1. Introduction To Truth And Knowledge
- Theories of Knowledge - Blithering Genius
- Views - Blithering Genius
- Veritasium: The Illusion of Truth
- The Frequency of Patterns and Stimuli affects how true or false we judge things in the world.
- Cognitive Load
- Cognitive Ease
- Cognitive Difficulty
- The Mere Exposure Effect
- Epistemology: The Puzzle of Grue - Wireless Philosophy
- What Is Random? - VSauce
- What Is Not Random? - Veritasium
- What is Truth? - AntiCitizenX
I like the last video, but I recommend ignoring how he promotes the Pragmatist Theory of Truth at the end since Pragmatism is incorrect. The cerebral cortex is a generic pattern-abstraction and recognition device that learns from embodied experience. In order to learn anything, we need to observe data and detect patterns that help us understand the data.
Since it’s impossible for someone to know literally everything, it’s also impossible for there to exist a universal ends-all-be-all fact-checker for truth. The best way for truth and fact-checkers to work in a society would be for the most dominant fact-checkers to cite the primary expert/institution/authority/knowledge/facts that they appeal to when determining the truth value of something. Likewise, there should be several competing truth fact-checkers, similar to how it’s a good idea for there to be several competing products on the market, several competing currencies, or several competing reviewers/peer-reviewers. It’s up to everyone in society to decide who they want to agree with.
1.1. The Raven Paradox
Even though there are lots and lots of wrong philosophical positions, it is still important to know them, the arguments in favor of them, and why they are all wrong because this helps us to better understand the correct philosophical positions by contrast. Due to the nature of belief networks, the only way to determine the best philosophical positions is to rigorously argue them back and forth until we inductively determine the best ones.
1.2. The Sorites Paradox
The Sorites Paradox: If a heap is reduced by a single grain at a time, the question is: at what exact point does it cease to be considered a heap?
The Sorites Paradox is related to the Raven Paradox. The proposed solutions (including ones by analytic philosophers) to Sorites Paradox don’t actually solve it. They’re just playing language games.
Knowing how to solve the Sorites Paradox is helpful for understanding:
- The Emergence of Consciousness
- Races as Clusters of Genes
- Dialect Continuums
- The Ship of Theseus
- Slippery Slope Fallacies
- Wittgenstein’s Concept of Family Resemblance
- Many other things
2. Empiricism, The Origin Of Knowledge
All knowledge originates from observing reality. We learn about reality by sensing it, making mistakes, and learning from those mistakes. All learning is a process of inductive reasoning.
Empiricism and Rationalism don’t (and shouldn’t) contradict each other. Sensory Input is just one part of the Reasoning Process.
3. The Three Nested Definitions Of Knowledge
The ability to predict (the ability to do the reasoning process).
The most specific definition is the ability to predict, and that involves models and representations of reality. Prediction requires representing reality. There’s no such thing as prediction without a model.
“To forecast, foretell, or estimate an unknown event on the basis of reasoning and existing knowledge.”
The ability to do things (procedural knowledge).
We might say he knows how to skate, he knows how to dance, he knows how to sink a 3-pointer, etc.
The ability to fit form to function (FFF) (the most general definition of knowledge).
For example, We might say the flower “knows” how to attract bees.
These three things are nested in the sense that the ability to predict enables you to do things, and the ability to do things is part of this more general biological concept of fitting a form to a function. All three of these definitions imply that any acquired knowledge under any of these three definitions is ultimately aimed at solving problem.
A fourth definition of knowledge would be descriptive knowledge, which can be used to aid the actions of doing the procedural or prediction based definitions of knowledge, although it cannot be used to solve problems by itself alone.
Note that there should be a further distinction of sensory, emotional, and experiential knowledge (SEMEX).
Just as reason is useless in a world that is completely absent of problems, knowledge would also be useless if there are:
- No problems to solve,
- No problems that can be solved, or
- No problems that the reason-endowed being wants/chooses to solve.
