Philosophy of Science

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# Philosophy of Science
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### MSA 2025
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# "Scientific Laws are Derived from the Facts"

What do you think about this statement? Is it true?

But _how_? How are scientific laws _derived_ from the facts? The issue is this: In what ways do facts help support scientific laws?

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# Example

**“All metals expand when heated.”**

- What is the scope of this assertion?
- What could provide support for this assertion?

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# An inductive argument

1. Metal `\(x_1\)` expanded when heated on occasion `\(t_1\)`. 2. Metal `\(x_2\)` expanded when heated on occasion `\(t_2\)`. n. Metal `\(x_n\)` expanded when heated on occasion `\(t_n\)`. Conclusion: All metals expand when heated.

What do you think about this argument?

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# Inductive arguments

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 1. I am a turkey that has been feed on morning `\(m_1\)`. 2. I am a turkey that has been feed on morning `\(m_2\)`. n. I am a turkey that has been feed on morning `\(m_n\)`. Conclusion: I will be fed every morning.

What happens on Christmas Eve?
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## A Potential Principle of Induction

Under precisely what circumstances is it legitimate to assert that a scientiﬁc law has been ‘derived’ from some ﬁnite body of observational and experimental evidence?

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**Principle of Induction**: If an inductive inference from observable facts to laws is to be justiﬁed, then the following conditions must be satisﬁed:

1. The number of observations forming the basis of a generalization must be large.
2. The observations must be repeated under a wide variety of conditions.
3. No accepted observation statement should conﬂict with the derived law.
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]

What problems do you foresee with this principle?

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Potential problems:
- What counts as a large number of observations?
- Which conditions must be relevantly varied so the observations can be repeated properly?
- What happens if an observation conflicts with the derived law?

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# The Problem of Induction

- Inductive arguments are not logically valid (the conclusion does not follow necessarily from the truth of the premises). How to fix this?

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# Uniformity of Nature

- Maybe we can assume that the course of nature will continue uniformly. In other words, perhaps we can assume that _the future will be like the past_.

- But how can we support the assumption of the uniformity of nature?

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# Uniformity of Nature

How can we support the idea of the uniformity of nature (that the future will resemble the past)? 1. Given our experience, past futures have resembled past pasts. ... n. Therefore, the future will resemble the past.

An option:

1. Given our experience, past futures have resembled past pasts.
2. **The future will resemble the past**
3. Therefore, the future will resemble the past.

Problem: Argument is **circular**.

How to solve the problem of induction?

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## Karl Popper: Conjectures and Refutations

According to Popper, we should understand scientific reasoning not as inductive, but as a deductive process based on conjectures:

1. We begin with a conjecture `\(C\)`.
2. We derive logical implications of `\(C\)` that can be tested.
3. If the implication passes the test, then `\(C\)` is corroborated (but not proven or verified).
4. If the implication fails the test, then `\(C\)` is refuted—we know for certain that `\(C\)` is false.
5. When `\(C\)` is refuted, it must be revised, or a new conjecture must be formulated to fit what we know.

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## Conjectures and Refutations - Example

1. All metals expand when heated.
2. Therefore, metal `\(x_1\)` will expand when heated on test made attain `\(t_1\)`.
3. If metal `\(x_1\)` expands when heated on test made attain `\(t_1\)`, then the conjecture "all metals expand when heated" is **corroborated**.
4. If metal `\(x_1\)` does not expand when heated on test made attain `\(t_1\)`, then the conjecture "all metals expand when heated" is **refuted**.

Is this how science should work?

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### Dealing with incongruent data: Lakatos

> The story is about an imaginary case of planetary misbehaviour. A physicist of the pre-Einsteinian era takes Newton’s mechanics and his law of gravitation, `\(N\)`, the accepted initial conditions, `\(I\)`, and calculates, with their help, the path of a newly discovered small planet, `\(p\)`. But the planet deviates from the calculated path. Does our Newtonian physicist consider that the deviation was forbidden by Newton’s theory and therefore that, once established, it refutes the theory `\(N\)`? No. He suggests that there must be a hitherto unknown planet `\(p_1\)` , which perturbs the path of `\(p\)`. He calculates the mass, orbit, etc. of this hypothetical planet and then asks an experimental astronomer to test his hypothesis. The planet `\(p_1\)` is so small that even the biggest available telescopes cannot possibly observe it; the experimental astronomer applies for a research grant to build yet a bigger one. In three years time, the new telescope is ready. Were the unknown planet `\(p_1\)` to be discovered, it would be hailed as a new victory of Newtonian science. But it is not. Does our scientist abandon Newton’s theory and his idea of the perturbing planet?

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### Dealing with incongruent data: Lakatos

> ... Does our scientist abandon Newton’s theory and his idea of the perturbing planet? No. He suggests that a cloud of cosmic dust hides the planet from us. He calculates the location and properties of this cloud and asks for a research grant to send up a satellite to test his calculations. Were the satellite’s instruments (possibly new ones, based on a little-tested theory) to record the existence of the conjectural cloud, the result would be hailed as an outstanding victory for Newtonian science. But the cloud is not found. Does our scientist abandon Newton’s theory, together with the idea of the perturbing planet and the idea of the cloud which hides it? No. He suggests that there is some magnetic field in that region of the universe which disturbed the instruments of the satellite. A new satellite is sent up. Were the magnetic field to be found, Newtonians would celebrate a sensational victory. But it is not. Is this regarded as a refutation of Newtonian science? No. Either yet another ingenious auxiliary hypothesis is proposed or... the whole story is buried in the dusty volumes of periodicals and the story never mentioned again. (Lakatos, 1970)