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24\begin{document}
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26%-----------------------------------------------------------
27% First page
28\begin{minipage}[t]{\textwidth}
29\begin{textblock*}{50mm}(0mm,0mm)
30\textbf{$\bullet$ Names}\\
31\textbf{Sammelweis:} Two hospitals. Washing hands with calcium hypochlorite reduced death rate. Discovered that washing hands between touching dead people and touching women giving birth decreases the chance that women the women dies. Cleaned hands with "calcium hypochlorite"\\
32\textbf{Alan Turing:} Turning test,If a computer is belived to be a human and, turning machine.\\
33\textbf{Francis Bacon:} Observations of nature, u should observe nature and recognize patterns and formulate scientific laws.\\
34\textbf{René Descartes:} Logical deductions, u should use your own logical reasoning to understand the laws of nature. Invented the cartesian coordinate system.\\
35\textbf{Karl Popper:} Falsification, rejection of the classical inductivist views on the scientific method, theory in the empirical sciences can never be proven, but
36it can be falsified, meaning that it can and should be scrutinised by decisive experiments.\\
37\textbf{David Hume:} Induction cannot be proved to be correct using logic nor proved using induction. Popper solves induction: We can never verify hypotheses. We can only falsify them.\\
38\textbf{Kepler:} Stated laws of planetary motion.\\
39\textbf{Newton:} Formulated the laws of gravity.\\
40\textbf{Darwin:} Published a theory of evolution by natural selection.\\
41\textbf{Lavoisier:} Disproved the phlogiston theory of combustion.\\
42\textbf{Mendeleyev:} Created the periodic table.\\
43\textbf{Carl Hempe:} The D-N Model and HD\\
44\textbf{Hans Reichenbach:} Reichenbach’s principle.\\
45\textbf{Thomas Kuhn:} Introduced the term paradigm shift. A paradigm consists of terms, methods, norms and ways of viewing thing.  It defines
46our way of understanding the world (or at least a part of it). Normal science is science as
47it is done within the paradigm. In revolutionary science we reject the old paradigm and
48replace it with a new one.\\
49\textbf{Aristotle:} Causes in nature, kinds of causes. Invented formal logic and syllogisms.
50\\
51\textbf{Euclid:} Formal mathematics, constructed geometry from axioms. 
52He listed a set of undeniable truths (axiom) and 
53showed how theorems can be deduced from the 
54axioms in a rigorous way.
55\\
56\textbf{Galilei:} Discovers a law for the movements of pendulums. Bodies with different weights fall equally fast. He constructs telescopes. He discovers mountains on the surface of the moon.
57Discovered Jupiter’s moons using a telescope.
58\\
59\textbf{Descartes:} Program for how research should be done. He presents a totally mechanistic worldview: Everything can be explained by interactions
60between physical bodies. He invents analytical geometry.\\
61\textbf{Kurt Gödel:} Incompleteness theorem, Some true statements have no proof.\\
62\textbf{Merton:} Characterize the scientific method\\
63\textbf{Kant:} Stated that duty ethics has a categorical imperative.\\
64$\cdot$ He had a theory about the way we view everything around us that can ”explain” science\\
65$\cdot$ He said that we have certain categories through which we understand what we see\\
66$\cdot$ We cannot say that the world is ”really” three-dimensional but we are forced to see it that way\\
67$\cdot$ We cannot tell if time really exists but we are forced to experience it\\
68$\cdot$ We don’t know if causes exist but we are forced to believe that they do\\
69$\cdot$ Science is built from our categories, the way we are forced to see things
70\\
71\textbf{Paul Feyerabend:} Freedom of science (like freedom of religion), He argues that there is no method common for all sciences.\\
72\textbf{Nietzsche:}\\
73$\cdot$ Regarded as one of the first to deny that objective truth exists.\\
74$\cdot$ Said that all truth is matter of Ideologyideologically driven.\\
75$\cdot$ Said that Christianity is a slave moral
76
77\textbf{Derrida: } Deconstruction, two types of problems: those that come from nature and those from humans.\\
78\textbf{Thomas Bayes: } Bayes formula: He found an important formula connecting different types of conditional probabilities, conditional probabilities, this formula is the basis for so called Bayesian Statistics.\\
79\textbf{Copernicus:} Introduced heliocentric world view.\\
80\textbf{William James:} One of the founders of Pragmaticism.\\
81\textbf{John Stuart Mill, Jeremy Bentham:} Created Consequentialism -Utilitarianism\\
82\textbf{Thomas Hobbes: } Contract Ethics\\
83\textbf{Frege:} He tried to construct all mathematics with logic.\\
84\textbf{Bertrand Russell:} Frege's axiom leads to contradictions\\
85\textbf{William of Occam:} Occam's razor\\
86\textbf{Headwood:} Proved that every plane graph can be coloured with no more than five colors. Weakening of the four-color theorem but his proof shows that an erroneous proof (by Kempe) can still be useful.\\
87\textbf{Sven Ove Hansson:} Proposed seven characteristics of pseudoscience\\
88\textbf{Goodman:} Goodman’s paradox.\\
89\textbf{Von Neumann:}
90Founded game theory based on the assumption of people's rationality.\\
91\textbf{Zeno:} 
92Pre-Socratic paradox creator. Achilles and the tortoise\\
93\textbf{Einstein:} Developed the general theory of relativity.\\
94\textbf{Robert Millikan:} Millikan determined the electron mass.\\
95\textbf{:}\\
96\textbf{:}\\
97\textbf{:}\\
98\textbf{:}\\
99\textbf{:}\\
100
101\textbf{Tomas Möre:} Theorem of chair breaking. Livet är ett smör.\\
102\textbf{:}\\
103\\\\\\
104\textbf{$\bullet$ Panel discussions:}\\
105A panel discussion is a public debate in front of an audience.\\
106The panel consists of experts, chosen to reflect different opinions.\\
107The moderator keeps the discussion going by asking the panelists questions, moderating the discussion, and ensuring that each panel member has en equal opportunity to speak.\\
108moderator, panelist, audience.
109\\\\
110\textbf{$\bullet$ The Renaissance}\\
111During the Renaissance several scientific 
112developments took place.
113The human body and the circulation of the 
114blood
115Copernicus' heliocentric  world view 
116\\\\
117\end{textblock*}
118
119%-----------------------------------------------------------
120\begin{textblock*}{50mm}(52mm,0mm)
121\begin{tabular}{|l}
122\begin{minipage}{50mm}
123\textbf{$\bullet$ Causes}\\
124\textbf{Sufficient cause:} A is a sufficient cause of B if      
125A => B.\\
126\textbf{Necessary cause:} A is a necessary cause of B if 
127not A => not B (B => A).
