4. Epistemology
Epistemology is the branch of philosophy concerned with the theory of knowledge.
Epistemology is the study, or theory of knowledge, including the questions: What is
knowledge? How is or should it be acquired, tested, stored, revised, updated, and
retrieved?
Much of the debate in epistemology centers on four areas:
1. The philosophical analysis of the nature of knowledge and how it relates to such
concepts as truth, belief, and justification,
2. Various problems of skepticism,
3. The sources and scope of knowledge and justified belief, and
4. The criteria for knowledge and justification.
The eventual demarcation of philosophy from science was made possible by the
notion that philosophy's core was "theory of knowledge," a theory distinct from the
sciences because it was their foundation... Without this idea of a "theory of
knowledge," it is hard to imagine what "philosophy" could have been in the age of
modern science.
— Richard Rorty, Philosophy and the Mirror of Nature
5. Meta Knowledge
Metaknowledge or meta-knowledge is knowledge about a preselected knowledge.
Metaphilosophy
Metaphilosophy (sometimes called philosophy of philosophy) is "the investigation of the nature of philosophy".
• Its subject matter includes the aims of philosophy, the boundaries of philosophy, and its methods.
• is considered by some to be a subject apart from philosophy, while others see it as automatically a part of philosophy
Defining philosophy and its boundaries is itself problematic;
Nigel Warburton has called it "notoriously difficult".
As Bertrand Russell wrote:
"We may note one peculiar feature of philosophy. If someone asks the question what is mathematics, we can give him a
dictionary definition, let us say the science of number, for the sake of argument. As far as it goes this is an uncontroversial
statement... Definitions may be given in this way of any field where a body of definite knowledge exists. But philosophy cannot
be so defined. Any definition is controversial and already embodies a philosophic attitude. The only way to find out what
philosophy is, is to do philosophy."
Bertrand Russell (1959). The Wisdom of the West: A Historical Survey of Western Philosophy in Its Social and Political Setting. Doubleday. p. 7.
6. Meta-epistemology
Meta-epistemology is a metaphilosophical study of the subject, matter, methods and
aims of epistemology and of approaches to understanding and structuring our
knowledge of knowledge itself.
In epistemology, there are two basic meta-epistemological approaches: traditional "normative" epistemology, and naturalized
epistemology.
Naturalized epistemology had its beginnings in the twentieth century with W. V. Quine. Quine's proposal, which is commonly
called "Replacement Naturalism," is to excise every trace of normativity from the epistemological body. Quine wanted to
merge epistemology with empirical psychology such that every epistemological statement would be replaced by a
psychological statement.
Some goals of meta-epistemology are to identify inaccurate traditional assumptions, or hitherto overlooked scope for
generalization.
Thus whereas epistemology has usually been seen as a branch of philosophy, the discussion below also takes examples from biology which
seem equivalent in relevant ways. Also, insofar as philosophy is involved, there may be a case for extending it beyond its traditional domain of
word-based definitions
7. Evolutionary epistemology
Evolutionary epistemology refers to three distinct topics:
1. the biological evolution of cognitive mechanisms in animals and humans,
2. a theory that knowledge itself evolves by natural selection, and
3. the study of the historical discovery of new abstract entities such as abstract number or abstract value that
necessarily precede the individual acquisition and usage of such abstractions.
"Evolutionary epistemology" can refer to a branch of epistemology that applies the concepts of biological evolution to the growth of
animal and human cognition.
It argues that the mind is in part genetically determined and that its structure and function reflect adaptation, a nonteleological
process of interaction between the organism and its environment.
A cognitive trait tending to increase inclusive fitness in a given population should therefore grow more common over time, and a trait
tending to prevent its carriers from passing on their genes should show up less and less frequently.
"Evolutionary epistemology" can refer to a branch of epistemology that applies the concepts of biological evolution to the
growth of animal and human cognition
"Evolutionary epistemology" can also refer to the opposite of (onto)genetic epistemology, namely phylogenetic epistemology as the
historical discovery and reification of abstractions that necessarily precedes the learning of such abstractions by individuals.
