Deductive reasoning
The syntactic approach, by contrast, focuses on rules of inference, that is, schemas of drawing a conclusion from a set of premises based only on their logical form.
Mental logic theories hold that deductive reasoning is a language-like process that happens through the manipulation of representations using rules of inference.
In philosophy, the geometrical method is a way of philosophizing that starts from a small set of self-evident axioms and tries to build a comprehensive logical system using deductive reasoning.
[6][7] Logical consequence is knowable a priori in the sense that no empirical knowledge of the world is necessary to determine whether a deduction is valid.
[8] A similar formulation holds that the speaker claims or intends that the premises offer deductive support for their conclusion.
That brings with it an important drawback of this definition: it is difficult to apply to concrete cases since the intentions of the author are usually not explicitly stated.
It is based on the idea that the sentences constituting the premises and conclusions have to be interpreted in order to determine whether the argument is valid.
[23] This is similar to the valid rule of inference named modus ponens, but the second premise and the conclusion are switched around, which is why it is invalid.
[24][25] This is similar to the valid rule of inference called modus tollens, the difference being that the second premise and the conclusion are switched around.
So given a set of premises, they are faced with the problem of choosing the relevant rules of inference for their deduction to arrive at their intended conclusion.
[13][26][27] This issue belongs to the field of strategic rules: the question of which inferences need to be drawn to support one's conclusion.
This includes the study of the factors affecting their performance, their tendency to commit fallacies, and the underlying biases involved.
[3][5] A notable finding in this field is that the type of deductive inference has a significant impact on whether the correct conclusion is drawn.
On the other hand, even some fallacies like affirming the consequent or denying the antecedent were regarded as valid arguments by the majority of the subjects.
[3][5] These findings suggest that the deductive reasoning ability is heavily influenced by the content of the involved claims and not just by the abstract logical form of the task: the more realistic and concrete the cases are, the better the subjects tend to perform.
The increased tendency to misjudge the validity of this type of argument is not present for positive material conditionals, as in "If the card has an A on the left, then it has a 3 on the right.
These theories aim to explain how deductive reasoning works in relation to the underlying psychological processes responsible.
Mental logic theories see deductive reasoning as a language-like process that happens through the manipulation of representations.
[3][1][46][45] This is done by applying syntactic rules of inference in a way very similar to how systems of natural deduction transform their premises to arrive at a conclusion.
In the latter case, the additional cognitive labor required makes deductive reasoning more error-prone, thereby explaining the increased rate of error observed.
In this sense, it has been claimed that humans possess a special mechanism for permissions and obligations, specifically for detecting cheating in social exchanges.
[3][50][51] Some theorists hold that the thinker has to have explicit awareness of the truth-preserving nature of the inference for the justification to be transferred from the premises to the conclusion.
One consequence of such a view is that, for young children, this deductive transference does not take place since they lack this specific awareness.
Deductivism states that such inferences are not rational: the premises either ensure their conclusion, as in deductive reasoning, or they do not provide any support at all.
It consists in the challenge of explaining how or whether inductive inferences based on past experiences support conclusions about future events.
[57] Hypothetico-deductivism is a closely related scientific method, according to which science progresses by formulating hypotheses and then aims to falsify them by trying to make observations that run counter to their deductive consequences.
[64][65] The term "natural deduction" refers to a class of proof systems based on self-evident rules of inference.
[66] Natural deduction, on the other hand, avoids axioms schemes by including many different rules of inference that can be used to formulate proofs.
[70] It gets its name from the forms of mathematical demonstration found in traditional geometry, which are usually based on axioms, definitions, and inferred theorems.
[69] One recurrent criticism of philosophical systems build using the geometrical method is that their initial axioms are not as self-evident or certain as their defenders proclaim.
