Philosophy of Science

TEXTBOOKS

Sanguineti, Juan Jose. Logic. Manila: Sinagtala, 1992. (Part IV)

Bittle, Celestine OMCap. The Science of Correct Thinking. New York: Bruce Publishing, 1935.

1. INDUCTION

[See Sanguineti, Logic, pp 155-166; Bittle, Science of Correct Thinking, pp 270-319]

1.1 The Principles of Reasoning [p 155]

In DEDUCTION, we start from universal knowledge to particular. But the question is where does that knowledge come from?

Some philosophers say they are

    • a priori or innate; others that they are, or
    • made up in our minds--mental constructs.

Is that what Aristotle and St Thomas teach? Is that realistic?

In fact, the universal knowledge we need for DEDUCTION comes from INDUCTION.

Are the two exclusive? No no no no no! They are related, of course! "Both induction and deduction are necessary for truth: induction for its DISCOVERY, and deduction for its PROOF. The mind FIRST argues from the EFFECT to the CAUSE, and then from the CAUSE to the EFFECT." (Bittle, 272)

There are two types of INDUCTION:

    1. ESSENTIAL induction (mind grasps in experience the necessary link between a subject and a property) and
    2. EMPIRICAL induction (intellect simply generalises the existence of a link between a subject and a property on the basis of the repetition of facts, but without knowing whether this relation is essential or not).

1.2 Essential Induction [p 156]

DEFINITION. What is essential induction? It is the discovery that the intellect makes of a necessary and universal link between a subject and a property when it [the intellect] comes in contact with reality (through the senses and then to the intellect via abstraction).

Propositions can either be

    1. propositions per se notae, which, in turn, are divided into
        • per se notae quoad se, and
      • per se notae quoad nos
    2. propositions per aliud notae

Is there anyone who denies the possibility of essential induction? Yes. Conventionalism rejects the possibility of essential induction. [p 166]

1.3 Empirical Induction [p 162]

DEFINITION. What is empirical induction? It is the generalisation of a connection between a subject and a predicate, not on the basis of seeing an essential and necessary link between them, but because of the repeated occurence of a natural event.

KINDS

    1. Induction by complete enumeration: possible only if the number of individuals in a group is finite.
    2. Induction by incomplete enumeration (statistical count): merely probably, but sufficiently reliable in practice.
        • Yields physical certainty (not metaphysical certainty).
        • Passage from some to all.
        • This is the method most frequently employed by the experimental sciences.
        • Requires sampling of events.
        • BUT appropriate qualifications should be added to the generalisations.
        • Sample: "The law is true given certain conditions, which may or may not be known to us."
        • Not only detect trends, but may point to a real causal relation.
        • Always calls for an explanation, an investigation into the causes. In the experimental sciences (unlike in philosophy), this is also by means of empirical induction.

What is the foundation of empirical induction?

    • NOT mere psychological conditioning (Hume)
    • NOT an a priori form (Kant)
    • BUT from what we know about
        1. causaliity,
        2. order in the world, and
        3. the relation between a nature and its operations.

2. NATURE AND OBJECT OF SCIENTIFIC KNOWLEDGE

[See Sanguineti, Logic, pp 155-166]

2.1 Notion of Science [p 177]

DEFINITION. What is science? Science is the systematic and mediate knowledge of beings and their properties, by means of causes. Aristotle defined it as certain knowledge through causes. But he also added that science should study necessary, not contingent, judgments about things (which need not be the case--science can also study possibilities.)

The notion of science is analogical.

PURPOSE OF SCIENCE. What is science for?

    1. SPECULATIVE: To give us a knowledge of the world, ourselves and God.
    2. PRACTICAL: To enable us to respond to the needs of life.

Spontaneous knowledge is necessary for science.

2.2 The Object of Science [p 183]

    1. What is the MATERIAL OBJECT of science? The material object of science is the reality studied by each science.
    2. What is the FORMAL or PROPER OBJECT of science? It is the particular aspect of the material object studied by science.

