### Logic & Science

“Reasonable reflective thinking that is focused on deciding what to believe or do. More precisely, it is assessing the authenticity, accuracy, and/or worth of knowledge claims and arguments. It requires careful, precise, persistent and objective analysis of any knowledge claim or belief to judge its validity and/or worth.” Source: definition of critical thinking

The practice of critical thinking sets out to assess the validity of premises, logic of arguments, and reliability of conclusions. In practice, discerning the truth of an argument is not always a simple task. Core Concepts in Critical Thinking Introduction to Statements or Claims

An argument is a set of statements. The premises – facts or propositions – are intended to provide support for the conclusion. The conclusion is asserted to be true on the basis of the premises. If an argument is cogent, then a true conclusion follows logically from true premises.

Logic can be symbolic or informal. Symbolic logic examines the precise symbolic representation of logical concepts, the abstract relationships between these concepts, and the systematization of these relationships. Informal logic involves the application of logical principles to assessment the types of informal arguments and claims that we encounter in daily life.

Propositional logic is a branch of symbolic logic dealing with propositions as units and with their combinations and the connectives that relate them – if, then compound statements. Propositional Logic Terms and Symbols Proposition evaluator. Categorical logic and categorical syllogisms are more concrete than is propositional logic – some, all, and/not. Venn diagram evaluator. An understanding of Fallacies of Logic – recognized structural errors in argumentation – provides a shortcut to assessing the cogency of an argument.

We most often encounter prepositional arguments in daily life, while the logic of science, and of mathematics in particular, is more often categorical. In special cases such as the behavior of gases, at different temperatures, and under pressure, the “problem of induction” can be disregarded and predictive equations are termed Laws (The Gas Laws).

Scientific predictions, however, represent a subset of experimentation and are propositional – if this hypothesis is correct, then we will observe such and such a phenomenon. Failure to observe the predicted phenomenon might be taken to disprove the hypothesis. However, the failure might be a result of experimental or observational error, or might result from faulty predictions based upon a reasonable hypothesis. Alternatively, the hypothesis may be incorrect, but the predicted phenomenon is observed because of a mechanism not yet hypothetically considered.

For these reasons peer-reviewed scientific papers include analyses of current thinking, descriptions of methods, and statements of results so that other researchers might attempt replication. In science, unlike the case for mathematics, proof is not possible, while disproof – falsification – is possible. For this reason, hypotheses to be experimentally tested are ideally framed in such a way that they may be disproved – falsifiable hypotheses. When an empirically based, logical hypothesis, which has not been disproved after repeated testing, is deemed satisfactory by consensus within the scientific community, then the hypothesis graduates to the status of Theory (capitalized to differentiate the scientific term from its vernacular usage). In practice, much of science proceeds upon positive results – repeated observations of a phenomenon under particular conditions. In the softer sciences, such as the social sciences, statistical analyses of results play an important role. Some sciences, such as paleontology are by their nature outside the possibility of experimentation – we cannot resurrect dinosaurs and recreate meteor impacts – and must proceed on the basis of accumulated evidence.

The practice of critical thinking sets out to assess the validity of premises, logic of arguments, and reliability of conclusions. In practice, discerning the truth of an argument is not always a simple task. Core Concepts in Critical Thinking Introduction to Statements or Claims

An argument is a set of statements. The premises – facts or propositions – are intended to provide support for the conclusion. The conclusion is asserted to be true on the basis of the premises. If an argument is cogent, then a true conclusion follows logically from true premises.

Logic can be symbolic or informal. Symbolic logic examines the precise symbolic representation of logical concepts, the abstract relationships between these concepts, and the systematization of these relationships. Informal logic involves the application of logical principles to assessment the types of informal arguments and claims that we encounter in daily life.

Propositional logic is a branch of symbolic logic dealing with propositions as units and with their combinations and the connectives that relate them – if, then compound statements. Propositional Logic Terms and Symbols Proposition evaluator. Categorical logic and categorical syllogisms are more concrete than is propositional logic – some, all, and/not. Venn diagram evaluator. An understanding of Fallacies of Logic – recognized structural errors in argumentation – provides a shortcut to assessing the cogency of an argument.

We most often encounter prepositional arguments in daily life, while the logic of science, and of mathematics in particular, is more often categorical. In special cases such as the behavior of gases, at different temperatures, and under pressure, the “problem of induction” can be disregarded and predictive equations are termed Laws (The Gas Laws).

Scientific predictions, however, represent a subset of experimentation and are propositional – if this hypothesis is correct, then we will observe such and such a phenomenon. Failure to observe the predicted phenomenon might be taken to disprove the hypothesis. However, the failure might be a result of experimental or observational error, or might result from faulty predictions based upon a reasonable hypothesis. Alternatively, the hypothesis may be incorrect, but the predicted phenomenon is observed because of a mechanism not yet hypothetically considered.

For these reasons peer-reviewed scientific papers include analyses of current thinking, descriptions of methods, and statements of results so that other researchers might attempt replication. In science, unlike the case for mathematics, proof is not possible, while disproof – falsification – is possible. For this reason, hypotheses to be experimentally tested are ideally framed in such a way that they may be disproved – falsifiable hypotheses. When an empirically based, logical hypothesis, which has not been disproved after repeated testing, is deemed satisfactory by consensus within the scientific community, then the hypothesis graduates to the status of Theory (capitalized to differentiate the scientific term from its vernacular usage). In practice, much of science proceeds upon positive results – repeated observations of a phenomenon under particular conditions. In the softer sciences, such as the social sciences, statistical analyses of results play an important role. Some sciences, such as paleontology are by their nature outside the possibility of experimentation – we cannot resurrect dinosaurs and recreate meteor impacts – and must proceed on the basis of accumulated evidence.