Studying logic, you are recommended to read Concise Logicals in the Oxford Commons series, by Graham Prist, a philosophy professor in logic research.
This book is not one of those thick, logical equations, but a philosophical approach to interesting logical questions, such as the existence of God? Is time passing? How to calculate probability? How can best be made?
This thin little book is like a simple copy of the logical travel map, and each chapter discusses a logical philosophical question without a standard answer. Read as a whole, you have a basic understanding of all aspects of logic, which is an excellent logical literacy book.
So I’m going to focus on three important and interesting points of knowledge in the next book, and I’m going to tell you why they’re important and why they’re interesting.
The first knowledge point is called the True Value function.
The second knowledge point is called a model algorithm.
The third knowledge point is called fuzzy.
First knowledge point: the real value function. To that end, we need to know what the proposition is. To put it simply, the subject is a statement of truth and falsehood. For example, “Hitler is the President of France” Andy Lee, “The Mass Lover” and “The Mount of Everest is the highest in the world” and “Ruthour was born in Zhejiang Shao Xing.” The first two are fake, the second are true and the last two are not true.
Let us pause and reflect on why the first two sentences are false, the second in the middle are true and the last two are not true.
From a common sense point of view, we will say that because the first two sentences are not true, the middle two are true. Anything that expresses the truth is true. If the facts are not expressed, they are false. More precisely, the truth is the state of the real world. A statement consistent with the facts is a statement that correctly describes the state of the world, that is, a statement of truth. A statement that is not true is a statement that does not properly describe the state of the world.
And “Have you eaten yet? It’s a question, it’s a question, it’s a question, it’s not a description of the state of a world. “Please help me to break the cap” is a prayer sentence, which indicates a request or an order from someone else and does not describe the state of the world, so there is no real difference between the two sentences. In our real world, Mount Everest is indeed the highest in the world, and Lu Xuan was born in the Zhejiang Shao Xing. But Hitler is not the President of France, and I am not a popular lover at least for the time being. So these words either describe the state of the real world or outline some unrealistic state of affairs. They are true and false. The first two sentences are true and the latter two are false.
People may think it’s real, it’s fake, it’s fake. In fact, it is difficult to analyse what is real and what is fake. Let’s think, “Sun Goku’s 72nd change, “The Red Child is the son of the Iron Fan Princess.” They describe the situation in fictional stories and it is difficult to say that they correspond to reality in the world. But it’s both false and it doesn’t sound right.
So, is there no truth in this fictional story? This is a question without a standard answer. However, in order to facilitate the discussion, we consider sentences that correspond to the facts of the real world to be the real and the factual ones to be false. And a sentence without a real one is not a proposition. And “real” and “false” are real. Although some scholars believe that “real” and “uncertain” can be set. These are the three real values, but we usually set only “real” and “false” values. So one proposition is not true, it is false and there is no third possibility.
Go back to the knowledge point of the real value function. We already know what’s real and what’s the function? The function is like a machine that enters a value into it, and it outputs a value. For example, the f(x+1) function, enter one in, it will output 2; enter 67 in, it will output 68. Or, the f(x dad) function, which enters into the inside, it will export Cao Cao; it will enter in the inside, it will export Sun Kin.
The real-value function in logic is very similar to that in mathematics, and it also enters values and outputs values. Here we need to know the three most common real functions. The first one is called “No,” and it’s done in a simple way, and if the title P is true, then the title P’s denial is fake. If the title P is fake, then the title P’s denial is true. In other words, the denial of this real-value machine reverses the true value of the sentence entered. The input is a fake, the input is a fake.
For example, Beijing is the capital of China, and the proposition is true. So when the real-value machine is rejected, the proposition becomes “Beijing is not China’s capital”, and it’s fake. And the idea that Shanghai is Russia’s capital is in fact a lie, and when it is entered to deny this real-value machine, it becomes “Shanghai is not Russia’s capital” and becomes real.
The second real-value function is called “joined”, “consolidated” and “intake” “take”. “Access” is a real-value function machine that requires statements to be entered into it to be true. If you enter a statement inside, even if it’s only one fake, it’s going to export the fake value.
For example, the three propositions of “Andy Lee is a man” and “Andy Lee has learned psychology” and “Andy Lee has learned logic” are true, and they’re all integrated into the machine and become “Andy Lee is a man who has learned logic and psychology.” And “Andy Lee is a girl” and “Andy Lee has learned psychology” and “Andy Lee has learned logic” and at least one is not true. Together, they become “Andy Lee is a girl who has learned psychology and logic,” a proposition that, while partly true, seems to be false.