3. PHILOSOPHY AND THE PARTICULAR SCIENCES

[See Sanguineti, Logic, pp 155-166]

3.1 The Scope of Particular Sciences [p185]

What is the scope of particular sciences? A particular science studies the proximate principles of a specific type of being.

Do particular sciences need philosophy? Yes! Every particular science presupposes certain basic notions which belong to the strictly philosophical order, and which therefore lie beyond the scope of the [particular] science itself.

3.2 Philosophy

What is the difference between Philosophy and the particular sciences? (Note that we are assuming that Philosophy is also a science--it is a systematic and mediate knowledge through causes as well.)

The distinction between philosophy and the particular sciences is NOT rigid.

What is POSITIVISM? It denies the possibility of knowing the nature of things, because essence is either non-existent or unknowable. Science can only study phenomena or observable events. NEO-POSITIVISM maintains a similar position.

4. ORDER (I.E., CLASSIFICATION) OF THE SCIENCES

[See Sanguineti, Logic, pp 155-166]

4.1 The General Picture [p 193]

Sciences can either be:

    • human or theological;
    • speculative or practical;
    • deductive or experimental (inductive);
    • physical, mathematical or metaphysical (according to the degree of abstraction or intellection used)

4.2 Physical, Mathematical and Metaphysical Approaches to Reality [p 194]

These are also called degrees of abstraction (at least for the first two).

    1. PHYSICAL INTELLECTION. Sciences using physical intellection or physical abstraction employ concepts which signify natures existing in sensible matter and which should be understood in sensible matter. Only the individuating matter is left aside. Biology and Physics usually use this kind of intellection.
    2. MATHEMATICAL INTELLECTION. Mathematics uses another kind of intellection, where the concepts leave aside the verifiable aspects of material things in order to signify quantitative structures in the abstract. Mathematics can also include beings of reason--mental constructs.
    3. METAPHYSICAL INTELLECTION. This is proper to philosophy. Metaphysical concepts signify those aspects of things which are intelligible apart from sensible matter, and which can be found in immaterial beings.

4.3 The Physico-Mathematical Order [p 200]

The aforementioned division is NOT rigid. There are intermediate sciences as well.

4.4 The Human Sciences [p 201]

These include history, pedagogy, psychology, economics and sociology. These are closely related to philosophy. Unlike the physical or mathematical science, these sciences cannot admit of rigid "laws" because human freedom is involved in the realities that they study.

4.5 Unity and Subalternation of the Sciences [p 203]

The classification above should not lead one to separate the sciences into watertight compartments. They are related to one another. In fact, some sciences depend on the truths of another science. This is called subalternation or subordination of sciences. It can take place in many ways, depending on the criteria of hierarchy among the sciences. But it is important to remember the following:

    • The particular sciences are formally subordinated to philosophy.
    • The practical sciences are subordinated to ethics

5. THE SCIENTIFIC METHOD

[See Sanguineti, Logic, pp 155-166]

5.1 Method in General [p 205]

When we speak of "method", we mean an orderly manner of arriving at one's end. The scientific method is the orderly way of arriving at truths in a given scientific discipline. What science basically does is a combination of induction and deduction:

    1. FIRST, it draws principles from OBSERVATION and EXPERIENCE. (INDUCTION)
    2. One makes a HYPOTHESIS as to the PROBABLE CAUSE of the phenomenon observed.
    3. The hypothesis is put to a test--it is VERIFIED.
    4. The LAW is explained.
    5. The law is APPLIED to all similar cases. (DEDUCTION) [cf Bittle, p 275]

5.2 Scientific Experimentation (or Observation) [p 209; Bittle 298-306]

    • Scientific knowledge starts from observation.
    • This observation can be produced artificially, through experiments.
    • Observations can be enriched with the use of special instruments of observation and measurement.
    • The objects of the sciences are more difficult to study the more withdrawn they are from sensible experience.
    • The philosophy of Aristotle and St Thomas also begin from observation.