Criteria that problems must meet to be worth attempting to solve:
- There is a problem to solve,
- It is possible to solve the problem, and
- Some reason-endowed being would want/choose to solve the problem.
4. The Subject-Object Dichotomy
Main Article: What is Subjectivity? - Blithering Genius
A subject is a being who has a unique consciousness (will and awareness) and/or unique personal experiences, or an entity that has a relationship with another entity that exists outside itself (an object).
An object is a philosophical term often used in contrast to the term subject. A subject is an observer and an object is a thing observed.
A subject has a mind. Something is “subjective” if it is mind-dependent or perspective-dependent. Subjectivity is not random or arbitrary. Subjectivity is a concept for describing properties of the mind, like knowledge, truth, emotions, value, will, awareness, etc.
A subject can be viewed as both a subject and an object. Philosophy and psychology are the self thinking about itself. This is achieved by viewing subjects from the perspective as if they were objects.
The conditions of being a subject within objective reality:
- Biological Desires for sustaining the subject’s life.
- Truth and Knowledge that provides only a limited scope of reality.
- Free Will (Deterministic as an object, “free will” as a subject)
- Limited lifespan with eventual mortality where all biological processes cease to continue.
- Designed to reproduce (a consequence of evolution).
|Knowledge / Truth||Reality|
We cannot understate how important the Subject-Object Dichotomy and its implications are for forming an accurate and coherent philosophy and understanding of the world.
Note: It seems that it’s easier to learn the subject-object dichotomy inductively rather than deductively, i.e. by learning the more specific applications, and only then looking at the big picture.
5. The A Priori And A Posteriori Distinction
|Epistemology||A Priori||A Posteriori|
|Explained||Cannot be false||Can be false|
The a priori and a posteriori distinction was central to Immanuel Kant’s entire philosophy. Kant proposed that Knowledge of Metaphysics is Synthetic, A Priori Knowledge. Metaphysics is supposed to be definition-based knowledge about the world that seeks deeper meaning.
- For example, it is one thing to know that a triangle has three sides, but it’s another thing to know that all the angles in a triangle add up to 180 degrees, and is thus equivalent to traveling in the exact opposite direction.
- In this example, a triangle is defined as having three sides because that is the most distinguishing characteristic that the human mind uses to define a triangle when first learning about it (distinguishing characteristics are most important for classifying and categorizing concepts).
Kant believed that the pinnacle of Metaphysics and Mathematics was to understand the world’s less obvious characteristics, beyond its most obvious characteristics. Metaphysics isn’t supposed to be a bunch of empty definitional truths, metaphysics is supposed to discover truths that are necessary and universal. Metaphysics is supposed to extend our knowledge, to be ampliative.
Informative Video: Kant On Metaphysical Knowledge- Wireless Philosophy.
A Priori knowledge is defined as being justified by appealing to the senses.
Philosophical Distinctions Table
Philosophical Distinctions Table (Transposed)
|Epistemology||A Priori||A Posteriori|
6. The Nature of Concepts
6.1. The Definition Of Concepts And Properties
- A concept is anything or any idea that the human mind can think about.
- Every concept has an implicit (or explicit if more conscious) definition in our brains.
- Every concept has a definition
- All properties are technically concepts by this definition since we can think about them.
- Properties are simpler concepts that can be identified as being parts of more complex concepts.
- Properties are used to define complex concepts.
- Properties are simpler concepts that can be identified as being parts of more complex concepts.
- Complex concepts may be defined by properties as part of their definition, and properties have their own definitions.
- So the definition of complex concepts that are defined by properties is really just a definition composed of other definitions.
- If more complex concepts are described in simpler and simpler terms until there are no properties left to describe them, definitions that are free from properties are used instead.
- At some point, things just can’t be more simply described, so definitions are used to communicate what our brains are indescribably and abstractly thinking about.
- Definitions have two purposes:
- To explain things that we don’t understand.
- To provide concrete descriptions of what we are talking about.
