Saturday, December 31, 2022

Mnemonic devices for remembering symbolic representations

Here are a few examples of mnemonic devices that could be used to remember symbolic representations:

For the symbol ∀ (for all), you might use the phrase "For All Xs." This helps you remember that the symbol represents the idea of "for every" or "for all" in a statement.

For the symbol ∃ (there exists), you might use the phrase "Exists at least one." This helps you remember that the symbol represents the idea of "there is at least one" or "there exists" in a statement

For the symbol → (implies), you might use the phrase "If, then." This helps you remember that the symbol represents the idea of "if this is true, then that must also be true" in a statement.

For the symbol ∈ (belongs to), you might use the phrase "In set." This helps you remember that the symbol represents the idea of "belongs to" or "is a member of" a particular set.

Remember, these are just a few examples, and you may find that other mnemonic devices work better for you. The important thing is to find a device that helps you remember the meaning of the symbols and use it regularly as you practice and learn.

Monday, December 26, 2022

A game theoretic representation of the three little pigs

It’s interesting having technology represent physically what one may have as a passing thought. Here's chatGPT giving an example of a bayesian game using the three little pigs.

Sure, we can represent the story of the three little pigs as a Bayesian game. In this game, the players are the wolf and the little pigs, and the payoffs to the players depend on the strategies chosen by the players and the state of the game.

To represent the story of the three little pigs as a Bayesian game, we can use a tuple (S,A,P,u), where S is the set of possible states of the game, A is the set of possible actions (or strategies) for each player, P is the probability distribution over the possible states of the game, and u is the utility function that assigns a payoff to each player for each combination of strategies and states.

Here is an example of the three little pigs represented as a Bayesian game:

S = {house of straw, house of sticks, house of bricks}

A = {blow, hide}

P = {0.4, 0.3, 0.3}

u(wolf,blow,house of straw) = 1

u(wolf,hide,house of straw) = 0

u(pig,blow,house of straw) = -1

u(pig,hide,house of straw) = 0

u(wolf,blow,house of sticks) = 1

u(wolf,hide,house of sticks) = 0

u(pig,blow,house of sticks) = -1

u(pig,hide,house of sticks) = 0

u(wolf,blow,house of bricks) = 0

u(wolf,hide,house of bricks) = 0

u(pig,blow,house of bricks) = 1

u(pig,hide,house of bricks) = 0

In this example, the set S represents the possible states of the game (the house of straw, the house of sticks, or the house of bricks), the set A represents the possible actions (or strategies) for each player (blow or hide), the probability distribution P represents the likelihood of each state occurring, and the utility function u assigns a payoff to each player for each combination of strategies and states.

For example, the utility function u(wolf,blow,house of straw) = 1 indicates that if the wolf chooses to blow and the pig is in the house of straw, the wolf gets a payoff of 1. Similarly, the utility function u(pig,hide,house of bricks) = 0 indicates that if the pig chooses to hide and is in the house of bricks, the pig gets a payoff of 0.

I hope this helps! Let me know if you have any other questions.

Thursday, December 22, 2022

How definite descriptions improve critical thinking

Testing chatGPT and thought this collection of ideas was helpful. There are many questions to explore with this technology.

In symbolic logic, a definite description is a phrase of the form "the X" where X is a property or a set of properties. For example, "the tallest building" or "the prime numbers" are definite descriptions. The use of definite descriptions allows us to talk about unique objects or sets of objects, such as a specific building or a particular set of numbers, in a formal and precise way.

Here is an example of a definite description being used in symbolic logic:

Suppose we want to say that the capital city of France is Paris. We could express this statement using the definite description "the capital city of France" as follows:

Let C be the capital city of France. Therefore, C = Paris.

In this example, "the capital city of France" is a definite description that refers to a unique object, namely the city that is the capital of France. The statement "C = Paris" asserts that this unique object is in fact Paris. This allows us to make a precise and formal statement about the capital city of France using the symbolic language of logic.

