Core Philosophical Concepts Explained

Fundamental Philosophical Concepts

Pre-Rational Ideas & Justification

These concepts often precede or underpin rational thought:

  • Theoretical Justification: The basis for understanding.
  • Imagination: A key faculty in forming ideas.
  • Grounded Understanding: Comprehending the whole tradition.
  • Ultimate Justification: The final and justifying principle.
  • Supernatural: Concepts beyond natural explanation.
  • Arbitrariness: Lack of inherent reason or order.
  • Symbolic: Representation through symbols.

Core Characteristics

Read More

Primary Language Skills & CLIL Integration

Primary Language Skill Development

Listening Skills Progression

Years 1 & 2 Primary

  • Understand a tale told by the teacher with necessary interactional modifications.
  • Understand a very simple dialogue (audio recording) with visual aid.
  • Understand words and phrases (audio recording).
  • Understand a song or chant (audio recording).
  • Follow single instructions given by the teacher in English for general classroom management or specific tasks.

Years 3 & 4 Primary

  • Understand a tale told by the teacher with
Read More

Venezuela’s Historical Border Disputes: Colombia, Brazil, Guyana

Venezuela’s Historical Border Disputes

The Michelena-Pombo Treaty (1833)

On December 14, 1833, three years after the dissolution of Gran Colombia, Lino de Pombo, representing Colombia, and Santos Michelena, representing Venezuela, signed a treaty of friendship, alliance, commerce, navigation, and limits. This treaty, however, was rejected by Venezuelan congress members.

Subsequent Agreements with Colombia

After the Michelena-Pombo treaty, another agreement was signed on July 23, 1842, focusing on friendship,

Read More

Nephron: Kidney Structure, Function, and Regulation

The nephron is the functional unit of the kidney. Each kidney contains approximately 1 million nephrons, which do not regenerate if destroyed. From age 40, approximately 1% of nephrons are lost each year.

Components of the Nephron

The nephron is primarily formed by the glomerulus and the tubular system.

Glomerulus

An afferent arteriole, originating from the renal artery, reaches the glomerulus and branches into glomerular capillaries. These capillaries are highly permeable—approximately 400 times

Read More

Mastering Vermicomposting: Stages & Essential Care

Introduction to Vermicomposting

Vermicomposting is a bio-oxidative process in which earthworms convert organic waste into nutrient-rich compost known as vermicompost or worm castings. This method is eco-friendly, cost-effective, and highly efficient in recycling organic matter. It not only helps in waste management but also improves soil health, fertility, and crop yield naturally.

The process depends on the activity of decomposer organisms, mainly earthworms such as Eisenia fetida, Eudrilus eugeniae,

Read More

Spanish Economic Shifts: Colonial Trade and Fiscal Challenges

ITEM 3: Colonial Trade and Fiscal Crises

Contradictions in Colonial Trade and Fiscal Crisis

Colonial Trade Crisis

Spain’s economy faced challenges due to its colonial trade. The nation imported more food and manufactured goods than it produced, as it primarily exported raw materials. After the loss of colonies, imports of food and manufactured goods were initially prohibited. While this succeeded for food, it failed for manufacturing due to widespread smuggling.

The economy was underdeveloped, exporting

Read More

Corporate Governance Essentials: Principles, Theories, and Best Practices

Corporate Governance: Definition & Core Principles

Corporate governance is the system of rules, practices, and processes by which a company is directed and controlled. It involves balancing the interests of various stakeholders such as shareholders, management, customers, suppliers, financiers, government, and the community.


Key Principles of Corporate Governance (OECD Framework)

  1. Transparency – Accurate and timely disclosure of financial and operational information.
  2. Accountability – Clear responsibilities
Read More

Brazilian Folklore, Personal Journeys, and Language Insights

The Legend of Saci-Pererê

Saci-Pererê is a well-known character in Brazilian folklore. He is a mischievous, one-legged Black boy who smokes a pipe and wears a red cap that grants him magical powers. He appears like a whirlwind and enjoys playing pranks on animals and people. His favorite tricks include making objects disappear and disrupting cooks’ work by swapping salt and sugar containers or causing food to burn. Additionally, he is the guardian of herbs and medicinal plants, skilled in preparing

Read More

Quantitative Methods & Machine Learning Essentials

Likelihood Function

The likelihood function describes how observed data depends on the model parameters, θ. It is often denoted as p(x|θ).