• Piaget dismissed this possibility
One of the hallmarks of evolutionary epistemology is the notion that empirical testing alone does not justify the pragmatic
value of scientific theories, but rather that social and methodological processes select those theories with the closest "fit" to a
given problem.
For the evolutionary epistemologist, all theories are true only provisionally, regardless of the degree of empirical testing they
have survived
8. Genetic epistemology
Genetic epistemology is a study of the origins (genesis) of knowledge (epistemology).
The discipline was established by Jean Piaget.
Piaget's genetic epistemology is halfway between formal logic and dialectical logic.
Piaget's genetic epistemology is midway between objective idealism and materialism.
Piaget believed that knowledge is a biological function that results from the actions of an individual through change. He also stated
that knowledge consists of structures, and comes about by the adaptation of these structures with the environment.
Piaget proposes three types of knowledge: physical, logical mathematical, and social knowledge.
9. Constructivist epistemology
Constructivist epistemology is a branch in philosophy of science maintaining that scientific knowledge is constructed
by the scientific community, who seek to measure and construct models of the natural world.
Natural science therefore consists of mental constructs that aim to explain sensory experience (and measurements).
Constructivism opposes the philosophy of objectivism, which embraces the belief that a human can come to know the truth about the
natural world not mediated by scientific approximations, with different degrees of validity and accuracy.
According to constructivists, the world is independent of human minds, but knowledge of the world is always a human and social
construction
According to constructivists there is no single valid methodology in science, but rather a diversity of useful methods
Cultural constructivism
Radical constructivism
Critical constructivism
10. Metaphysics
Metaphysics is a branch of philosophy investigating the fundamental nature of reality.
Topics of metaphysical investigation include existence, objects and their properties, space and time, cause and effect, and possibility.
Another branch is metaphysical cosmology: which seeks to understand the origin and meaning of the universe by thought alone.
Some philosophers and scientists, such as the logical positivists, reject the entire subject of metaphysics as meaningless, while others
disagree and think that it is legitimate.
• Metalogic
• Metamathematics
• Metaphysics
• Meta-ethics
• Meta-ethics
• Metatheory
12. Knowledge
• Sources of Knowledge
• Types of Knowledge
• Levels of Knowledge
• Taxonomies of Knowledge
13. Structure of Knowledge and Justification
• Foundationalism
• Coherentism
Foundationalism
• According to foundationalism, our justified beliefs are structured like a building: they are divided into a foundation and a
superstructure, the latter resting upon the former.
• Beliefs belonging to the foundation are basic.
• Beliefs belonging to the superstructure are nonbasic and receive justification from the justified beliefs in the foundation.
Coherentism
• Foundationalism says that knowledge and justification are structured like a building, consisting of a superstructure that rests upon a
foundation.
• According to coherentism, this metaphor gets things wrong.
• Knowledge and justification are structured like a web where the strength of any given area depends on the strength of the
surrounding areas.
Coherentists, then, deny that there are any basic beliefs.
As we saw in the previous section, there are two different ways of conceiving of basicality. Consequently, there are two corresponding
ways of construing coherentism: as the denial of doxastic basicality or as the denial of epistemic basicality.
15. Sources of Knowledge
Perception
Our perceptual faculties are our five senses: sight, touch, hearing, smelling, and tasting.
Perceptual experience is fallible.
The world is not always as it appears to us in our perceptual experiences.
According to direct realism, we can acquire such knowledge because we can directly perceive such objects. For example, when you see a
tomato on the table, what you perceive is the tomato itself.
According to indirect realism, we acquire knowledge of external objects by virtue of perceiving something else, namely appearances or
sense-data. An indirect realist would say that, when you see and thus know that there is a tomato on the table, what you really see is not
the tomato itself but a tomato-like sense-datum or some such entity.
Direct and indirect realists hold different views about the structure of perceptual knowledge.
16. Sources of Knowledge
Introspection
Introspection is the capacity to inspect the, metaphorically speaking, "inside" of one's mind.
