Knowledge
The value of knowledge
From tropisms to proper knowledge: The adaptative value for living organisms of "knowing" their environment. Examples range from plants to animals to rational animals (us): more sensory organs and bigger brains were selected by nature because they increase our chances of survival.
Definition and degrees of knowledge
What is knowledge?
When can we say we know something? Which are the conditions an agent has to fulfill for afirming they know.
Four degrees: form ignorance to knowledge passing through doubt and belief. Can you define each one? Differences between them?
Skepticism
Between dogmatism and relativism.
Two kinds of skepticism: absolute and methodological.
Skepticism as one of the pillars of critical thinking.
Perspectivism
The metaphor of knowledge as the result of observing the world from a perspective. Perspectives are objective as well as plural:
Two people in the same place share the same perspective and therefore agree on the same truths.
Not all perspectives are equally good for obtaining kowledge. Like our horizon in a ship, it can be enlarged or reduced depending on our position on the ship.
But there is not a privileged perspective that captures the whole truth.
Sources of knowledge
We know some things because of our senses. Empiricism is the philosophical doctrine that affirms that all of our knowledge comes from experience.
We know some (other) thinks because of our reason: Rationalism is the philosophical doctrine that affirms that all of our knowledge comes our reason.
Scientific methods
The sciences are one, but not the only source of knowledge. A key characteristic of sciences, wether they are formal sciences such as mathematics or logic or experimental such as physics or medicine, is their methods.
An important part of a scientist's education is to learn the methods to be employed for acquiring new knowledge. Three methods are commonly employed:
Deduction
Induction
Hypothesis and deduction
Deduction
What separates Pythagoras from the rest of people that knew how to apply it to right triangles?
Why prove the theorem? What do we gain when we have a proof?
What is in general a theorem?
Starting and supporting points of a demostratation: axioms and lemmas. Define both concepts.
Which two lemmas appear in the demonstration? Can you demonstrate at least of them?
Towards the demonstraton of a theorem: logical resoning steps. Can you identify some of those steps in the demostration?
Induction
Who was Francis Bacon?
Which are the starting points of inductive reasoning?
What kind of results are the product of induction?
Which sciences use induction most?
Explain induction with an example.
Differences between deduction and induction.
Hypothesis plus deduction
Who was Galileo?
Which is the starting point of the hypothetical-deductive method?
What is an hypothesis? Where hypothesis come from?
How deduction intervenes in the method?
Observation and experiment: Which is the key difference between them?
Which sciences use the hypothetical-deductive method most?
What kind of results are the product of the hypothetical-deductive method?
Is this method a way of combining rationalism and empiricism? Give reasons in favour of an affirmative answer.
Facts and theories
Bricks and buildings: a metaphor for facts and theories
Facts are like bricks: they can be part of different buildings. Bricks are not rocks that we just find on the ground, bricks are made purposefully by scientists: proofs and computations, experiments and observations are the bricks of scientific theories.
Theories are like buildings: they are built by people using available bricks. Sometimes, a building is abandoned because a new brick does not fit in, other times because there is a better way of rearranging all the existing bricks into a better building.
Discoveries
Some facts are more important than others; they are called great discoveries. These discoveries may fit into an existing building, reinforcing it in critical places. But they may not fit no matter how hard we try; then a new building is needed.
However important, discoveries are just bricks. Like any other brick, they have to be made, even by mistake or unexpectedly. But once made, they can not be ignored; bricks are hard and resist the collapse of the building they are part of.
Theories are provisional
In the same way that we need buildings for shelter, we need theories for making sense of facts. A pile of bricks is of little use; brute facts need explanations and they don't make predictions.
Empirical theories are built and reinforced as new facts are added to them. So theories are seldom complete, new knowledge is required for parts that need development and holes that need to be filled.
A building with cracks and holes is better than no building at all. So scientists do not abandon an empirical theory until a better one is ready to accomodate the known facts, to provide better explanations and more accurate predictions.
We move into a new building because it has no apparent cracks or holes, because is larger or better located. In the same way, we change to a new theory because all known facts fit in, because it predicts or explains new facts or because it makes connections with other theories.
No building is perfect, sooner or later it develops cracks and faults. Or maybe we need more room or have to move to another city. No empirical theory is perfect, but there are better and worse theories.
We can easily check if a brick is broken, but buildings usually have hiddent faults that only appear later. We can verify facts (that is why they resist change), but we can not verify experimental theories (that is why we can change them).