Why are Good Theorys Good- Review
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Why are Good Theorys Good- Review
- 1. WHY ARE GOOD THEORIES GOOD ? REFLECTIONS ON EPISTEMIC VALUES , CONFIRMATION, AND FORMAL EPISTEMOLOGY Sinu G S Student MICS Selected Topics in Artificial Intelligence University of Luxembourg
- 2. THEME OF PAPER This paper discusses about Comparison of Theory of Confirmation and Theory of Verisimilitude or Truthlikeness. Connection between Logic of Confirmation with Logic of Acceptability Connection of Confirmation Theory with Naturalism,Intertheoretic Reduction and Explanation. 2
- 3. AGENDA OF PRESENTATION Introduction Approaches of Confirmation Problems in Confirmation Huber‟s Theory of Confirmation Confirmation and Truthlikeness Many Senses of Confirmation Naturalism and Bayesian Tinkering Belief Framework for modeling realistic cognitive agents (Research Assistant Systems) 3
- 4. Introduction Approaches of Confirmation Problems in Confirmation Huber‟s Theory of Confirmation Confirmation and Truthlikeness Many Senses of Confirmation Naturalism and Bayesian Tinkering Belief Framework for modeling realistic cognitive agents (Research Assistant Systems) 4
- 5. INTRODUCTION Epistemology Theory of Knowledge and justified belief Theories and Evidence Theory Real World Data(Evidence) Predictions Confirmation 5
- 6. Introduction Approaches of Confirmation Problems in Confirmation Huber‟s Theory of Confirmation Confirmation and Truthlikeness Many Senses of Confirmation Naturalism and Bayesian Tinkering Belief Framework for modeling realistic cognitive agents (Research Assistant Systems) 6
- 7. APPROACHES OF CONFIRMATION Inductive Logic Induction proceeds from the specific case to the general case: “probable inference” All swans we have seen have been white; therefore all swans are white. 7
- 8. INDUCTIVE LOGIC METHOD Initial observation Prediction suggests generates hypothesis NO, modify hypothesis experiments and data New observations Do new observations match predictions? YES, confir m hypothesis “Accepted truth” 8
- 9. APPROACHES OF CONFIRMATION Deductive Logic Deduction proceeds from the general case to the specific case: “certain inference” For every action, there is an opposite and equal reaction. This rifle will recoil when it is fired. 9
- 10. HYPOTHETIC-DEDUCTIVE LOGIC METHOD Initial observation suggests hypothesis Prediction A hypothesis hypothesis Prediction B Prediction C New observations NO, falsify hypothesis Do new observations match predictions? hypothesis Prediction D YES, repeat attempts to falsify 10 “Accepted Multiple truth” failed falsifications
- 11. Introduction Approaches of Confirmation Problems in Confirmation Huber‟s Theory of Confirmation Confirmation and Truthlikeness Many Senses of Confirmation Naturalism and Bayesian Tinkering Belief Framework for modeling realistic cognitive agents (Research Assistant Systems) 11
- 12. PROBLEMS OF CONFIRMATION What makes an observation count as evidence ? This piece of copper conducts electricity This confirms (increases the credibility of) Hypothesis “All pieces of copper conduct electricity” Law Like Hypothesis This man performs scientific experiments This confirms(increases the plausibility) of all man perform scientific experiments Accidental Hypothesis idea 12
- 13. PROBLEMS OF CONFIRMATION How do observations confirm a scientific theory ? You can know only what you observed and you have never observed a “Law of Nature” Russell‟s Chicken Story Moral of the story: You cannot always induce the truth from past experience! 13
- 14. PROBLEMS OF CONFIRMATION Raven‟s Paradox P1 : All ravens are black. P2 : Everything that is not black is not a raven E1 : This raven, is black. E2 : This red (and thus not black) thing is an apple (and thus not a raven). 14
- 15. PROBLEMS OF CONFIRMATION Moral of Raven‟s Paradox Theory of Confirmation “With in certain limits,what is the true of evidence statements is true of the whole „universe of discourse‟ Evidences may depends on Context. 15
- 16. PROBLEMS OF CONFIRMATION A logical consequence of any theory T is T or S. “Earth is center of solar system or I am 23 years old” I am actually 23 years old. This means Earth is center of Solar System (Logical Sequence of I am 23 years old ) is confirmed by observing „ I am 23 years old‟ Can nature of solar system be confirmed by my age ? 16
- 17. Introduction Approaches of Confirmation Problems in Confirmation Huber’s Theory of Confirmation Confirmation and Truthlikeness Many Senses of Confirmation Naturalism and Bayesian Tinkering Belief Framework for modeling realistic cognitive agents (Research Assistant Systems) 17