Through introspection, one knows what mental states one is in: whether one is thirsty, tired, excited, or depressed.
Compared with perception, introspection appears to have a special status.
It is easy to see how a perceptual seeming can go wrong: what looks like a cup of coffee on the table might be just be a clever hologram
that's visually indistinguishable from an actual cup of coffee.
But could it be possible that it introspectively seems to me that I have a headache when in fact I do not?
It is not easy to see how it could be. Thus we come to think that introspection has a special status. Compared with perception,
introspection seems to be privileged by virtue of being less error prone. How can we account for the special status of introspection?
First, it could be argued that, when it comes to introspection, there is no difference between appearance and reality; therefore,
introspective seemings are necessarily successful introspections.
According to this approach, introspection is infallible.
Critics of foundationalism have argued that introspection is certainly not infallible.
Might one not confuse an unpleasant itch for a pain?
Might I not think that the shape before me appears circular to me when in fact it appears slightly elliptical to me?
17. Sources of Knowledge
Memory
Memory is the capacity to retain knowledge acquired in the past.
What one remembers, though, need not be a past event.
It may be a present fact, such as one's telephone number, or a future event, such as the date of the next elections.
Memory is, of course, fallible
One issue about memory concerns the question of what distinguishes memorial seemings from perceptual seemings or mere imagination.
Some philosophers have thought that having an image in one's mind is essential to memory, but that would appear to be mistaken. When one
remembers one's telephone number, one is unlikely to have an image of one's number in one's mind.
18. Sources of Knowledge
Reason
Some beliefs would appear to be justified solely by the use of reason. Justification of that kind is said to be a priori: prior to any kind of
experience.
What exactly counts as experience? If by ‘experience’ we mean just perceptual experiences, justification deriving from introspective or
memorial experiences would count as a priori. For example, I could then know a priori that I'm thirsty, or what I ate for breakfast this morning
Justification and knowledge that is not a priori is called ‘a posteriori’ or ‘empirical’.
Several important issues arise about a priori knowledge.
1. First, does it exist at all?
2. Second, if a priori justification is possible, exactly how does it come about?
3. Third, if a priori knowledge exists, what is its extent?
1. Empiricists have argued that a priori knowledge is limited to the realm of the analytic, consisting of propositions of a somehow
inferior status because they are not really "about the world". Propositions of a superior status, which convey genuine information
about world, are labeled synthetic. a priori knowledge of synthetic propositions, empiricists would say, is not possible. Rationalists
deny this. They would say that a proposition such as "If a ball is green all over, then it doesn't have black spots" is synthetic and
knowable a priori.
4. A fourth question about the nature of a priori knowledge concerns the distinction between necessary and contingent truths. The received
view is that whatever is known a priori is necessarily true, but there are epistemologists who disagree with that.
19. Sources of Knowledge
Testimony
Testimony differs from the sources we considered above because it isn't distinguished by having its own cognitive faculty.
The epistemological puzzle testimony raises is this: Why is testimony a source of knowledge?
An externalist might say that testimony is a source of knowledge if and only if it comes from a reliable source.
But here, even more so than in the case of our faculties, internalists will not find that answer satisfactory.
Suppose you hear someone saying ‘p’. Suppose further that person is in fact utterly reliable with regard to the question of whether p is the
case or not. Finally, suppose you have no evidential clue whatever as to that person's reliability. Wouldn't it be plausible to conclude that,
since that person's reliability is unknown to you, that person's saying ‘p’ does not put you in a position to know that p? But if the reliability of a
testimonial source is not sufficient for making it a source of knowledge, what else is needed? Thomas Reid suggested that, by our very nature,
we accept testimonial sources as reliable and tend to attribute credibility to them unless we encounter special contrary reasons. But that's
merely a statement of the attitude we in fact take toward testimony. What is it that makes that attitude reasonable? It could be argued that, in
one's own personal experiences with testimonial sources, one has accumulated a long track record that can be taken as a sign of reliability.