The third real-value function is called “diagnosing” and “analyzing” the “dialysis”. To read the statement entered in the real-value machine, as long as one is true, the whole is true. It’s all fake. The whole thing is fake. It is also possible to read “or”. So we’re going to read it “or.”
A few examples. Andy Lee is a rocker, Andy Lee is a chick, Andy Lee is a programming expert. All three words are fake, so they’re all fake, and they’re all fake. But if it turns out that “Andy Lee is a rock star or a programming expert or a man,” because the proposition “Andy Lee is a man” is true, then the whole complex proposition, though mostly fake, is true.
This is the point of knowledge about real-value functions. Now, let’s look at the second knowledge point, which is a model algorithm.
And in real life, if we say “Andy Lee is cute, Andy Lee is programming expert,” then neither of these words is true, and it’s fake. But if we say, “Andy Lee may be cute, and Andy Lee may be a programming expert,” then those two words are not necessarily fake.
Likewise, the two words “Andy Lee is male, Andy Lee has learned psychology” are true, but if the word “andy Lee” has become “andy Lee must be male, and Andy Lee must have learned psychology” they are not necessarily true.
The words “necessarily” and “possibly” are simulators. These two model algorithms can be converted to each other. If 1+1 is necessarily equal to 2, then 1+1 cannot be equal to 2. In other words, “necessarily” is equivalent to “no no.” “It’s not necessarily a beautiful woman.” “Possible” is equivalent to “not necessarily”. It’s obnoxious, but it’s intuitive to write it in a logical symbol.
We can’t deduce the reals from the reals of the reals. For example, I’m actually a man, but I’m not necessarily a man, and I could have had a sex-transformation operation. This means that, in fact, it does not mean that it is necessary. However, 1+1 actually equals 2 and 1+1 necessarily equals 2. Here, this mathematical formula is actually real, and it’s bound to be true.
In order to fully understand the model algorithm, we need to use the concept of a possible world. The “Possible World” and the parallel universe in science fiction films are a little similar to the multiple universes in physics. In short, we can imagine a possible world that is very similar to, but not necessarily identical to, our real world. In that possible world, there are solar systems and the Earth, which happens to have evolved organisms and formed human civilization. The historical development of this human civilization is almost identical to our real world, where there is a person like me, Andy Lee.
In this case, if that Andy Lee is a pretty girl, then we say “Andy Lee may be a pretty girl,” and if that Andy Lee is a programming master, we say “Andy Lee may be a programming master.” In other words, the “possibly” model algorithm means that, at least in a possible world, the phrase fits that possible world.
And the “necessarily” simulator means that in all conceivable worlds, words are true. For example, 1+1 = 2. In all possible scenarios, 1+1 equals 2.
In other words, a proposition is bound to be true, that is, it is true in every possible world that can be envisaged. And a proposition is bound to be fake, and it is fake in all possible worlds. A proposition may be true, that it is true in at least one possible world. A proposition may be fake, but it’s fake in at least one possible world.
After an in-depth understanding of the concept of a possible world, we will find it particularly useful. It can explain what is possible and what is inevitable. Although not here, some philosophers use it to explain causality. So the question is, what is this possible world? Is it the product of our human imagination or is it another universe that exists?
The philosopher David Lewis believes that perhaps the world is as real as our real world. Or rather, our real world is realistic for us, but it is only possible for the inhabitants of another possible world. And those who may be the real world for the people who live there. For example, in another possible world, I’m a little girl. The world is very real for me as a woman. At this moment, I might even imagine that that woman, Andy Lee, is a man in another possible world?
Of course, there are also philosophers who believe that perhaps the world is just a theoretical model that we humans have conceived and that it does not exist. The same goes for me personally, and I do not think that the world may be real. But that does not prevent us from recognizing the importance of a possible world. You know, in order to understand the real world, we must envisage a possible world. In history studies, for example, we often imagine how history can change if there is an event in history or if there is no event in history. The East Wind is not with Zhou Zhang, Bronze Springs locks Zi Jo. If Cao Cao wins the Red Wall War, how will the history of the three countries follow? At this point in time, we are using this model of the possible world to imagine that in another possible world, Cao Cao did win the battle of the Red Wall, and would he be able to put two pieces into his hands?
And we’re talking about model algorithms. Then let’s look at the third knowledge point, ambiguity.
Let me start with a story. There’s a wooden boat that we call Panda. Every time it returns, we replace its old parts with a new one. It was just a few years later that all parts of the Panda were replaced. So the question is, is this Panda still Panda?
If you ask the sailors on board, you might think it’s the Panda. These sailors and the Panda are together in the morning and evening, although they have all the parts on the whole, which, in terms of physical properties, is no longer the same thing. But sailors generally do not notice this change. Like human beings, as time passes, we continue to metabolize and each molecule is different, but we still believe that we are the same person, and that there is little change every day, after all.
