Chapter 1: Intellectual Preparation for Logic
Highlightg(yellow) - 02 Confirming Facts > Page 15 · Location 154 The objective existence of facts comes in two basic forms: things (objects) and events. Things are entities that exist, such as animals, vegetables, or mineral deposits. For example, the White House can be seen as a representative of a thing, while Lincoln’s assassination can be seen as a representative of an event.
Highlightg(yellow) - 02 Confirming Facts > Page 15 · Location 158 To confirm the existence of a thing, you simply need to conduct an on-site investigation.
Highlightg(yellow) - 02 Confirming Facts > Page 15 · Location 162 However, how do we prove the authenticity of an event, such as Lincoln’s assassination?
Highlightg(yellow) - 02 Confirming Facts > Page 15 · Location 164 We can only rely on certain things that can serve as indirect evidence. For instance, official records (police reports, death certificates, etc.), contemporary newspapers, photographs, memoirs, diaries, and congressional archives. All these authoritative sources from different fields can only be explained by the fact that Lincoln was assassinated.
Highlightg(yellow) - 02 Confirming Facts > Page 15 · Location 167 Facts can be considered objective or subjective. Things and events are objective; they exist in the public domain and are, in principle, accessible to everyone. A subjective fact is a fact confirmed either through personal experience or indirectly through the experience of others. For example, a headache is a subjective fact; if I experience a headache, I have firsthand evidence of its authenticity. But if you have a headache, not me, I can only establish my concept of a headache by indirectly hearing you describe your headache. Therefore, the confirmation of a subjective fact completely depends on the reliability of the person claiming to have the headache.
Highlightg(yellow) - 02 Confirming Facts > Page 16 · Location 174 Just as with indirectly verifying the authenticity of a thing, when verifying the truth or falsity of an event using indirect evidence, we must pay sufficient attention, because seriously scrutinizing the authenticity and reliability of the evidence source is the most important thing.
Highlightg(yellow) - 03 Concepts and Their Objects > Page 16 · Location 180 A correct concept faithfully reflects the objective order of its object; conversely, an incorrect concept is a distorted expression of the objective world.
Highlightg(yellow) - 05 Concepts and Facts > Page 18 · Location 198 Human cognition is mainly formed by three parts: (1) objective things; (2) the reflection of those things in the brain; and (3) the language we create for them, through which we can communicate with others. Taking the cat as an example, first there must be a cat, and only then can we establish the concept of a cat, followed by the universally recognized word “cat.” Everything originates from the objective existence of the cat; without this objective existence, there can be no concept or language about the cat.
Highlightg(yellow) - 05 Concepts and Facts > Page 19 · Location 206 Complex concepts refer to concepts that do not correspond one-to-one with objective things. Such concepts usually have multiple sources in the objective world. For example, democracy—is it a clear and specific concept? At least subconsciously, yes, because we can link it to the objective world. However, the connotation of democracy has rich sources: people, events, constitutions, legislative actions, the old regime, and the new regime, among others. If I want to discuss democracy with others, to avoid falling into the subjective trap and being unable to communicate, I must discuss things that everyone understands in reality; I must constantly involve various events in reality, and these events are the real soil of the democratic connotation.
Highlightg(yellow) - 06 Expressing Concepts in Language > Page 20 · Location 226 Language must faithfully express the original appearance of objective things, thereby giving our communication a solid factual basis. Note - 06 Expressing Concepts in Language > Page 20 · Location 227 Thus, language can also be poisoned to deceive the masses.
Highlightg(yellow) - 07 Effective Communication > Page 21 · Location 238 In logic, a statement has a specific meaning; it is a specific linguistic expression that applies only to propositions that can be judged as true or false.
Highlightg(yellow) - 07 Effective Communication > Page 21 · Location 239 Words are called the foundation of language, and propositions are the foundation of logic.
Highlightg(yellow) - 07 Effective Communication > Page 21 · Location 240 Logic itself is the study of discovering the truth and separating it from error.
Highlightg(yellow) - 07 Effective Communication > Page 21 · Location 243 Communication. If a person doesn’t even understand what they are thinking, how can they clearly express it to others?
Highlightg(yellow) - 07 Effective Communication > Page 22 · Location 246 Don’t assume that your audience will grasp the meaning you haven’t directly expressed.
Highlightg(yellow) - 07 Effective Communication > Page 22 · Location 248 Ignorance. When we are unsure, it is best to clearly state the background information; rambling is always better than missing a critical point.
Highlightg(yellow) - 07 Effective Communication > Page 22 · Location 249 Use complete sentences.