- Every known concept and property has a definition in our brain, even if we can’t verbally describe it.
- Definitions have two purposes:
7. The Representationlist Theory Of Truth
This may also be called the Information Compression Theory of Truth, or the Model of Models Theory Of Truth. I don’t have an exact name for it.
Different levels of truth are distinguished by lossey information compression (information is lost the more simplified the knowledge is).
If Knowledge is non-lossey, then the parimoniousness of the knowledge is additional knowledge, because high-quality knowledge is supposed to be parsimonious.
7.1. Why Objective Truth Doesn’t Exist
To put it most concisely, the reason why objective truth does not exist is that it’s not possible to have absolute, omniscient knowledge of reality. Conscious minds can only have subjective, perspective-dependent models of objective reality. No proposition can ever be truly be labeled as “objectively true” because it’s always possible to be wrong about that said propositions if further knowledge of reality invalidates that proposition’s truth value assignment. Truth is essentially the same thing as knowledge, because whatever people know is what they will assert to be “true”.
There is no foundation for truth, any more than there is a biggest number.
- Suppose that X is the biggest number. Now add 1 to X. X + 1 is bigger than X. Thus, X is not the biggest number.
- Suppose that F is the ultimate foundation of truth and value. Now question F. Thus, F is not the ultimate foundation of truth and value.
“There is no truth.”
This is a valid performative contradiction. Whether truth is subjective or objective, saying this statement contradicts itself.
“(The truth is that) There is no objective truth.”
This is not a true performative contradiction since truth is relative by definition. For that reason, asserting this statement does not have to assume that propositions are objectively true. It can be more clearly shown why there is no contradiction in this statement if we rephrase the statement with two other statements that have equivalent meaning:
“There is no objective truth.” = “Nothing is objectively true.”
“Nothing is objectively true.” = “All truth is relative.”
A common theme among mastering different academic fields is to understand the finer details of something. The goal of mastery is make all the tiny, implicit details explicit and rigorous. Examples:
- For math, everything must be rigorous and verbose. One reason is to avoid assuming things that need to be proven
- In programming, telling instructions to the computer often requires lots of tiny steps we would never think about.
- When learning a foreign versus a natural language, one must be aware of lots of small details often overlooked by natives.
- For physics, all small details must be considered when calculating physics problems, though they are often ignored in idealized models and situations used for teaching physics concepts.
7.2. Example: “The Sky Is Blue”
A common phrase that many people utter for asserting the supposed obviousness of objective truth is “The sky is blue”, but this is ironically a great example for demonstrating how truth is all about information compression. For one thing, the sky isn’t always blue. Sometimes, it has orange/sunset colors, sometimes it’s gray when it’s cloudy and raining outside, sometimes it’s pitch black at night, and it can even appear red during wildfires, yellow near hurricanes, or white if there’s nothing but clouds. Since Truth is information compression, saying that “the sky is blue” omits the information that the sky isn’t always blue all the time (because it’s the simplest statement we can say about the sky’s color), even if it may be the case that the sky is blue most of the time.
Furthermore, the vast majority of the world’s languages don’t make a native distinction between blue and green, most likely because the human eyes have fewer blue cones for detecting blue light within them, in comparison to the number of red cones. Many languages don’t even have a native word for “blue/green”. And to make things even more complicated, Russian makes a native three-way distinction between green, light blue, and dark blue.
- Green = зеленый
- Light Blue = голубой (also incidentally the term for gay)
- Dark Blue = синий
So, Russians would say that the sky is “light blue” or “cyan”, instead of just “blue”, if they are making the simplest, most information-compressed statement about the sky’s color.
The two main takeaways here regarding the complexity of truth are: 1. truth exists at different levels of provided information, and 2. the specificity/ambiguity of language affects the truth values of propositions. If we insist that the statement “the sky is blue” is definitively and unquestionably true, then we are omitting important information about the sky and choosing to be willingly misleading about it. Since the Correspondence Theory of Truth is unable to account for situations where a subject believes a proposition to be true when it’s actually false given more information about reality, this implies that it’s not sufficient enough for understanding the true nature of truth.