- 18. HUBER‟S THEORY OF CONFIRMATION Problem of Theory of Theory Assessment How we compare and evaluate theories in the light of available evidence? Given Hypothesis or Theory H Set of data,the Evidence E Some Background information B How good is H given B ? What is the value of H in view of E and B ? 18
- 19. HUBER‟S THEORY OF CONFIRMATION Qualitative Theory of Hypothetico-Deductivism (H&B) E Aims at informative theories Increasing Function of Logical Strength of Theory Quantitative Theory of probablistic inductive logic P(H|E&B)>=r , r (.5,1) Aims at plausible or true theories Decreasing Function of Logical Strength of Theory 19
- 20. HUBER‟S THEORY OF CONFIRMATION Conflicting Concepts of Confirmation Informativeness If E confirms H and H0 logically implies H, then E confirms H0 . E |∼ H, H0 H ⇒ E |∼ H0. Plausibility If E confirms H and H logically implies H0, then E confirms H0. E |∼ H, H H0 ⇒ E |∼ H0 A good theory is true & informative 20
- 21. HUBER‟S THEORY OF CONFIRMATION 2 virtues a good theory Truth (or „plausibility‟) Strength (or „informativeness‟) f (H, E, B) Epistemic value of Hypothesis If E entails H → H’, then f (H, E) ≤ f (H’, E) If ￢E entails H’ → H, then f (H, E) ≤ f (H’, E) f (H, E) = p (H, E) + p (¬H,¬E) 21
- 22. Introduction Approaches of Confirmation Problems in Confirmation Huber‟s Theory of Confirmation Confirmation and Truthlikeness Many Senses of Confirmation Naturalism and Bayesian Tinkering Belief Framework for modeling realistic cognitive agents (Research Assistant Systems) 22
- 23. CONFIRMATION AND TRUTHLIKENESS Knowledge Justified True Belief Belief An Idea Some one has about the world True Corresponds with facts Justified Not just a coincidence 23
- 24. CONFIRMATION AND TRUTHLIKENESS Karl Popper‟s view Belief What if every one lost all their beliefs about engineering Justified Circular Argument Why A ? Because B Why B ? Because A Criticise Beliefs,Don‟t Justify them Knowledge is useful truth. 24
- 25. CONFIRMATION AND TRUTHLIKENESS Acceptable theories Not Only High degree of confirmation But Also Capacity of explaining or predicting the empirical evidence Epistemic value of a theory depends on two factors Coherence or Similarity between H and E How Informative our Empirical Evidence is ? Vs (H, E) = [p (H&E) /p (HvE)] [1/p (E)] = p (H, E) /p (HvE) 25
- 26. CONFIRMATION AND TRUTHLIKENESS High Similarity High Informative H is more verisimilar than H‟ 26
- 27. CONFIRMATION AND TRUTHLIKENESS Properties of Empirical Verisimilitude 27
- 28. CONFIRMATION AND TRUTHLIKENESS Properties of Empirical Verisimilitude 28
- 29. Introduction Approaches of Confirmation Problems in Confirmation Huber‟s Theory of Confirmation Confirmation and Truthlikeness Many Senses of Confirmation Naturalism and Bayesian Tinkering Belief Framework for modeling realistic cognitive agents (Research Assistant Systems) 29
- 30. MANY SENSES OF CONFIRMATION Acceptance of Theory H can be „acceptable‟ in the sense that the community allows that individual scientists accept H Best one confirmed H can be „acceptable‟ in the sense that the community commands its members to accept it Mostly Confirmed What makes theory so good that it is legitimate to accept it ? Alternative Theorems What makes theory so good that it is compulsory to accept it ? Certified Knowledge 30
- 31. MANY SENSES OF CONFIRMATION X ,the set of all possible mutually exclusive sets of consequences that the choice of a demarcation level β will have for scientist i, then,the optimal choice for that scientist will correspond to: pi(x,b) is obviously the probability with which i judges that the choice of b will lead to consequences x, ui(x) is the utility that i would experiment under x. 31
- 32. Introduction Approaches of Confirmation Problems in Confirmation Huber‟s Theory of Confirmation Confirmation and Truthlikeness Many Senses of Confirmation Naturalism and Bayesian Tinkering Belief Framework for modeling realistic cognitive agents (Research Assistant Systems) 32
- 33. NATURALISM AND BAYESIAN TINKERING Problem of theory evaluation‟ is not a „philosophical‟ problem, but a problem for the communities of fleshand-bone scientists Inter Theoretical Reduction increases epistemic values Showing that a theory can be reducible to another increases the verisimilitude of both theories 33
- 34. EXPLANATORINESS AND CONFIRMATION A Theory H explains the facts F for the scientific community C if and only if F can be derived from H by C, and the members of C understand H, i.e., if H is „intelligible‟ for them Coeteris paribus, if X is easier to understand than Y, then p(Y) < p(X). 34
