An appeal to skepticism about reasoning

Unaided and aided reasoning Humans reason about many things. Some things are more complex than other things. The more complex a thing is, the more probably it is that one will reason wrongly about it. For simple things the probability of unaided reasoning reasoning wrongly is not high. For complex things the probability of unaided…

Continue Reading

Complete arguments

A complete argument is as argument that is stated or presented such that: 1. One can see all the propositions in the argument. 2. All the propositions in the argument are numbered. 3. It is explained what kind of purpose all the propositions have. (Premise, inference or assumption.) 4. All inferences are stated, it is…

Continue Reading

Validity and necessary truths

Validity is defined in a couple of ways. I like to define it like this: An argument is valid iff the superconjunction1 of all the premises and the negation of the conclusion is impossible. It sounds a bit unusual at first but it is worded that way to prevent confusion about modalities. A more common…

Continue Reading

Truth tables and necessary truths

In the essay Validity and necessary truths I used truth tables with necessary truths and impossibilities in it. I did it like this: P □Q P→□Q T T T F T T Note that the modal operator is placed in the truth table also. It could also be done like this: P Q P→Q T…

Continue Reading

Sound arguments and rationally convincing arguments

I’ve read many times and places that an argument is sound iff 1.      The argument is valid. 2.      All the premises of the argument are true. [1] Let’s call this the standard definition of a sound argument. Now consider this argument: 1.      If the Earth is a planet, then there is a satellite above Denmark…

Continue Reading

The term non-sequitur

As Wikipedia notes,i the term is used in everyday speech to deny a conditional (if-then statement), and it is also used in logic to mean an invalid argument. This together with the fact that in normal language people do not write the complete arguments when they argue, makes it very easy to confuse things. Suppose…

Continue Reading

Contraries and contradictories

Contraries If one looks in a general dictionary one will not a find a definition of contrary that is philosophically useful.i I looked the word up in a philosophical dictionary but that was not satisfied with the provided definition: A pair of categorical propositions which (provided that we assume existential import) cannot both be true,…

Continue Reading

Tough modal logic formalization

Source. Gamgee wrote: In the Ontological Argument, Anselm refutes Guanilo’s Perfect Island criticism by stating that God has Aseity. Anselm does not, as far as i know, make any attempt to prove that God has Aseity, or even if Aseity is logically possible. I argue that it is not, for the following reason: 1) We…

Continue Reading