128\\\\
129If we have multiple causes but if we want to choose just one cause?
130We can choose the one  that is most unlikely to occur.  
131\\\\
132Aristotle gave a description of causes in nature. There are four 
133kinds of causes: \\
134A. Material causes \\
135B. Efficient causes \\
136C. Formal causes \\
137D. Final causes 
138\\\\
139\textbf{$\bullet$ Explaination}\\
140\textbf{Causal explanation:} If something causes P, it also explains P.\\
141\textbf{Functional explanation:} P has some good function and this fact explains P.\\
142\textbf{Explanation by purpose:} There is some mind that has wanted P.\\
143\textbf{Pragmatic explanation:} The explanation is adapted to the type of answer the questioner wants.\\
144\textbf{Explanations with unifying theories:} A unifying theory is a theory that explains a lot of observations (almost everything).\\
145\textbf{Explanations by reduction:} An attractive way of explaining observations is to reduce them to a basic theory and restate them in the language of the theory.\\
146\\
147If we want a theory of explanation that focuses on deduction and scientific laws, the D-N model seems to be the best alternative.\\
148\\\\
149\textbf{$\bullet$ Models}\\
150\textbf{$\circ$ DN-model} Theory -> Reality, (Carl Hempel) Deductive-nomological Define what explanations are, looks at statements, observations and laws in isolation.  \\ %not sure about Define what explanations are.
151We have a fact P in a situation 
152S. In the D-N model this fact is 
153explained in the following way:
1541. A general scientific law L.\ 
155(I => P)
1562.  An I initial condition that applies in S.
1573.Conclusion: P
158\textbf{Cons:}
159Could be too strong. Can exclude a possible cause even if it should be considered a cause.
160Could be too weak. Can classify something as a cause even if it should not.
161A high-level method for determining causes. Sometimes needs to be complemented by low-level methods.
162\\
163\textbf{$\circ$ HD-model} Reality -> Theory, 
164Used for falsification Hypothetico-Deductive  Method. 
165Combines deductions with 
166observations.
167The general method for handling observations.
168Solution to Induction problems.
169Is a proposed description of scientific method. According to the HD-method, scientific inquiry proceeds by formulating a hypothesis in a form that can be falsifiable, using an observable data where the outcome is not yet known. A test outcome that could have, but does not run contrary of the hypothesis corroborates the theory. Used in physics and chemistry.\\
170Example:
171We have a hypothesis and want to show that it is false.
172We have a set of observations E1, E2, ..., En.
173Assume that there is an observation Ei such that H => not Ei.
174Then Ei falsifies H.
175\\
176\textbf{$\circ$ Induction}\\
177We make observations and try to see a pattern in them.
178If the observations are many and all agree with the pattern we conjecture that the pattern always
179One motivation for induction is the Principle of Uniformity of Nature (PUN).
180\textbf{Principle of Uniformity of Nature (PUN):}
181$\cdot$ The idea is that there are regularities in nature 
182$\cdot$ If there are a lot of regularities to be found out there, then there is a big chance that an observed regular pattern can be an instance of a basic regularity 
183$\cdot$ If this is the case then it seems as if induction could be a logically meaningful tool for finding regularities
184\\\\
185\textbf{$\bullet$ Reichenbach’s principle}\\
1861. A is the cause of B\\
1872. or B is the cause of A\\
1883. or there is a third factor C that is the cause of both A and B.
189\\
190\textbf{$\bullet$ Hypothesis strengthening}\\
191hypothesis H and an observation E/\\
192\textbf{E strengthens H} if P(H|E) > P(H) or if P(E|H) > P(E) or if P(E|H) >
193P(E|notH).\\
194\textbf{E Weakens H} if P(H|E) < P(H) or if P(E|H) < P(E) or if P(E|H) <
195P(E|notH).
196\\\\
197\textbf{$\bullet$ Merton}\\
198\textbf{Communalism:} knowledge should be accessible for all people.\\
199\textbf{Universalism:} everyone should have the right to contribute.\\
200\textbf{Disinterestedness:} Science should be objective, not ruled by special interests.\\
201\textbf{Originality:} the results should be new.\\
202\textbf{Skepticism:} scientists should be open to criticism
203\\\\
204\textbf{$\bullet$ Homeopathy}\\
205Homeopathy was developed at the end of the 18th 
206century by Hahnemann.\\
207$\cdot$ One of the cornerstone of homeopathy is the principle 
208Like cures like. \\
209$\cdot$ Hahnemann’s favorite example was Cinchona bark 
210which cures malaria and gives malaria-like symptoms 
211if eaten (?)\\
212$\cdot$ The second principle is the 
213principle of dilution which makes a substance more potent if is diluted, given that 
214the dilution is done by a process called 
215succussion.\\
216$\cdot$ A third, more modern, principle is that water has a 
217memory of substances
218
219\textbf{$\bullet$ Types of errors}\\
220If we have two hypotheses $H_0$
221and $H_1$ and do a test like the ones mentioned and we
222assume that one of the hypotheses is true,
223we can get two types of errors.\\
224Type 1: We conclude that $H_1$
225is true while, in fact, $H_0$
226is true. The probability for this
227happening will be called $\alpha$.\\
228Type 2: We conclude that $H_0$
229is true while,
230in fact, $H_1$
231is true. The probability for this
232happening will be called $\beta$.\\
233In the tests we have described we have focused
234on designing the test so that
235$\alpha$ is small. But
236at the same time it can happen that
237$\beta$ is big. Ideally, we would like
238$\alpha$ and $\beta$ to be small at
239the same time, but is not always possible.
240The best way to make this possible is to do
241not just one test but n tests and compute
242$\Theta = \frac{1}{n}\sum_{i} \Theta _i$
243and use this value to tell which
244of $H_0$ and $H_1$ is true.
245\\\\
246\textbf{$\bullet$ Computer Simulations}\\
247There is one area of science that seems to
248be relatively unexplored: The Philosophy of
249Computer Simulation. Normally we observe
250reality and make observations. We can use
251computer methods to analyze data. But we
252can make computer simulations of ”reality”
253instead.
254Let us assume that we have a process P that
255we want to simulate.
256We might believe that we understand the
257process.
258We then try to write a program simulating
259the process.
260When we write the program we might run in-
261to difficulties which forces us to rethink our
262understanding of the process.
263So even without running the program we might
264gain understanding of the model which the
265process is part of.