The actual best answer to what color the sky is that it depends on the location, the time of day, and the atmospheric conditions, but people don’t typically say that because it requires more words (information) to say. The other reason is that the phrase that the sky is blue has been repeated so many times is that most people’s minds are classically conditioned to believing that it’s obvious statement.
Another example of an oversimplified truth is stating that the Earth is a sphere. The Earth is technically better described as an oblate spheroid since the speed at which the Earth rotates causes the mass around the equator to be farther away from the center of the Earth, compared to all other points around the Earth. Since the Earth is close enough to being shaped like a sphere, and since spheres are a more familiar concept that is easier to understand, nearly everybody refers to Earth as being a sphere in casual discourse.
7.3. The Extent of Truth
Propositions can also be “mostly true”, “somewhat/kind of true/false”, or “mostly false”. In these situations, it is either the case that:
- Some of the proposition’s components are true while the other components are false, or
- There is too much information compression of reality to the extent that the proposition model reality very inaccurately, or
- Both  and  to some extent each.
7.3.1. Bloom’s Taxonomy
7.4. An Example of Information Compression
Among the first conceptions of the Earth’s position in space was Ptolemaic system and epicycles. Further knowledge revealed that the Earth actually orbits the Sun, and the Heliocentric Model was formed. Later, the center of the Milky Way Galaxy was discovered, and it was realized that we live in an ever expanding, unimaginably huge universe.
Each of these different conceptions of Universe not only vary by their accuracy, but also by the amount of information gathered about objective reality that is compressed into the mental models formed from sensory experience. Even if the Ptolemaic Model is clearly wrong with the modern knowledge that we now have about the Universe, it was formed during a time when people could only gaze at the stars and notice that the stars in the sky would vary depending on the time of day and time of year. So if that’s the only information we have to base our model of the Universe on, that model is still “true” according to that limited sensory experience of the Universe. When more information is gathered about the Nature of the Universe, the simpler model becomes false because we have more information to make a truth judgment that is more representative of reality.
7.5. A Second Example of Information Compression
7.6. Examples Of False Beliefs Formed From Incomplete Knowledge Of Reality
A small sampling of all the inaccurate thoughts ever brainstormed in history is:
- The universe is controlled by a powerful all-mighty god?
- The universe revolves around the Earth?
- The universe is composed of earth, water, air, and fire?
- The species of the world developed according to creationism?
- The Earth is flat?
- The brain is responsible for blood circulation and the heart is responsible for our thinking and thoughts?
- The bones in an embryo are the first structures to develop?
- The expansion of the universe is slowing down due to gravity?
- The great dinosaur extinction was caused by a violent volcano?
- The best system to guarantee human rights is communism?
- Supernatural gods are responsible for the sun, moon, and every other unexplained phenomenon in this universe?
We must keep in mind that all these inaccurate beliefs were formed from incomplete models of reality.
8. Evaluating Platonism
8.1. Arguments Against Platonism
Arguments Why The Platonic Realm Does Not Exist:
- The Platonic Realm doesn’t have any explanatory power.
- Believing in the Platonic Realm is not necessary for explaining how we understand the world, if our models of objective reality and the associated sensory data and reasoning that generates said models are stored completely within systems of reasoning that exist within our own minds.
- Why does a Platonic Realm containing every possible pattern have to exist, when we can instead understand that patterns are information stored in the brain about the characteristics and relations about many different things (genes, mathematical structures, etc) that exist within the physical world?
- If the Platonic Realm doesn’t exist physically, then where does it exist?
- Where is the empirical evidence that the Platonic Realm exists?
- Where is the empirical evidence that ontological primitives exists?
- How do we have access to the Platonic Realm?
- Why do we have unequal access to all the propositions in the Platonic Realm?
