Phi 2010 HONORS

I remember Professor Barr's adage in my Statistical Analysis class: if you find two compelling reasons for a mistake (outside the research), it's not a mistake.

What an error in statistics?

Observational error (or Measurement error) is the difference between a measured value of a quantity and its true value. In statistics, an error is not necessarily a "mistake."

The reason is that variability is an inherent part of the results of measurement processes.

Measurement errors can be divided into two: random and systematic.

Random errors are errors in measurement that lead to inconsistent measurable values when repeated measurements of a constant attribute or quantity are taken (errors can get repeated even if looking for proof)

Systematic errors are not determined by chance but are introduced by repeatable processes inherent to the system.

Put differently, the house would lose if randomness was true.

A systematic error is not determined by chance but by a repeatable process inherent to the system. In gambling parlance, Casino bias is part of the game; otherwise, the House loses!

Now, is complete randomness REAL? Some think not.

If not, how do you argue?

Tuesday, October 1, 2024

Mi salsa de tomate (muy importante)

Pincha aquí.

why is 7+5 =12 synthetic apriori?

find the answer here.

Tuesday, September 24, 2024

Homework #4 Epistemology

click here for more information.

Chapter 6: Epistemology

Epistemology's main characters,

A brief history of epistemology,

Some necessary epistemological concepts,

A PBS video to help you see these ideas,

Criteria of adequacy of scientific theories (importante)

The features of what distinguishes a good theory from a bad one:

1. Consistency: Lack of internal contradictions.

2. Simplicity: Quality of relying on only a small number of assumptions.

3. Scope: The amount of diverse phenomena observed.

4. Conservatism: Quality of fitting well with existing theories.

5. Fruitfulness: The number of new facts predicted of problems solved.

Monday, September 23, 2024

Some excellent Math texts I recommend

Tom Apostol Vol. 1, & Volume 2, (PDF) for Calculus 1, 2 & 3.

Advanced Calculus (PDF), by Lynn Loomis and Schlomo Sternberg.

A great Linear Algebra Introduction (PDF).

Intro to Abstract Algebra, by Michael Artin (2nd Edition).

Differential Equations, PDF, by Paul Blanchard.

Applied Partial Differential Equations, PDF, David Logan.

Introduction to Set Theory PDF, by Herbert Enderton, PDF.

Thursday, September 19, 2024

Logical and causal possibility (think of mind experiments)

Logical Possiblity:

Something is logically possible if and only if it violates a law of logic.

Here is one logical possibility: "President J. F. Kennedy was not killed by Larry Oswald in Texas on November 22, 1963."

He was indeed killed that day. So, why is it still logically possible? There's no contradiction in assuming Larry Oswald missed his shot or that Kennedy was hurt but survived.

Causal Possibility:

Something is causally possible if it does not violate law of nature.

Law of non-contradiction:

Nothing can have and lack property at the same time.

Examples: "A triangle of four sides," "2 + 2 = 5", "A married bachelor," etc.

Conceivability:

1. If p is conceivable, it is imaginable (imagination is a mental faculty linked to rationality). An example of that is mind experiments in physics and math.

Is Superman logically possible? The first step in the evidence that p is possible is to be able to conceive it. Just that.

We say p is conceivable if its implication can be drawn without it being contradictory, i.e.,

Can Superman be conceived?

Yes, that's why we talk about him and can even watch him in a movie.

Now, Clearly, not everything that is conceivable is possible. For example, Superman, dragons, gremlins, and succubi are all conceivable but not possible.

Why not? They violate laws of nature.

Remember: If p is conceivable, then from 2. It's logically possible.

finally,

3. p is causally possible if it doesn't violate a law of nature.

Now, let's talk a little bit about LAWS OF NATURE:

Laws differ from scientific theories in that they do not posit a mechanism or explanation of phenomena; they are merely distillations of the results of repeated observation.

A law's applicability is limited to circumstances resembling those already observed, and the law may be found to be false when extrapolated.

How do logical possibility (LP) and causal possibility (CP) relate?

If something is logically impossible, it is causally impossible.

If something is causally possible, it is logically possible.

LI → CI
CP → LP

Clearly, LI is sufficient for CI. Is it necessary? It would be if CI cannot exist without LI. Let's pursue this point further.

Something cannot be and not be at the same time.

But time is a causal variable, not a logical one. If time is outside us, then "same time" is sort of cheating for a logical category.