However, when we think of the sheer breadth of the knowledge we derive from testimony, one wonders whether one's personal experiences
constitute an evidence base rich enough to justify the attribution of reliability to the totality of the testimonial sources one tends to trust. An
alternative to the track record approach would be to declare it a necessary truth that trust in testimonial sources is justified. This suggestion,
alas, encounters the same difficulty as the externalist approach to testimony: it does not seem we can acquire knowledge from sources the
reliability of which is utterly unknown to us.[
20. Knowledge - Definition
A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols).
Definitions can be classified into two large categories,
• intensional definitions (which try to give the essence of a term) and
• extensional definitions (which proceed by listing the objects that a term describes).
• Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out
examples.
Definitions have one of the following three limitations
1. Infinite Regression
2. Circulaity/ Recursive
3. Rely upon some Primitive Notions
Many philosophers have chosen instead to leave some terms undefined.
• The scholastic philosophers claimed that the highest genera (the so-called ten generalissima) cannot be defined, since a higher genus
cannot be assigned under which they may fall. Thus being, unity and similar concepts cannot be defined.
• Locke supposes in An Essay Concerning Human Understanding that the names of simple concepts do not admit of any definition.
• Mill also argued that individuals cannot be defined.
Wittgenstein, rejected the need for any undefined simples.
He rejected the very idea that every explanation of the meaning of a term needed itself to be explained: "As though an explanation hung
in the air unless supported by another one",claiming instead that explanation of a term is only needed to avoid misunderstanding.
Limitations of Definition
21. Knowledge - Definition
Fallacies of definition are the various ways in which definitions can fail to explain terms
Fallacies of Definition
• Three major fallacies are
1. overly broad,
2. overly narrow, and
3. mutually exclusive definitions.
• Fourth is incomprehensible definitions
The most common is circular definitions
22. Starting Basis
In epistemology (theory of knowledge), a self-evident proposition is one that is known to be true by understanding its meaning without
proof,[citation needed] and/or by ordinary human reason.
Epistemology - Self-evidence
Some epistemologists deny that any proposition can be self-evident.
The following proposition is often said to be self-evident: A finite whole is greater than, or equal to, any of its parts
In informal speech, self-evident often merely means obvious, but the epistemological definition is more strict.
A famous claim of the self-evidence of a moral truth is in the United States Declaration of Independence, which states, "We hold these Truths
to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these
are Life, Liberty and the pursuit of Happiness."; philosophically, these propositions' self-evidence is debatable.
23. Starting Basis
A truism is a claim that is so obvious or self-evident as to be hardly worth mentioning, except as a reminder or as a rhetorical or literary
device, and is the opposite of falsism.
Rhetoric - Truism
In philosophy, a sentence which asserts incomplete truth conditions for a proposition may be regarded as a truism. An example of such a
sentence would be "Under appropriate conditions, the sun rises." Without contextual support – a statement of what those appropriate
conditions are – the sentence is true but incontestable. A statement which is true by definition (for example, the Lapalissade "If he were not
dead, he would still be alive") would also be considered a truism.
The word may also be used with a different sense in rhetoric, to disguise the fact that a proposition is really just an opinion.
Similarly, stating an accepted truth about life in general can also be called a truism.
• A falsism is a claim that is clearly and self-evidently wrong. A falsism is usually used merely as a reminder or as a rhetorical or literary
device. An example is "pigs can fly." It is the opposite of truism.
• A falsism is similar to, though not the same as, a fallacy
Falsism
24. Starting Basis
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.‘
Among the ancient Greek philosophers an axiom was a claim which could be seen to be true without any need for proof.
Mathematics - Axiom
In mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms".
In both senses, an axiom is any mathematical statement that serves as a starting point from which other statements are logically derived.
Within
In informal speech, self-evident often merely means obvious, but the epistemological definition is more strict.
A famous claim of the self-evidence of a moral truth is in the United States Declaration of Independence, which states, "We hold these Truths
to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these
are Life, Liberty and the pursuit of Happiness."; philosophically, these propositions' self-evidence is debatable.