- If there is a Platonic Realm, then why are so many situations where we can’t perfectly model natural phenomena?
- How would Platonists verify truth propositions under their theory of truth?
- How are the arguments in favor of the Platonic Realm any different from the fallacious Transcendental Argument for God (TAG)? (We have to have a Platonic Realm (God) to understand anything)
- If we should assume that there are aspects of reality that are not empirically observable without evidence for their existence (e.g. the Platonic Realm), how is this any different from arguing that we should believe in an omniscient omnipotent God, when God is not empirically observable either (under the most common definitions of “God”)?
- Believing in a Platonic Realm does not prevent an infinite regress of knowledge, since it’s actually an Inverse Homunculus Fallacy.
- You don’t solve the problem of meaninglessness by attaching it to an ontology that’s assumed to exist. You give terms meaning by grounding them in embodied experience.
Believing in a Platonic Realm only creates more unanswered questions than it solves. Occam’s Razor is sufficient to conclude that the Platonic Realm simply doesn’t exist, since it’s easier to explain truth as being a model representation of reality.
8.2. Arguments For Platonism
Arguments Why The Platonic Realm Does Exist:
- It supposedly gives explanatory power for proving or disproving existential and universal propositions within certain frameworks.
- A Platonic Realm is supposedly necessary in order to prevent an infinite regress of knowledge.
- Godel’s Completeness Theorems allegedly affirm the existence of unfalsifiable and undecidable statements.
8.3. Arguments Why The Objectivity Or Subjectivity Of Truth Is Unfalsifiable
Arguments Why The Existence of the Platonic Realm Is Unfalsifiable:
- Neither side ever said that can definitively disprove the other’s claims.
- The nature of truth makes it impossible to prove whether some statements are true or false. Humans also have limited knowledge of reality.
9. The Problems With Justified True Belief (JTB)
Justified True Belief doesn’t define what “true”, “justified”, or “belief” (knowledge) are.
The three nested definitions of knowledge are superior to Justified True Belief (JTB):
- They don’t require defining terms like “truth”, “belief”, or “justified”.
- The definition of prediction implies that prediction must be done based on given information within some scheme. So unlike JTB, defining knowledge as the ability to predict is not far removed from sensory experience.
- This definition of knowledge also doesn’t conflict with any of the Gettier Problems.
10. The Problems With The Correspondence Theory Of Truth
The correspondence theory of truth assumes that truth is objective and that it exists outside the mind, so it proposes no meaningful difference between truth and reality. Under my representationalist theory of truth, there is no meaningful difference between truth and knowledge because they’re both recognized to be subjective concepts. Both theories of truth/knowledge agree that knowledge and reality are definitely different from each other.
The main problem with describing truth as “conforming to reality” is that there can be no universal, infallible decider for truth since not everybody can agree on what the “Truth” is. Determining “Truth” faces the same exact obstacles that must be faced with determining “Knowledge”. Strangely, Rand acknowledges that it’s possible for knowledge to be wrong when admitting that it’s not possible to have omniscience or infallible knowledge of reality, yet she still describes knowledge and truth as “corresponding” to reality. Knowledge and truth cannot correspond to reality if they’re wrong, so it would be more accurate to say that knowledge and truth represent a (fallible) model of reality, from the perspective of a subject.
Truth claims are about objective reality, but there is no way to objectively verify or falsify them. We subjectively verify or falsify them, from our own perspectives, based on the data we have available to us, and using the mental abilities that we possess. At most, people can build a mental model of what they think reality is by sensing it, making mistakes, and correcting those mistakes. If the model is wrong, then they can and should correct their knowledge to form a more accurate model of reality. Beyond that, we can’t know much else about what reality is like because we cannot escape our subjectivity.
“A proposition is either true, or it isn’t. And your model is flawed, or it isn’t”
This statement is wrong as soon as it left the gate. By using the word model, it automatically implied that Truth isn’t about whether a statement corresponds to reality. Truth is about models of reality.