Logic is aprioristic. And yet, Kant has argued that time is not outside. Of course, being a physicist, you will swear that time is outside since you can work with it mathematically. But that doesn't contradict Kant's point (though we don't have time to pursue that here).

Tuesday, September 17, 2024

¿Qué es un experimento mental? (mind experiment)

DEF: The description of a possible situation in which a concept should apply or a condition should be met if the theory in question is true.

Es decir, un experimento mental es un recurso de la imaginación empleado para investigar la naturaleza de las cosas. La mente es el laboratorio del filósofo. Mind experiments nos ayudan a ver concebir las condiciones de posibilidad de las cosas.

Varias teorías o posturas filosóficas se fundan en los resultados de experimentos mentales:

el dilema del tranvía, en ética,

la tabla de Carneades, en ética,

la habitación china, en filosofía de la mente,

la tierra gemela, en filosofía del lenguaje,

el cerebro en una cubeta y...

el cuarto de Mary en filosofía de la mente.

Homework #3 (causation & fallacies)

click here for more information.

¿Qué es la verdad?

En clase les he dicho que la verdad es complicada. Y lo es, pero eso no significa que la filosofía no haya definido el concepto de verdad.

En general tenemos tres definiciones:

1. Correspondence Theory of Truth (la verdad como correspondencia),

A proposition is true by its correspondence with reality.

Ejemplo: Un vertebrado es un animal que tiene un esqueleto con columna vertebral y cráneo, y cuyo sistema nervioso central está formado por la médula espinal y el encéfalo.

2. The Coherence Theory of Truth (la verdad como coherencia con lo que ya se cree).

Truth is what best coheres with our existing knowledge.

Ejemplo: En cosmología, se entiende por Big Bang, o Gran Explosión, al comienzo del universo, es decir, el punto inicial en el que se formó la materia, el espacio y el tiempo.

3. The Pragmatic Theory of Truth (la verdad pragmática).

Truth is, whatever best does the job at hand.

Ejemplo: El cuadro Guernica de Picasso es una obra maestra de la pintura del siglo XX.

Lista de algunos paradigmas científicos que han cambiado

pincha aquí.

Thursday, September 12, 2024

Cause and effect can betray even the smartest amongst us!

When is C a cause of E?

Take this simple example: Pluto's barking causes Dick to wake up.

We need four steps:

1. The cause must precede the effect,

2. It's nearly impossible for the cause to happen and the effect not to happen. Another way of saying it: if the cause had not happened, the effect would not have happened.

3. The cause makes a difference, (without the cause, there's no effect),
4. There's no common cause, Think of a person suffering from depression. You could frame their depression using the common-cause relationship as well. Depression leads to a lack of motivation AND a lack of appetite.

so, we have:

1. The barking precedes Dick's waking up,
2. It's nearly impossible for Pluto to bark and Dick not to wake up,

3. Without the barking, there's no waking up,
4. Suppose both the barking and waking up is caused by a person jumping Dick's fence and making a noise which causes Pluto to bark and Dick to wake up).

necessary, sufficient, and contributory causes:

Pluto's barking is a necessary cause of Dick's waking up if the barking precedes the waking, but it doesn't imply the latter will occur, i.e., Dick may not wake up (it's not guaranteed).

Pluto's barking is a sufficient cause of Dick's waking up if the the barking necessarily imply the waking, although another cause may also contribute to Dick's waking (noise coming from the bathroom where Dick's wife was taking a shower). Here the presence of the waking doesn't guarantee the prior occurrence of the barking.

A cause is a contributory cause if it's one among several co-occurrent causes. In general, there is no implication that a contributory cause is necessary, though it may be so.

Reciprocally, a contributory cause is not sufficient for the effect, because it is by definition accompanied by other causes, which would not count as causes if they are sufficient, for your information, most causes are contributory, i.e., there are more than one.

Want one paramount example of contributory causation?

Climate change, with all its contributory causes: sun, orbital variations of the earth, low cloud cover, oceans, albedo effect, man-made C0₂, etc.

REMEMBER, VERY IMPORTANT...

CORRELATION DOESN'T MEAN CAUSATION

Fallacies (watch out, most of info you get from sources is fallacious)

A fallacy is an argument which provides poor reasoning in support of its conclusion. Here are some examples:

Begging the Question: The argument's conclusion is used as one of its premises. Basically the proof is assumed.

A: He's mad right now.
B: How do you know?
A: Because he's really angry.