Definite descriptions are often used in logical arguments to make precise and formal statements about unique objects or sets of objects. This can help improve critical thinking in several ways.

First, using definite descriptions allows us to be more precise and clear in our reasoning and arguments. This can help us avoid confusion or misunderstandings, and make it easier for others to follow our line of thinking.

Second, using definite descriptions forces us to be more precise and explicit in our assumptions and premises. In order to use a definite description, we need to clearly specify the properties that define the unique object or set of objects we are talking about. This can help us identify any assumptions or implicit premises in our arguments, and make sure they are stated explicitly and clearly.

Third, using definite descriptions can help us evaluate the validity of an argument by examining the relationship between the premises and the conclusion. In a logical argument that uses definite descriptions, the premises must be sufficient to support the conclusion. If the premises do not logically entail the conclusion, then the argument is not valid. This can help us improve our critical thinking skills by encouraging us to carefully evaluate the logical structure of an argument.

Here are some examples of how using definite descriptions can improve critical thinking in the ways described above:

1. Precise and clear reasoning:

Suppose we are having a discussion about the tallest building in the world. Without using definite descriptions, our conversation might go something like this:

Person 1: I heard that the tallest building in the world is in Dubai.

Person 2: No, I heard it's in Shanghai.

Person 1: But I read an article that said it's in Dubai.

Person 2: Well, I saw a documentary that said it's in Shanghai.

In this conversation, there is a lot of confusion and disagreement because it is not clear which building we are talking about. By using a definite description, we can be more precise and clear in our reasoning:

Person 1: I heard that the building with the highest architectural height is in Dubai.

Person 2: No, I heard that the building with the highest occupied floor is in Shanghai.

Person 1: Ah, I see what you're saying. So they are different buildings with different records.

Person 2: That's right.

In this revised conversation, the use of definite descriptions ("the building with the highest architectural height" and "the building with the highest occupied floor") helps us avoid confusion and have a more productive conversation.

2. Precise and explicit assumptions and premises:

Suppose we are trying to prove that all prime numbers are odd. Without using definite descriptions, our proof might go something like this:

Proof:

Let P be a prime number.
P is not even, because if it were, it could be divided by 2.
Therefore, P is odd.

In this proof, the second step is not explicitly stated, so it is not clear what the proof is based on. By using a definite description, we can be more precise and explicit in our assumptions and premises:

Proof:

Let P be a prime number.
Let E be the set of even numbers.
P is not an element of E, because if it were, it could be divided by 2.
Therefore, P is odd.

In this revised proof, the use of definite descriptions ("the set of even numbers" and "an element of E") helps us make our assumptions and premises explicit and clear.

3. Valid logical structure:

Suppose we are trying to prove that all triangles have three sides. Without using definite descriptions, our proof might go something like this:

Proof:

Let T be a triangle.
T has three sides.
Therefore, all triangles have three sides.

In this proof, the second step does not logically follow from the first step, so the argument is not valid. By using a definite description, we can make the logical structure of the argument more clear:

Proof:

Let T be a triangle.
Let S be the set of polygons with three sides.
T is an element of S.
Therefore, all triangles have three sides.

In this revised proof, the use of definite descriptions ("the set of polygons with three sides" and "an element of S") helps us make the logical structure of the argument more clear and valid.

Monday, December 19, 2022

Symbolic Logic and Law

I was talking to chatGPT about logic. It was asked to show how symbolic logic is used in law. the AI provides great introductions to subjects. However, one still has to do one’s own research to understand them beyond a shallow level.

Symbolic logic is often used in law to help reason and argue more effectively and rigorously. In law, logical arguments are used to support or challenge the validity of legal principles, rules, and decisions. Symbolic logic provides a formal and precise language for representing and analyzing these arguments, which can help lawyers and judges evaluate their quality and validity.

One way in which symbolic logic is used in law is to represent and analyze the logical structure of legal arguments. In symbolic logic, we can represent the premises and conclusion of a legal argument using logical symbols and operators, such as the connectives "and," "or," and "if-then." This allows us to clearly and precisely express the logical relationships between the premises and the conclusion of the argument, and evaluate whether the argument is valid or invalid.