But if we take the parts off the panda and reassemble them into a boat, it’s exactly the same as the new panda. The question is, who is the Panda? Is that a boat with sailors sailing? Or reassemble the ship with parts?
I also have no standard answer to this question. Interested friends can search for relevant information again. Then we have to think about the ambiguity behind this. In other words, most of what we say in our daily lives is vague and not very precise. For example, if a person has no money, we say that he is a poor person. But if we give this man a dollar, we’ll still say he’s poor. Give him another dollar, he’s still poor. If this process continues until one million dollars is paid to him, then he already has a million dollars in property or is he poor?
The statement of the poor is vague, as is the statement of the rich. Even the term “blank” is vague. A bald head grows a hair, and he’s still bald. One more hair, he’s still bald. If you think about it, you’ll find that words like “blue” “beauty” “expert” “child” are vague. We know that when the blue paint is mixed with yellow paint, it becomes green paint. Well, a big bunch of blue paint mixed into a drop of yellow paint doesn’t seem to make the whole pigmention green. So, what about the second drop and the third drop? How many drops will it turn green? A three-year-old is definitely a child. After a day, this three-year-old is still a child. One more day, this three-year-old child is still a child. So how many days will it take for this kid to become an adult?
Such vague questions indeed make it difficult for us to answer. But in real life we sometimes have to answer. For example, at the time of the examination, the rule of 60 points is below the level of failure and requires re-examination. But when we think about it, we’ll think of 60 points and 59 points. Why doesn’t the former have to retake it, and the latter needs to retake it? For example, article 236 of the Criminal Code of the People’s Republic of China provides that “the rape of a minor under the age of 14 shall be punished by a heavier penalty”. But when you’re under 14, it’s only a day away, and it’s probably only 12 in the night. However, rape is punishable under 14 years of age and may not be considered a crime of rape if it reaches 14 years of age after one day. That sounds incredible, but the actual rules do.
That is to say, while many statements are vague, we have to draw precise criteria in particular cases. There’s an example of a new bike in this book. If we went to the bike shop to buy a new bike, we’d expect the bike to be never used. But if it’s for a bike race, we’ll think that 9 is a new bike, and it’s not badly worn, and it’s as good as a brand-new bike.
In short, in different circumstances, our quest for precision is different. There are times when special precision is required and no ambiguity is present. At times, however, it is particularly accurate and not interesting. For example, Ming said to Mei, “My love for you is like the moon, and never changes.” But, think about it, the moon was formed about 4.5 billion years ago and has been slowly changing ever since. There are countless round hills on the Moon, which are craters that were hit by meteorites. In a very long time, the moon will be very different from today. But, while the moon, to be precise, is not always the same, let us not care about those details when we talk romanticly.
These are the three points of knowledge that I have shared with you today.
The first knowledge point is called a real value function. True is true and false. The real value of a proposition is that it is true. The real value of a proposition is false, and it is not true. The function is like a machine, and when you enter some values, you output some values. We understand three real-value functions. The first is called “no,” which is to turn the value entered into the opposite. The input is fake, the input is fake. The second is called “Acquire.” All the calls for input are true. The output is real. Even if it was just a fake one, it would be a fake one. The third one is called “Analysis”. This function only enters at least one real question, and the real question is exported as a whole; if you enter all false questions, the false question is exported as a whole.
The second knowledge point is called a model calculator. There are only two models, one called “necessarily” and the other called “probably”. They can be transformed into one another, and they must be true, that is, they cannot be. In order to understand the model algorithm, we know the world again. Maybe the world is the world we thought of. If in all possible worlds I’m a little girl, I’m definitely a little girl. If in a possible world, I’m a pretty girl, I could be a pretty girl. That is to say, what is necessarily required of all possible worlds, and perhaps only of at least one possible world.
The third knowledge point is called fuzzy. Much of what is said in everyday life is vague, that is to say, minor changes do not lead to a denial of this claim. A child grew up a day later and was a child. A poor person is a poor person after one dollar. In some cases, however, we must also seek precision and eliminate ambiguity. At this point, some boundary lines need to be drawn arbitrarily. For example, more than 60 is qualifying, less than 60 is not. Although 60 points and 59 points don’t seem much different.
My recommendation for this book is here. I hope it will help you. If you’re interested in the book, you might want to read the original book, read the charts and the formulae, and see what the logical symbols we’re talking about look like. If you have a greater interest in logic, you can find a special course on logic. Record number: YX11v19bNNr
I don’t know.
Keep your eyes on the road.