Maximum Likelihood Estimation (MLE)

The Maximum Likelihood Estimator (MLE), δ(x), is defined as:

AD_4nXens3ikERhLz2M8HRO4dfpKx9_w9BgUbx73ALHG41CGRjsBxhIsjOw4BzE1BphWCTk53xzdyxIzHr1I422n2rEii-8h4nn-e_ANVu9Lfvd-9gTgwuMjXiTVHu3h94h_Pp-zzdZm?key=LHRE6LkDAk3aauFWnXAY3w

or equivalently:

AD_4nXcBOqTKdnd_44nT9SvCEN_DC3fTsTRA6L92Ma8KuAwJFiqJw1ob3yLLhFBxcIFmvg5br9WC97OQbtxEoadi3MJZmlNWDP--HzQmzGYYOHlE92JvAyaLrwZrPv1hOvQE0-1bhjRPHw?key=LHRE6LkDAk3aauFWnXAY3w

The Gaussian log-likelihood is shown above.

Asymptotic Distribution of MLE

When n is large, the asymptotic distribution of the MLE is given by:

AD_4nXcfhoYKSvG5j_M-BufAmuQPVt-n61jGX9AFGHH72am8FJwK1jJwpVhCbd18IozHsGDa5vglE6F4FYN9cMiEDAVGKnnwWcmgNHuaykwujgCqRVwcUUjRoQhM2WOLFu1X5v91vhpY8g?key=LHRE6LkDAk3aauFWnXAY3w

where:

AD_4nXfMjcWPVzPNV0KN67nEqo0BJIubRYV7FNxAznDQ2qrpYrVa_i36aynPjaomQ_CdQ1IZCCPIVU7aX2iaVZXGbVsUBaDXxn1wfyL61ohsq4xQrN0ndXHz4z62whJP9c9NWJ44fj8o?key=LHRE6LkDAk3aauFWnXAY3w

Examples include:

  • Gaussian: AD_4nXcrVSk61EBxOo-Yfcy7NovkHFiXR9vRQ1oDMDZJ3PDU1456xscUf4UlFihY50DKAC01kl1PrBCg8QvDmEYTZP7OGzMwky8IW5kWMc5-UBMyy14DWAuL8TqaPuoFOkeG2gWp4UrM?key=LHRE6LkDAk3aauFWnXAY3w
  • Exponential: AD_4nXdH3ZJbiU6DQ5fU66ztOanYvjMdHipMqQE66STpcJ_EYuBzRVH8grFgu9sedLQyeyMJmQZnD7hJ4i4SMSNcovoOpwfxK5RMHGPMLsJU-r_CtmogiS2jFbspG7UWBymWywXcp607?key=LHRE6LkDAk3aauFWnXAY3w

Bayesian Estimation

The Bayesian forecast is given by:

AD_4nXcQACF6aLi-R_oXFCxI00TGSzp-SYj3jT4-te79_CYDkkQzjHqVCY84UHTLI03s8qaHtVH0-f6QJk3J2FkjzwpsQlsphLkRnAtWxyBhAwwowcACKqZ2xphX_gASIN2w4wWDn5_MSw?key=LHRE6LkDAk3aauFWnXAY3w

Assume the

Read More

Ethical Dimensions: Free Will, Society, and Business Accountability

Understanding Free Will: Debates and Perspectives

Free will controls our own decisions, meaning we can choose what we do without being forced. Philosopher Sam Harris, however, argues that free will is an illusion.

The concept of free will is often based on two premises:

  • We are free to behave differently than in the past.
  • We consciously control our thoughts and actions.

Harris contends that the choices we make stem from prior causes we cannot see or control. He suggests that understanding this can shift

Read More