Relevant Reading: What is Subjectivity? - Blithering Genius
11. The Problems With The Pragmatist Theory Of Truth
AntiCitizenX’s video promotes the Pragmatist Theory of Truth in the last several minutes, but it’s misguided. If someone does not have enough information to make the best decision possible, they are not using the Pragmatist Theory of Truth to navigate themselves through life. What they are actually doing is they are using compressed (incomplete) information to form the premises that are used in their decisions. Not everything that we gather about reality from our senses is the big picture of reality is. We often only have a very simplified understanding of reality for many different things.
When we do make mistakes, it’s because the model of reality that we have in our minds is not comprehensive enough. Different truth judgments result from people having levels of understanding and models of reality that vary in their level of details.
Under this understanding of truth, the essential reason why “objective truth” doesn’t exist is because it’s not possible to create a hypothetical model of reality that has 100% accurate precision for all its details. Or in other words, it’s not possible to be omniscient and know everything there is to know about reality because that is a fundamental condition of being a subject (philosophical).
Models are not supposed to be absolutely true. Models are true in a matter of degree, since models (often generalizations) can be very abstract to their particulars.
12. The Consensus Theory Of Truth
The Consensus Theory of Truth is decided by what group of people collectively affirm to be true.
The Consensus Theory of Truth cannot stand by itself since each person within the group of people (including the people who agree with the consensus) each arrived at their verdict via the Information-Compression Theory of Truth, which works on individual scales. Nonetheless, the Consensus Theory of Truth has popular appeal in many situations, especially when it’s most important that decisions should be made based on popular support. The Consensus Theory of Truth is often used in court systems and in informal situations that have a similar nature to deciding guilt verdicts.
12.1. “The Wikipedia Theory of Truth”
The Wikipedia Theory of Truth is that Wikipedia is more likely (but not guaranteed) to be correct than most opinions out there, because it was created by a consensus of dozens to hundreds or even thousands of well-educated people who tend to be smarter than the average person, and are often “experts” in their own fields, as they are members of Academia.
For January-November of 2021, this was more or less the theory of truth that I operated under until I read Blithering Genius’s essay on Why Most Academic Research Is Fake. At that point, I realized that Wikipedia can’t be trusted because Academia is not infallible. In fact, Academia is rigged and as susceptible to ideological biases as any other person out there. When I went through this phase, I was probably the most leftist/humanist that I had ever been at any other point in my life, but I’m glad that I snapped out of very quickly.
13. The Meaninglessness of the Standpoint Theory of Truth
Slavery and the Holocaust are some of people’s favorite sacred moral narratives. When people are abusing the Exploitative Rhetoric, they often compare injustices to slavery or the Holocaust. When people who oppose these comparisons hear them, they often respond by saying “That’s offensive to Holocaust Survivors or Actual Slaves”.
If we’re going to take the Standpoint (STFU) Theory of Truth for granted, then there are plenty of examples for showing how ridiculous it is. If you look hard enough, you can always find an example of someone who went through a heinous tragedy who compares a completely different phenomenon to the hardship that they experienced:
- Example of a slave who claimed that taxation is worse than slavery: Former Slave: Frederick Douglass.
- Example of a Holocaust survivor who compared modern slaughterhouses to the Holocaust: Vegan Holocaust Survivor: Alex Hershaft.
- Example of a Holocaust survivor who compared the COVID-19 lockdowns to the Holocaust: 92 year-old Holocaust survivor compares COVID response to Nazi Germany.
- Example of a Holocaust survivor who compared Islamic indoctrination as using the same indoctrination tactics used in Nazi Germany: [I can’t remember the name of the person who made this comparison, but if I find it, I’ll post it here.]
The point of making this list was to show that it’s rather meaningless to compare perceived hardships to sacred moral narratives like slavery or the Holocaust because dozens of other perceived forms of oppression can be compared to these sacred moral narratives as well. Conversely, it’s equally meaningless to attempt to use standpoint theory to argue against such comparisons since we can always find someone who went through the actual hardships who agrees with the comparison.
