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College aantekeningen

Coursera Quantitative Methods
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I've made notes of every single video(clip) of this Coursera course, every week. Everything you need to know to pass your quizzes and to study the material thoroughly is included.

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  • 9 augustus 2021
  • 31
  • 2020/2021
  • College aantekeningen
  • Annemarie zand scholten
  • Alle colleges

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Voorbeeld van de inhoud

Quantitative methods
When and from whom do you accept a description or explanation as true?
From someone with authority: a teacher, a boss, a scientist, an expert in the field, your father.
When they can back up their statement with solid sounding arguments.

1.01 Non-scientific methods
- Intuition/belief
- Consensus
- Authority (opinions)

- Casual observation > better than ^, people are not good at observing, we selectively observe,
we remember things that agree with our beliefs (selective perception, bias)
- Informal logic > reasoning (biased, flawed)

We can’t depend on subjective, unreliable sources like opinions. We need systematic observation,
free from any bias, combined with consistently applied formal logic: we need the scientific method.

What principles come to mind when you hear scientific method?
Replicable, research, reliable, lots of data.

1.02 Scientific method
- Systematic observation
- Formal logic, consistently applied
So: better chance of valid explanations, evaluate plausibility of hypothesis.

Six principles of the scientific method for hypothesis
1. Empirically testable: it’s possible to collect empirical or physical evidence or observations
(data)
2. Replicable: able to consistently repeat or replicate the original study (no accidental
outcomes)
3. Objective: it shouldn’t matter who is performing the study to get the same results > clear
assumptions, concepts and procedures: independently
4. Transparency: researchers need to publicly share the assumptions, concepts, procedures and
any other relevant information for accurate replication
5. Falsifiable: possible to find observations that contradict the hypothesis > it’s pointless
otherwise since the conclusion is already drawn
6. Logically consistent/coherent: there shouldn’t be any internal contradiction

Which is more certain, a hypothesis or a theory?
Theory. You base a theory on a hypothesis and can apply it in the real world.

1.03: Scientific Claims

Observation: an accurate or inaccurate representation of the world, an observation is not
informative because it doesn’t describe and explain a general relation. Observations are the building
blocks of the empirical sciences, but they’re not very useful on their own. They come useful when
they can be used to confirm or contradict a hypothesis.

,Hypothesis (law): describes/explains a pattern or general relation between properties. Laws are
strongly supported, but don’t show much connection between properties. For examples Newton’s
gravity law.

Theory: a broad overarching explanation of many related phenomena. A theory is build out of
hypothesis that are very strongly supported by empirical evidence. A theory is highly plausible when
it’s supported by logical grounds, historical and qualitative analyses.

Theories are the most well established explanations, the closest thing to certainty. They consist of
hypothesis that have survived the scientific method. This doesn’t mean that they’re certain or true.
In science there is no certainty, only a provision, best explanation.

1.04: Classical Period

Plato was a philosophical realist. He said that reality exists independently of human thought. Plato
says we can’t learn/get knowledge about the nature of reality through sensory experience, but
through reasoning. Plato is therefore called a rationalist.

Aristotle, student of Plato, was a realist just like Plato. To Aristotle, reality is the physical world.
Unlike Plato, he says that there’s no separate plane of existence where abstract forms live. Also
unlike Plato, Aristotle was an empiricist and believed our sensory experience gives us an accurate
representation of reality. Knowledge comes through observation. He still saw reasoning as the best
way to understand and explain nature. He developed formal logic > syllogism. (logische redenering)

According to Aristotle, the fundamental premises (premises that you accept as undisputedly true)
can be determined through observation of basic patterns or regularities in the world.

Plato’s and Aristotle’s views were dominant for almost 2000 years. At the end of the 16 th century,
people realised that Plato and Aristotle’s views were flawed (flawed, selective, observations).

The ancient Greek Ptolemy described the movement of planets by placing the earth at the centre of
the universe with the planets each moving in their own cycle along their orbital path.

New scientific discoveries weren’t made until a huge scientific revolution started at the end of the
16th century: the age of enlightenment.

In the 10th century, Arab and Persian scholars started using systematic observation and
experimentation, emphasising unbiased observation and not just logical reasoning.

Englishmen Grosseteste and Roger Bacon advocated the use of induction and deduction.

Induction: using particular observations to generate general explanations.
Deduction: predicting particular outcomes based on general explanations.

The printing press was the third important development. It created the perfect conditions for a
scientific revolution: easily spreading knowledge to more people,

The fourth development ahead of the scientific revolution was Copernicus model about planetary
motion where the sun is central of all planets. This was contrary to the church’s theory, where the
earth was central, according to Ptolemy and Aristotle. First he was afraid to publish it to avoid
punishment by the church, eventually he did with a note to the church about the same freedoms as
Ptolemy.

,1.05: Enlightenment

Galilei is considered the father of modern science because he separated science from philosophy,
ethics and theology, which were under control of the catholic church. He was the first to explicitly
advocate for a scientific approach based on observation and experimentation in stead of just
theological reasoning and appose several of Aristotle’s theories.