Of course smoking causes cancer. The smoke from cigarettes is a carcinogen!

Prosecutor to defendant: So how did you feel when you killed your wife?

Ad hominem (or Against the Person): When someone tries to win an argument by denigrating its presenter (favorite fallacy used by politicians and the media to put down an enemy)

"You claim that this man is innocent, but you cannot be trusted since you are a criminal as well."

"Hey, Professor Moore, we shouldn't have to read this book by Freud. Everyone knows he used cocaine."

Argumentum ad Populum (Literally "Argument to the People"): Using an appeal to popular assent, often by arousing the feelings and enthusiasm of the multitude rather than building an argument.

Ex: "The Bold and the Listless must be a great book. It’s been on the best seller list for 8 weeks."

Appeal to ignorance (ad ignorantiam): It has two forms: The fallacy occurs when you argue that your conclusion must be true, because there is no evidence against it. Ad ignorantiam wrongly shifts the burden of proof away from the one making the claim.

"She hasn't said she doesn't like you, right? So she's probably interested. Call her up."

"Nobody has conclusively proven that the Yeti doesn't exist, therefore it must exist."

"I thought I had every reason to think I was doing fine leading the group; no one complained."

Hasty Generalization: You are guilty of hasty generalization when jumping into conclusion about all things of a certain type based on evidence that concerns only a few things of that type (favorite argument used by politicians and ideologues).

"The department of law enforcement in Miami is corrupt. Five police officers in three different departments were involved in drug dealing in 2017" (right answer: Miami has 4,780 police employees, i.e., 5 corrupt officers are 0.16% of the force).

"Men are toxic! It's crystal clear: They perpetrate over 76% of the violent crime in the US." (right answer: violent men committing violent crimes constitute 6% of the population of males in the US).

Appeal to Authority: A claim is accepted because not because of its merit, but because of the authority (power, fame, etc) of the person saying it.

"Pacifism is a good idea because the brilliant scientist Einstein advocated it."

"If the Pope says it, it must be true."

"Nobody is a better judge than public opinion."

Red Herring: This fallacy consists in diverting attention from the real issue by focusing instead on an issue having only a surface relevance to the first.

Daughter: "I'm so hurt that Todd broke up with me, Mom."
Mother: "Just think of all the starving children in Africa, honey. Your problems will seem pretty insignificant then."

Appeal to Fear: To use threat or harm to advance an argument. Ex: "If we don’t stop petroleum consumption, global warming will increase. Therefore, we need to stop petroleum consumption immediately."

False Dilemma: It presumes that there are only two alternatives to a given problem, when in fact there are more than two.

"Either science can explain how she was cured or else, it's a miracle."

"Since there is nothing good on TV tonight, I will just have to get drunk."

"If you are don't accept our climate catastrophe, then you're a denier!"

False Cause: Supposing that two events are connected when in fact they are not.

"They had a very successful business. Then they decided to adopt a child, and the business went immediately into the red."

Inconsistency: A person commits the fallacy of inconsistency when he or she makes contradictory claims.

"I'm a strong believer in freedom of speech. However, when a person like John Dean can influence our youth , you have to draw a line and say no more."

"This is the truth: truth is subjective."

Etimological fallacy: Believing that the present day meaning of a word of concept should necessarily be similar to its historical meaning.

"So-and-so" (a phrase used in the 19th Century) should not be used anymore. It's very offensive!

Necessary and sufficient conditions

Necessary conditions:

X is a necessary condition for Y,

if X is not present, Y doesn't happen.

(yet, to say that X is a necessary condition for Y does not mean that X guarantees Y)

Having gasoline in my car (gasoline engine cars) is a necessary condition for my car to start. Yet, having gasoline in the car does not guarantee that my car will start. There are many other conditions needed for my car to start.

Having oxygen in the earth's atmosphere is a necessary condition for human life. However, having oxygen will not guarantee human life. There are many other conditions needed for human life other than oxygen in the atmosphere.

Sufficient conditions:

X is a sufficient condition for Y,

if X is present, Y happens (X guarantees Y)

Rain pouring from the sky is a sufficient condition for the ground to be wet (not necessary, since the ground could be wet for other reasons).
______

Test yourself:

*Is sunlight a necessary or sufficient condition for the flowers to bloom?

*Is earning a final grade of C a necessary or sufficient condition for passing the course?

*Is being a male a necessary or sufficient condition for being a father?

*Is having AIDS a necessary or sufficient condition for having the HIV virus?