- 35. Introduction Approaches of Confirmation Problems in Confirmation Huber‟s Theory of Confirmation Confirmation and Truthlikeness Many Senses of Confirmation Naturalism and Bayesian Tinkering Belief Framework for modeling realistic cognitive agents (Research Assistant Systems) 35
- 36. CONCEPTUAL BELIEF FRAMEWORK (RESEARCH ASSISTANT SYSTEMS) Acceptability Hypothetico Deductive Supportability Truthfulness Background Knowledge Informativeness Inductive Supportability 36
- 37. CONCEPTUAL BELIEF FRAMEWORK (RESEARCH ASSISTANT SYSTEMS) Acceptability Relativism Truthfulness Evidence Informativeness Totality(among set of enclosure) 37
- 38. CONCEPTUAL BELIEF FRAMEWORK (RESEARCH ASSISTANT SYSTEMS) Relativism Acceptability Supportability Truthfulness Theory Informativeness Reducibility 38
- 39. 39
Notas del editor
- Epistemolgy in sense of knowledge What is necessary & sufficient conditions of knowledge,what are it’s sources,structure,limils ?Epistemolgy in sense of justified beliefHow we are to understand the concept of justification ?What makes justified beliefs justified ?Is justification internal or external to one’s own mind ?Scientific research is complicated, and there are different scientific disciplines. But generally speaking, we can identify four main components in scientific research :Theories - Here we include all the hypotheses, laws and facts that are about the empirical world.The world - The objects, processes and properties of the universe.Predictions - We use our theories to make predictions about the world. They are often predictions about the future, but we can also have predictions about the past. For example, a geological theory about the earth's history might predict that certain rocks contains a high percentage of special metals. A crucial part of scientific research is to test a theory by checking whether its predictions are correct or not.Data (evidence) - The information that is gathered from empirical observations or experiments. We use data to test our theories. They might also inspire new directions in research.When we describe a scientific claim as a "theory", we are highlighting the fact that it is a claim about the world that can be true or false. It does not imply that we are unsure of the claim or that we do not have evidence for it.
- Statistics is an inductive process: we are trying to draw general conclusions based on a specific, limited sampleInductive reasoning is the process of reasoning from the specific to the general. Inductive reasoning is supported by inductive logic, for example:From specific propositions such as:This raven is a black bird.To general propositions: All ravens are black birds.The conclusions may or may not be valid
- For example, if I observe 10,000 dogs, and every dog has fleas, I may conclude "All dogs must have fleas." The conclusion is a conjecture or a prediction. Further evidence may support or deny my conclusion. The 10,001st dog may not have fleas. Therefore, with an inductive argument, anyone can affirm all my premises (10,000 dogs with fleas, yet deny my conclusion (all dogs have fleas) without involving himself in any logical contradictionAn argument must meet 2 conditions to justify believing the conclusion (hypothesis): (1) the premises (assumptions, experimental/initial conditions must themselves be justified. (2) there must be sufficient connection between the premises and conclusionGiere's 3 criteria of good test provides the basis for judging this connection. 1) prediction is deducible from the hypothesis together with the initial conditions. 2) prediction is improbable when considered out of context from hypothesis 3) prediction is verifiableThe experiment determines the truth and falsity of the prediction.If the prediction is successful the hypothesis is justified.If the prediction fails the hypothesis is refuted.Theoretical hypothesis: Insects always have 6 legsPremise: All creatures with 3 body parts are insects (assumption)Prediction: Each individual captured will have 6 legsPremise: They all have 6 legs (prediction true)Conclusion: Insects probably always have six legs
- Deductive reasoning is the process of reasoning from the general to the specific. Deductive reasoning is supported by deductive logicEgFrom general propositions: For every action, there is an opposite and equal reaction.To specific propositions such as: This rifle will recoil when it is fired.In contrast to inductive reasoning, the conclusions of deductive reasoning are as valid as the initial assumption. Deductive reasoning was first described by the ancient Greek philosophers such as Aristotle.