He’s most famous for the Aristotelian and Ptolemaic view that the earth is the centre of the universe,
supporting Copernicus’s heliocentric view. Galilei made such observations of Venus that could only
be explained if the planets revolved around the sun so he did claim that the earth revolves around
the sun, in contrast to Copernicus only saying the heliocentric model just saving the phenomenon.

René Descartes rejected many of Aristotle’s ideas but agree that knowledge should be based on first
principles. Our senses and mind can be deceived easily, so he discarded every notion that he
doubted. He was only left with one certainty: he thought, therefore he must exist. Cogito, ergo sum.
Concluding we only know the true nature of the world through reasoning.

Francis Bacon also believed that scientific knowledge should be based on first principles, but he
believed it should happen through inductive methods. Generating explanations based on sensory
experiences, which makes him the father of empiricism (relating to experience, observation).

David Hume took empiricism to the extreme by only accepting sensory data as source of knowledge
and disqualifying theoretical concepts that didn’t correspond to directly observable things, called
scepticism: the true nature of reality consist only of the features of objects, not of the physical
objects themselves (cat).

No amount of confirmatory observation can ever conclusively show that a scientific statement about
the world is true (swan). So if you require that all knowledge must be based on just observations, you
can never be sure about anything.

German Idealism became popular at the start of the 19 th century (partly because of Hume’s
scepticism). It says that we mentally construct reality, meaning that our experience of the world is a
mental reconstruction. Scientific inquiry should therefore focus on what we can know through our
own reasoning. They got criticised a lot for using overly complicated language and scientists lost
patience with the idealists. Their musings on the nature of being became less relevant in a period
where scientific, medical and technical advances were made rapidly.

Logical positivism: a new philosophy of science that radically swinged back to empiricism.

1.06: Modern science
After the first world war, a group of mathematicians, scientists and philosophers formed the Wiener
Kreis, the Vienna Circle. They were unhappy with the German idealists, who focused on first
principles of knowledge and a fundamental nature of being. According to members of the Vienna
Circle, idealist questions about the self and existence were meaningless because they were
unanswerable. So they came up with a new philosophy of science:

Logical Positivism;
Science: the study of meaningful statements in the world
Meaningful: verifiable (verification criteria) – it should be possible to determine the truth of a
statement

, Two types of meaningful statements
- Analytic statements: statements that are necessarily true (tautological). They are a priori
statements, like definitions and purely logical statements (squares have four sides, bachelors
are unmarried).
- Synthetic statements: statements that depend on the state of the world. they are a posteriori
and can only be verified through observation > these statements should always be publicly
accessible according to the logical positivists.

In logical positivism, statements are not allowed to refer to unobservable entities like electron of
gravity because they can’t be observed directly. The statement is meaningless if it makes reference
to an unobservable entity, is not tautological or not logically or empirically verifiable.
Subjects like theology and ethics were thereby excluded from science.

1. The criteria and verification through observation couldn’t deal with the problem of induction
since no amount of confirmatory evident is ever enough to definitely prove or verify a
statement.
2. Also not allowing reference to unobservable entities crated big problems, science entities like
gravity and depression cannot be observed directly but are indispensable in scientific
explanations.

Those two problems led to a more moderate version of positivism:
Logical Empiricism;
Karl Popper argued that a statement is meaningful only if it’s falsifiable (instead of verifiable) because
we can never conclusively verify or prove a statement with observations, but we can conclusively
disprove it with contradictory evidence. Therefore Popper proposes that scientists should actively
engage in risky experiments to maximize the chance of finding evidence that contradicts our
hypothesis > improve hypothesis. This way, the hypothesis is provisionally supported if contradictory
evident is absent. According to Popper, if contradictory evidence is found, the scientific explanation is
wrong and should be rejected.

Quine showed that this criterion is also problematic. In the Duhem-Quine thesis, he stated that no
hypothesis can be tested in isolation but that there are always background assumptions and
supporting hypotheses. According to Quine, we could always reject one of the background
assumptions or supporting hypothesis to salvage the original hypothesis.

Thomas Kuhn pointed out that science doesn’t develop out of either the verification or falsification
principle and that hypotheses aren’t immediately rejected or revised if the data don’t agree with
them because science takes places within a certain framework or paradigm. After all, hypothesis are
generated within a certain paradigm. Contradictory results lead to revision of the hypothesis, but
only if those results fit the framework. More contradictory evidence? Crisis > paradigm shift and the
cycle begins again.

Today’s scientists follow the hypothetico-deductive method, combining induction and deduction.
Requiring falsifiability and accepting repeated confirmation only as a provisional support for a
hypothesis. Bas van Fraassen’s constructive empiricism is in line with that method. He states that a
scientific statement is accepted as true as far as our observations go, whether the statements
truthfully represents the unobservable entities, simply can’t be determined. So, knowledge requires
observation, but unobservable entities are allowed.

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