Here's my first set of Logic notes. In case anyone is interested, I'm constantly fine-tuning how I go about my studies in order to maximize understanding and retention. My current process is:
- Read for five minutes
- Handwritten notes for what I can actively recall from memory.
- Repeat 1 & 2 for a thirty-minute study session (I'll normally only have two five minute segments for a full ten minutes of newly read material before going back and re-reading/reviewing from where I started reading on a given day for the remainder of the full thirty minute session; the handwritten notes can take a good chunk of time).
- Review notes at the end of the day.
- The following morning review notes again and type them into a document
- Review of the pages covered in the source material in order to add anything I missed that seems important.
I might have a different study system in the next week. All depends on what I think is working best for me. This is an extremely taxing subject, but I believe that suffering is worth it in the end to stretch my mind well beyond where it currently is.
Do take my notes with a grain of salt. I very much doubt that I'll get it all the first time around. So, don't take it to be the Truth. And feel free to comment suggestions and/or corrections. 😊
I --
Socratic Logic - concepts, judgements, and arguments are represented in a logical argument as 1) terms(concepts), 2) propositions (judgements), 3) argument, which is commonly given in the form of a syllogism (e.g. “All men are mortal. I am a man. Therefore I am mortal).
Logic unlike language isn’t artificial. It’s discovered. It’s a natural property of the universe such as mathematics.
Terms are simple: Man is a concept based off of abstraction. Propositions such as “All men are mortal” are judgements made concerning abstracted aspects of “man.” Propositions will contain a subject (man) and a predicate (are mortal) that is then subjected to the argument which draws a conclusion from the terms and propositions: If men are mortal, and I am a man; then I must be mortal.
An argument is theoretically composed of two premises (both containing a subject and predicate) and a conclusion (containing a subject, predicate, and the truth statement that is extracted from the comparison of the two.
Terms are either clear/unclear. Propositions are either True/False. And Conclusions are either valid/invalid.
Terms are concerning with what a thing is. Propositions with the existence of a thing as it is. And Arguments with cause/why a thing is as it is. An arguments takes the propositions built off of terms in order to conclude whether a valid conclusion about why something is as it is can be made.
A true, valid conclusion can only be reached with clear, unambiguous terms, True premises, and valid logical conclusions/arguments. If any of these three parts is compromised the logic is ambiguous and inconclusive.
II -- Logic (32-37) - How to define Truth: to paraphrase Aristotle, what one says exists and it does exists is Truth. What one says exists and doesn’t exist is not Truth. Truth can be a tricky concept since the definition can be concrete, but the methods by which we observe and gather facts for Truth can be faulty and led people into existential crises about the subjective, rather than objective, nature of reality.
Three questions to continually ask when hearing someone else’s argument: 1) What do you mean? (define terms properly), 2) What’s the point? (what is being proved/what’s your conclusion?), 3) Why? (defend why you’re correct).
To make your own case you must 1) have clear and unambiguous terms, 2) true premises, and 3) valid logic in order to come to a true conclusion.
Funny story: Aristotle had described in a lecture the three levels of intelligence: 1) gods, 2) men, 3) brutes. He said that the gods know too much to ask questions while the brutes knew too little to ask questions. So, when his students had no questions afterwards he asked if he should be proud they’d risen to the level of gods through his lecture or if he should lament that they’d fallen to the level of brute through his lecture.
The ability to question is part of what truly separates us from animals and computers. Computers never question. They only do with the data we give them what we have already programmed them to do. There’s nothing intelligent and conscious about them.
Animals can show some degree of problem-solving (e.g. gorillas stacking crates to escape an enclosure or animals learning certain behaviors hoping it will lead to treats), but they still don’t have a quantifiable ability to abstract. Though there is some interesting research into animal “intelligence.” But the differences in degree and quality between humans and animals is an unbridgeable gap currently.
Concepts (the essence and nature of things) defies the laws of nature. They are not reliant on space and time. A man can think of two cities that are thousands of miles apart at the same time to compare them. His concept of the cities bridges the gap created by time and space. I know; not the strongest argument. But I hope to revisit the thought.
Question: for concepts being able to defy/transcend time and space, did the concept of a house exist before the first house was built?
Concepts are dependent on our minds. But the objects that our minds understand (simple apprehension) are independent of our minds.
III -- Logic - Concepts are 1) Spiritual/immaterial, 2) Abstract, 3) Universal, 4) Necessary, and 5) Unchanging/Immutable
Spiritual means that concepts are without physical properties. They have no weight, color, size, energy, etc. A thought (as is different from a “concept”) can potentially be considered to have a physical element through its processing in the brain and the resulting phantasm that results in the symbolic communication of the immaterial concept that started the process.