- Championed by the philosopher of science Karl Popper (1902-1994)The goal of these tests is not to confirm, but to falsify, the hypothesisThe accepted scientific explanation is the hypothesis that successfully withstands repeated attempts to falsify it Example Good Here is an illustration :Suppose your portable music player fails to switch on. You might then consider the hypothesis that perhaps the batteries are dead. So you decide to test whether this is true.Given this hypothesis, you predict that the music player should work properly if you replace the batteries with new ones.So you proceed to replace the batteries, which is the "experiment" for testing the prediction.If the player works again, then your hypothesis is confirmed, and so you throw away the old batteries. If the player still does not work, then the prediction is false, and the hypothesis is disconfirmed. So you might reject your original hypothesis and come up with an alternative one to test, e.g. the batteries are ok but your music player is broken1. A scientific hypothesis must be testableThe HD method tells us how to test a hypothesis, and a scientific hypothesis must be one that is capable of being tested.2. Confirmation is not truthIn general, confirming the predictions of a theory increases the probability that a theory is correct. But in itself this does not prove conclusively that the theory is correct.If H then P.P.Therefore H.Here H is our hypothesis "the batteries are dead", and P is the prediction "the player will function when the batteries are replaced". This pattern of reasoning is of course not valid, since there might be reasons other than H that also bring about the truth of P. For example, it might be that the original batteries are actually fine, but they were not inserted properly. Replacing the batteries would then restore the loose connection. So the fact that the prediction is true does not prove that the hypothesis is true. We need to consider alternative hypotheses and see which is more likely to be true and which provides the best explanation of the prediction. (Or we can also do more testing!)3) Disconfirmation need not be falsityVery often a hypothesis generates a prediction only when given additional assumptions (auxiliary hypotheses). In such cases, when a prediction fails the theory might still be correct.If Hypothesis and Initial Conditions (are true), then the Prediction (is true).Initial Conditions (are true) but not Prediction.Thus, hypothesis not true.If(H and IC), then P.Not P and IC.Thus, Not H.If the premises are true, and the prediction is false, then the hypothesis must be false.Example of refuting argument:Theoretical hypothesis: insects always have 6 legsPremise: Insects beget other insects (assumption)Prediction: Fly larvae will have six legsPremise: Maggots don't have 6 legs (prediction false)Conclusion: Insects don't always have six legs (conclusion: reject hypothesis)
- Similarity in logical structureThis X is a Y, Hence all X’s are Y …Hence Confirmation is not just a function of logical structure of scienceThere has to be something that the hypothesis themselves that makes a difference.
- Hume says “Future is under no obligation to mimic the past”On a farm, there was a flock of chickens. One chicken started talking with another, remarking "How good our farmer has been to us. I think he is an awfully nice man, because he comes every morning to feed us." The other chicken nodded in agreement, adding "and he has been feeding each and everyone of us here every day like clockwork, every day without fail since we were all just little baby chicks." Indeed, when queried, most of the other chickens clucked in agreement about how benevolent their farmer was.But there was one chicken, intelligent but eccentric, who countered saying "How do you know he is all that good? I remember, not too long ago, that there were some older chickens who were taken away, and I haven't seen them since. What ever happened to them?"Some of the chickens may have slept a little uneasy that night, but in the morning the farmer came as usual, this time scattering even more corn around. The chickens ate this with gusto, and this dispelled any remaining doubts about the benevolence of the farmer. "You see, there is nothing to worry about. Our farmer had a little extra food, so he gave it to us because he likes us! He is a good man," remarked one chicken to the others, and they all nodded in agreement, all of them, that is, except one.The intelligent but eccentric chicken became even more agitated. "He is just fattening us up! We are going to be slaughtered in a weeks time!" he squawked in alarm. But nobody listened. All the other chickens just thought he was a troublemaker.A week later, all the chickens were placed into cages, loaded onto a truck, and driven to the slaughterhouse.