5.3 Demonstration [p 213]

    • Aside from experience and observation, science can lay down postulates.
    • It then moves on to the demonstrative phase. In this discussion, "demonstration" is the use of reasoning in science.
    • There are two kinds of demonstration which sciences use together, depending on the availability of data:
      1. PROPTER QUID ("on account of which") demonstration: it goes from causes to effects. Starting from the cause or nature of a thing, we demonstrate its effects and properties. We start from what is prior in being to something posterior. This is why it is also called A PRIORI demonstration. It is also called DEDUCTION.
      2. QUIA ("because") demonstration: from effects to causes. The reasoning process begins with what is posterior in being, though it is first in our knowledge.

6. THE PRINCIPLES OF SCIENTIFIC KNOWLEDGE

[See Sanguineti, Logic, pp 155-166]

6.1 Notion of Principle [p 225]

DEFINITION. What is a principle? A principle (or arche in Greek), is that from which something else proceeds.

Scientific principles are the universal and indemonstrable propositions which constitute the premises of the demonstrations.

6.2 Kinds of Scientific Principles [p 226]

There are many kinds of principles. Among them are the following:

    • COMMON AND PROPER PRINCIPLES. These are also called FIRST or METAPHYSICAL PRINCIPLES. They are the immediate and most certain truths that refer to the properties of being, or at least to some basic characteristics of reality. They are easily grasped through spontaneous knowledge. Examples:
        • the principle of non-contradiction
        • the principle of causality
        • the principle of comparative identity ("two things identical to a third are identical to each other")
        • the principle of finality (in human actions)
        • the principle of moral good ("good must be done, and evil avoided")
        • the principle of the intelligibility of being ("man is capable of knowing the truth")
    • ARTICLES OF FAITH in Theology.
    • PRINCIPLES SPECIFIC TO A PARTICULAR SCIENCE
    • NORMS/RULES/LAWS of the PRACTICAL SCIENCES

6.3 Mathematical and Logical Principles [p 228]

    • Mathematical principles are FORMAL, not necessarily real. They are called AXIOMS or POSTULATES.
    • SOME mathematical principles are not derived from induction but are PURE IDEAL CONSTRUCTS.
    • SOME mathematical principles are REAL principles since they express the laws of quantity as such.
    • Nonetheless, they are NOT ARBITRARY because they are governed by the principle of non-contradiction. Furthermore, they are formulated by means of an abstraction which has its foundation in real quantity.

The axiomatic method is used by the deductive sciences (e.g. mathematics and formal logic), where one begins with a few indemonstrable axioms.

6.4 Physical Principles [p 232]

6.4.1 Physical Laws [p 232]

    • Physical principles are UNIVERSAL propositions which express certain properties of SENSIBLE THINGS.
    • Physical LAWS express the natural inclination of material things to act in a certain way.
    • DEFINITION. A physical law can be defined as a UNIVERSAL ENUNCIATION of a property or of a regular pattern found in the behaviour of phenomena. (This is synonymous to the definition above of "physical principles".)
    • These laws are usually expressed in the form of mathematical equations, or as statistics, or as approximate measurements.
    • Physical laws are usually abstract or schematic in character. Why? Because they leave out various factors which are actually involved in the changes undergone by phenomena.

6.4.2 Hypotheses [p 234]

What is a hypothesis? HYPOTHESES are universal or particular propositions that have not yet been conclusively proven. It involves HYPOTHETICAL DEDUCTIVE REASONING.

This involves the following phases:

    1. a probable cause is given for some observable facts (imperfect demonstration quia);
    2. a number of effects are deduced from this hypothesis, showing that this is the best hypothesis that can account for these effects.

Are there any CRITERIA FOR THE FORMULATION OF VALID HYPOTHESES? Absolutely!

    • COHERENCE with other branches of the science.
    • Sufficient EMPIRICAL VERIFICATION.
    • FECUNDITY, or the capacity to explain new phenomena which other hypotheses cannot explain.
    • SIMPLICITY, such that the hypothesis can explain different kinds of phenomena with only a few causes.

Theoretical MODELS sometimes form part of hypotheses.

6.4.3 Scientific Theories [p 237]

DEFINITION. A theory is an organised set of scientific propositions derived from a number of principles and observations.

