whether they hold is analytic, not synthetic.

30. What is primitive psychologism in logic? Does Carnap agree with primitive psychologism? State two reasons Carnap gies for his position.

Primitive psychologism holds that logic is about how people actually think. Carnap disagrees with this because:
  1. Logic would be part of psychology, and accordingly could be investigated empirically.
  2. Logical laws would be false.


31. What is qualified psychologism in logic? Does Carnap agree with qualified psychologism? State a reason Carnap gives for his position.

Qualified logic holds that logic is about correct or rational thinking. Carnap objects to this as he thinks the reference to thinking is superfluous.

32. How can induction be justified according to Carnap? What is Carnap's basis for claiming that this justification is not circular?

Carnap asks if we can justify a man acting in accordance with probability1.
Justification:
1.If x acts in accordance with probability1 and the world is probably1 highly uniform, then x will probably1 be successful in the long run.
2.The world is probably1 highly uniform.
Therefore 3. If x acts in accordance with probability1, then x will probably1 be successful in the long run.
Carnap claims that this justification is not circular because Premise 2 is an analytical claim, not synthetic.

33. What is an effective procedure?

A procedure which has rules that uniquely determine each step, and the solution has a finite number of steps.

34. Is inductive reasoning less subject to effective procedures than deductive reasoning is, according to Carnap? Justify your answer by stating the kinds of problems for which each kind of logic does and does not provide effective procedures.

No, it is not less subject to effective procedures. To find a conclusion, there is no effective procedure in deductive or inductive logic. To examine a result there is no effective procedure in deductive or inductive logic. However, to examine a proof, there is an effective procedure in deductive and inductive logic.

35. Why are creativity and intuition needed in inductive reasoning? Does it follow from this that there cannot be exact rules of inductive logic? Justify your answer (for example, by making a comparison with deductive logic).

Because there are problems of inductive logic for which there are no effective procedures so one must use creativity and intuition. It does not follow because in deductive logic we observe that even if there exists an effective procedure for a subject, it does not necessarily become mechanical. You need to use creativity and intuition to reach a conclusion.

36. The “four-color theorem” states that four colors are sufficient to color a map so that regions with a common boundary are colored differently. For a long time mathematicians were unable to either prove or disprove this theorem but in 1976 it was proved using a computer.

(a) Which of Carnap’s three kinds of problems was the computer being used to solve?

Examining the results

(b) Computers follow mechanical rules. So is the fact that a computer proved this theorem a counterexample to Carnap’s claim about the need for creativity and intuition in this kind of problem? Why, or why not?

No, the computer only works for a specific case, whereas an effective procedure has to work in every case. In this situation, the computer only works in this specialized case.

37. Do good scientists follow Popper’s rules of scientific method? Support your answer with an example.

'No, Newton did not form a new auxiliary hypothesis when he found an anomaly in his theory concerning the calculated and observed movement of the moons apogee. This anomaly was resolved in 1750, and was due to using the wrong mathematical approach. Newton followed Popper's method, his theory would have been wrongly abandoned.'

38. What must happen in order for scientists to give up a paradigm, according to Kuhn?

The following must happen for a paradigm to be rejected:
  1. The anomalies must be severe and prolonged, resisting all attempt to deal with them. (This causes a sense of crisis.)
  2. These must be a better alternative paradigm.

39. Can the following claims of Kuhn be explained in terms of what is probable given the evidence? Justify your answers.

(a) Anomalies normally don’t cause a paradigm to be abandoned.

Since it's a paradigm, it's a hugely successful theory, and there is so much evidence to support it that it is probably correct. Hence, since anomalies are probably mistakes, they normally don't cause a paradigm to be abandoned.

(b) Severe and persistent anomalies cause a sense of crisis.

Initially one would say the anomaly is due to a mistake, however if they become severe and persistent it becomes clear that there is a bigger problem. It becomes probably that something is deeply wrong - i.e. something about the paradigm is not right.

(c) Paradigms are not abandoned without a better alternative.

The paradigm has been enormously successful, so will probably continue being be very useful. So despite the severe and persistent anomalies there must be some truth to the paradigm. It does not make sense to change to a theory that's not at least as good.

40. What is Kuhn’s argument for his claim that debate between proponents of different paradigms must be circular?

P1: Paradigms contain not only theories but also standards that a scientific work must meet.
P2: Different paradigms have different standards as well as different theories.
So, debates between proponents of different paradigms is necessary circular since each proponent will use different standards.

41. What is a historical example that Kuhn uses to illustrate his claim that debate between proponents of different paradigms must be circular? Does this example support or contradict Kuhn’s claim? Justify your answer.

Kuhn's example contradicts his claim/argument. He uses a comparison between Newton and Descartes - allegedly two paradigms with different standards - but Newton's paradigm did not adopt different standards than Descartes. Newton himself believed in Descartes' standards as he searched for a mechanical explanation for gravity. So this example contradicts P2 of his argument.

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