Another way in which symbolic logic is used in law is to identify and evaluate the assumptions and implications of a legal argument. In symbolic logic, we can represent the assumptions and implications of an argument using quantifiers and variables, such as "all" and "some." This allows us to clearly and precisely express the scope and implications of a legal argument, and evaluate whether the assumptions and implications are reasonable and consistent with the law.

Overall, the use of symbolic logic in law can help lawyers and judges reason and argue more effectively and rigorously, and improve their critical thinking skills. By using the tools and techniques of symbolic logic, they can better evaluate the quality and validity of legal arguments, and make more informed and reasonable legal decisions.

Here is an example of how symbolic logic might be used in a legal case:

Suppose a defendant is charged with the crime of robbery. The prosecution's case against the defendant is based on the following three pieces of evidence:

1. A witness saw the defendant leaving the scene of the robbery with a bag of money. 2. The defendant was arrested shortly after the robbery with a bag of money in his possession. 3. The victim of the robbery identified the defendant as the perpetrator.

In this case, the prosecution might use symbolic logic to represent and analyze the logical structure of their argument as follows:

1. Let W be the witness who saw the defendant leaving the scene of the robbery with a bag of money. 2. Let D be the defendant. 3. Let B be the bag of money. 4. Let A be the arrest of the defendant. 5. Let V be the victim of the robbery.

Premise 1: W saw D leaving the scene of the robbery with B. Premise 2: A occurred, and during A, D had B in his possession. Premise 3: V identified D as the perpetrator.

Conclusion: Therefore, D is guilty of robbery.

In this argument, the premises are statements 1-3, and the conclusion is statement 6. The relationship between the premises and the conclusion is that the premises provide evidence or support for the conclusion.

This argument can be evaluated for its logical validity by using the rules of symbolic logic. For example, we can use the rule of modus ponens to show that the premises logically imply the conclusion:

1. If W saw D leaving the scene of the robbery with B, and A occurred and during A, D had B in his possession, and V identified D as the perpetrator, then D is guilty of robbery. (This is the rule of modus ponens.) 2. W saw D leaving the scene of the robbery with B. (This is premise 1.) 3. A occurred and during A, D had B in his possession. (This is premise 2.) 4. V identified D as the perpetrator. (This is premise 3.)

Therefore, D is guilty of robbery. (This is the conclusion.)

In this way, symbolic logic can be used to represent and analyze the logical structure of a legal argument, and evaluate its validity. This can help lawyers and judges reason and argue more effectively and rigorously, and make more informed and reasonable legal decisions.

Friday, December 16, 2022

How are premises and conclusions different from assumptions and implications?

I was talking to chatgpt about logic and how it works. This question arose since in natural language premises and assumptions are similar, as well as conclusions and implications. These concepts are used in specific ways in logic. I thought the AI gave useful explanations and examples as to how they are different. More could be said about implication though.

In a logical argument, the premises are the reasons or evidence that are offered to support the conclusion. The conclusion is the main point or claim that the argument is trying to establish. The relationship between the premises and the conclusion is that the premises are supposed to provide evidence or support for the conclusion.

In contrast, assumptions and implications are not directly part of the argument itself, but are related to the argument in other ways. Assumptions are the background beliefs or conditions that are necessary for the argument to be valid or reasonable. Implications are the logical consequences or implications of the argument.

For example, consider the following argument:

Premise: All dogs are mammals.

Premise: Fido is a dog.

Conclusion: Therefore, Fido is a mammal.

In this argument, the premises are "All dogs are mammals" and "Fido is a dog," and the conclusion is "Fido is a mammal." The relationship between the premises and the conclusion is that the premises provide evidence or support for the conclusion.

Now suppose that one of the assumptions of this argument is that "mammals are a type of animal." This assumption is not explicitly stated in the argument, but it is necessary for the argument to be valid. Without the assumption that mammals are a type of animal, the conclusion "Fido is a mammal" would not be meaningful or relevant.