266\end{minipage}
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268\end{textblock*}
269
270\begin{textblock*}{50mm}(106mm,0mm)
271\begin{tabular}{|l}
272\begin{minipage}{50mm}
273\textbf{$\bullet$ Falsification}\\
274If we have a theory T, we try to find a testable consequence E of T.
275If E turns out t be false, then T is falsified.
276Then we must reject T.\\
277A statement hypothesis, or theory has falsifiability (or is falsifiable) if it is contradicted by a basic statement, which in an eventual successful or failed falsification, must respectively correspond to a true or hypothetical observation.\\
278\textbf{Demarcation criterion:} 1) Logical part (stated in terms of rules of interference - ways to logically infer new statements from existing statements) 2) Methodological part (Stated in terms of rules that do not claim to prove anything) The methodological rules define falsification. They should not be confused with the logical rules of interference used to define falsifiability which is about the logical form of the theory. 
279We can never be certain that a theory is true. We can only know that it has not been falsified this far.
280\textbf{$\circ$ Criticism of falsificationism:} \\
281$\cdot$ The theory doesn't seem to agree well with how science is done in real life.
282$\cdot$ Scientist don't always (perhaps never) try to falsify their theories.
283$\cdot$ Well established theories have more than once been temporarily falsified.
284\\\\
285\textbf{$\bullet$ Theorems and such}\\
286\textbf{$\circ$ Benford’s Law:}\\
287“Thirty percent of all numbers start with the digit 1”.
288Supposedly true for collections of numbers with widely varying orders of magnitude, like populations of cities or byte sizes of files.\\
289\textbf{$\circ$ Gödel’s incompleteness theorems:}\\
290First Incompleteness Theorem: "Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.\\
291States that some true statements have no proof.
292\\
293Gödel’s second incompleteness theorem says that the system cannot be proved to be consistent with methods inside the system.
294\\
295Demonstrated the inherent limitations of every formal axiomatic system capable of modelling basic arithmetic. 
296"if we have a list of axioms which we can enumerate with a computer, and these axioms are sufficient to develop the basic laws of arithmetics, then our list of axioms cannot be both consistent and complete."
297\\
298\textbf{$\circ$ The Phlogiston Theory:}\\
299When an object is burning it is phlogiston leaving the object. 
300The Phlogiston Theory was falsified by Antoine Lavoisier.
301\\
302\textbf{$\circ$ Occam’s razor:}\\ The idea is to choose the simplest explanation.\\
303\textbf{$\circ$ The Four-colour Theorem}\\
304Every (planar) map can be coloured with 
305four colours. A colouring is required to be 
306such that no adjacent countries have the 
307same colour.   
308\\
309\textbf{$\circ$ Four-colour Theorem prorf}\\
310The path towards the proof of the FCT starts with a return to Kempe's
311failed proof from 1879. The proof uses ideas that Kempe had.
312The proof uses induction over the size of the graph. Then we observe
313that a planar graph must have a set of unavoidable subgraphs.
314Then we prove that the subgraphs are reducible. This means that if the
315rest of the graph can be four-coloured, then this colouring can be
316extended to the subgraph with some minor changes to the original
317colouring.
318Kempe found the a simple unavoidable subgraph in form of a node with
319degree at most five. But he failed to prove that the subgraph is
320reducible (it is not).
321Appel and Haken had the idea that they should try to find more
322complicated unavoidable subgraphs.
323\\\\
324Every (planar) map can be coloured with 
325four colours. A colouring is required to be 
326such that no adjacent countries have the 
327same colour.
328\\\\
329If a proof is erroneous, it means that there is a 
330counterexample.
331Counterexamples come in two forms:\\
332$\cdot$ Global counterexample - An example which 
333shows that the statement in the theorem is false.\\
334$\cdot$ Local counterexample - An example which shows 
335that a step in the proof is incorrect.
336\\\\
337We can 
338weaken 
339the theorem by replacing A or B 
340with other statements. The weaker theorem can 
341perhaps be proven.\\\\
342\textbf{$\bullet$ Data}\\
343A part of research is to handle data of different types. It appears that one can describe data in several ways.\\
344$\cdot$ Description after level of abstraction.\\
345$\cdot$ Split into primary and secondary data.\\
346$\cdot$ Quantitative and qualitative data.\\
347$\cdot$ Measurement for different types of scale.\\
348\\\\
349\textbf{$\bullet$ The rational person}\\
350$\cdot$ A rational decides what his/her goals are.\\
351$\cdot$ The goals and pursued in a rational way.\\
352$\cdot$ Rational probably means that they are pursued in a way most likely to achieve the goals.\\
353$\cdot$ But the goal should also be rational.\\
354$\cdot$ But then - what is a rational goal?\\
355$\cdot$ Do we need ethics to find out?
356\\\\
357\textbf{$\bullet$ Philosophical analysis of science}\\
358$\cdot$ Normative - It tells you how science should be\\
359$\cdot$ Descriptive - It tells you have science is actually done\\
360\\
361\textbf{$\bullet$ Mathematics and Natural Science}\\
362Truth: An objective truth. \\
363Method: In essence deduction and 
364hypothetical - deductive method linked to  
365experiments. \\
366Objectives: Knowledge of the objectively 
367existing world and the mathematical world.\\
368\textbf{$\bullet$ The Humanities}\\
369Truth: Very diverse perceptions. \\
370Method: The hermeneutic method 
371( understanding) seems the most important. \\
372Goal: Very diverse perceptions. Most likely, 
373they are all about understanding the world in 
374all aspects related to humans.\\
375\\
376\textbf{$\bullet$ Collectivism versus individualism}\\
377\textbf{Methodological individualism:} Analyze what the 
378most important actors in the historical process did 
379and thought. \\
380\textbf{Methodological collectivism:} Analyze the ideas and 
381forces that existed in society and what they led to. 
382\\\\
383\textbf{$\bullet$ Examples of pseudoscience}\\
384Classic examples of areas that are usually 
385regarded as pseudoscience is: \\
386$\cdot$ Astrology \\
387$\cdot$ Freudian psychology \\
388$\cdot$ Marxist theory 
389\\\\
390\textbf{$\bullet$ An alternative way to recognize 
391pseudoscience:}\\
392$\cdot$ It does not do any real problem solving. \\
393$\cdot$ It has for a long developed to a much 
394lesser degree than other "similar" theories.
395\\\\
396\textbf{$\bullet$ Users of formal systems:}\\
397$\cdot$ Mathematicians - use them to prove 
398mathematical theorems.\\
399$\cdot$ Computer scientists - use them to design 
400algorithms that solve problems.\\
401$\cdot$ Philosophers - use them to define and analyze 
402things.
