1. Falsifiability - 1
In science and philosophy of science, falsifiability, contingency, and defeasibility are roughly equivalent terms referring to the property of empirical statements that they must admit of logical counterexamples.
This stands in contradistinction to formal and mathematical statements that may be tautologies, that is, universally true by dint of definitions, axioms, and proofs.

2. Falsifiability - 2
Some philosophers and scientists, most notably Karl Popper, have asserted that no empirical hypothesis, proposition, or theory can be considered scientific if it does not admit the possibility of a contrary case.
For example, the proposition "all swans are white" would be falsified by observing a black swan, which would in turn depend on there being a black swan somewhere in existence.

3. Falsifiability - 3
A falsifiable proposition or theory must define in some way what is, or will be, forbidden by that proposition or theory.
For example, the existence of a black swan is forbidden by the proposition in question. The possibility in principle of observing a black swan as a counterexample to the general proposition is sufficient to qualify the proposition as falsifiable.

4. Falsifiability - 4
The falsification of statements occurs through modus tollens, via some observation.
Suppose some universal statement U implies an observation O :
U → O
An observation conflicting with O , however, is made:
¬ O
So by modus tollens :
¬ U

5. Falsifiability - 5
It is always possible to revise the universal statement or the existential statement so that falsification does not occur.
On hearing that a black swan has been observed in Australia, one might introduce the ad hoc hypothesis, "all swans are white except those found in Australia".
The universal statement is defeasible through exceptions. And there may be exceptions to the exceptions.

6. Falsifiability - 6
Naïve falsification considers scientific statements individually. But scientific theories are formed from groups of these sorts of statements, and it is these groups that must be accepted or rejected by scientists. Scientific theories can always be defended by the addition of ad hoc hypotheses.
As Popper put it, a decision is required on the part of the scientist to accept or reject the statements that go to make up a theory or that might falsify it.

7. Falsifiability - 7
At some point, the weight of the ad hoc hypotheses and disregarded falsifying observations will become so great that it becomes unreasonable to support the base theory any longer, and a decision will be made to reject it.
In place of naïve falsification, Popper envisioned science as evolving by the successive rejection of falsified theories, rather than falsified statements.
Falsified theories are to be replaced by theories that account for the phenomena which falsified the prior theory, i.e. with greater explanatory power.

8. Falsifiability - 8
Popper proposed falsification as a way to determine if a theory is scientific. If a theory is falsifiable, then it is scientific; if it is not, then it is not science. A theory not open to falsification requires faith that it is not false. He uses this criterion of demarcation to draw a sharp line between scientific and unscientific theories.
Falsifiability was one of the criteria used by Judge Overton to determine that 'creation science' was not scientific and should not be taught in public schools. It was enshrined in United States law for whether scientific evidence is admissible in a jury trial.

9. Belief Revision- 1
Belief revision is the process of changing beliefs to take into account a new piece of information.
The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents.
What makes belief revision non-trivial is that several different ways for performing this operation may be possible.

10. Belief Revision- 2
E.g., the current knowledge includes the 3 facts: “A is true”, “B is true” and “if A and B are true then C is true”.
The introduction of the new information “C is false” can be done preserving consistency only by removing at least one of the 3 facts. In this case, there are at least 3 different ways for performing revision.
In general, there may be several different ways for changing knowledge.

11. Belief Revision- 3 Two kinds of change are usually distinguished:
Update. New information is about the present, while the old beliefs refer to the past; update is the operation of changing the old beliefs to take into account the change.
Revision. Both the old beliefs and the new information refer to the same situation; an inconsistency between them is explained by the possibility of old information being less reliable than the new one; revision is the process of inserting the new information into the set of old beliefs without generating an inconsistency.

12. Belief Revision- 4
The main assumption of belief revision is that of minimal change: the knowledge before and after the change should be as similar as possible.
In the case of update, this principle formalizes the assumption of inertia.
In the case of revision, this principle enforces as much information as possible to be preserved by the change.

13. Scientific method - 1
Scientific method is a body of techniques for investigating phenomena and acquiring new knowledge, as well as for correcting and integrating previous knowledge. It is based on observable, empirical, measurable evidence, and subject to laws of reasoning.
Although specialized procedures vary from one field of inquiry to another, there are identifiable features that distinguish scientific inquiry from other methods of developing knowledge.

14. Scientific method - 2
Scientific researchers propose specific hypotheses as explanations of natural phenomena, and design experimental studies that test these predictions for accuracy.
These steps are repeated in order to make increasingly dependable predictions of future results.
Theories that encompass whole domains of inquiry serve to bind more specific hypotheses together into logically coherent wholes.

15. Scientific method - 3
This in turn aids in the formation of new hypotheses, as well as in placing groups of specific hypotheses into a broader context of understanding.
Among other facets shared by the various fields of inquiry is the conviction that the process must be objective so that the scientist does not bias the interpretation of the results or change the results outright.