Highlightg(yellow) - 07 Effective Communication > Page 22 · Location 253 Don’t treat a subjective view as an objective fact. Mount Tai is between Shandong and Shanxi—this is a proposition based on objective facts; it is either true or false. But if I say, “Mount Tai is beautiful,” this proposition mixes subjective and objective factors. In this case, we absolutely cannot arbitrarily judge the truth or falsity of a subjective proposition, as we just did. The truth or falsity of an objective proposition is undisputed, but that of a subjective proposition is not. If I want a certain subjective proposition to be accepted by everyone, I must argue for it.
Highlightg(yellow) - 07 Effective Communication > Page 23 · Location 257 Avoid double negatives.
Highlightg(yellow) - 07 Effective Communication > Page 23 · Location 261 Choose language appropriate to the object.
Highlightg(yellow) - 08 Avoiding Vague and Ambiguous Language > Page 24 · Location 276 One way to avoid ambiguity is to ensure that the words you use reflect your intended meaning as specifically as possible, so that the reader or listener does not have to strain to guess what you mean.
Highlightg(yellow) - 08 Avoiding Vague and Ambiguous Language > Page 24 · Location 279 Words like “love,” “democracy,” “fairness,” “kindness,” and “evil” inherently have unclear meanings. This is not just because they lack a fixed referent, but also because their meanings are too broad. Therefore, even if two people use the same word (e.g., “love”), their meanings can be vastly different, or even contradictory. This is why, when using such words, they must be accurately understood. Before you try to convince someone that something is unfair, you must tell them how you define “unfair.”
Highlightg(yellow) - 09 Avoiding Evasive Language > Page 25 · Location 289 Try to speak plainly and directly to reduce the possibility of the listener misunderstanding your intended meaning. But this doesn’t mean you should be unrestrained; a person should be able to perfectly combine conciseness with elegance.
Highlightg(yellow) - 10 Truth > Page 26 · Location 297 All logical reasoning and all arguments have only one purpose: to find the truth of a certain thing.
Highlightg(yellow) - 10 Truth > Page 26 · Location 300 Truth comes in two basic forms: ontological truth and logical truth. Ontological truth is the more fundamental. Ontological truth refers to truth concerning existence. If a thing is deemed to be an ontological truth, and it truly is, then it must exist somewhere. A lamp on a table is an ontological truth because it genuinely exists there, not merely as an illusion. The opposite of ontological truth is a false illusion.
Highlightg(yellow) - 10 Truth > Page 26 · Location 306 Definition of a Proposition: A linguistic expression that can be judged as true or false. To affirm a proposition is to judge it as true, and vice versa.
Highlightg(yellow) - 10 Truth > Page 27 · Location 311 Confirming the truth means achieving the unification of the subjective and the objective.
Highlightg(yellow) - 10 Truth > Page 27 · Location 314 The basis for determining the truth or falsity of a proposition is the actual situation, and logical truth is built upon the foundation of ontological truth.
Highlightg(yellow) - 10 Truth > Page 28 · Location 325 Language logic should be based on factual logic.
Chapter 2: Basic Principles of Logic
Highlightg(yellow) - 01 Basic Principles > Page 31 · Location 332 Logic is the analysis of thought.
Highlightg(yellow) - 01 Basic Principles > Page 31 · Location 340 Law of Identity: A thing can only be itself. This explains the rich and colorful reality, which is composed of countless individuals, and each individual is unique. A thing can only be itself, and not something else. An apple is an apple; it cannot be an orange, a banana, or a pear.
Highlightg(yellow) - 01 Basic Principles > Page 32 · Location 343 Law of Excluded Middle: For any judgment about a thing under certain conditions, there must be a clear “is” or “is not”; there is no intermediate state. This explains that a thing either exists or does not exist, with no middle ground. A lamp on a table—this statement is either true or false, with no other possibility.
Highlightg(yellow) - 01 Basic Principles > Page 32 · Location 353 Law of Sufficient Reason: Everything has a sufficient reason for its existence. This principle can also be called the principle of causality. It embodies the content that the existence of all things in the universe has a sufficient basis.
Highlightg(yellow) - 01 Basic Principles > Page 33 · Location 362 Law of Contradiction: At the same time, a thing cannot be both X and not-X in the same respect. This principle can be seen as an extension of the Law of Identity: if X is X (Law of Identity), then at the same time, it cannot be not-X (Law of Contradiction). The qualifier “in the same respect” refers to the mode of existence. At the same time, a thing can be both and not at different respects, which is not a contradiction.
Highlightg(yellow) - 02 Gray Areas and Man-Made Gray Areas > Page 36 · Location 400 Negation can only be confirmed when the positive is known.