403\\\\
404\end{minipage}
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411\textbf{$\bullet$ Argument}\\
412The reasons offered within the argument are called “premises”, and the proposition that the premises are offered for is called the “conclusion”\\
413\textbf{A premise:}, which
414$\cdot$ since
415$\cdot$ because
416$\cdot$ if
417$\cdot$ assuming that
418$\cdot$ given that
419\\
420\textbf{A conclusion:}
421$\cdot$ therefore
422$\cdot$ this proves that
423$\cdot$ then
424$\cdot$ consequently
425$\cdot$ thus
426\\\\
427\textbf{$\bullet$ Two types of logical reasoning}\\
428\textbf{inductive reasoning}, which
429entails moving from repeated observations to a general conclusion, and
430\textbf{deductive reasoning}, which entails going from a general principle (called a
431premise) to a conclusion about a particular case.
432\\\\
433\textbf{$\bullet$ Fallacies}\\
434\textbf{$\circ$ Formal fallacies}\\
435are those where the logical structure underpinning the
436argument is faulty in some way.\\
437\textbf{$\circ$ Informal fallacies}\\
438also come in many guises. These are misleading – not
439so much because the logical steps are incorrect, but because they make false
440analogies, use emotional and misleading claims, and jump to unjustified
441conclusions on evidence that is skimpy, irrelevant or untrue.
442\\\\
443\textbf{$\bullet$ Constructing an argument}\\
444One is to argue
445for a statement by providing evidence that will support it. The other is to
446refute a statement by providing evidence that undermines it. Between these
447opposites can be a combination of the two, which entails a less black-andwhite
448approach by arguing for a revision or refinement of the statement to get
449nearer to the truth, again based on the evidence presented. Another
450combination compares two – usually opposing – statements, and argues that
451one is right and the other is wrong.
452\\\\
453%--------------------------------------------
454\textbf{$\bullet$ yourlogicalfallacyis.com}\\
455\textbf{$\cdot$} You misrepresented someone's argument to make it easier to attack.\\
456\textbf{$\cdot$} You said that if we allow A to happen, then Z will eventually happen too, therefore A should not happen.\\
457\textbf{$\cdot$} Because you found something difficult to understand, or are unaware of how it works, you made out like it's probably not true.\\
458\textbf{$\cdot$} You used a double meaning or ambiguity of language to mislead or misrepresent the truth.\\
459\textbf{$\cdot$} You assumed that one part of something has to be applied to all, or other, parts of it; or that the whole must apply to its parts.\\
460\textbf{$\cdot$} You cherry-picked a data cluster to suit your argument, or found a pattern to fit a presumption.\\
461\textbf{$\cdot$} You presumed that a real or perceived relationship between things means that one is the cause of the other.\\
462\textbf{$\cdot$} You asked a question that had a presumption built into it so that it couldn't be answered without appearing guilty.\\
463\textbf{$\cdot$} You appealed to popularity or the fact that many people do something as an attempted form of validation.\\
464\textbf{$\cdot$} You made what could be called an appeal to purity as a way to dismiss relevant criticisms or flaws of your argument.\\
465\textbf{$\cdot$} You used a personal experience or an isolated example instead of a sound argument or compelling evidence.\\
466\textbf{$\cdot$} You attempted to manipulate an emotional response in place of a valid or compelling argument.\\
467\textbf{$\cdot$} You moved the goalposts or made up an exception when your claim was shown to be false.\\
468\textbf{$\cdot$} You said that because an authority thinks something, it must therefore be true.\\
469\textbf{$\cdot$} You judged something as either good or bad on the basis of where it comes from, or from whom it came.\\
470\textbf{$\cdot$} You argued that because something is 'natural' it is therefore valid, justified, inevitable, good or ideal.\\
471\textbf{$\cdot$} You claimed that a compromise, or middle point, between two extremes must be the truth.\\
472\textbf{$\cdot$} You presumed that because a claim has been poorly argued, or a fallacy has been made, that the claim itself must be wrong.\\
473\textbf{$\cdot$} You avoided having to engage with criticism by turning it back on the accuser - you answered criticism with criticism.\\
474\textbf{$\cdot$} You said that 'runs' occur to statistically independent phenomena such as roulette wheel spins.\\
475\textbf{$\cdot$} You presented two alternative states as the only possibilities, when in fact more possibilities exist.\\
476\textbf{$\cdot$} You attacked your opponent's character or personal traits in an attempt to undermine their argument.\\
477\textbf{$\cdot$} You presented a circular argument in which the conclusion was included in the premise.
478\\\\
479%--------------------------------------------
480\textbf{$\bullet$ Math}\\
481\textbf{$\circ$ Series}\\
482\textbf{$\cdot$ Geometric}\\
483$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\cdots$
484is geometric, because each successive term can be obtained by multiplying the previous term by 1/2.
485Geometric series are among the simplest examples of infinite series with finite sums, although not all of them have this property. Historically, geometric series played an important role in the early development of calculus, and they continue to be central in the study of convergence of series.
486\\
487\textbf{$\cdot$ Harmonic}\\
488The harmonic series is the divergent infinite series:\\
489$\sum_{n}^{\infty} \frac{1}{n} = 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\cdots$
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506\textbf{$\bullet$ Theories}\\
507\textbf{$\circ$ Ad hoc hypotheses}\\
508If H => not E and E has been observed, someone
509might want to save H. This can maybe be done by assuming that the
510implication has the form ( H\&A => not E). Then we
511substitute A1 for A and get (H\&A1 => E).If A1 seems very unlikely, 
512if considered by itself, we call
513A1 an ad hoc hypothesis.\\
514Added to a theory in order to save it from being falsified.
515Example: Add santa claus is invisible condition to avoid having him being disproved.
516\\
517\textbf{$\circ$ Realism:} The goal of science is to describe reality as it is.
