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| public:t-713-mers:mers-25:concepts_terms [2025/08/19 10:58] – [Models] thorisson | public:t-713-mers:mers-25:concepts_terms [2025/08/19 12:27] (current) – [Correlation, Knowledge, Causation] thorisson |
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| ====Correlation, Knowledge, Causation==== | ====Correlation, Knowledge, Causation==== |
| | Correlation | Some factors/variables co-vary when changes in one variable are related with changes in the other, negative or positive. | | | Correlation | Some factors/variables co-vary when changes in one variable are related with changes in the other, negative or positive. | |
| | Correlation: Powerful source of information | Any variables in the world can be measured for correlation (i.e. to see if they are correlated). Only two variables are needed (independent and dependent) for doing correlation studies. | | | Correlation: Powerful source of information | Any variables in the world can be measured for correlation (i.e. to see if they are correlated). Only two variables are needed (independent and dependent) for doing correlation studies. | |
| | Main operating principle behind correlation | There is no causation without correlation. \\ BUT: It is not guaranteed to be measurable. | | | Main operating principle behind correlation | There is no causation without correlation. \\ BUT: It is not guaranteed to be measurable. | |
| | Correlation: Pitfall | Correlation does not imply causation between the variables measured! \\ BUT: ALL correlation that is NOT a coincidence has a cause. | | | Correlation: Pitfall | Correlation does not imply causation between the variables measured! \\ BUT: ALL correlation that is NOT a coincidence has a cause. | |
| | Quasi-experimental designs | Purpose: Where true experimental design is not possible, approximate it. \\ If direct control over dependent/independent variables is not possible. | | | Modeling Correlation | A model that makes use of observed correlation between A and B is only good for prediction, not for manipulation; to be useful for manipulation (goal-directed behavior and planning) it must include the causal direction of the relationship between A and B. | |
| | How it works | 1. One-shot case study (no control group) \\ 2. Single group pre- and post-test (minimal control) \\ 3. ABAB: Single-group repeated measures (slightly less minimal control) | | | Causal Relations are Invisible | Causal relations do not jump out at us when we observe something unfamiliar because the cause and effect are "spread out" over time -- cause-effect happens over time, as the cause must happen before the effect. | |
| | Limitations | Much greater uncertainty as to the internal and external validity of the quasi-experiments than true experimental designs | | | Modeling Cause-Effect | Intelligent agents can model cause and effect with many methods; two of them are invention (coming up with a wild idea for the relationship betweeen A and B, e.g. that spirits make people sick) and discovery (through observation and experimentation with A and B, e.g. that unclean surgical knives can bring disease-carrying material between people). | |
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| | How it relates to logic | If causal relations are rules, and the world has regularity, then the world is rules-based. Reasoning is the method of following logic when working with rules. It means we can reason about the world. | | | How it relates to logic | If causal relations are rules, and the world has regularity, then the world is rules-based. Reasoning is the method of following logic when working with rules. It means we can reason about the world. | |
| | Types of \\ (basic) \\ causal relations | A->B & A->C : A causes B and C. \\ A->B->C : A causes B and B causes C \\ [A+B]->C : A and B together cause C. \\ A->C, B->C : Both A and B are sufficient to cause B. | | | Types of \\ (basic) \\ causal relations | A->B & A->C : A causes B and C. \\ A->B->C : A causes B and B causes C \\ [A+B]->C : A and B together cause C. \\ A->C, B->C : Both A and B are sufficient to cause B. | |
| | Time and Causation | The temporal relation between cause and effect is strict on time: Effects cannot happen before causes. | | | Time and Causation | The temporal relation between cause and effect is strict on time: Effects cannot happen before causes! | |
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| ====Reasoning==== | ====Reasoning==== |
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| | What is Reasoning? | A systematic way of considering implications. | | | What is Reasoning? | A systematic way of considering statements and their implications. | |
| | How is it done? | Via processes that observe rules. | | | How is it done? | Via processes that observe rules, called "reasoning processes". | |
| | What are \\ the main reasoning \\ process types? | **Deduction**: All men are mortal. Socrates is a man. Hence, Socrates is mortal \\ **Abduction**: How did this come about? (Sherlock Holmes) \\ **Induction**: What is the general rule? \\ **Analogy**: 'This' is like 'that' (in 'this' way). | | | What are \\ the main reasoning \\ process types? | **Deduction**: All men are mortal. Socrates is a man. Hence, Socrates is mortal \\ **Abduction**: How did this come about? (Sherlock Holmes) \\ **Induction**: What is the general rule? \\ **Analogy**: 'This' is like 'that' (in 'this' way). | |
| | How are they used \\ in science? | In empirical science to unearth the "rules of the universe". \\ In mathematics as axioms. \\ In philosophy as a way to construct arguments. \\ In computer science to write code. | | | How are they used \\ in science? | In empirical science to unearth the "rules of the universe". \\ In mathematics as axioms. \\ In philosophy as a way to construct arguments. \\ In computer science to write code. | |
| | Why does it work? | Because the world's behavior is/seems rule-based. | | | Why does it work? | Because the world's behavior is/seems rule-based. | |