*Is studying for a test a necessary or sufficient condition for passing a test?

*Is completing all the requirements of your degree program a necessary or sufficient condition for earning your degree?

Friday, September 6, 2024

homework #2

click here for more information.

Tuesday, September 3, 2024

deductive and inductive arguments

PREMISE:

A premise is a reason given.

ARGUMENT:

An argument is a set of premises and a conclusion.

DEDUCTIVE ARGUMENTS

An argument is a set of premises and a conclusion. Look at this argument:

"Socrates is a man"  first premise
"Men are mortal"   second premise
________
"Socrates is mortal" conclusion

Now, there are deductive and inductive arguments.

Deductive argument are “truth preserving”, because the truth of its premises guarantees the truth of its conclusion.

Deductive arguments can be valid or invalid. If VALID, then the conclusion necessarily follows from the premises (even if the premises were false).

"Socrates is a man" (T)
"Men are mortal"    (T)
________
"Socrates is mortal" (T)

the above argument is valid. in addition the premises are true. if the argument is VALID and its premises true, the conclusion must be true. we call this kind of argument SOUND.

now let's play a bit with truth values:

"Socrates is a man" (T)
"Men are immortal" (F)
__________
"Socrates is immortal" (F)

the above argument IS VALID, i.e, though the conclusion follows from the premises, though one premise is false. We have a false premise and a false conclusion, yet the above argument is VALID, but UNSOUND

See that deduction is independent from experience beause the reasoning is self contained in the premises. Remember that the premises could be false and the argument still be valid.

DEDUCTION IS APRIORISTIC. MATHEMATICS IS AN EXAMPLE OF AN APRIORISTIC DISCIPLINE.

______________

INDUCTIVE ARGUMENTS:

An inductive argument establishes a conclusion with high degree of probability. Here the truth of their premises does not guarantee the truth of their conclusion.

Every windstorm observed so far in this area comes from the north. We can see a big cloud of dust in the distance. So, probably a new windstorm is coming from the north.

Analysis: The above argument is a strong inductive argument. The "so far" in the premise is simple and cautious, and the conclusion uses "probably." Strong inductive arguments establish the conclusion with high probability IF the premises were true.

There are three kinds of inductive arguments:

Inductive generalization: It goes from a premise about a sample to a conclusion about the population, or it derives general principles from specific observations.

Analogical Induction: The process of analogical inference involves noting the shared properties of two or more things and from this basis inferring that they also share some further property:

Example:

Athenians and spartans are similar with respect to speaking the same language & being Pantheists
An Athenian has been observed to have further property X
Therefore, a Spartan probably also has property X.

Enumerative Induction: It reasons from particular instances to all instances.

Example: If one observes 100 swans, and all 100 are white, one might infer "All swans are white."

(As you can see, even if the premises are true, it does not entail the conclusion's truth. The conclusion might be true, and might be thought probably true, yet it can be false).

Inference to the best explanation IBE:

Phenomenon Q.

E provides the best explanation for Q.

Therefore, it is probable that E is true.

________________

As you can see, a big difference between deduction and induction is that the latter depends from experience.

INDUCTION IS BASICALLY A POSTERIORI.

SO, WE CAN SAY THAT SCIENTIFIC THEORIES ARE A POSTERIORI, NEVER ABSOLUTELY CERTAIN.

axis of knowledge

In the Y axis, I know that I know (certainty)

In the X axis, I know I don't know (doubt, duda, la filosofía)

In the -Y axis, I don't know, I know (self deceit, autoengaño)

In the -X axis, I don't know I don't know (blissful ignorance or self-deceit)

la naturaleza de la hipótesis

Henri Poincaré

La hipótesis (hypo: debajo, thesis: conclusión) es el recurso par excellence del descubrimiento científico.

Es el recurso esencial para descubrir el mundo. Qué sería de la ciencia, incluso el conocimiento más elemental... sin la posibilidad de hipotetizar. Ahora bien, la hipótesis comienza "debajo"... y esto es bueno, debajo es substrato, no es lo obvio, pero tampoco eso significa que sea verdad.

Recuérdese. Hypótesis no es conclusión, es meramente un postulado plausible. La hipótesis necesita confirmación. Esa confirmación se da en las matemáticas en forma absoluta. No así en las demás ciencias experimentales.

¿Qué garantías tenemos que nuestra hipótesis funcione?

De esto vamos a hablar muy pronto.