518“Realists, unlike instrumentalists, think that scientific theories can answer metaphysical questions.”\\
519\textbf{$\circ$ scientific anti-realism}\\
520believe that science can only describe
521the observable parts of reality and that the theories
522often are only fictions or models about which we
523cannot say that they are true or false. The goal of science is to describe the observable part of reality as it is.We
524cannot say anything about the non-observable part of reality.\\
525\textbf{$\circ$ Pseudo science}\\
526Sven Ove Hansson proposed seven characteristics of pseudoscience:\\
527\textbf{$\cdot$ Authoritarianism:} Some people are accorded such great ability to decide what is true and false.\\
528\textbf{$\cdot$ Experiments that can not be repeated}\\
529\textbf{$\cdot$ Hand-picked examples:} hand-picked examples, instead of random.\\
530\textbf{$\cdot$ Reluctance to real testing:} Does not try test the theory against reality.\\
531\textbf{$\cdot$ Indifference to contradictory facts:} Evidence against the theory are ignored.\\
532\textbf{$\cdot$ Subterfuges:} Only tests the theory under such conditions that it can only be confirmed, never contradicted.\\
533\textbf{$\cdot$ Explanations are abandoned without being replaced:} One abandons sustainable explanations without putting something in place so that the new theory leaves more unexplained than the old one.\\
534\textbf{$\circ$ Hermeneutics}\\
535It is the theory and methodology of interpretation, especially the interpretation of biblical texts, wisdom literature, and philosophical texts. (Understanding the world in
536all aspects related to humans?)\\
537\textbf{$\circ$ Paradigm shifts}, (Tomas Kuhn)\\
538A paradigm consists of terms, methods, norms and ways of viewing thing.  It defines
539our way of understanding the world (or at least a part of it). Normal science is science as
540it is done within the paradigm. In revolutionary science we reject the old paradigm and
541replace it with a new one.\\
542\textbf{$\circ$ Creationism} (E.g. classical Christianity)\\
543Creationism is the belief that the world and all living things in whole or in part is the
544result of divine intervention or supernatural means.\\
545\textbf{$\circ$ Intelligent Design}\\
546The notion that life on Earth is too complex to have arisen and developed exclusively by random variation and natural selection as biology’s theory of evolution
547says. It is customary to give examples of organs that are irreducibly complex.\\
548\textbf{$\circ$ Postmodernism}\\
549By tradition, it is consider important to distinguish between 
550symbols and reality. A new brilliant insight: Everything's symbols!
551Postmodernism questions everything: Science, scientific methods, logic...\\
552Ideology in denying that truth exists.
553The theories of the modernist movement is and product of the Enlightenment, and inseparable link between knowledge and power. There is no universal fact or truth. 
554\\
555\textbf{$\circ$ Behaviorism}\\
556All scientific statements about 
557consciousness must be based 
558on observation.Consciousness is a fiction that 
559describes these observations. (kind of reductionism)\\
560\textbf{$\circ$ Realism:} there is a mathematical reality that exists independently of us. 
561Mathematicians are exploring this reality. Also called \textbf{Platonism}.\\
562\textbf{$\circ$ Constructivism:} the mathematics are designed by us. 
563Only what is constructed or potentially possible to construct is real.  This view (or a variant of it) is also known as \textbf{Intuitionism}.\\
564\textbf{$\circ$ Formalism:} Mathematics is just a sort of game with symbols. 
565Mathematicians examine the consequences of the different rules of the game. Everything that does not lead to a contradiction is allowed. This view is a form of anti-realism.\\
566\textbf{$\circ$ Metaphysics} is concerned with questions such as:\\
567What is it to be?\\
568Who are we?\\
569What is knowledge?\\
570What are things?\\
571What is time and space?\\
572One extreme is Idealism, another is Materialism. (Opposite ends of a spectrum)\\
573\textbf{$\circ$ Epistemology} is the theory of knowledge, especially regarding its
574validation and the methods used. It deals with how we know things and what
575we can regard as acceptable knowledge in a discipline. It is concerned with
576the reliability of our senses and the power of the mind. As for the methods of
577acquiring knowledge, the two basic approaches are Empiricism and Rationalism.
578\\
579The relative merits of these approaches have been argued ever since the
580ancient Greeks – Aristotle advocating the first and Plato the second.\\
581\textbf{$\circ$ Idealism}
582Advocates that reality is all in the mind; that everything that exists is in some way dependent on the activity of the mind. Hence, as phenomena are reliant on mental and social factors they are therefore in a state of constant change – e.g. music is not just sound, it is an
583emotional experience;\\
584\textbf{$\circ$ Materialism (or Reductionism)}
585Insists that only physical things and their interactions exist and that our minds and consciousness are wholly due to the active operation of materials. Hence, phenomena are
586independent of social factors and are therefore stable – e.g. music is just
587vibrations in the air.\\
588\textbf{$\circ$ Reductionism}
589For example, a reductionist regarding mathematics might take any given mathematical theory to be reducible to logic or set theory. Or, a reductionist about biological entities like cells might take such entities to be reducible to collections of physico-chemical entities like atoms and molecules.
590\\
591\textbf{$\circ$ Empiricism} (Logical Empiricism or Logical Positivism)\\
592Knowledge gained by sensory experience (using inductive reasoning).\\
593One of the principles of LP is the requirements we must put on a statement S in order for it to be meaningful.\\
594Let S be any statement put in a form that indicates that it should be true or false. It is meaningful if either:\\
595$\cdot$ it in principle can be proved or disproved using logical methods\\
596$\cdot$ there are some observations that would confirm or disconfirm the statement\\
597All other statements are meaningless.\\
598The idea with logical positivism is to ask the question:\\
599What kind of test would we perform to see if this statement is true?
600
601\textbf{$\circ$ Rationalism} 
602Knowledge gained by reasoning (using deductive
603reasoning).\\
604\textbf{$\circ$ Relativism} 
605The world around us is a creation of our mind. We can only experience it personally through perceptions influenced by our preconceptions, beliefs and values.\\
606\textbf{$\circ$ Instrumentalism}
607“scientific theories need not be believed to be true, but rather should be thought of as useful or convenient fictions.”\\
608\textbf{$\circ$ }\\
609\textbf{$\circ$ }\\
610\textbf{$\circ$ }\\
611\end{textblock*}
612
613\begin{textblock*}{50mm}(52mm,0mm)
614\begin{tabular}{|l}
615\begin{minipage}{50mm}
616\textbf{$\bullet$ Realism and Anti-realism}\\
617$\cdot$ Realists believe that science is an accurate
618description of reality, even those parts of it that
619cannot be observed directly.\\
620$\cdot$ Anti-realists believe that science can only describe
621the observable parts of reality and that the theories
622often are only fictions or models about which we
623cannot say that they are true or false.\\
624$\cdot$ 
625\\\\
626\textbf{$\circ$ Arguments for Anti-realism}\\
627$\cdot$ In the history of science, there are many examples of theories that explains observable data very well but still proved to be incorrect.\\
628$\cdot$ It is possible to realize that there is always a variety of theories that may explain these data. The theories are being under-determined.\\
629$\cdot$ If you are using a theory to explain the data, it is just an arbitrary tool for the explanation.
