Benjamin Meixner, 12302260

1. Distinction in Hume’s Enquiry

Definition: “Relations of ideas” refer to a type of knowledge that is intuitively or demonstrably certain. These truths are not dependent on empirical observation and are known through reason alone.
Examples:
1. “2 + 2 = 4” — A fundamental arithmetic truth.
2. “All bachelors are unmarried men” — A logical statement that is true by definition.
Questions: i) Are relations of ideas independent of us?
- Yes, they are independent of human experience; their truth is self-evident through logic.
ii) How are they known?
- They are known through logical deduction and reasoning, devoid of empirical validation.
iii) Does the negation or denial of statements about relations of ideas lead to a contradiction?
- Yes, negating these truths leads to contradictions, as they are intrinsically true.

Definition: “Matters of fact” are statements contingent upon empirical observation. They rely on experiential data to assert their truth.
Examples:
1. “The sun rises in the east.”
2. “It is raining today.”

According to Hume, the foundation for all reasoning about matters of fact is the relation of cause and effect.

Example: If one finds a watch on a deserted island, one might infer that it was left there by a shipwrecked individual.
Assumption: Hume suggests that we assume a past event caused the presence of the watch.

Causal relationships cannot be proven solely through deduction. Hume argues that necessary connections between events require empirical observation.

Hume contends that it is impossible to justify beliefs in causal relations because they rely on empirical observation, rather than logical necessity.

Fire and Heat: The presence of fire produces heat.
Motion and Object: A ball moves when it is pushed.
Eating and Nourishment: Consuming food results in the feeling of nourishment.

Hume maintains that causality cannot be established through observation alone; we can only identify correlations, not necessary connections.

Deduction: Reasoning from general principles to specific instances.
Induction: Reasoning from specific instances to general principles.
Induction is often viewed as a valid inference form when assuming the uniformity of nature. However, Hume critiques the justification of induction.

Patterns include:
1. Generalizing from Sample to Population: Inducing that all swans are white based on observing a specific white swan population.
2. Causal Inference: Concluding that smoke causes fire when smoke is frequently observed alongside fire.
3. Statistical Correlations: Assuming that high coffee consumption leads to increased alertness based on observed trends.

Increased ice cream sales correlated with higher drowning incidents during the summer months—both occur simultaneously, but one does not cause the other.
Higher education levels correlate with higher income, yet education alone does not guarantee greater earnings.
An individual carrying an umbrella correlates with rain; however, carrying the umbrella does not cause the rain.

The Phillips Curve presents a correlation between inflation and unemployment rates.
Prediction Basis: It suggests that a decrease in unemployment correlates with an increase in inflation.
Foundation of Prediction: The prediction relies on historical data, invoking inductive reasoning. However, there is considerable debate regarding whether this correlation implies a causal relationship.