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Anaximander posited that every element had an opposite, or was connected to an opposite (water is cold, fire is hot). Thus, the material world was said to be composed of an infinite, boundless apeiron from which arose the elements (earth, air, fire, water) and pairs of opposites (hot/cold, wet/dry). There was, according to Anaximander, a ...
In natural language, an instance of the paradox of entailment arises: It is raining. And It is not raining. Therefore George Washington is made of rakes. This arises from the principle of explosion, a law of classical logic stating that inconsistent premises always make an argument valid; that is, inconsistent premises imply any conclusion at all.
The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol → {\displaystyle \rightarrow } is interpreted as material implication, a formula P → Q {\displaystyle P\rightarrow Q} is true unless P {\displaystyle P} is true and Q {\displaystyle Q} is false.
Therefore, it is not opposite day, but if you say it is a normal day it would be considered a normal day, which contradicts the fact that it has previously been stated that it is an opposite day. Richard's paradox : We appear to be able to use simple English to define a decimal expansion in a way that is self-contradictory.
Materialism is a realist philosophy of science, [17] which holds that the world is material; that all phenomena in the universe consist of "matter in motion," wherein all things are interdependent and interconnected and develop according to natural law; that the world exists outside consciousness and independently of people's perception of it ...
These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...
Using the terminology of Aristotle, Bacon demands that, apart from the "laws of nature" themselves, the causes relevant to natural science are only efficient causes and material causes, or, to use the formulation which became famous later, natural phenomena require scientific explanation in terms of matter and motion.
Kant says, "Although all our cognition begins with experience, it does not follow that it arises from [is caused by] experience." [13] According to Kant, a priori cognition is transcendental, or based on the form of all possible experience, while a posteriori cognition is empirical, based on the content of experience: [13]