Highlightg(yellow) - 03 Everything Has Its Origin > Page 37 · Location 411 There must be a fundamental similarity between every cause and its effect. This means that a cause must lead to the observed effect and leave its specific imprint on the result; in turn, every effect, to some degree, reflects the characteristics of its origin.
Highlightg(yellow) - 04 Don’t Give Up the Search for Causes > Page 37 · Location 421 The search for causes should not be abandoned halfway. Causes are often a series. For example, A is the cause of B occurring, and B’s occurrence leads to C. We can represent their relationship graphically: A → B → C. Let’s assume C represents a difficult problem in an event that needs to be remedied. We find that C is caused by B. Following the correct method for solving issues, we decide to focus on the cause of C, which is B. This logical approach is commendable, but it hasn’t gone far enough. B is indeed the direct cause of C, but it is not the root cause. The source of the causal chain is A, so A is the fundamental cause of problem C.
Highlightg(yellow) - 05 Distinguishing Causes > Page 39 · Location 439 Let’s analyze the “Four Causes” using the example of a birdcage. Its efficient cause is Fried, who manufactured it; its material cause is pine wood, nails, screws, and paint; its formal cause is the specific shape of the birdcage (which distinguishes it from, say, a filing cabinet or a window lattice); and its final cause is providing a place for small birds to perch.
Highlightg(yellow) - 05 Distinguishing Causes > Page 40 · Location 456 Even the best tool in the hands of an unqualified person will not yield the best results. Bookmark - 05 Distinguishing Causes > Page 40 · Location 457
Highlightg(yellow) - 06 Defining Terms > Page 40 · Location 459 The most effective way to avoid semantic confusion and ambiguity in a logical argument is to define terms. When we say “define terms,” we are actually defining the objective thing that the term represents. The process of definition is the process of giving it a precise “position” based on how it relates to other things (the thing being defined).
Highlightg(yellow) - 06 Defining Terms > Page 40 · Location 464 The logical process of defining terms is divided into two steps: First, placing the term to be defined into the closest category; second, determining its distinguishing characteristics from other things within that category.
Highlightg(yellow) - 06 Defining Terms > Page 41 · Location 466 The classic definition of a human is “a rational animal.” In this definition, “animal” is the closest category, the category most closely related to humanity. Why?
Highlightg(yellow) - 06 Defining Terms > Page 41 · Location 473 In Aristotle’s definition of man, “rationality” is the characteristic that distinguishes man from other animals. A specific distinguishing characteristic is called a genus (or property/attribute), and it determines a specific category and distinguishes it from other categories.
Highlightg(yellow) - 06 Defining Terms > Page 41 · Location 477 Justice: Step 1: “Justice is a social virtue…” Step 2: “…through justice, every member of society receives what is due to them.”
Highlightg(yellow) - 06 Defining Terms > Page 42 · Location 484 Fear: Step 1: “Fear is an emotion…” Step 2: “…that prompts us to avoid perceived danger.”
Highlightg(yellow) - 06 Defining Terms > Page 42 · Location 489 If we want to define “mobile phone,” Step 1 can be quite simple: the category is “communication device”; then, we must emphasize several specific distinguishing characteristics to differentiate it from other existing communication devices in the world.
Highlightg(yellow) - 06 Defining Terms > Page 42 · Location 490 The unique value of a logical definition lies in its ability to reveal the essence of the defined thing.
Highlightg(yellow) - 07 Assertive Propositions > Page 43 · Location 499 The most effective arguments have conclusions that are assertive propositions, clearly and explicitly telling us what the truth of a thing is.
Highlightg(yellow) - 07 Assertive Propositions > Page 44 · Location 504 A proposition may be assertive in form, but the content it expresses may still be incorrect. A person might say, “The Chicago Cubs are the best baseball team.” This is an assertive proposition, but it only tells us the speaker’s firm belief. It describes a subjective fact because it is merely the speaker’s opinion and does not reflect any objective reality.
Highlightg(yellow) - 08 Universal Propositions > Page 45 · Location 528 Logic is the technology that allows us to believe in the truth.
Chapter 3: Argumentation: The Language of Logic
Highlightg(yellow) - 01 Constructing an Argument > Page 48 · Location 534 A logician does not need to have seen or heard the Atlantic Ocean or Niagara Falls with their own eyes; they can infer the possibility of their existence from a single drop of water.
Highlightg(yellow) - 01 Constructing an Argument > Page 49 · Location 547 The most effective argument always tries to reach the simplest and clearest conclusion.
