Philosophical logic
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Understood in a narrow sense, philosophical logic is the area of philosophy that studies the
application of logical methods to philosophical problems, often in the form of extended logical
systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the
study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as
identical to the philosophy of logic, which includes additional topics like how to define logic or a
discussion of the fundamental concepts of logic. The current article treats philosophical logic in
the narrow sense, in which it forms one field of inquiry within the philosophy of logic.
An important issue for philosophical logic is the question of how to classify the great variety of
non-classical logical systems, many of which are of rather recent origin. One form of
classification often found in the literature is to distinguish between extended logics and deviant
logics. Logic itself can be defined as the study of valid inference. Classical logic is the dominant
form of logic and articulates rules of inference in accordance with logical intuitions shared by
many, like the law of excluded middle, the double negation elimination, and the bivalence of
truth.
Extended logics are logical systems that are based on classical logic and its rules of inference but
extend it to new fields by introducing new logical symbols and the corresponding rules of
inference governing these symbols. In the case of alethic modal logic, these new symbols are
used to express not just what is true simpliciter, but also what is possibly or necessarily true. It is
often combined with possible worlds semantics, which holds that a proposition is possibly true if
it is true in some possible world while it is necessarily true if it is true in all possible worlds.
Deontic logic pertains to ethics and provides a formal treatment of ethical notions, such as
obligation and permission. Temporal logic formalizes temporal relations between propositions.
This includes ideas like whether something is true at some time or all the time and whether it is
true in the future or in the past. Epistemic logic belongs to epistemology. It can be used to
express not just what is the case but also what someone believes or knows to be the case. Its rules
of inference articulate what follows from the fact that someone has these kinds of mental states.
Higher-order logics do not directly apply classical logic to certain new sub-fields within
philosophy but generalize it by allowing quantification not just over individuals but also over
predicates.
Deviant logics, in contrast to these forms of extended logics, reject some of the fundamental
principles of classical logic and are often seen as its rivals. Intuitionistic logic is based on the
idea that truth depends on verification through a proof. This leads it to reject certain rules of
inference found in classical logic that are not compatible with this assumption. Free logic
modifies classical logic in order to avoid existential presuppositions associated with the use of
possibly empty singular terms, like names and definite descriptions. Many-valued logics allow
additional truth values besides true and false. They thereby reject the principle of bivalence of
truth. Paraconsistent logics are logical systems able to deal with contradictions. They do so by
, avoiding the principle of explosion found in classical logic. Relevance logic is a prominent form
of paraconsistent logic. It rejects the purely truth-functional interpretation of the material
conditional by introducing the additional requirement of relevance: for the conditional to be true,
its antecedent has to be relevant to its consequent.
Contents
1 Definition and related fields
2 Classification of logics
3 Classical logic
4 Extended logics
o 4.1 Alethic modal
o 4.2 Deontic
o 4.3 Temporal
o 4.4 Epistemic
o 4.5 Higher-order
5 Deviant logics
o 5.1 Intuitionistic
o 5.2 Free
o 5.3 Many-valued
o 5.4 Paraconsistent
5.4.1 Relevance
6 References
Definition and related fields
The term "philosophical logic" is used by different theorists in slightly different ways.[1] When
understood in a narrow sense, as discussed in this article, philosophical logic is the area of
philosophy that studies the application of logical methods to philosophical problems. This
usually happens in the form of developing new logical systems to either extend classical logic to
new areas or to modify it to include certain logical intuitions not properly addressed by classical
logic.[2][1][3][4] In this sense, philosophical logic studies various forms of non-classical logics, like
modal logic and deontic logic. This way, various fundamental philosophical concepts, like
possibility, necessity, obligation, permission, and time, are treated in a logically precise manner
by formally expressing the inferential roles they play in relation to each other.[5][4][1][3] Some
theorists understand philosophical logic in a wider sense as the study of the scope and nature of
logic in general. On this view, it investigates various philosophical problems raised by logic,
including the fundamental concepts of logic. In this wider sense, it can be understood as identical
to the philosophy of logic, where these topics are discussed.[6][7][8][1] The current article discusses
only the narrow conception of philosophical logic. In this sense, it forms one area of the
philosophy of logic.[1]
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Understood in a narrow sense, philosophical logic is the area of philosophy that studies the
application of logical methods to philosophical problems, often in the form of extended logical
systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the
study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as
identical to the philosophy of logic, which includes additional topics like how to define logic or a
discussion of the fundamental concepts of logic. The current article treats philosophical logic in
the narrow sense, in which it forms one field of inquiry within the philosophy of logic.