630\\\\
631\textbf{$\circ$ Arguments for realism}\\
632$\cdot$ Anti-realism is based on the supposed fact that we can divide the world into observable and non observable parts.\\
633$\cdot$ But can we really do that in a consistent way?\\
634$\cdot$ There are, for example. a gradual transition from observability with the eye to observability with electron microscopes. It is the first one a genuine observability but not the other one?
635%-------------------------------------------
636\\\\
637\textbf{$\bullet$ Science vs Pseudoscience}\\
638$\cdot$ Hand-picked examples vs random samples.\\
639$\cdot$ Experiments can not be repeated vs can be repeated.\\
640$\cdot$ 
641%-------------------------------------------
642\\\\
643\textbf{$\bullet$ Creationism is not a science. Three reasons.}\\
644$\cdot$ it is not falsifiable.\\
645$\cdot$ It is not guided by natural law.\\
646$\cdot$ Its conclusions are tentative, i.e., are not necessarily the final word.
647%-------------------------------------------
648\\\\
649\textbf{$\bullet$ Computer Science research?}\\
650$\cdot$ Categorize problems by complexity class.\\
651$\cdot$ Evaluate the performance of an algorithm.\\
652$\cdot$ Find Correlation between data sets.\\
653$\cdot$ Predict the outcome of an event using an algorithm.
654%-------------------------------------------
655\\\\
656\textbf{$\bullet$ Is Computer Science science?}\\
657\textbf{For:}\\
658$\cdot$ Computers itself are man-made however the problem about how we process data in the best way or how humans 
659interact with different interfaces are not anything man-made, so the claim that everything is artificial is false.\\
660$\cdot$ The problem is to correctlydivide all the different areas which are constantly popping up as advancesare made, which is not feasible.  And since some areas clearly are sciencethen the whole group has to be classified as science\\
661$\cdot$  Even if the research was made poorly does not mean the field is not a science. \\
662\textbf{Against:}\\
663$\cdot$ Computer Science deals with the artificial and human made concept, while a science should deal with non-artificial and laws of nature\\
664$\cdot$ Computer Science is a mismatch of several different fields, where some are clearly not science. \\
665$\cdot$ The way we do science is not scientific enough. A lot of hypotheses are not being tested.\\
666\\\\
667\textbf{$\bullet$ Paradox}\\
6681) Premise - consisting of facts and established truths,\\
6692) argument - which is a logical derivation of the premise and\\
6703) Conclusion - which seems to be fake.\\
671In each paradox, either the argument is inadequate, the premise wrong or the conclusion is actually true.
672%----------------------------------------------
673\\\\
674\textbf{$\bullet$ Raven paradox - Hypothesis “All ravens are black”}\\
675Observing a non-black raven would falsify the hypothesis, and observing a black raven would strengthen it.\\
676The hypothesis may be expressed in predicate logic as follows:\\
677H1: $\forall x R(x) \implies B(x)$\\
678But there is another, logically equivalent, way of writing this:\\
679H2: $\forall x \neg B(x) \implies \neg R(x)$\\\
680Thus All non-black objects are non-ravens. \\
681An observation of a non-black raven would still falsify the hypothesis, but now any observation of a non-black non-raven, such as a yellow banana, ought to strengthen it!              
682Hempel’s principle of symmetry:
683If a theory can explain facts then it also predicts facts and vice versa.
684%----------------------------------------------
685\\\\
686\textbf{$\bullet$ Goodman’s paradox}\\ 
687$\cdot$ An object is grue if it has been observed and was green or has not been observed (yet) and is blue. \\
688$\cdot$ All observed emeralds have been grue.\\
689$\cdot$ Should we conclude that all emeralds are grue?\\
690$\cdot$ Another way of defining grue is that x is grue if observed before September 18th 2018 and was green or x will be blue after the same date.\\
691$\cdot$ So emeralds are grue?
692
693\textbf{$\bullet$ Achilles and the tortoise}\\
694In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
695\\
696False because geometric series converges.
697%----------------------------------------------
698\\\\
699\textbf{$\bullet$ The Axiom of Choice}\\
700The paradox says that it is possible to divide a sphere with volume 1 into a number 
701of parts and put the parts together and form two spheres which both have volume 
7021!The paradox "works" because we can it divide the sphere into parts that do not 
703have measurable volumes.\\
704\textbf{$\circ$ Intelligent Design on Axiom of Choice}\\
705$\cdot$ We can believe that there is an objective answer to the question about the axiom of choice is true or not. We must try to understand the mathematical reality better. This approach is called realism.\\
706$\cdot$ We choose to only deal with such mathematics can be proved constructively. We cannot know if The axiom of choice is true. This approach is known as constructivism.\\
707$\cdot$ We can choose to accept the axiom of choice as true or false, depending on what we want.Have it your way! This approach is called formalism.
708%-------------------------------------------
709\\\\
710\textbf{$\bullet$ Ethics}\\
711\begin{tabular}{|c|c|c|c|}
712    \hline
713    Theory & Intuitive & Operational & Logical \\
714    \hline
715    Consequentialism & No & ? & Yes\\
716     \hline
717    Deontology & Yes & ? & No\\
718     \hline
719    Contract & ? & Yes & Yes\\
720     \hline
721\end{tabular}
722
723\textbf{$\bullet$ How to define a scientific theory}
724To be more specific, he used these five points to describe 
725the difference between a scientific theory and a pseudo-
726scientific theory. A scientific theory must fulfill this: \\
727It is guided by natural law. \\
728It has to be explained by reference to natural law. \\
729It is testable against the empirical world. \\
730Its conclusions are tentative, i.e., are not necessarily the 
731final word. \\
732It is falsifiable.
733\\
734\textbf{$\bullet$ Examples of pseudoscience}\\
735Classic examples of areas that are usually 
736regarded as pseudoscience is: \\
737$\cdot$ Astrology \\
738$\cdot$ Freudian psychology \\
739$\cdot$ Marxist theory 
740\end{minipage}
741\end{tabular}
742\end{textblock*}
743
744\begin{textblock*}{50mm}(106mm,0mm)
745\begin{tabular}{|l}
746\begin{minipage}{50mm}
747\textbf{$\bullet$ What is Ethics?}\\
748We can say it is a system for guiding our
749choices in different situations.
750But it is not just rational choices. It is about
751situations where our conceptions of right and
752wrong and good and bad play roles.
753We could say that ethics tries to be a logical
754theory about something - perhaps - irrational.