Finally, suppose that one of the implications of this argument is that "Fido is not a reptile." This implication is not directly stated in the argument, but it follows logically from the premises and conclusion. If we accept the premises and conclusion of the argument, then it logically follows that Fido cannot be a reptile, because reptiles are not mammals.

In summary, the difference between premise and conclusion vs. assumption and implication is that premises and conclusions are directly part of the argument, while assumptions and implications are related to the argument in other ways. Premises provide evidence or support for the conclusion, while assumptions are necessary for the argument to be valid, and implications are logical consequences of the argument.

Saturday, August 13, 2022

On the conflict between omniscience, omnipotence, and omnibenevolence

It is simply easier to reason without employing a god, especially a god with the omni-powers. Such a being wreaks havoc on the foundations of logic. Most people don’t study formal logic. They know of certain rules from their observations of natural language, but it is always a swirl of thoughts if we utilize no systemization. Add this to the fact that belief in a god isn’t difficult given certain circumstances (indoctrination, tragedy, ignorance, etc.).

Unfortunately, one can’t prove a negative. I can only define the terms and attempt to show how they disagree.

Omniscience means you have all knowledge, a complete epistemology.

Perhaps some may ask where omnipresence is. Well, it is contained in omniscience. There’s no difference between knowing everything and seeing everything, though seeing all differs from knowing all. The human must use time to utilize knowledge. Our observation of the present becomes a record of the past that we use to predict the future. Knowledge also uses truth, as the connections between various ideas and facts have to be determined as kept or thrown.

As one could guess, an omniscient being simply knows the future. How can one know the future before it has occurred? You could be the one creating everything in the space. Of course, how can one know one’s creation is working without running it, I don’t know. To test the creation is to lack confidence in one's omniscience, but to not test the creation is to not have proof of one’s absolute correctness. The internal conflicts of omniscience would be claimed to be solved by omniscience. But our mortal brains need proof for claims. All honorable things are willing to pass through logic, surely omniscience would use truth's greatest tool!

Omnipotence means you have the power to do anything, full control over ontology.

The word "omnipotence" means that you have the power to do anything, including fully change your mind about things. In other words, if an omnipotent being wanted to destroy the Earth and all of humanity with a single thought, it could. Omnipotence is also defined as "omnipotence" in philosophy or theology; thus, there are two types of divine omnipotence: one which is limited (or not unlimited) and another which is unlimited (or not limited). Of course, a true god would have to have unlimited power.

What more can be said about a being that can do anything? Words are meaningless in the face of such power.

Omnibenevolence means you are perfectly good, never stray from the path of ethics.

Omnibenevolence is the belief that you are perfectly good, meaning that your actions always result in goodness. It is difficult to be good in nature. The more knowledge you gain, the more responsibility is expected from you. One has to be unselfish and want the happiness of the other for the sake of the other. One has to study the other and the world to provide optimal service. However, ethics doesn’t ask that we needlessly suffer for others who wouldn’t suffer for us. A problem so complex for a human ought to be nothing for a god.

Some may claim relativity for ethics. They may appeal to culture and the various things people would consider good. Unfortunately, there are no perfectly ethical cultures. This forces one to investigate every culture and pick out those parts that are ethical. An omnibenevolent being would know all the correct actions, but this is merely knowing all the win-win situations.

A god with all three properties cannot exist.

If god is omniscient, he can know everything that has happened and will happen. He could also foresee every possible outcome of any decision or event in the future, which means that he could have known what was going to happen before it happened. If god is omnipotent, then he has unlimited power over all things: himself included! This means that if there were some event or situation where his actions were required (like sending someone away from Jesus), then he could use his own power to make it happen with no help from anyone else. But if we say “God cannot do this because…” then we're saying something about our beliefs about how things work around here; not necessarily facts about reality itself!