25. Starting Basis
• In mathematics, logic, and formal systems, a primitive notion is an undefined concept.
• In particular, a primitive notion is not defined in terms of previously defined concepts, but is only motivated informally, usually by an
appeal to intuition and everyday experience.
Logic - Primitive Notion
An inevitable regress to primitive notions in the theory of knowledge was explained by Gilbert de B. Robinson:
To a non-mathematician it often comes as a surprise that it is impossible to define explicitly all the terms which are used. This is not a
superficial problem but lies at the root of all knowledge; it is necessary to begin somewhere, and to make progress one must clearly state
those elements and relations which are undefined and those properties which are taken for granted.
Gilbert de B. Robinson (1959) Foundations of Geometry, 4th edition, page 8, University of Toronto Press
Examples
• Set theory, the concept of the set is an example of a primitive notion.
• Euclidean geometry, under Hilbert's axiom system the primitive notions are point, line, plane, congruence, betweeness, and incidence.
• Euclidean geometry, under Peano's axiom system the primitive notions are point, segment, and motion.
• Philosophy of mathematics, Bertrand Russell considered the "indefinables of mathematics" to build the case for logicism in his book The
Principles of Mathematics (1903).
26. Starting Basis
• A premise or premiss is a statement that an argument claims will induce or justify a conclusion.
• In other words: a premise is an assumption that something is true.
Philosophy- Premise
Aristotle held that any logical argument could be reduced to two premises and a conclusion.
Premises are sometimes left unstated in which case they are called missing premises, for example
Socrates is mortal because all men are mortal.
It is evident that a tacitly understood claim is that Socrates is a man.
Syllogism
All men are mortal - Premise
Socrates is a man - Premise
Socrates is mortal - Conclusion
The proof of a conclusion depends on both the truth of the premises and the validity of the argument.
27. Starting Basis
• In the branch of linguistics known as pragmatics, a presupposition (or PSP) is an implicit assumption about the world or background
belief relating to an utterance whose truth is taken for granted in discourse.
Linguistics - Presupposition
A presupposition must be mutually known or assumed by the speaker and addressee for the utterance to be considered appropriate in
context. It will generally remain a necessary assumption whether the utterance is placed in the form of an assertion, denial, or question, and
can be associated with a specific lexical item or grammatical feature (presupposition trigger) in the utterance.
Examples
Jane no longer writes fiction.
Presupposition: Jane once wrote fiction.
Have you stopped eating meat?
Presupposition: you had once eaten meat.
Have you talked to Hans?
Presupposition: Hans exists.
Crucially, negation of an expression does not change its presuppositions:
Example
I want to do it again and I don't want to do it again both presuppose that the subject has done it already one or more times;
My wife is pregnant and My wife is not pregnant both presuppose that the subject has a wife
28. Starting Basis
• A principle is a law or rule that has to be, or usually is to be followed, or can be desirably followed, or is an inevitable consequence of
something, such as the laws observed in nature or the way that a system is constructed.
• The principles of such a system are understood by its users as the essential characteristics of the system, or reflecting system's designed
purpose, and the effective operation or use of which would be impossible if any one of the principles was to be ignored
Principle
Exemplary principles include First, do no harm, the golden rule and the doctrine of the mean
The principle of legality is the legal ideal that requires all law to be clear, ascertainable and non-retrospective
Principle of excluded middle
Moral Law
Juridic law
29. Starting Basis
• In the law of evidence, a presumption of a particular fact can be made without the aid of proof in some situations.
• The types of presumption include a rebuttable discretionary presumption, a rebuttable mandatory presumption, and an irrebuttable or
conclusive presumption.
• Presumptions are sometimes categorized into two types: presumptions without basic facts, and presumptions with basic facts
• An example of presumption without basic facts is presumption of innocence.
• An example of presumption with basic facts is Declared death in absentia, e.g., the law says if a person has been missing for seven years or
more (basic fact), that person is presumed dead
• In the United States, mandatory presumptions are impermissible in criminal cases, but permissible presumptions are allowed.
