Ah, Euclid you're like a Guardian Angel watching over us.

Ingrid asked us if we could construct the given triangles in Proposition 4, Book I. It became chaos, believe me. People went crazy, some shut their ears, some didn't understand what was happening. But at the end we decided to divide in groups to make this work.

So, now we're divided in 3 groups. My group is Marce, Kata, Carmen, Grace and I. We decided to accomplish certain standards (these were the core of them):

• Drawings have to be understood in our notebook.
• Logical structure
• Rhetoric and understandable explanation

This chapter talks about the different methods of thinking that are introduced in the preface. Is the mental process in which our language conjunctions happen associative or pure memory?

Pinker describes the two different theories: Chomsky and Halle's, and Rumelhart and McClelland's. Chomsky and Halle talk about how our mind is full of memorized rules, while Rumelhart and McClelland talk about how our mind is a network of associations. This is a debate that brings the matter to a more profound field: philosophy. The two schools of thinking: empiricism and rationalism. Chomsky and Halle's theory would be the rational, therefore, etc. (As my friend Euclid would say.)

Pinker mentions that the way language works, is a combination these two methods of thinking:

"Prince and I have proposed a hybrid in which Chomsky and Halle are basically right about regular inflection and Rumelhart and McClelland are basically right about irregular inflection. Our proposal is simply the traditional words-and-rules theory with a twist. Regular verbs are computed by a rule that combines a symbol for a verb stem with a symbol for the suffix. Irregular verbs are pairs of words retrieve from the mental dictionary, a part of memory. Here is the twist: Memory is not a list of unrelated slots, like RAM in a computer, but is associative, a bit like the Rumelhart-McClelland pattern associator memory. Not only are words linked to words, but bits of words are linked to bits of words."

Bert shared with us a set of rules for dialogue that his previous students in the U.S. made. The rules were really good and the ones that really we thought of adding to our rubric were:

• Speak to the question
• Do not fear rejection/controversy
• Don't steal the learning experience of others

The latter is of real importance, and we haven't thought as a culture much of it. It is really interesting to question people and let them explore their own understanding and mind. Just answering and telling people what they should think blocks the learning experience of the individual.

And that is one of the things that also a reader and learner should also know when they let Wikipedia steal their own understanding. (I'm not saying that Wikipedia is a bad source, but one must learn when sources are necessary or when they're just telling us the whole answer.)

Diego's morning meeting was great! I had so much fun, we saw so many different things. We had a little bit of everything.
First of all, he gave us some mathematical problems to deal with like doubling numbers or dododoubling them. (Yes, it's 3 times doubling a number). We received a prize if we actually did the problem and it was complex, I have to admit. At least I received one prize. Also, I notice my pupils where dilated. Haha, kidding, but I notice that some people gave up easily.

After this, we watched a little Hayek vs. Keynes. Rap. AMAZING. I love these videos, I would watch them again and again. (Notice the Bible joke)

After this, Dieguito was on fire! He brought us MPC cupcakes :) (but, we had to eat them like educated people)

Composition and Reading.

This chapter introduces different forms of communicating ideas : it focuses on the rhetoric. The communicator, in order to transfer his thoughts correctly must create a state of mind and make a connection with the previous knowledge of the receptor. That is why in order to say something interesting, one must observe.

This chapter introduces rules of writing and reading for different kinds of compositions, being poetry, essays, etc.

This chapter is a brief summary to induction.

Logic deals with all things as they are, in order to attain truth. But, there's something really important that Miriam Joseph mentions is that there is a relation of the mind and the material. "We're not all logical after all".

We absorb from the outside and create our thoughts... the will seeks food, but the intellect searches for truth. We have faith in either a god or a person. We believe and based on that beliefs we see the world.

As agents, we cause things. We search for patterns, for laws in nature. Our metaphysical inductions we try to turn into scientific. There's a greater complex whole.

"Deduction leads to consistency in the conceptual order, and induction leads to the assurance that this conceptual order truly represents the real order."

We're surrounded by an incredible amount of false arguments, lies which sometimes, like a virtual virus, affect society in silence until it becomes so affecting that it can even hurt humanity.

For example, the problem of socialism is based on a fallacy of Statement or Secundum Quid. This fallacy states that some partial trues are made absolute trues.

Ad Populum, I related to the Corn Pone opinions. The Ad Misericordiam I related to the false charity motivation.

Everywhere, every time. I dare to say that we're surrounded by lies and these are not part of reality. That is why, somehow that strange force that I will call truth surges out of that cultivation of fallacies.

This chapter talks about simple syllogisms. As mentioned in the chapter before, the syllogism is a tool of reasoning and it is used to acquire new knowledge. Also, it is essential for proving the logical truth of something.

Syllogisms are composed by three propositions: two premises and one conclusion. The subject of the conclusion is the minor term and the predicate of the conclusion is the major term encountered in the premises.
                               
But these syllogisms, since they connect with other premises that might be true, can get really complex. So the conclusions of a syllogism can become a premise of a new syllogism.

                    "Relations of Simple Propositions"
The propositions are related by:

• Conjunction: When two or more propositions join.
  
• Opposition: See illustration down, it explains how the different propositions oppose.
  
• Eduction: This relation explores the argument. It transforms the proposition from explicit to implicit. Not every kind of proposition can be submitted to this process.
  
• Syllogism: This is one of the really important relations of propositions, because it is used for reasoning. For discovering truth. They can be simple, hypothetical, disjunctive or a dilemma.
  

In this chapter, Sister Miriam Joseph introduces the Liberal Arts and how it is useful in our lives. She emphasizes in the importance of the liberal arts in order to explain the trivium, which is the main subject of the book.

She also explains which are the liberal arts, which are classified in the trivium and quadrivium. The trivium is composed by logic, grammar, rhetoric; and the quadrivium is composed by music, astronomy, geometry and mathematics.

The importance of the Trivium is that it settles standards so we can communicate ideas, therefore, we can gain new knowledge and understand the world. The thing that the trivium seeks is the truth.

And to get clearer, there's no necessity of having a subject called "trivium" in order to understand and learn; but the intrinsic learning of the trivium in different subjects is absolutely interesting. It can be observed in Euclid, when he settles his definitions and has a logical expression of it!