| | Deduction | Mathematical deduction is axiomatic - always Boolean (true or false). \\ Scientific deduction is **never** axiomatic - it can always be disproven. | | | Deduction | Mathematical deduction is axiomatic - **always** Boolean (true or false). \\ Scientific deduction is **never** axiomatic - it can always (potentially) be disproven. \\ // IRL we do deduction (of the latter kind) all the time, e.g. when picking option B to meet when you already said you cannot do option A.// | |
| | Abduction | Mathematical deduction can be completely verified. \\ Scientific abduction can always be challenged. | | | Abduction | Mathematical abduction can be completely verified through its axioms. \\ Scientific abduction can always be challenged. \\ //IRL: Choosing the side-entrance when we see that the front door is locked (which might still be wrong).// | |
| | Induction | The best method for verifying induction in mathematics is //mathematical proof.// \\ In science, induction can never be proven. This is why scientific theories must be formulated in a way that they can be //disproven// (cf. Karl Popper). | | | Induction | The best method for verifying induction in mathematics is //mathematical proof.// \\ In science, induction can never be proven. This is one reason why scientific theories must instead be formulated in a way that they can be //disproven// (cf. Karl Popper). \\ // IRL: Generalizations are made in the form of rules of thumb all the time; mostly we don't care whether they are always true or not, only how useful they are in particular situations for particular purposes.// | |
| | Analogy | Used by scientists and mathematicians alike to come up with new ideas, compare and contrast, and analyze their subject matter. | | | Analogy | Used by scientists, mathematicians, and average Joe and Jane to come up with new ideas, compare and contrast, and analyze anything the heart desires. | |
| | Reasoning in \\ Maths vs. Science | Reasoning is different in maths than in science because to do math we //must know all the rules completely up front//. The main role of maths is to inspect what the rules imply. \\ In science //all rules are hidden.// The main role of science is to //uncover the rules//. | | | Reasoning in \\ Maths vs. Science | Reasoning is different in maths than in science because to do math we //must know all the rules completely up front//. The main role of maths is to inspect what the rules imply. \\ In science //all rules are hidden.// The main role of science is to //uncover the rules//. | |
| | Axiomatic vs. \\ Non-axiomatic | In axiomatic reasoning we know for a fact \\ 1. we have the complete set of rules \\ 2. all the rules are true, and that \\ 3. if we follow the rules we will have absolute truth. \\ In non-axiomatic reasoning, none of the above holds. \\ //So how can we reason, then?// | | | Axiomatic vs. \\ Non-axiomatic | In axiomatic reasoning we know for a fact \\ 1. we have the complete set of rules \\ 2. all the rules are true, and that \\ 3. if we strictly follow the rules we will have absolute truth every time. \\ In non-axiomatic reasoning, none of the above holds. \\ //So how is it then that we can reason?// | |
| | Empirical Reasoning | For reasoning in the physical world, we must assume that we possibly got things wrong. But //some things are more wrong than others.// To ensure that we use the best knowledge we have for any task X, we must do bookkeeping about //what works and what doesn't in what situations//. | | | Empirical Reasoning | For reasoning in the physical world, we must assume that we possibly got things wrong. But //some things are more wrong than others.// To ensure that we use the best knowledge we have for any task X, we must do bookkeeping about //what works and what doesn't in what situations//. | |
| | | Defeasible Reasoning | Reasoning that is based on assumptions and conclusions that can be refuted is called //defeasible reasoning//. | |
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| | A scientific theory gives us the big picture | A good scientific theory relates together, in a coherent way, some part of the world -- in general the bigger the part, the better the theory. | | | A scientific theory gives us the big picture | A good scientific theory relates together, in a coherent way, some part of the world -- in general the bigger the part, the better the theory. | |
| | Occam's Razor | A good scientific theory cannot be simplified; it is the shortest and most accurate explanation of a phenomenon. Einstein is quoted as saying: "A theory should be as simple as possible, but not simpler". | | | Occam's Razor | A good scientific theory cannot be simplified; it is the shortest and most accurate explanation of a phenomenon. Einstein is quoted as saying: "A theory should be as simple as possible, but not simpler". | |
| | A scientific theory can be **disproven** | A scientific theory or hypothesis is a statement that is //disprovable//. To count as "scientific" a theory //must// be disprovable. For this there must exist some measures and actions that are //possible// (in theory, but better yet, practic) whose results would possibly - should the measurements come out a particular way - disprove the theory. \\ Applying this criterion strictly means that //all scientific theories to date have been disproven - i.e. proven incorrect.// \\ This is not a bug but a //**feature!**:// Exposing the limits of our theories by demonstrating in which contexts they are incorrect allows us to come up with better theories. | | | \\ A scientific theory can be **disproven** | A scientific theory or hypothesis is a statement that is //disprovable//. To count as "scientific" a theory //must// be disprovable. For this there must exist some measures and actions that are //possible// (in theory, but better yet, practic) whose results would possibly - should the measurements come out a particular way - disprove the theory. \\ Applying this criterion strictly means that //all scientific theories to date have been disproven - i.e. proven incorrect.// \\ This is not a bug but a //**feature!**:// Exposing the limits of our theories by demonstrating in which contexts they are incorrect allows us to come up with better theories. | |
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