An important issue for philosophical logic is the question of how to classify the great variety of
non-classical logical systems, many of which are of rather recent origin. One form of
classification often found in the literature is to distinguish between extended logics and deviant
logics. Logic itself can be defined as the study of valid inference. Classical logic is the dominant
form of logic and articulates rules of inference in accordance with logical intuitions shared by
many, like the law of excluded middle, the double negation elimination, and the bivalence of
truth.
Extended logics are logical systems that are based on classical logic and its rules of inference but
extend it to new fields by introducing new logical symbols and the corresponding rules of
inference governing these symbols. In the case of alethic modal logic, these new symbols are
used to express not just what is true simpliciter, but also what is possibly or necessarily true. It is
often combined with possible worlds semantics, which holds that a proposition is possibly true if
it is true in some possible world while it is necessarily true if it is true in all possible worlds.
Deontic logic pertains to ethics and provides a formal treatment of ethical notions, such as
obligation and permission. Temporal logic formalizes temporal relations between propositions.
This includes ideas like whether something is true at some time or all the time and whether it is
true in the future or in the past. Epistemic logic belongs to epistemology. It can be used to
express not just what is the case but also what someone believes or knows to be the case. Its rules
of inference articulate what follows from the fact that someone has these kinds of mental states.
Higher-order logics do not directly apply classical logic to certain new sub-fields within
philosophy but generalize it by allowing quantification not just over individuals but also over
predicates.
Deviant logics, in contrast to these forms of extended logics, reject some of the fundamental
principles of classical logic and are often seen as its rivals. Intuitionistic logic is based on the
idea that truth depends on verification through a proof. This leads it to reject certain rules of
inference found in classical logic that are not compatible with this assumption. Free logic
modifies classical logic in order to avoid existential presuppositions associated with the use of
possibly empty singular terms, like names and definite descriptions. Many-valued logics allow
additional truth values besides true and false. They thereby reject the principle of bivalence of
truth. Paraconsistent logics are logical systems able to deal with contradictions. They do so by
, avoiding the principle of explosion found in classical logic. Relevance logic is a prominent form
of paraconsistent logic. It rejects the purely truth-functional interpretation of the material
conditional by introducing the additional requirement of relevance: for the conditional to be true,
its antecedent has to be relevant to its consequent.
Contents
1 Definition and related fields
2 Classification of logics
3 Classical logic
4 Extended logics
o 4.1 Alethic modal
o 4.2 Deontic
o 4.3 Temporal
o 4.4 Epistemic
o 4.5 Higher-order
5 Deviant logics
o 5.1 Intuitionistic
o 5.2 Free
o 5.3 Many-valued
o 5.4 Paraconsistent
5.4.1 Relevance
6 References
Definition and related fields
The term "philosophical logic" is used by different theorists in slightly different ways.[1] When
understood in a narrow sense, as discussed in this article, philosophical logic is the area of
philosophy that studies the application of logical methods to philosophical problems. This
usually happens in the form of developing new logical systems to either extend classical logic to
new areas or to modify it to include certain logical intuitions not properly addressed by classical
logic.[2][1][3][4] In this sense, philosophical logic studies various forms of non-classical logics, like
modal logic and deontic logic. This way, various fundamental philosophical concepts, like
possibility, necessity, obligation, permission, and time, are treated in a logically precise manner
by formally expressing the inferential roles they play in relation to each other.[5][4][1][3] Some
theorists understand philosophical logic in a wider sense as the study of the scope and nature of
logic in general. On this view, it investigates various philosophical problems raised by logic,
including the fundamental concepts of logic. In this wider sense, it can be understood as identical
to the philosophy of logic, where these topics are discussed.[6][7][8][1] The current article discusses
only the narrow conception of philosophical logic. In this sense, it forms one area of the
philosophy of logic.[1]