- This problem was proposed by the logician Carl Gustav Hempel in the 1940s to illustrate a contradiction between inductive logic and intuition. A related issue is the problem of induction and the gap between inductive and deductive reasoning.[Hempel describes the paradox in terms of the hypothesis:[2][3](1) All ravens are black. In strict logical terms, via contraposition, this statement is equivalent to:(2) Everything that is not black is not a raven. It should be clear that in all circumstances where (2) is true, (1) is also true; and likewise, in all circumstances where (2) is false (i.e. if a world is imagined in which something that was not black, yet was a raven, existed), (1) is also false. This establishes logical equivalence.Given a general statement such as all ravens are black, a form of the same statement that refers to a specific observable instance of the general class would typically be considered to constitute evidence for that general statement. For example,(3) Nevermore, my pet raven, is black. is evidence supporting the hypothesis that all ravens are black.The paradox arises when this same process is applied to statement (2). On sighting a green apple, one can observe:(4) This green (and thus not black) thing is an apple (and thus not a raven). By the same reasoning, this statement is evidence that (2) everything that is not black is not a raven. But since (as above) this statement is logically equivalent to (1) all ravens are black, it follows that the sight of a green apple is evidence supporting the notion that all ravens are black. This conclusion seems paradoxical, because it implies that information has been gained about ravens by looking at an apple. SolutionP1: All ravens are black.P2: All nonblack things are nonravens.E1: This raven is black.E2: This white thing is not a raven.P1 and P2 are logically equivalent, i.e., any evidence that supports P1 supports P2 to the same extent. But E1 and E2 are not equivalent. E1 provides much stronger support for both propositionsTo see why this is so, consider an aviary in which there are exactly two ravens among 100 birds.P3: All ravens in the aviary are black.P4: All nonblack birds in the aviary are nonravens.E3: This raven is black.E4: This white bird is not a raven.E3 represents 50% of the evidence needed to prove P3. Less obviously but equally true, it represents 50% of the evidence needed to prove P4. (If the only other raven is found to be black, P4 must be true.)By checking all 98 nonblack birds and verifying that they are not ravens, an investigator could prove P3. The proof would apply just as convincingly to P4. But a single nonblack nonraven would be less useful than a single black raven, because the former would represent 1/98th of the necessary evidence and the latter 50%.E1 and E3 are more significant than E2 and E4 because they account for a greater proportion of the total number of cases under consideration. Nevertheless, E2 to a trivial extent and E4 to a much greater extent, account for something – a nonblack nonraven eliminates one potential falsifier of the proposition “All ravens are black.”© Prof. F. Leavitt 1997ReferenceC.G. Hempel (1945) ‘Studies in the logic of confirmation’. Mind, 54: 1-26.Fred Leavitt is a professor in the Psychology Department at California State University
- Co-relation Problem among statements..
- Qualitative Hypothetico_Deductivisn HDH is confirmed by evidence E relative to background knowlewdge B iff the conjunction of H and B logically implies E in some suitable way
- The idea is that a sentence or proposition is the more informative, the more possibilitiesit excludes. Hence, the logically stronger a sentence, the more informativeit is. On the other hand, a sentence is more plausible the fewer possibilities itexcludes, i.e. the more possibilities it includes. Hence, the logically weaker asentence, the more plausible it is. The qualitative counterparts of these two comparativeprinciples are the defining clauses above. If H is informative relativeto E, then so is any logically stronger sentence H0. Similarly, if H is plausiblerelative to E, then so is any logically weaker sentence H0.
- Unified ‘logic of confirmation’, one that respects both the idea that a hypothesis H is confirmed by empirical evidence E if H can be formally inferred from E (i.e., if the theory derives from the data) and also the idea that H is confirmed by E if we can formally infer E from HAccording to Huber, the reason of this conflict is that there are (at least) two virtues a good theory must have, truth (or ‘plausibility’) and strength (or ‘informativeness’), and there is a trade-off between them (i.e., the kind of things we can do to improve the ‘truth’ of our theories usually go against what we can do to improve their ‘strength’, and vice-versa).So, imagine we try to define some measures f of the epistemic value of a hypothesis H given the evidence E and background knowledge B; functions f (H, E, B) may have many different mathematical properties, but the following ones are what wouldallow to call it, respectively, ‘truth responsive’ and ‘strength responsive’ on the basis of evidence1 (see Huber 2008a, pp. 92–93):(1) (a) If E entails H -> H, then f (H, E) ≤ f (H , E)(b) If ￢E entails H -> H, then f (H, E) ≤ f H, E)The condition in (1.a) means that, within the states allowed by E, all the states allowed by H are also allowed by H’, i.e., H’ covers a bigger portion than H of the states of the world consistent with our evidence; so, if f behaves in the way stated by (1.a), itwill give a higher value to theories that would be true in a bigger proportion of the states that we know might be true. The condition in (1.b) means, instead, that in the states that are not allowed by E, H’ covers a smaller portion of them than H, and so,the more content that we know is false a hypothesis has, the better (recall that the content of a proposition is inversely related to the magnitude of the states it is consistent with). Fig. 1 allows to clearly understand these two conditions ((1.a) refers to what happens ‘inside’ E, whereas (1.b) refers to what happens ‘out’ of E; the square represents the set of states consistent with background knowledge B).
