Key Concepts in Philosophy and Science: A Concise Overview
Q cannot deduct any other. A set of rules or transformation (q interference) allows us to move from one well-formed formula (wff) to another wff.
Deductive-Perfect Systematization: Ideal logical rigor, no tacit assumptions, inability to obtain a contradiction in the system, a lesser number of axioms. Consistency requirements (not leading to internal contradictions), completeness (sufficient means to derive all valid statements q can form in their language), decidability (possibility to determine whether any formula is valid or not in the system), independence of the axioms (q none obtainable from the other).
Hypothetico-Deductive Method (better results in empirical sciences):
- From observation, I register a certain phenomenon (experience). This is compared to others, leading to previous problems.
- The comparison allows me to make the first classification/generalization (universal statements) concerning constant relations among phenomena, and attempt to build a solution (hypothesis). The hypothesis is a universal statement on experience.
- It is necessary to derive appropriate consequences deduced from the hypothesis: observable empirical predictions.
- Contrast the hypothesis; see if the deduction is supported or not (verification/falsification) by experience.
- If the hypothesis is confirmed, a second generalization: the statement of laws or scientific theories explain the facts.
Main Epistemological Theories:
Neopositivism: The goal of science is to explain facts subsumed under laws. The laws are justified inductively. Science differs significantly because its propositions have a proposition (law or theory). It is meaningless when it is not verifiable. A proposition is verifiable when experiences would make it true or false.
Popperian Falsificationism: Science tries to solve problems. To solve problems, hypotheses and theories are developed. A theory can be considered scientific if it is falsifiable. A falsifiable theory can point out when it would be false.
Theory of Scientific Revolutions: Science begins with a collection of random facts (prescience). At one time, a paradigm is proposed to explain a number of these acts. When anomalies are discovered in the functioning of a paradigm, an ad hoc hypothesis is intended to address them. When the number of anomalies is very big, the paradigm is in crisis, beginning a stage of proliferation of new paradigms, imposing a new paradigm that implies a totally different and unique conception of reality.
Refined Falsifiability: Science attempts to solve problems. To solve them, hypotheses and theories are constructed. A theory is considered valid if it is falsifiable and has been confirmed in at least one falsifiable case. If a theory seeks to replace existing theories within research programs, any research program consists of a core and an unfalsifiable protective circle. Any modification made in the protective circle must also be falsifiable. A research program degenerates when it is unable to predict new facts.
Problems of the Middle Ages:
Christianity: 1. Establish in philosophy what the relationship between reason and faith is, and above all, establish what is most relevant. 2. Responses: conciliatory (Aquinas), separator (William of Ockham). The relationship with God and creatures has to do with the idea of whether we are free or if we are determined. The relationship between essence and existence (contingent essence is in all beings except God). No being is necessary; therefore, all possible combinations have been due to St. Anselm’s ontological argument: if someone says God does not exist, God exists. Problem of universals: are there universal concepts? And if any, what characteristics? Solutions: Plato (universals are real), conceptual terms, etc. State: The Church-State goal is the relevance of the state, supported by the will of Constantine (donation of empire to the papacy).
Rationalism and Empiricism:
Similarities: Their philosophical systems are built in and from consciousness. They have ideas as knowledge. They are core-mounted on a prior theory of knowledge. They share an intimate relationship between philosophy and science; the scientific method is fundamental.
Differences: Rationalists believe in the existence of innate ideas (latest matches directly; q need not verification through experience), modeled by knowledge of maths, given in the continent (Descartes, Spinoza, Leibniz). Empiricists believe experience is the only source of knowledge; therefore, innate ideas do not exist as a model. They take empirical science knowledge, which develops mainly in the British Isles (Locke, Berkeley, Hume).
Enlightened Reason is autonomous, needs no faith or tradition, is limited (internal boundaries), critical, rejects damages and tradition/idolatry, is an analyst looking to find the rationality, secular or secular (not atheist!).
Sophists: After the wars against the Persians, visa policy intensified. It became necessary to have a new education not reduced to the aristocratic ideal but satisfying the demands of leadership imposed by the rise of democracy. Sophists were itinerant teachers who charged for useful knowledge capable of providing success. The curriculum was based on two disciplines: Rhetoric (the art of leading others by the word) and Dialectic (the art of contesting and discussing). They were primarily concerned with man, civilization, customs, and trends; skeptical, relativistic, and subjective.
Socrates had an educational mission in his life. He used dialogue as a method and focused his activities on human cognitive work activity. He did not charge for teaching positions. Against skeptical, relativist, subjectivist ideas and the pursuit of success, Socrates taught a universal truth that is valid for all human beings and expressed in a universal context.
Axiomatic Formal System: A system of true statements, starting from a set of sentences, some of which are called axioms (q principle is self-evident, needs no proof).
It consists of: A board of symbols or alphabet, a code of rules and formula training, a list of axioms or postulates that are the system’s primitive formulas, containing the least possible number, and are evident from.