Reason, Truth, and Science: Exploring Formal and Material Truths
IV. Reason, Truth, and Science
IV.1. Formal and Material Truths, Deduction and Induction
True statements can be categorized into two types: those true due to facts (empirical truths) and those true due to reasoning (formal truths).
IV.1.1. Material Truth
Empirical or material truths are based on experience and observation. They are contingent, meaning they could be otherwise under different circumstances. For example, the statement “There are no trees on the Doctor Marañón High School courtyard” is contingently false, as it could become true if the trees were removed.
Immanuel Kant referred to these as synthetic truths, as they combine concepts with properties derived from experience. These truths are known a posteriori, meaning “after experience.”
IV.1.2. Formal Truth
Formal or necessary truths are true by virtue of their logical structure and could not possibly be false. They are true in any possible world. For example, “2 + 2 = 4” is a necessary truth.
Kant called these analytic truths, as they are true based on the analysis of concepts. They are known a priori, meaning “independent of experience.”
Examples of analytic propositions include:
- Definitions: “A bachelor is unmarried.”
- Axioms and theorems: “Only one straight line crosses two different points in a plane.”
- Logical truths (tautologies): “Either the Universe is infinite or it isn’t.”
IV.1.3. Arguments
Deductive arguments are those where the conclusion necessarily follows from the premises. They are explanatory and do not provide new factual knowledge.
Inductive arguments, on the other hand, amplify the range of the premises, making the conclusion only probable. The truth of the premises does not guarantee the truth of the conclusion. Inductive arguments can be based on causal relations, correlations, or analogies.
IV.2. The Scientific Method and the Problem of Demarcation
IV.2.1. Classes of Sciences
Empirical sciences, such as physics, chemistry, biology, psychology, and history, deal with facts and events in the world. They rely on material truth and inductive reasoning.
Formal sciences, such as logic and mathematics, deal with relations between symbols and have no empirical content. They rely on formal truth and deductive reasoning.
IV.2.2. Methods in Science
Science primarily uses deduction, both within axiomatic systems (formal sciences) and as a link between hypotheses and their consequences (empirical sciences).
The Axiomatic Methodology
An axiomatic system consists of axioms (unproved statements assumed to be true) and theorems (statements derived from axioms or other theorems). Euclid’s Elements of geometry is a classic example of an axiomatic system.
The Hypothetical-Deductive Method
The hypothetical-deductive method is a hybrid approach used in empirical sciences. It involves the following steps:
- Observation of an unexplained event.
- Formulation of a hypothesis to explain the event.
- Deduction of consequences from the hypothesis.
- Verification of consequences through experimentation.
If the consequences are not met, the hypothesis is refuted. If they are met, the hypothesis is corroborated.
IV.2.3. The Demarcation of Science
The problem of demarcation is concerned with distinguishing science from pseudo-science. Key features of science include:
- Inclusion of laws and theories
- Rigorous language with precise definitions
- Systematic and coherent structure
- Empirical verifiability of statements
Karl Popper argued that the defining characteristic of science is the falsifiability of its laws and theories. A theory is scientific if it can be potentially disproven by observation or experiment. Pseudoscientific theories, on the other hand, are often ambiguous, overly general, or rely on ad hoc hypotheses to avoid falsification.