16. Scientific method - 4
Another basic expectation is that of making complete documentation of data and methodology available for careful scrutiny by other scientists and researchers, thereby allowing other researchers the opportunity to verify results by attempted reproduction of them.
This also allows statistical measures of the reliability of the results to be established.

17. Scientific method - 5
There are multiple ways of outlining the basic method shared by all of the fields of scientific inquiry.
The following facets are typical classifications of the most important components of the method on which there is very wide agreement in the scientific community and among philosophers of science.

18. Scientific method - 6
Observation. A constant feature of scientific inquiry.
Description. Information must be reliable, i.e. replicable (repeatable) as well as valid (relevant to the inquiry).
Prediction. Information must be valid for observations past, present, and future of given phenomena, i.e. purported "one shot" phenomena do not give rise to the capability to predict, nor to the ability to repeat an experiment.

19. Scientific method - 7
Control. Actively and fairly sampling the range of possible occurrences, whenever possible and proper, as opposed to the passive acceptance of opportunistic data, is the best way to control or counterbalance the risk of empirical bias.
Falsifiability, or the elimination of plausible alternatives. This is a gradual process that requires repeated experiments by multiple researchers who must be able to replicate results in order to corroborate them.

20. Scientific method - 8
All hypotheses and theories are in principle subject to disproof. There might be a consensus about a particular hypothesis or theory, yet it must in principle remain tentative.
As a body of knowledge grows and a particular hypothesis or theory repeatedly brings predictable results, confidence in the hypothesis or theory increases.

21. Scientific method - 9
Causal explanation. The following requirements are generally regarded as important to scientific understanding:
Identification of causes. Identification of the causes of a particular phenomenon to the best achievable extent.
Covariation of events. The hypothesized causes must correlate with observed effects.
Time-order relationship. The hypothesized causes must precede the observed effects.

22. Scientific method - 10
Testability, a property applying to an empirical hypothesis, involves two components:
The logical property described as contingency, defeasibility, or falsifiability, meaning that counterexamples to the hypothesis are not logically impossible.
The practical feasibility of observing a reproducible series of such counterexamples, if they do exist.
In short, a hypothesis is testable if there is some real hope of deciding whether it is true or false of real experience.

23. Scientific method - 11
The predictive power of a scientific theory refers to its ability to generate testable predictions.
Theories with strong predictive power are highly valued, because the predictions can often encourage the falsification of the theory.
The concept of predictive power differs from explanatory or descriptive power (where phenomena that are already known are retrospectively explained by a given theory) in that it allows a prospective test of theoretical understanding.

24. Scientific method - 12
Scientific ideas that do not confer any predictive power are considered at best "conjectures", or at worst "pseudoscience". Because they cannot be tested or falsified in any way, there is no way to determine whether they are true or false, and so they do not gain the status of "scientific theory".
Theories whose "predictive power" presupposes technologies that are not currently possible constitute something of a grey area.

25. Scientific method - 13
Reproducibility is one of the main principles of the scientific method, and refers to the ability of a test or experiment to be accurately reproduced, or replicated.
The term is very closely related to the concept of testability and, depending on the particular field, may require the test or experiment to be falsifiable.

26. Scientific method - 14
The results of an experiment performed by a group of researchers are generally evaluated by other independent researchers by reproducing the original experiment.
They repeat the same experiment themselves, based on the original experimental description, and see if their experiment gives similar results to those reported by the original group.
The result values are said to be commensurate if they are obtained (in distinct experimental trials) according to the same reproducible experimental description and procedure.

27. Scientific method - 15
Experiments which cannot be reliably reproduced are generally not considered to provide useful scientific evidence.
Results which prove to be highly reproducible are given more credence than those which are less reproducible, although this is based on an intuitive application of the principle of induction, rather than on the strict application of the principles of falsifiability.

28. Science features – summary 1
Science is the organized, systematic enterprize that gathers knowledge about the world and our theorizations and condenses it into testable laws and principles.
The features of science that distinguish it from pseudoscience are: repeatability, economy, mensuration, heuristics, consilience.

29. Science features – summary 2
Repeatability: The same phenomenon is sought again, preferably by independent investigation, and the interpretation given to it is confirmed or discarded by means of novel analysis and experimentation.
Economy: Scientists attempt to abstract the information into the form that is both simplest and aesthetically most pleasing – the combination called elegance – while yielding the largest amount of information with the least amount of effort.

30. Science features – summary 3
Mensuration: If something come be properly measured, using universally accepted scales, generalizations about it are rendered unambiguous.
Heuristics: The best science stimulates further discovery, often in unpredictable new directions; and the new knowledge provides an additional test of the original principles that led to its discovery.
Consilience: The explanations most likely to survive, of different phenomena, are those that can be connected and proved consistent with one another.