Abstract means that the concept has been mentally separated from the perceived object. Consider a red rose, you can abstract the color red from it and perceive that the color is able to exist in objects other than the singular red rose. You even go so far as to imagine potential/unreal objects with the abstracted quality of red imposed upon it (e.g. a rose red cat. At least to my knowledge they do not naturally exist, but it can exist in the mind after I’ve abstracted the color rose red and imposed it onto the phantasm of cat in my mind). You cannot physically separate the color from a flower, but you’re able to separate color from flower through your intellect.
Universal means that the concept applies to all things with that essence at all time. The different kinds of trees, despite how technically different they may appear, still have the same “essence” of tree that we’ve abstracted to label them all trees. Fun excerpt from Orthodoxy by Gilbert K. Chesterton :
“Then there is the opposite attack on thought: that urged by Mr. H.G.Wells when he insists that every separate thing is ‘unique,’ and there are no categories at all. This also is merely destructive. Thinking means connecting things, and stops if they cannot be connected. It need hardly be said that this scepticism forbidding thought necessarily forbids speech; a man cannot open his mouth without contradicting it. Thus when Mr. Wells says (as he did somewhere), ‘All chairs are quite different,’ he utters not merely a misstatement, but a contradiction in terms. If all chairs were quite different, you could not call them ‘all chairs.’”
IV -- Logic - continuing the Five elements of a concept:
Spiritual/immaterial (i.e. a concept has some weight, height, depth, taste, etc.)
Abstract (i.e. formed by the intellect from observation)
Universal (i.e. the concept applies to all things, at all places [e.g. the concept tree applies to all trees everywhere at once; not just the current tree being perceived])
Necessary (i.e. the concept must contain within it the abstractions that are intrinsic to the entity's existence [e.g. a triangle only exists with three sides and a sum of 180 degrees]) Concepts such as trees are a harder to pin down due to so many variables, but without being able to write down a concrete, defined list I can still understand what the concept tree applies to and infers.
Unchanging (i.e. what a concept applies to can change materially [e.g. two bunnies + two bunnies might = more than four bunnies eventually], but the concept will always remain the same [e.g. 2 + 2 = 4])
Metaphysics is the study of being. Being is intrinsic to everything else. Without being there can be nothing else.
The nature of being is intrinsic to Logic. By creating the conception of a house you have implied that house has being in addition to the form, substance, etc. “The House is blue” has the implicit understanding that the House is.
Concepts are private and wholly within the mind of the individual’s intellect. Terms are an extrinsic extension of concepts for social utilization that are communicated via words (the material means of communicating [e.g. speaking, written symbols]) Terms can be expressed by differents words in different words in different languages.
Propositions are made of terms: An apple is a fruit. The terms “apple” and “fruit” are used. Terms can only be clear/unclear (aka ambiguous/unambiguous) while propositions are either True or False.
Concepts to 2) judgments to 3) arguments
Terms to b) propositions to 3) syllogisms.
V -- Logic (42-44) - Does beauty literally exist or just beautiful things (i.e. the immaterial concept itself or just a physical manifestation)? Plato believed in what is coined “Extreme Realism” (i.e. there is a physical world and an equally real spiritual world populated by immaterial things).
William Ockham was a founder of Nominalism in opposition to such ideas as “Extreme Realism” by stating that concepts do not exist but that humans create names that are imperfect shorthand to classify individuals that are imprecisely lumped together by the subjective human intellect (i.e. “All chairs are quite different.”)
Personal Note: it seems to me that Nominalism has a fundamental error in giving the individual matter of a given object far more importance compared to the abstracted essence that can be apprehended by the human intellect.
Aristotle took a middle ground by proclaiming that concepts do exist in and because of the intellect (they don’t have an existence outside the intellect). Some theorize that if concepts did exist outside the intellect that this would lead to the valuing of concepts above the existing individuals identified by the concepts.
Personal note: I imagine that believing concepts exist outside the intellect does have a danger in belittling the importance of the individual. But to have intellect (which exists independently in all individuals) be the origin and home of concepts gives equal importance to each individual instead of allowing the individuals who defy certain concepts to be devalued for not conforming to the ideal that exists outside the person.
Concepts must have a universality to them that extends to a class that encompasses more than merely the current and presently perceived being to avoid the danger of having everything be of subjective importance to the whims of each individual’s apprehension.
Having concepts that extend to a group of like individuals that includes more than the single being that is perceived at any given moment is the only way to adequately categorize and understand the world.
Terms have extension (e.g. “Man” extends to either all 7+ billion people or to a single individual man depending on context) and comprehension (e.g. “Man” is comprehended as a “rational animal”).
Extension is a quantitative with how it can measure the connection/reference a term has with the physical/real world (e.g. you measure how many people “Man” extends to). Comprehension is qualitative since it cannot be measured (e.g. the nature/aspect “rational animal” as a comprehension of “Man” cannot be measured; only abstracted and understood).
Divisions and outlines measure a term’s extension. The definition of a term analyzes its comprehension.
