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The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a necessary consequence of its premises. An argument that is not valid is said to be "invalid". An example of a valid (and sound) argument is given by the following well-known syllogism:
In this example, the first premise is a conditional statement in which "P" is the antecedent and "Q" is the consequent. The second premise "affirms" the antecedent. The conclusion, that the consequent must be true, is deductively valid. A mixed hypothetical syllogism has four possible forms, two of which are valid, while the other two are invalid.
The hypothesis of Andreas Cellarius, showing the planetary motions in eccentric and epicyclical orbits. A hypothesis (pl.: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or ...
Formal logic and mathematical rules are examples of rigorous consistency. An example would be: if all As are Bs and all Bs are Cs, then all As are Cs. While this standard is of high value, it is limited. For example, the premises are a priori (or self-apparent), requiring another test of truth to employ this criterion. Additionally, strict ...
Auxiliary hypotheses that are independently testable: "An auxiliary hypothesis ought to be testable independently of the particular problem it is introduced to solve, independently of the theory it is designed to save." (For example, the evidence for the existence of Neptune is independent of the anomalies in Uranus's orbit.)
If the null hypothesis is valid, the only thing the test person can do is guess. For every card, the probability (relative frequency) of any single suit appearing is 1/4. If the alternative is valid, the test subject will predict the suit correctly with probability greater than 1/4. We will call the probability of guessing correctly p. The ...
These assumptions or beliefs will also affect how a person utilizes the observations as evidence. For example, the Earth's apparent lack of motion may be taken as evidence for a geocentric cosmology. However, after sufficient evidence is presented for heliocentric cosmology and the apparent lack of motion is explained, the initial observation ...
Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logically possible. The practical feasibility of observing a reproducible series of such counterexamples if they do exist. In short, a hypothesis is testable if there is a possibility of deciding whether it is true or false based on experimentation by anyone.