• The ancient Jewish law code, the Talmud, included reasoning from presumptions (hazakah), propositions taken to be true unless there was
reason to believe otherwise, such as "One does not ordinarily pay a debt before term.“
• The same concept was found in ancient Roman law, where, for example, if there was doubt as to whether a child was really the issue of
someone who had left money in a will, the presumption was in favour of the child
• Medieval Roman and canon law graded presumptions according to strength: light, medium or probable, and violent.
• These gradings and many individual presumptions were taken over into English law in the seventeenth century
Presumption
30. Starting Basis
Specific presumptions
Examples of these presumptions include:
The presumption of death. A person who has been absent for seven years without explanation and "gone to parts unknown" is presumed
dead at common law.[6] The time period it takes for the presumption to arise has often been modified by statute.[7]
The presumption of sanity. A person who faces criminal trial is presumed sane until the opposite is proved. Similarly, a person is presumed to
have testamentary capacity until there is evidence to undermine that presumption.
The presumption of innocence, which holds that the prosecution bears the burden of proof in a criminal case with the result that the accused
may be acquitted without putting forward any evidence.
The presumption of legitimacy or presumption of paternity, which presumes that a husband is the biological father of a child born to his wife
during the marriage, or within nine months after the marriage is ended by death, legal separation, or divorce.[8] Some jurisdictions also hold
that a presumption of paternity arises when a father accepts a child into his home, or publicly represents that he is the child's father.[9]
A presumption of survivorship has referred to a number of different presumptions. The term is sometimes used to refer to presumptions that
one or another of two persons lived the longer when they died together in the same accident.[10] The presumption that two or more people
who establish a joint account intend for the survivors to have the assets put into the fund upon the death of one of the joint account holders
has also been called the "presumption of survivorship".[11]
The presumption of mailing presumes that a properly addressed letter delivered to the post office or a common carrier was in fact delivered
and received by the addressee.[12]
The presumption of fraud or undue influence arises where a person in a position of trust over another, such as a guardian or the holder of a
power of attorney applies the other person's assets to his or her own benefit.[13]
The presumption of validity is another way of expressing a burden of proof: the official acts of courts are presumed valid, and those who
would challenge them must overcome this presumption.[14] This is also termed the presumption of regularity.[15]
The presumption of advancement in relation to transfers from husbands to wives and from fathers to children.
In the law of the United States, the presumption of constitutionality presumes that all statutes are drafted in accordance with Federal and
state constitutional requirements. The party challenging the constitutionality of a statute bears the burden of proof, and any doubts are
resolved against that party. If there are two reasonable interpretations of a statute, one of which is constitutional and the other not, the
courts choose the path that permits upholding the statute.[16
Presumption
31. Starting Basis
Dogma is an English term transliterated in the 17th century from Latin (Latin dogma) meaning "philosophical tenet", derived from the Greek
'dogma' (Greek δόγμα) meaning literally "that which one thinks is true" and 'dokein' (Greek dokeo) "to seem good.“
Religion - Dogma
The term "dogma" is sometimes used metaphorically, often disparagingly, to refer to a body of positions held in a non-religious contexts such
as in politics and science.
A notable use of the term can be found in the Central Dogma of Molecular Biology. In his autobiography, What Mad Pursuit, Francis Crick
wrote about his choice of the word dogma:
"I called this idea the central dogma, for two reasons, I suspect. I had already used the obvious word hypothesis in the sequence hypothesis,
and in addition I wanted to suggest that this new assumption was more central and more powerful. ... As it turned out, the use of the word
dogma caused almost more trouble than it was worth."
32. Starting Basis
A creed (also known as a confession, symbol, or statement of faith) is a statement of the shared beliefs of a religious community in the form of
a fixed formula summarizing core tenets.
Religion - Creed
Muslims declare the shahada, or testimony: "I bear witness that there is no god but (the One) God (Allah), and I bear witness that Muhammad
is God's messenger."