755We could demand that an ethical theory should work
756$\cdot$ Intuitively: It should to some extent agree with
757generally accepted notions (whatever that is)
758$\cdot$ Operationally: It should give working guidelines for
759our behavior
760$\cdot$ Logically: It should be amendable to some form of
761logical analysis
762\\\\
763\textbf{$\bullet$ Ethics}\\
764\textbf{$\circ$ Consequentialism -Utilitarianism:} (John Stuart Mill, Jeremy Bentham)
765We act so that we maximize the goodness of the results. Utilitarianism <=> maximize the total happiness in a society.\\
766\textbf{Pros:}\\
7671. Its logical clarity makes it believable.\\
7682. Handles impartiality in a good way.\\
7693. Detailed analysis of different alternative options.\\
770\textbf{Cons:}\\
7711. Calculations of happiness possible in practice?\\
7722. Defend injustices and indifferences to a person’s suffering by many people’s happiness.\\
7733. Justify almost any type of actions.\\
774\textbf{$\circ $Duty Ethics- Deontology} (Immanuel Kant)\\
775Make an assessment of the acts themselves.
776Certain actions are prohibited regardless of the consequences.\\
777\textbf{Pros:}\\ 1. easy to understand\\2. it is intuitive\\3. evident how to use.\\
778\textbf{Cons:}\\ 1. defend act with bad consequences.\\2. different moral laws might conflict.\\
779\textbf{$\circ $ Contract Ethics} (Thomas Hobbes) A code of ethics is a set of rules that you agreed to follow. A contract.\\
780The main idea is that we need ethics in form of laws in order to make co-operation between humans possible 
781In a way it is more important to have rules even if they are bad rules than to have no rules at all
782A code of ethics is a set of rules that you agreed to follow. We have, so to say, drawn up a contract. 
783According to Hobbes, ethics is such a social contract that all citizens must be aware of. 
784We can think of a profession that has rules for how its members should act. If you do not follow the rules, you are not in the profession any longer. 
785\\
786\textbf{$\circ $ Other theories}\\
787\textbf{Subjectivism:} What I think is right, is right (for me).\\
788\textbf{Relativism:} What is right or wrong depends on what culture you live in.\\
789\textbf{Emotivism:} It is all emotions. It is good, yeah!!\\
790\textbf{Virtue ethics:} The important thing is to be a good person.\\
791\textbf{Supernaturalism:} Only what GOD commands is right.\\
792\textbf{Intuitionism:} We should follow our intuition on true moral values\\
793\textbf{Deontology:} There are a few general rules that must be followed unconditionally.
794\\
795\textbf{$\circ $ A proposal for scientific ethics}\\
796follow 10 principles:\\
797$\cdot$ Honesty: Scientists shall not falsify or distort the results.
798They must be objective and impartial in the
799research process.\\
800$\cdot$ Accuracy: Scientists should avoid errors in research caused by
801carelessness and uncritical thinking. They should
802avoid self-deception and conflicts of interest. \\
803$\cdot$ Openness: Scientists should share data, methods, and
804ideas with others. They shall permit criticism. \\
805$\cdot$ Freedom: Scientists should allow all kinds of research,
806ideas and theories. They shall, however,
807criticize research, ideas and theories they
808perceive as wrong. \\
809$\cdot$ Recognition: Scientists should give recognition to those who
810deserve it, above all at the publication of
811books and articles. \\
812$\cdot$ Teaching: Scientists should devote part of their time to
813teaching. They should also strive to inform the
814public about science.  \\
815$\cdot$ Social responsibility: Scientists should avoid research that harms society.
816They should try to produce good effects. Scientists
817are responsible for their research and to inform the
818public about the possible negative consequences of
819it. \\
820$\cdot$ Opportunity for all: Scientists should avoid research that harms society.
821They should try to produce good effects. Scientists
822are responsible for their research and to inform the
823public about the possible negative consequences of
824it. \\
825$\cdot$ Mutual respect: Scientists should treat colleagues with
826consideration and respect.\\
827$\cdot$ Respect for human (and
828animal) subjects in
829experiments: Scientists should treat human subjects and
830laboratory animals with dignity. Scientists
831should not violate anyone's rights or privacy. 
832%-------------------------------------------
833\\\\
834\textbf{$\bullet$ Famous theories}\\
835$\cdot$ Utilitarism - We should increase happiness in the
836world\\
837$\cdot$ Subjectivism - It is up to everyone to find his/her
838moral values\\
839$\cdot$ Relativism - Ethics is something defined by your
840culture. Different ethics are equally true\\
841$\cdot$ Intuitionism - We should follow our intuition on true
842moral values\\
843$\cdot$ Deontology - There are a few general rules that
844must be followed unconditionally\\
845$\cdot$ Supernaturalism - Moral rules are commands given
846by a supernatural being\\
847$\cdot$ Emotivism - Saying that X is good means the same
848thing as saying: ”Hurrah for X!”\\
849$\cdot$ Virtue ethics - You should try to be a good person.
850Then good actions follow naturally There exists virtues e.g.
851Honest, generous, kind, understanding. And if you as such have these virtues, one's actions become moral.
852\\\\
853\textbf{$\bullet$ Philosophical Terms}\\
854\textbf{Naive Realism:} Reality is more or less as we experience it.\\
855\textbf{Critical Realism:} Reality exists but we cannot experience it 
856directly. There is, however, a close connection between reality 
857and our experiences of it.\\
858\textbf{Idealism:} Reality does not exist. The only existing things are 
859our (or just my) experiences. \\
860\textbf{Phenomenalism:} Reality exists but we can only know it through 
861constructions based on observations made by our senses.
862%-------------------------------------------
863\\\\
864\textbf{$\bullet$ Cognitive theories}\\
865\textbf{$\circ$ Emotivism-Morality}\\
866Is just about the feelings we have for something.
867Ethics based on intuition - Works best with Duty Ethics\\
868\textbf{$\circ$ Cognitivism-Morality}\\
869Is something objectively existing and we can have knowledge about this something.
870Ethics based on rationality - Works best with Consequence Ethics
871%-------------------------------------------
872\\\\
873\textbf{$\bullet$ Truth}\\
874\textbf{Correspondence Truth:} A statement is true if what it says is a fact existing in reality
875(observations of reality.)\\
876\textbf{Coherence Truth:} A statement is true if it is a part of a consistent system of statements.
877(Prove statements with logical methods.)\\
878\textbf{$\circ$ ``Subjective truth''}\\
879\textbf{Intuitive truth:} Something is true if there is no way we can believe it is false (strong
880conviction).\\
881\textbf{Pragmatic truth:} If we cannot prove that something is true or false we can choose to
882believe it is true if that choice has good consequences for us.