To quote from Blithering Genius on Standpoint Theory:
Standpoint theory is basically the belief that marginalized groups have special insight – their experiences are more truthy. In other words: complete bullshit. It isn’t a theory of knowledge. It’s a rhetorical trick to “win” a debate by retreating into the swamp of relativism and solipsism. It’s like saying “You can’t see your privilege because you are a white male, so let me tell you about it”. Or, in other words, “Listen and Believe”. Or in other other words, STFU.
Standpoint Theory has gotten so ridiculous that the United States Holocaust Memorial Museum has insisted that other traumatic events cannot be compared to the Holocaust, because in their moralist worldview, only the Holocaust can be the worst event to have ever happened in human history, mainly because the Holocaust is their favorite thing to virtue-signal about.
The United States Holocaust Memorial Museum unequivocally rejects efforts to create analogies between the Holocaust and other events, whether historical or contemporary. That position has repeatedly and unambiguously been made clear in the Museum’s official statement on the matter – a statement that is reiterated and reaffirmed now.
The Museum further reiterates that a statement ascribed to a Museum staff historian regarding recent attempts to analogize the situation on the United States southern border to concentration camps in Europe during the 1930s and 1940s does not reflect the position of the Museum.
The Museum deeply regrets any offense to Holocaust survivors and others that may have been engendered by any statement ascribed to a Museum historian in a personal capacity.
This poses a problem for other moral ideologues who insist that their favorite thing to virtue-signal about can and should be compared to the Holocaust. Since standpoint theory hardliners will argue and virtue-signal against each other about their sacred moral narratives, it’s all just more evidence that standpoint theory is not a meaningful or epistemically sound theory of truth.
14. Unfalsifiable / Undecidable Concepts
Unfalsifiable: Not able to be proven false, but not necessarily true.
A conjecture is undecidable, relative to some formal system, if neither it or its negation can be proven within that system.
15. What is Mathematics?
Mathematics is a system of reasoning for number, quantity, space, and change, given a set of premises.
Mathematical foundations is “how”, philosophy of maths is “why”.
… the sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work—that is, correctly to describe phenomena from a reasonably wide area – John Von Neumann
When people use the term ’Mathematics’, they usually mean at least one of three things:
- Using reason, logic, theorems, and axioms to prove new theorems that can enable us to make conclusions about abstract situations, or invent new mathematical methods for doing things.
- Modeling a situation using abstract objects.
- Solving the abstract model of a situation, which often pertains to a real situation.
These three things can be summarized as: 1. creating the tools to solve a problem (theory building), 2. modeling a problem, and 3. solving a problem (problem solving).
16. Philosophical Mathematics
Nowadays, we have branches of mathematics that didn’t exist in the past that can be used to answer philosophical questions.
Philosophical Topics That Can Be Better Understood By Using Some Branch Of Applied Mathematics:
- Free Will and Determinism: Chaos Theory
- Time: Temporal Interval Logic
- Epistemology/Structure of Knowledge: Classical Logic
- Evidence/Certainty: Evidential Logic
- Ethics: Deontic Logic
- Rational Egoism: Game Theory
- Moral Relativism: Game Theory
- Philosophy of Information: Graph Theory
- Language: Formal Language Theory
- Language Semantics: Logic & Set Theory
- Philosophy of Music: Set Theory, Abstract Algebra, Numbers, Series, Category Theory, Topology
- Physics: Calculus, Partial Differential Equations, Linear Algebra, Etc
- Aesthetics: Mathematical Beauty
- Calculation of Land Rent and Land Value Tax: For some components of land value, Calculus can calculate land value approximately as a gradient of value that stretches from urban centers and the suburbs out to the rural areas.
And of course, there are also all the situations where mathematics can be used to model real-world phenomenon and thus increase our understanding of them.
Input is usually provided by biological sensors when unspecified, but it could also be a model or representation, or an imagined set of premises.