The first thing to note is that a god with all three properties cannot exist. A god with omniscience knows everything and therefore has no need for anything else; hence it would be impossible for such a being to be omnipotent. Omnipotence means having the ability to do anything that can be done in principle (for example, create something out of nothing). But if you aren't able to create something out of nothing then how could your power not be limited and restricted?

Similarly, if your power is limited by its own nature then what need does it have for benevolence? If there are limits on how much good or bad someone else can do before they're punished by fate itself—which seems like an awfully cruel way of doing things—then why bother helping them at all?

Omnibenevolence means having good intentions toward others, even though you might not like their behavior or think they should change their ways. If you had no reason to feel bad about yourself (and therefore didn't care about how other people felt), then why would it matter if others did?

Omniscience is a property that would make a god all-knowing. If god were omniscient, he would know everything there is to know about everything, including you and me. But this would conflict with the idea that god is omnipotent because if he could do anything in the universe then it would be impossible for anything else to exist (because by definition if something exists then it cannot be nothing). And if god has all power within himself, then he wouldn’t be able to create anything new.

If such omniscience were possible, then there would be no need for any kind of punishment or reward system because everything would already have been decided by fate itself (which is also impossible since fate doesn't exist). This also means that anything that happens after death couldn't happen at all since there wouldn't be anything else left besides an empty void where nothing exists anymore except perhaps some vague notion about possibly existing beings like ourselves who might exist in some form after death but not necessarily us ourselves!

If a god exists, then it must be omnipotent and omniscient. But if a god exists, then we can't be sure that he's omnibenevolent. If a god is omnibenevolent, then he would want us all to be happy; but if he wanted us all to be happy and didn't have any control over our actions or emotions (which many people believe), then how could one person's happiness affect another?

These two ideas contradict each other: either we're not responsible for our own actions or emotions—or else our personal suffering affects everyone else around us unavoidably. Either way, this contradiction proves that no one can know whether god exists without knowing something else first: namely whether there are other minds in the universe besides their own.

There are three ways for a god to exist. First, the god could be omniscient and omnipotent—that is, it would know everything about the world and control everything in it. Second, the god could be omnibenevolent—that is, it would care about everyone equally and want everyone to live happily in this world. Thirdly (and finally), we can imagine a god who doesn't have any of these properties: instead of knowing everything or caring about every single person equally or even existing at all!

Now let's consider what happens if we combine these three properties together into one entity: our god-like being would know everything there is to know about everything in existence without ever having experienced anything himself which means he wouldn't have any personal knowledge or experience related specifically towards his own life because he experienced nothing personally before creating each individual human being out of nothing but dust! So how does such an entity even begin considering itself? How could anyone possibly conceive such an idea?

Conclusion

What is the point of giving up one’s logical reasoning for the false belief in a god? We do much waste and suffering in the name of deities who should be universes unto themselves. It would be an abusive relationship if god were real. Logic shows that a god with the omni-powers is absurd. Letting go of false propositions will help one organize one’s epistemology, creating more true connections, and leading to better predictions.

Tuesday, June 21, 2022

PWIP 45

There appear to be two “scales” in ethics. There are the extremes of good and bad. These scales don’t allow for gradation, a thing is either good or bad, and there is no middle ground. This can perhaps be called a classical scale. The second kind of scale is Aristotle’s golden mean. Instead of the good being one end of two extremes, it is the midpoint between two vices.

Let’s relate these scales to economics. In the traditional scales, being poor is seen as bad, and being rich is seen as good. This is, of course, because the rich hold much of the power in society, and thus influence values. The golden mean would entail that there’s an ethical place that exists between being impoverished and being filthy rich. Society doesn’t think there should be a ceiling for wealth and a floor for poverty. This runs into the virtue of fairness, which requires a kind of equality and proportionality. Everyone should get what they need. If there’s more than what is necessary then an equal and proportional distribution is made. This appears to run into the problem of merit and ownership, i.e. distributing according to work done (or some other criteria) and distributing according to authority over goods.

