Abstract
The most basic assumption of science is that there is a reality to be known. Without the postulate of the independent existence of a real world the scientific effort would be in vain. I do not discuss this basic assumption here. I shall come back to this issue in the next chapter, devoted to ontology. Now I want to focus on how we represent the world in our attempts to understand it. Only some brain processes and statements can be true, false, or something in between. Propositions are constructs that inherit the truth value of the statements from which they are abstracted. A truth value cannot be assigned to a theory or to a worldview. A theory, however, can be truer than another. The same holds for worldviews. Science thrives for finding ever truer theories about the world.
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Notes
- 1.
By “the world” I mean the totally of existents, whatever they are.
- 2.
The Russell paradox: consider the class of all classes that are not members of themselves. Let us call this class A. Then if A ∈ A → A∉A and if A∉A → A ∈ A.
- 3.
Paradoxes of self-reference are like the Liar’s paradox: consider the statement “I lie”. If I lie, then what I say is false. Then “I lie” is false, and I say the truth. Then I do not lie, contrary to the hypothesis.
- 4.
If the variables are few, it is usual to adopt ‘x’, ‘y’, etc.
- 5.
These are stipulative definitions. For a discussion of the different kinds of definitions see Gupta (2015).
- 6.
Notice that the axioms are also trivially entailed by the axiomatic basis: A i ⊢ A i.
- 7.
I call ‘attribute’ to properties of constructs and other conceptual objects. The word ‘property’ itself is reserved for factual objects. ‘Attribute’ suggests that we are who ascribe the feature to the construct, i.e. that constructs are fictions.
- 8.
The sorites paradox (sometimes translated as the paradox of the heap because in Ancient Greek the word “sorities” means “heap”) is a paradox that arises from vague predicates. The classical example is a heap of sand. If you take away a grain of sand from the heap you still have a heap. So, the operation ‘heap minus 1 grain = heap’ holds for any heap. The application of the operation does not alter the heap. Repeat the operation a large number of times and, nevertheless, the heap will disappear. The paradox resides in the impossibility to determine how or when the heap disappears.
- 9.
A model of an abstract formula is a structure (e.g. an interpretation) that satisfies the formula within a formal theory.
- 10.
The reader can already foresee that I shall reject the usual definition of knowledge as true belief. See Chap. 2.
- 11.
A supertask is the implementation of an infinite number of physical operations (‘tasks’) in a finite time.
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Romero, G.E. (2018). Philosophical Semantics. In: Scientific Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-97631-0_2
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