Whether Judaism is creedal has been a point of some controversy. Although some say Judaism is noncreedal in nature, others say it recognizes
a single creed, the Shema Yisrael, which begins: "Hear, O Israel: the LORD our God, the LORD is one."[
One of the most widely used creeds in Christianity is the Nicene Creed, first formulated in AD 325 at the First Council of Nicaea.
33. Fact
A fact is something that has occurred or is correct.
The usual test for a statement of fact is verifiability—that is, whether it can be demonstrated to correspond to experience.
The fact-value distinction emerged in philosophy in the Enlightenment. In particular, David Hume (1711–1776) argued that human beings are
unable to ground normative arguments in positive arguments, that is, to derive ought from is.
• Virtually all modern philosophers affirm some sort of fact-value distinction, insofar as they distinguish between science and "valued"
disciplines such as ethics, aesthetics, or the fine arts.
• However, philosophers such as Hilary Putnam argue that the distinction between fact and value is not as absolute as Hume envisioned.
The fact-value distinction is the distinction between things that can be known to be true and things that are the personal preferences of
individuals.
Fact–value distinction
34. Logical atomism
The theory holds that the world consists of ultimate logical "facts" (or "atoms") that cannot be broken down any further.
The first principle of logical atomism is that the World contains "facts".
Having originally propounded this stance in his Tractatus Logico-Philosophicus, Wittgenstein rejected it in his later Philosophical Investigations
(secs. 46–49, 91 and sec. 81).
Ruseell also eventually rejected Logical Atomism.
Logical atomism is a philosophical belief that originated in the early 20th century with the development of analytic philosophy.
Its principal exponents were the British philosopher Bertrand Russell, the early work of his Austrian-born pupil and colleague Ludwig
Wittgenstein, and his German counterpart Rudolf Carnap.
35. Is–ought problem
The is–ought problem, as articulated by Scottish philosopher and historian David Hume (1711–76), states that many writers make claims
about what ought to be on the basis of statements about what is.
Indefinables are concepts so global that they cannot be defined; rather, in a sense, they themselves, and the objects to which they refer,
define our reality and our ideas. Their meanings cannot be stated in a true definition, but their meanings can be referred to instead by being
placed with their incomplete definitions in self-evident statements, the truth of which can be tested by whether or not it is impossible to think
the opposite without a contradiction. Thus, the truth of indefinable concepts and propositions using them is entirely a matter of logic.
Hume found that there seems to be a significant difference between positive statements (about what is) and prescriptive or normative
statements (about what ought to be), and that it is not obvious how one can coherently move from descriptive statements to prescriptive
ones.
The is–ought problem is also known as Hume's law, or Hume's guillotine.
Indefinables
37. Logicism
Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic
and therefore some or all mathematics is reducible to logic
Kurt Gödel's incompleteness theorem undermines logicism because it shows that no particular axiomatization of mathematics can decide all
statements.
Some believe that the basic spirit of logicism remains valid because that theorem is proved with logic just like other theorems.
Logicism was key in the development of analytic philosophy in the twentieth century.
The problem of presuming the "extralogical" notion of "iteration":
Kleene points out that, "the logicistic thesis can be questioned finally on the ground that logic already presupposes mathematical ideas in its
formulation. In the Intuitionistic view, an essential mathematical kernel is contained in the idea of iteration" (Kleene 1952:46)
38. Logic
Logic (from the Ancient Greek: λογική, logikḗ[1]), originally meaning "the word" or "what is spoken" (but coming to mean "thought" or
"reason"), is generally held to consist of the systematic study of the form of arguments.
There is no universal agreement as to the exact scope and subject matter of logic (see § Rival conceptions, below), but it has traditionally
included the classification of arguments, the systematic exposition of the 'logical form' common to all valid arguments, the study of inference,
including fallacies, and the study of semantics, including paradoxes.
Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid-1800s), and recently logic has been
studied in computer science, linguistics, psychology, and other fields.
Is Logic Empirical?