In order to be active in ethics, one needs a well-formed epistemology. Most people have corrupted epistemologies due to religion and other faulty ideologies. Religion is particularly heinous because it gives people the belief that they have an ultimate truth, destroying positive traits like humbleness, curiosity, and open-mindedness. They believe they know the ontology, which is profoundly absurd. They think belief in a thing they claim is omniscient somehow also gives them powers of omniscience. Many of these laypeople, being uneducated in philosophy, have no sound justification for their beliefs. The unsophisticated, informal methods of reasoning found in holy books (mostly fallacies of appeals to authority) are used for real-world problems.

Lies are easier to generate than the truth. Both are related to language and communication. Once one has a language that can express enough content, one can generate any piece of information and claim it is true. Obviously, obtaining the truth requires more than the mere communication of information.

People will by default appeal to the truth, rarely does one see them put in the work to express it proper. This is because the truth is multifaceted and complex. I can’t say I have the truth, merely that I seek the truth and discover what I hope are aspects of it. There seems to be a hierarchy of the truth. At the top of the hierarchy is big T Truth. This is ontology, the all, it is the dynamics of all things. We’ve spoken of the hierarchy because it is the same as philosophy.

Next is the process of discovering truth, which is perhaps akin to a flowchart or algorithm. First, is one coming from a place of ignorance or some knowledge, that is to say, is one building a foundation or upon a foundation. There’s likely no true pure ignorance without being part of nonexistence. The first tools for discovering truth are those provided by the body, primarily reason, the senses, and movement. The next tools are perhaps those discovered by reason itself, mainly mathematics, logic, and science. The next part is perhaps knowing which sources one can trust. One would need to record who is consistent and whose predictions come to pass.

Thursday, January 27, 2022

PWIP 44

One of the more difficult problems for the human is how resources should be distributed. Every animal seems to have to deal with the problem of resources in one way or another. They must somehow obtain nutrients. Many “lay claim” to a space or territory. They will defend their resources with violence.

There is perhaps an economical-like process in the brain. There are patterns and cycles in nature that affect the lifestyle of biological beings. Most animals are swayed by nature because of a lack in their physical structure, cognitive capabilities, social skills, and/or other features such as these. One may dominate nature to one’s desire, assuming one has the ability to do so safely. Although good economics is the efficient use of resources. The other generates the problem of ethics, which spreads through practically all interactions with the other, including economical interactions. Best practices are left to the business class, who may be practical, and even limited by the law, but not bound to ethics.

One would perhaps need to start from what the humans need and work backward from there. Like other animals, nutrients and space seem first. Ancient humans were known to hunt, farm, settle, and migrate. This is all pre-civilization, and thus before any formalization of mental content.

There appears to be a set of highly efficient ways to live in any given area that can be discovered through the scientific method. This notion can be extended to the planet and beyond. There are certain aspects of life the human would focus its attention towards in order to live well, though this isn’t an exhaustive list they are; medicine, technology, matter sciences, and brain sciences. The earth and the biological material seem resilient to destruction, the human is comparatively less so.

The resources society uses are represented in monetary exchange. An item’s value appears to represent its scarcity, desirability, and the resources put into the item. This generates for the merchant what seems like a game-theoretic problem of whether an individual who didn’t want the item then wants it now, and whether the individual that did want it before wants it again.

America has what seems like a nested rule. The federal government is on the top, then the state government down to the local level. Institutions run all the way through, so below the local level government there are businesses, schools, places of worship, etc., then finally personal homes. Yet we see the business class taking control of many aspects of life.

Proof of post-scarcity is the amount of waste. There seems to be massive waste from overuse and underuse. Technology makes it easy to reproduce perfect copies of images and sounds. This seems to have ended the scarcity of certain types of artists. The sun provides massive amounts of harvestable energy. We only use a fraction of the energy from the sun we could be using. We have enough knowledge and capability with farming to provide food for everyone. Not only do we not provide for everyone, but we waste tons of food. We can actively and passively teach everyone many different arts, but we force people into myopic lanes. It is a post-scarcity world, yet the humans do not act as if it is so. Perhaps the waste is based on an acknowledgment?