Lets look at what a “valid” argument is:
p | q | p then q | p and (p then q) | (p and (p then q)] then q
T | T | T | T | T
T | F | F | F | T
F | T | T | F | T
F | F | T | F | T
What is really satisfying is that I can complete this without learning, I just calculate truth tables. Its so easy (once you know the rules), that we can get a material computer to do it. But you know its strange, actually the fourth column of the truth table: p AND (p THEN q) is the same as just “p AND q”. Note that p AND q have the same truth values as p AND ( p THEN q) given the same truth values of p, q. (Compare truth values of 4th column above to 3rd column below)
p | q | p AND q
T | T | T
T | F | F
F | T | F
F | F | F
The idea of a valid argument is the same as:
Know: p AND q
We already knew q from (p AND q), however. All we did was take out our mental knife (or pen) and cut p out. Thats why its called “deduction”, you Take Away p from (p AND q), get q.
For example, I can teach my daughter “if you touch the hot pan then you get burned”, or I can teach her “Touch the hot pan and you will get burned”. The difference is subtle and purely rhetorical. My daughter would learn the same skill of not getting burned without the “if, then”.
So why do we do all this with our first truth table, calling a valid argument “p AND (p THEN q)” instead of just calling it “(p AND q)”? The “if, then” is reductive; it focuses the person on the result, cutting out the “fathering” premise. Interestingly, the etymology of the word “robot” has the same root as the word “orphan”. The “and” is inclusive. Because the idea of a “valid argument” persuades us that we are making “progress”. Eg. “this, then this, then this, …” The valid argument confuses us from seeing the simplicity of what we are actually doing. It is a rhetorical move. The foundations of logic are rhetorical in nature. Rhetoric is prior to logic. Saying “We know p and q, and so we know q” does not sound like progress. Logic- is it the right way to think? What is thought? The philosopher Wittgenstein decided this question could not be answered. “Thought this peculiar being” The reason is if you “really” answer this question your thoughts become a servant of your answer, which is simply mind-control.
An attitude of skeptical uncertainty, or simply by asking a lot of questions, we can avoid and defend against overusing logic and debilitating our minds.
“Don’t go by reports, by legends, by traditions, by scripture, by logical conjecture, by inference, by analogies, by agreement through pondering views, by probability, or by the thought, “This contemplative is our teacher.””
-Kalama Sutta, translated from the Pali by Thanissaro Bhikkhu
Questions are power, what do I mean? What are questions? Power is notoriously difficult to define. The idea that “knowledge is power” or “power is knowledge” leads to a very difficult discussion about what is knowable and definable. Claim: “Questions always involve an intention towards the unknown.” If you already know the answer, perhaps the unknown is whether or not someone else knows the answer. But perhaps you ask yourself something to make yourself more aware of what you already know. So it is unknown whether questions involve an unknown. It is also problematic to describe the question as an “intention.”
“Every mental phenomenon includes something as object within itself, although they do not all do so in the same way. In presentation something is presented, in judgment something is affirmed or denied, in love loved, in hate hated, in desire desired and so on. This intentional in-existence is characteristic exclusively of mental phenomena. No physical phenomenon exhibits anything like it. We could, therefore, define mental phenomena by saying that they are those phenomena which contain an object intentionally within themselves.” (Franz Brentano)
“In-existence” is referring to the object’s existence within an intention. If I am curious about a neutron star, the neutron star has an existence within my curiosity- just as I have an existence within my curiosity. What else has an existence within my curiosity? Now, the power of this question is its ability to easily indicate as its object just about anything I’ve ever directed my senses and mind toward, including my mind itself. I have stepped outside my mind and self with this question and asked about my asking, and it was easy enough to ask. The trouble is now I still don’t know where my mind or self stops and the material world begins, since it seems I can easily push that limit to wherever I want. There are interesting and relevant claims in Buddhism about meditation. In meditation Buddhists have described a state of “infinite consciousness” which seems to have the same intention as my question which has as its object all my previous consciousness- now, is that an object? Apparently through meditation it is possible that one “enters and abides in the base of neither-perception nor-non-perception.” (Sallekha Sutta: Sutta 8 Effacement, Majjhima Nikaya p. 125 trans. Bhikkhu Nanamol and Bhikkhu Bhodi), which is a mental phenomenon that does not need an object anymore.
The question shares a likeness with power in that it is also very difficult to define.
 The truth table of p AND (p THEN q) THEN q is the valid argument. “q” is the conclusion “p” and “p then q” are the propositions. The notion of a valid argument must be translated into basic logic, otherwise, according to Russell’s theory of types, valid arguments must be irrelevant to logic itself since a valid argument is about logic. Nonetheless, a “valid argument” is usually introduced with any beginning set of lectures on logic, but not this way.
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