Is Logic Empirical?" is the title of two articles (one by Hilary Putnam and another by Michael Dummett)that discuss the idea that the algebraic
properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about
quantum phenomena may provide grounds for revising classical logic as a consistent logical rendering of reality.
39. Different “Types” of Logic
Classical logic
Examples of classical logics
• Aristotle's Organon introduces his theory of syllogisms
• George Boole's algebraic reformulation of logic, his system of Boolean logic
• The first-order logic found in Gottlob Frege's Begriffsschrift.
Non-classical logics
Computability logic is a semantically constructed formal theory of computability—as opposed to classical logic, which is a formal theory of
truth—integrates and extends classical, linear and intuitionistic logics.
Many-valued logic, including fuzzy logic, which rejects the law of the excluded middle and allows as a truth value any real number between 0
and 1.
Intuitionistic logic rejects the law of the excluded middle, double negative elimination, and the De Morgan's laws;
Linear logic rejects idempotency of entailment as well;
Modal logic extends classical logic with non-truth-functional ("modal") operators.
Paraconsistent logic (e.g., dialetheism and relevance logic) rejects the law of noncontradiction;
Quantum logic
Relevance logic, linear logic, and non-monotonic logic reject monotonicity of entailment;
In Deviant Logic, Fuzzy Logic: Beyond the Formalism, Susan Haack divided non-classical logics into deviant, quasi-deviant, and extended
logics.
40. Classical logic
Classical logic (or standard logic) is an intensively studied and widely used class of formal logics. Each logical system in this class shares
characteristic properties:
1. Law of excluded middle and double negative elimination
2. Law of noncontradiction, and the principle of explosion
3. Monotonicity of entailment and idempotency of entailment
4. Commutativity of conjunction
5. De Morgan duality: every logical operator is dual to another
• While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include propositional and first-
order logics.
• Classical logic was originally devised as a two-level (bivalent) logical system, with simple semantics for the levels representing "true" and
"false“.
Deviant logic
Philosopher Susan Haack[1] uses the term "deviant logic" to describe certain non-classical systems of logic. In these logics,
• the set of well-formed formulas generated equals the set of well-formed formulas generated by classical logic.
• the set of theorems generated is different from the set of theorems generated by classical logic.
Achille Varzi in his review[2] of the 1996 edition of Haack's book writes that the survey did not stand well the test of time, particularly with the
"extraordinary proliferation of nonclassical logics in the past two decades—paraconsistent logics, linear logics, substructural logics,
nonmonotonic logics, innumerable other logics for AI and computer science." He also finds that Haack's account of vagueness "is now
seriously defective."
He concedes however that "as a defense of a philosophical position, Deviant Logic retains its significance."
41. Dialetheism
Dialetheism is the view that some statements can be both true and false simultaneously. More precisely, it is the belief that there can be a
true statement whose negation is also true. Such statements are called "true contradictions", dialetheia, or nondualisms.
Dialetheism is not a system of formal logic; instead, it is a thesis about truth that influences the construction of a formal logic, often based on
pre-existing systems.
Graham Priest defines dialetheism as the view that there are true contradictions.
The Jain philosophical doctrine of anekantavada — non-one-sidedness — states that[5] all statements are true in some sense and false in
another. Some interpret this as saying that dialetheia not only exist but are ubiquitous.
The Buddhist logic system named Catuṣkoṭi similarly implies that a statement and its negation may possibly co-exist.
Many modern Zen Buddhists are dialetheists. They use the term nondualism to refer to true contradictions.
Graham Priest argues in Beyond the Limits of Thought that dialetheia arise at the borders of expressibility, in a number of philosophical
contexts other than formal semantics.
According to dialetheists, there are some truths that can only be expressed in contradiction. Some examples include:
• The only certain knowledge we have outside of our immediate experience is that there is no certain knowledge outside of our immediate
experience.
• "All statements are true" is a false statement.
• "There are no absolutes" is an absolute.
According to dialetheists, these statements are not derived from logic, but are instead descriptions of experience.
Examples of true contradictions that
dialetheists accept
