LOGIC AND PHILOSOPHY OF SCIENCE

Logic

the study of correct reasoning — how to think clearly and make good arguments.

three laws of thought

1. Law of Identity

• Something is what it is.

• Example: A tree is a tree.

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2. Law of Non-Contradiction

• Something cannot be both true and false at the same time and in the same way.

• Example: The tree can’t be both alive and not alive right now.

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3. Law of Excluded Middle

• Something is either true or false; there’s no middle option.

• Example: The tree is either green or not green.

Syllogism

a form of logical reasoning where a conclusion is drawn from two given statements (premises).

STRUCTURE

• Major premise: A general statement

• Minor premise: A specific statement

• Conclusion: What follows from the two premises

EX

• Major premise: All humans are mortal.

• Minor premise: Socrates is a human.

• Conclusion: Socrates is mortal.

Validity

argument’s structure is correct — if the premises are true, the conclusion must be true.

• Validity is about the form of the argument, not whether the premises are actually true.

• An argument can be valid but still have false premises.

  Premise 1: All birds can fly.

• Premise 2: A penguin is a bird.

• Conclusion: A penguin can fly.

• This argument is valid (correct form), but the first premise is false, so the conclusion isn’t true.

Soundness

An argument is sound if it is both:

1. Valid (correct logical structure)

2. Has true premises

• A sound argument guarantees the truth of the conclusion.

  All sound arguments are valid, but not all valid arguments are sound.

Paradigm Shift

a big change in the way people think about or understand something, especially in science or knowledge.

• Happens when old ideas or theories are replaced by new ones.

• Changes the framework or “rules” for how we see the world.

Casuality

he principle that every event has a cause — one thing happens because something else made it happen.

If you knock over a glass, your action is the cause, and the glass breaking is the effect.

Falsificationism

idea that scientific theories should be tested by trying to prove them wrong rather than just confirming them.

• A theory is scientific only if it can be falsified (proven false).

• If a theory can’t be tested or potentially disproved, it’s not scientific.

Instrumentalism

the idea that scientific theories are tools or instruments for predicting and explaining things, not necessarily true descriptions of reality.

• Focuses on how useful a theory is, not whether it’s “true.”

• Theories are judged by their practical success.

Naturalism

belief that everything in the world can be explained by natural causes and laws, without needing supernatural explanations.

• The world operates through science and nature.

• Rejects supernatural or spiritual explanations.

Informal Fallacies

Mistakes in reasoning that happen because of errors in content or language, not just form.

• They look convincing but are logically flawed.

• Often rely on emotions, distractions, or irrelevant info.

Fallacies of Relevance

Errors in reasoning where the evidence or argument given is not actually relevant to the conclusion.

• They distract or mislead by using irrelevant information.

• Often appeal to emotions, authority, or personal attacks instead of facts.

• Ad Hominem: Attacking the person, not their argument.

• Appeal to Emotion: Trying to sway feelings instead of logic.

• Red Herring: Introducing an unrelated topic to distract.

• Appeal to Authority: Using an authority’s opinion as evidence when it’s not relevant.

Deductive

Starts with general truth → leads to specific conclusion. If premises are true, conclusion must be true.

Inductive

Starts with specific examples → generalizes to a conclusion. Can be strong, but not guaranteed true.

Limits to Science

Science is a powerful way to understand the natural world, but it has limits in what it can explain or prove.

Example Questions Science Can’t Fully Answer:

• What is the meaning of life?

• Is there life after death?

• What makes something beautiful?

• Cannot Answer Moral Questions:
  Science can tell us what is, but not what ought to be (e.g., what’s right or wrong).

NOMA Principal (Non-Overlapping Magisteria)

The NOMA principle says that science and religion deal with different areas ("magisteria") of knowledge, so they don’t conflict.

• Science covers the natural world: facts, experiments, how things work.

• Religion covers moral values, meaning, and spiritual purpose.

• Each has its own "domain" and shouldn’t interfere with the other.