The organise body of of scientific knowledge has several parts:

    1. SPECIFIC OBSERVATIONS which are recorded as BASIC PROPOSITIONS. These are not pure sense data, because the intellect has previously worked on them.
    2. LAWS that explain a series of facts.
    3. MORE UNIVERSAL PRINCIPLES which explain several laws and provide the entire science with its ESSENTIAL FOUNDATIONS

These parts are not rigidly distinguished from one another.

VALIDITY OF THEORIES. Conclusive evidence to the contrary may completely disprove a scientific theory, though in many cases, it does not completely invalidate a theory's elements.

Are theories necessarily hypothetical? No, not at all. Theories can become PHYSICALLY CERTAIN in the course of time. This does not mean that it cannot be perfected. The reason is that we can always grow in knowledge of reality.

6.5 Historical Panorama [p 240]

6.5.1 Ancient [p 240]

    • Born in ancient Greece, but with no clear distinction between experimental sciences and philosophy.
    • Geometry (Euclid), Astronomy (Hipparcus and Ptolemy), Mechanics (Archimedes), Medicine (Galen), Optics (Hero), Mathematics (Pythagoras and Platonic philosophy), Logic (Aristotle and the Stoics)

6.5.2 Medieval [p 240]

    • Christian writers inherited Graeco-Roman scientific knowledge
    • They developed it with Aristotle's Metaphysics and supernatural Theology.
    • Great thinkers of the period strove to show harmony between faith and reason, faith and science.
    • They also showed that human knowledge led to Theology. (See Stanley Jaki's "The Roads of Science and the Ways to God")
    • St Thomas defended Theology as a true science.
    • 13th century: acquisition of Aristotle's works and that of the Arabs stimulated interest in the natural sciences and mathematics, especially in Oxford and Paris. This is the beginning of modern science.
    • 14th century: gradual substitution of Aristotelian physics and application of physico-mathematical methods to the analysis of terrestrial phenomena in kinematics and dynamics.

6.5.3 Modern [p 241]

    • Mechanics, astronomy, mathematics: methodical and successful application of experimental method and mathematics to observable data.
    • 16th and 17th centuries. Copernicus, Kepler, Galileo, Newton
    • Mechanistic view arose with Descartes, Gassendi, Bacon.
    • 18th century. Encyclopaedists spread Scientism (physico-mathematical knowledge is the only valid kind of knowledge; philosophy and theology too abstract). Rejection of Metaphysics. RUPTURE BETWEEN SCIENCE AND FAITH.
    • 19th century: Classical Positivism (Comte, Stuart Mill, Spencer).

6.5.4 Contemporary [p 242]

    • Crisis of 19th century scientific dogmatism because of the advent of modern mathematics (especially non-Euclidian geometrics) and modern physics (theories of relativity and of quantum mechanics).
    • Relativism.
    • Principal modern epistemological theories
      • Poincaré (conventionalism): mathematics characterised by a certain degree of conventionalism; the supreme principles of physical theories are but elaborations of reason
      • Bergson, Husserl, Duhem: react by saying it's philosophy that gives a real knowledge of philosophy
      • Extreme relativistic positions: William James (pragmatism or instrumentalism); G. Mach (empirio-criticism); Lenin (dogmatic positivism)
      • Frege, Russell, Hilbert: trying to seek foundations of mathematics in logic.
      • Vienna Circle and verificationism (M Schlick; Ludwig Wittgenstein; Rudolf Carnap; Neurath; Reichenbach): rigidly anti-metaphysical positions. Karl Popper and falsifiability.
      • Some scientists held more realistic theses and rejected neo-positivism (Planck, Einstein, De Broglie, Schrödinger, Heisenberg)
      • Discussion on problems of the credibility and historical evolution of scientific theories (Thomas Kuhn, Stegmüller, Toulmin, Feyerabend, Lakatos, Bunge)

FINAL WORD: All science needs METAPHYSICS!!!

Please contact jmomandia at gmail dot com for any heresies found here.

First Edition. Taipei, 6 August 2007

Revised 21 August 2012, Taipei