Highlightg(yellow) - 01 Constructing an Argument > Page 49 · Location 557 The premise is the foundation of the argument; a correct argument relies on correct premises. Therefore, the first step of a correct argument is to confirm the correctness of the premises.
Highlightg(yellow) - 03 From Particular to Universal > Page 50 · Location 568 The process of arguing from universal to particular ensures the necessity of the conclusion, but the reverse is not guaranteed. For partially valid conclusions, we cannot definitively say that they hold true for the whole. In some examples, the process of arguing from particular to universal leads to clearly erroneous conclusions. “Some women are mothers” is an absolutely correct proposition, but this premise does not support the conclusion “All women are mothers.”
Highlightg(yellow) - 03 From Particular to Universal > Page 51 · Location 577 Just because certain characteristics are suitable for a part of the whole, it is not necessarily true that these characteristics are suitable for the whole. This is a clear fallacy. However, people often cannot avoid this fallacy, so when facing such situations, one should be extra careful. Hasty generalization is a kind of human nature, although it is not a good thing.
Highlightg(yellow) - 04 Assertion > Page 51 · Location 582 Assertion is the process of linking concepts by attaching a predicate to a subject.
Highlightg(yellow) - 04 Assertion > Page 52 · Location 583 If assertion is the process of aggregating and pairing concepts, then testing the correctness of the assertion lies in whether the aggregated concepts actually fit together in reality.
Highlightg(yellow) - 06 Comparison > Page 54 · Location 623 When we compare two things, we find that they are either completely similar, completely different, or partially similar.
Highlightg(yellow) - 07 Comparison and Argumentation > Page 57 · Location 657 Argument Summary: A possesses characteristics R, S, T, U, V, W, X, and Y. B possesses characteristics R, S, T, U, V, W, X, and Y. A possesses characteristic Z. Therefore, B also possesses characteristic Z. Analyzing this conclusion is not necessary, but it is highly probable. Based on the fact that two things possess many common characteristics, when one of them possesses another characteristic, it is very likely that the other one possesses it as well. Analogical argumentation is only applicable when we cannot directly prove that B possesses characteristic Z—of course, it can also be when B has not yet occurred, so it cannot be analyzed.
Highlightg(yellow) - 08 Correct Argumentation > Page 58 · Location 669 To make an argument correct and powerful, we must pay attention to its facts (content) and its form (structure).
Highlightg(yellow) - 08 Correct Argumentation > Page 58 · Location 679 Conjunctive Argumentation: The symbolic representation of conjunctive argumentation is: A $\cdot$ B. Here, A and B both represent a complete proposition. Using a simple example, for instance: “Anna is a sophomore at the University of Minnesota, majoring in Biology.” The symbol “$\cdot$” between A and B means “and,” and it is important because it signifies that both A and B are true. This is actually a chain reaction: if you assume one is false, you cannot assume the other is true. A $\cdot$ B can serve as a premise for an argument, from which two valid conclusions can be drawn: A $\cdot$ B $\rightarrow$ A $\rightarrow$ B. The contrapositive of A (not A) $\rightarrow$ B (not B) (i.e., Anna is not a sophomore at the University of Minnesota or she does not major in Biology) is also false, because it contradicts the premise of the argument.
Highlightg(yellow) - 10 Syllogism > Page 64 · Location 753 The basis of syllogistic reasoning is first determining that a certain part belongs to a whole, and then concluding that the members of that part also belong to the whole.
Highlightg(yellow) - 11 Truth of the Premise > Page 65 · Location 763 A syllogism, or any argument, if it is to yield a correct conclusion, must meet two basic requirements: first, it must have correct content, and second, it must have a sound structure.
Highlightg(yellow) - 15 Conclusion Must Reflect the Quantity of the Premise > Page 72 · Location 851 Some teenagers study Spanish. Some chess champions are teenagers. Therefore, some chess champions study Spanish. Analyzing the conclusion, it is not certain. It is possible that some chess players study Spanish. In fact, the probability is high. But this argument cannot prove that it is necessary.
Highlightg(yellow) - 15 Conclusion Must Reflect the Quantity of the Premise > Page 72 · Location 855 Two particular premises cannot yield a definite conclusion.
Highlightg(yellow) - 17 Inductive Argumentation > Page 75 · Location 884 Deductive argumentation yields necessary conclusions, while inductive argumentation can only yield probable conclusions.
Highlightg(yellow) - 17 Inductive Argumentation > Page 75 · Location 887 The basic principle of deductive argumentation is: starting from a proposition we know to be true (the major premise), through meticulous analysis (via the minor premise to the conclusion), we deduce what is implicitly contained within the original proposition.