- TraditinalEpistomoloy by ancient greek philosophers, Aristotle and Plateu
- Thoeries are modified by new theories,by improving to finding the final universal truth
- The main intuition under the notion of truthlikeness is that of the value of two false theories can be different, and even thatthe value of some false (or falsified) theories can be higher than the value of some true (or not yet falsified) theories. If truth and strength were the only relevant virtues of a hypothesis, then, if H and H’ have been falsified, then either both will have the same value, or the most informative of it will be better, but the latter entails that increasing the epistemic value of a falsified theory is a child’s playEpistemic value will not only depend on how much they say about the world, but also on something that has to do with what they say, inparticular, on what is the relation between what they say and the truth about the matterthat acceptable theories must have (if at all) a high degree of confirmation, and also other values, like the capacityof explaining or predicting the empirical evidenceThe naive definition asserts that the epistemic value of a theory depends on twofactors:a) how similar or coherent are the view of the world offered by the theory andthe view of the world that derives from our empirical evidence; andb) how informative our empirical evidence is (for being coherent with a veryshallow empirical knowledge is not as indicative of ‘deep truth’ as being coherent witha much richer corpus of empirical information).The coherence or similarity between H and E can be defined as p(H&E)/p(HvE),7whereas the informativeness of a proposition A can be measured by 1/p(A). Hence, thenaive definition of empirical verisimilitude would be as follows:(3) Vs(H,E) = [p(H&E)/p(HvE)][1/p(E)] = p(H,E)/p(HvE)
- The main intuition under the notion of truthlikeness is that of the value of two false theories can be different, and even thatthe value of some false (or falsified) theories can be higher than the value of some true (or not yet falsified) theories. If truth and strength were the only relevant virtues of a hypothesis, then, if H and H’ have been falsified, then either both will have the same value, or the most informative of it will be better, but the latter entails that increasing the epistemic value of a falsified theory is a child’s playEpistemic value will not only depend on how much they say about the world, but also on something that has to do with what they say, inparticular, on what is the relation between what they say and the truth about the matterthat acceptable theories must have (if at all) a high degree of confirmation, and also other values, like the capacityof explaining or predicting the empirical evidenceThe naive definition asserts that the epistemic value of a theory depends on twofactors:a) how similar or coherent are the view of the world offered by the theory andthe view of the world that derives from our empirical evidence; andb) how informative our empirical evidence is (for being coherent with a veryshallow empirical knowledge is not as indicative of ‘deep truth’ as being coherent witha much richer corpus of empirical information).The coherence or similarity between H and E can be defined as p(H&E)/p(HvE),7whereas the informativeness of a proposition A can be measured by 1/p(A). Hence, thenaive definition of empirical verisimilitude would be as follows:(3) Vs(H,E) = [p(H&E)/p(HvE)][1/p(E)] = p(H,E)/p(HvE)
- Once upon a time, positivist philosophers saw intertheoretical reduction as the fundamental road to scientific progress; the anti-positivist movement of the second part of the 20th century led a majority of philosophers to abandon, not only the idea that science progresses through reduction to some theories to others, but in many cases even the belief that intertheoretical reduction is logically possible at all
- Ceteris paribus or caA ceteris paribus assumption is often fundamental to the predictive purpose of scientific inquiry. In order to formulate scientific laws, it is usually necessary to rule out factors which interfere with examining a specific causal relationship. Under scientific experiments, the ceteris paribus assumption is realized when a scientist controls for all of the independent variables other than the one under study, so that the effect of a single independent variable on the dependent variable can be isolated. By holding all the other relevant factors constant, a scientist is able to focus on the unique effects of a given factor in a complex causal situation.eteris paribus is a Latin phrase, literally translated as "with other things the same," or "all other things being equal or held constant."
- Based on experts opinion