TheInfoList

Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BCE). Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular premises to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, distinguishing abduction from induction.

Various fields study how inference is done in practice. Human inference (i.e. how humans draw conclusions) is traditionally studied within the fields of logic, argumentation studies, and cognitive psychology; artificial intelligence researchers develop automated inference systems to emulate human inference. Statistical inference uses mathematics to draw conclusions in the presence of uncertainty. This generalizes deterministic reasoning, with the absence of uncertainty as a special case. Statistical inference uses quantitative or qualitative (categorical) data which may be subject to random variations.

## Definition

The process by which a conclusion is inferred from multiple observations is called inductive reasoning. The conclusion may be correct or incorrect, or correct to within a certain degree of accuracy, or correct in certain situations. Conclusions inferred from multiple observations may be tested by additional observations.

This definition is disputable (due to its lack of clarity. Ref: Oxford English dictionary: "induction ... 3. Logic the inference of a general law from particular instances."[clarification needed]) The definition given thus applies only when the "conclusion" is general.

Two possible definitions of "inference" are:

1. A conclusion reached on the basis of evidence and reasoning.
2. The process of reaching such a conclusion.

## Examples

### Example for definition #1

Ancient Greek philosophers defined a number of syllogisms, correct three part inferences, that can be used as building blocks for more complex reasoning. We begin with a famous example:

1. All humans are mortal.
2. All Greeks are humans.
3. All Greeks are mortal.

The reader can check that the premises and conclusion are true, but logic is concerned with inference: does the truth of the conclusion follow from that of the premises?

The validity of an inference depends on the form of the inference. That is, the word "valid" does not refer to the truth of the premises or the conclusion, but rather to the form of the inference. An inference can be valid even if the parts are false, and can be invalid even if some parts are true. But a valid form with true premises will always have a true conclusion.

For example, consider the form of the following symbological track:

1. All meat comes from animals.
2. All beef is meat.
3. Therefore, all beef comes from animals.

If the premises are true, then the conclusion is necessarily true, too.

Now we turn to an invalid form.

1. All A are B.
2. All C are B.
3. Therefore, all C are A.

To show that this form is invalid, we demonstrate how it can lead from true premises to a false conclusion.

1. All apples are fruit. (True)
2. All bananas are fruit. (True)
3. Therefore, all bananas are apples. (False)

A valid argument with a false premise may lead to a false conclusion, (this and the following examples do not follow the Greek syllogism):

1. All tall people are French. (False)
2. John Lennon was tall. (True)
3. Therefore, John Lennon was French. (False)

When a valid argument is used to derive a false conclusion from a false premise, the inference is valid because it follows the form of a correct inference.

A valid argument can also be used to derive a true conclusion from a false premise:

1. All tall people are musicians. (Valid, False)
2. John Lennon was tall. (Valid, True)
3. Therefore, Jo

Various fields study how inference is done in practice. Human inference (i.e. how humans draw conclusions) is traditionally studied within the fields of logic, argumentation studies, and cognitive psychology; artificial intelligence researchers develop automated inference systems to emulate human inference. Statistical inference uses mathematics to draw conclusions in the presence of uncertainty. This generalizes deterministic reasoning, with the absence of uncertainty as a special case. Statistical inference uses quantitative or qualitative (categorical) data which may be subject to random variations.

The process by which a conclusion is inferred from multiple observations is called inductive reasoning. The conclusion may be correct or incorrect, or correct to within a certain degree of accuracy, or correct in certain situations. Conclusions inferred from multiple observations may be tested by additional observations.

This definition is disputable (due to its lack of clarity. Ref: Oxford English dictionary: "induction ... 3. Logic the inference of a general law from particular instances."[clarification needed]) The definition given thus applies only when the "conclusion" is general.

Two possible definitions of "inference" are:

1. A conclusion reached on the basis of evidence and reasoning.
2. The process of reaching such a conclusion.

## Examples

### Example for definition #1

Ancient Greek philosophers defined a number of syllogisms, correct three part inferences, that can be used as building blocks for more complex reasoning. We begin with a famous example:

1. All humans are mortal.
2. All Greeks are humans.
3. All Greeks are mortal.

The reader can check that the premises and conclusion are true, but logic is concerned with inference: does the truth of the conclusion follow from that of the premises?

The validity of an inference depends on the form of the inference. That is, the word "valid" does not refer to the truth of the premises or the conclusion, but rather to the form of the inference. An inference can be valid even if the parts are false, and can be invalid even if some parts are true. But a valid form with true premises will always have a true conclusion.

For example, consider the form of the following symbological track:

1. All meat comes from animals.
2. All beef is meat.
3. Therefore, all beef comes from animals.

If the premises are true, then the conclusion is necessarily true, too.

Now we turn to an invalid form.

1. All A are B.
2. All C are B.
3. Therefore, all C are A.

To show that this form is invalid, we demonstrate how it can lead from t

This definition is disputable (due to its lack of clarity. Ref: Oxford English dictionary: "induction ... 3. Logic the inference of a general law from particular instances."[clarification needed]) The definition given thus applies only when the "conclusion" is general.

Two possible definitions of "inference" are:

Ancient Greek philosophers defined a number of syllogisms, correct three part inferences, that can be used as building blocks for more complex reasoning. We begin with a famous example:

1. All humans are mortal.
2. All Greeks are humans.
3. All Greeks are mortal.

The reader can check that the premises and conclusion are true, but logic is concerned with inference: does the truth of the conclusion follow from that of the premises?

The validity of an inference depends on the form of the inference. That is, the word "valid" does not refer to the truth of the premises or the conclusion, but rather to the form of the inference. An inference can be valid even if the parts are false, and can be invalid even if some parts are true. But a valid form with true premises will always have a true conclusion.

For example, consider the form of the following symbological track:

1. All meat co

The reader can check that the premises and conclusion are true, but logic is concerned with inference: does the truth of the conclusion follow from that of the premises?

The validity of an inference depends on the form of the inference. That is, the word "valid" does not r

The validity of an inference depends on the form of the inference. That is, the word "valid" does not refer to the truth of the premises or the conclusion, but rather to the form of the inference. An inference can be valid even if the parts are false, and can be invalid even if some parts are true. But a valid form with true premises will always have a true conclusion.

For example, consider the form of the following symbological track:

If the premises are true, then the conclusion is necessarily true, too.

Now we turn to an invalid form.

1. All A are B.
2. All C are B.
3. Therefore, all C are A.
4. Now we turn to an invalid form.

To show that this form is invalid, we demonstrate how it can lead from true premises to a false conclusion.

1. All apples are fruit. (True)
2. All bananas are fruit. (True)
3. T

A valid argument with a false premise may lead to a false conclusion, (this and the following examples do not follow the Greek syllogism):

1. All tall people are French. (False)
2. John Lennon was tall. (True)
3. Therefore, John Lennon was French. (False)
4. When a valid argument is used to derive a false conclusion from a false premise, the inference is valid because it follows the form of a correct inference.

A valid argument can also be used to derive a true conclusion from a false premise:

1. All tall people are musicians. (Valid, False)

A valid argument can also be used to derive a true conclusion from a false premise:

In this case we have one false premise and one true premise where a true conclusion has been inferred.