883%-------------------------------------------
884\\\\
885
886
887\end{minipage}
888\end{tabular}
889\end{textblock*}
890
891
892\begin{textblock*}{46mm}(160mm,0mm)
893\begin{tabular}{|l}
894\begin{minipage}{46mm}
895\textbf{$\bullet$ What is Science?}\\
896Science is a way to find absolute truths about nature.
897Another philosophy is that scientific theories don’t have to be strictly true. The important thing is that they give us a tool for predicting the future. This view is called Instrumentalism. Instrumentalists don’t deny the existence of truth, they just say that truth is not that important.
898\\\\
899\textbf{$\bullet$ What is scientific methodology?}\\
900$\cdot$ The HD-method for finding hypotheses.\\
901$\cdot$ Maximum Likelihood. Try to find H such that P(E | H) is maximal.\\
902$\cdot$ Use Baye's formula for computing P(H | E).\\
903$\cdot$ Deduction\\
904$\cdot$ Reichenbach’s principle
905$\cdot$ Probabilistic variant - We see how the HD-Method can
906be modified with probabilistic reasoning. We look at
907Bayesian methods
908\\\\
909\textbf{$\bullet$ Types of research}\\
910$\cdot$ Exploratory research.\\
911$\cdot$ Testing-out research.\\
912$\cdot$ Problem-solving research.
913\\\\
914\textbf{$\bullet$ Scientific method in project work}
915$\cdot$ Preparing Analysis\\
916$\cdot$ Finding hypotheses\\
917$\cdot$ Synthesis of partial results\\
918$\cdot$ Validation of results
919\\\\
920\textbf{$\bullet$ Three methods of analysis}\\
921$\cdot$ Content analysis: simply count the occurrences of something.\\
922$\cdot$ Data mining: use software to find pattern in data.\\
923$\cdot$ Meta-analysis: Analyze several of analyzes simultaneously and try to find patterns in them.\\
924$\cdot$ Linear Regression: Fitting a straight line to the data points.
925\\\\
926\textbf{$\bullet$ Probabilistic methods and problems}\\
927\textbf{$\circ$ Maximum Likelihood method:} if $P(E|H_1) > P(E|H_0)$ we should
928say that $H_1$ is more likely to be true.\\
929\textbf{$\circ$ Confidence intervals:}  Find and interval for 
930$I = [v-\epsilon, v+\epsilon]$ such that the probability that a value belongs
931to I is $\alpha$ where $\alpha$ is the chosen confidence level. (E.g. $\alpha = 0.95$)\\
932$\frac{v-\Theta}{\sigma}$ is N(0,1)-distributed.
933${P(v-q_{0.925}\sigma \leq \Theta \leq v+q_{0.925}\sigma )}{=0.95}$
934\\
935\textbf{$\circ$ Hypothesis testing:}\\
936Assume a hypothesis H to test. Compare it to a zero-hypothesis $H_0$. Design
937a test which gives us a value t. Define a set C such that we can reject $H_0$ if t
938is a membor of C. (That means that we accept H). The test is at a significant level 
939$\alpha$ if the $P(t\subset C) \leq \alpha$. If $t\subset C$, H passes the test on a significance level $\alpha$.
940\\\\
941\textbf{$\bullet$ Experiment design}\\
942Final stage(7):  Find some subjects. Randomly decide who is going to have a daily dosis of 
943vitamin C (group C) and who is going to have a pill that doesn't contain any active ingredient
944(group P). The subjects do not know ehther they belong to group C or P, and neither does the
945experiment leader. At the end of the trail period, we measure whether group C had fewer days of 
946infection than group P.\\
947\\
948$\cdot$ Control group \\
949$\cdot$ Randomly select who is part of the experiment 
950group and who is part of the control group \\
951$\cdot$  Placebo  \\
952$\cdot$  Double blind tests
953\\\\
954\textbf{$\bullet$ Components of a deductive system}\\
955\textbf{$\circ$ Vocabulary}\\
956In a deductive system the vocabulary is roughly the syntax of the language we use in
957the system. Less formally, we can say that the vocabulary defines the type of expressions you can expect to find in the system.\\
958\textbf{$\circ$ Deduction Rules}\\
959All deduction systems have some set of formal and informal rules which tells us what
960conclusions we can prove from other statements.\\
961\textbf{$\circ$ Axioms}\\
962Axioms are basic truths (intuitive truths maybe).
963Starting with axioms and using the deduction rules we create theorems.
964The axioms and theorems are the only truths in the system.
965In formal systems we divide the axioms into logical and non-logical axioms.
966In some systems with very strong deduction rules we have no logical axioms at all. Natural deduction is one example.
967\\\\
968\textbf{$\bullet$ Different ways interpreted probability:}\\
969\textbf{$\circ$ Axiomatic:} We postulate a set of equally probable elementary events. Every other event is expressed as a combination of these events. \\
970\textbf{$\circ$ Frequency:} The probability for an event is roughly the frequency with which the event will occur in repeated experiments. \\
971\textbf{$\circ$ Subjective:} We give a measure for the ”probability” of events without giving a formal basis for this measure.\\
972It seems as if the Bayesian view of verification relies on an extensive use of subjective probability. This is a problem since subjective probability is not universally accepted as a stringent scientific concept.
973\\\\
974\textbf{$\bullet$ Characterize science:}\\
975\textbf{$\circ$ Generalization:} When doing science we often try to generalize results we have obtained. We try to formulate general laws that are independent of special conditions. We carefully try to test the suggested laws and, if possible, try to prove them.
976\\
977\textbf{$\circ$ Verification and validation:} We can use scientific methods to prove special facts. (Even if
978they may not be classified as laws.) ”Now it is scientifically proved: Eating very little makes you Hungry.” Verification is normally done with strict statistical methods. We can also evaluate different engineering methods with similar methods.
979\\
980\textbf{$\circ$ Rigorous methodology:} Scientific methodology can mean a lot things. We will largely focus on the rules for writing scientific papers and for working together with other scientists. Science is mainly a communal enterprise. It is one of the main strengths of science (possibly the greatest one).
981\textbf{$\circ$ Underdetermination:} To each set of observations there are always different theories that fit the data.
982\\\\
983\textbf{$\bullet$ Scientific filter}\\
9841. We must put our solution in a broader scientific context. We must give references to
985other solutions and similar problems.\\
9862. We must prove scientifically that our solution is correct.\\
9873. We must publish our solution in the form of a report following scientific standards.
988\end{minipage}
989\end{tabular}
990\end{textblock*}
991
992
993
994
995\end{minipage}
996
997} %End tiny
998\end{document}