Highlightg(yellow) - 18 Evaluating Argumentation > Page 77 · Location 915 In the process of evaluating the correctness of an argument, the first step is to determine whether the argument being evaluated is a genuine argument.
Chapter 4: Roots of Non-Logical Thinking
Highlightg(yellow) - 01 Skepticism > Page 83 · Location 956 Logic is not satisfied with mere assertion. It pays no heed to the views of authorities, the prejudices of the masses, or the superstitions of the dead.
Highlightg(yellow) - 01 Skepticism > Page 83 · Location 965 The extreme skeptic claims that there is no such thing as truth in the world. This is clearly a self-contradictory conclusion, because if there is no truth in the world, then no proposition can be judged, making this conclusion baseless. The moderate skeptic reluctantly admits that truth might exist in the world, but insists that even if truth exists, humanity lacks the ability to discover it. At first glance, compared to the extreme skeptic, this conclusion seems to give truth a place, but in reality, it does not. If truth exists only theoretically and cannot be verified through practice, then it does not truly exist.
Highlightg(yellow) - 02 Evidential Agnosticism > Page 84 · Location 974 The agnostic neither denies the existence of truth nor considers it unattainable. They merely claim that people know very little about the truth of any definite thing.
Highlightg(yellow) - 05 Emotion and Argumentation > Page 86 · Location 1003 The more intense the emotion, the greater the difficulty in clear thinking and calm action.
Highlightg(yellow) - 05 Emotion and Argumentation > Page 87 · Location 1012 Never directly manipulate people’s emotions; strive to let people discover the truth themselves. Only truth is worth cheering for.
Highlightg(yellow) - 08 The Limits of Sincerity > Page 88 · Location 1026 Sincerity is a necessary condition for correct reasoning, but it is not a sufficient condition. If you do not believe in the view that you publicly advocate and vigorously defend, then you are abusing reasoning.
Chapter 5: Main Forms of Non-Logical Thinking
Highlightg(yellow) - 05 Begging the Question > Page 97 · Location 1111 Treating the view that needs to be proven as a self-evident premise.
Highlightg(yellow) - 05 Begging the Question > Page 98 · Location 1120 Its correctness is predicated on the correctness of the conclusion. If I don’t already know that Jim shaved, then I cannot be certain that everyone by the table has shaved. Therefore, the conclusion merely states a fact we already know. There is no true inference here.
Highlightg(yellow) - 06 False Assumption > Page 99 · Location 1132 A basic standard for judging an assumption is that the proposition must not violate the Law of Contradiction. In other words, it must not contradict itself.
Highlightg(yellow) - 07 Straw Man Fallacy > Page 100 · Location 1141 The Straw Man Fallacy is not an unintentional mistake because it involves deliberately distorting someone else’s argument.
Highlightg(yellow) - 08 Appeal to Tradition > Page 100 · Location 1145 Habit has a major influence on our lives. If we follow habits without analyzing whether they are actually worth following, we become slaves to habit.
Highlightg(yellow) - 09 Appeal to Force (Ad Baculum) > Page 101 · Location 1154 Precedent independently determines future behavior. In reality, precedent cannot provide effective support for future behavior; a completed action only has historical significance.
Highlightg(yellow) - 10 Appeal to Popularity (Ad Populum) > Page 102 · Location 1161 The Appeal to Popularity fallacy states that if the majority of people believe proposition X is correct, then we can conclude that X is correct.
Highlightg(yellow) - 11 Appeal to Person (Ad Hominem) > Page 102 · Location 1166 Principle: In an argument, we must focus on the argument itself, not on the person making the argument.
Highlightg(yellow) - 12 Appeal to Authority > Page 103 · Location 1176 People can only accept what is true when they are thinking freely, and they can only determine what is true when they are judging independently. Bookmark - 13 Abuse of Expert Opinion > Page 103 · Location 1178
Highlightg(yellow) - 13 Abuse of Expert Opinion > Page 103 · Location 1178 Abuse of Expert Opinion: An expert is an authority in a specific field. In an argument, consulting experts in the relevant field is a reasonable practice. However, when consulting experts, one must remain vigilant. Consider the following argument: Professor Smith says Project A is good. Professor Jones says Project A is good. Professor John says Project A is good. Therefore, we should accept Project A. Bookmark - 14 Quantification > Page 105 · Location 1194
Highlightg(yellow) - 16 Stopping at Analysis > Page 107 · Location 1218 The purpose of analysis is not simply to know what parts a thing is composed of, but to clarify how these components are interconnected and interact to form a whole. In purely quantitative terms, it is the whole being greater than the sum of its parts. If you fully understand the essence of a thing, then assembling the disassembled clock parts will still result in a clock.