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induction not justified in theory of knowledge
equivalent to saying "known by experience"
induction = proceed from singular statements to universals
singular statements known by experience
principle of induction is a universal statement
can we know its truth from experience? leads to infinite regress
or a priori true
inductive logic insurmountable
rejects probability on the same grounds as truth
psychology of knowledge deals with empirical facts
logic of knowledge deals with logical relation
belief in inductive logic due largely to confusion of psychology with epistemology
4 different ways in which the testing of a theory could be carried out
1. internal consistency (logical comparison of statements)
2. decide if it's empirical or tautological
3. compare with other theories to see if it's an advance in knowledge
4. testing theory by way of empirical applications of the conclusions that can be drawn from it
singular conclusions can be verified
temporarily support theory, but can always be overthrown
corroborated but not verified if withstands detailed and severe tests
demarcation between metaphysics and empirical sciences
older positivists wanted to accept only the concepts which were derived from experience
positivists, instead of proposing a suitable convention, are trying to discover a natural difference in which metaphysics is meaningless
Wittgenstein says every meaningful proposition must be reduced to elementary/atomic propositions
but this means no natural laws either, so empirical, natural science is left hurting
Popper's criterion of demarcation is a convention
he thinks the only way to defend it is by a value judgment: how useful is it?
Criteria for empirical systems:
1. Synthetic, non-contradictory
2. Must be not tautological/metaphysical, but describe a possible world of experience
3. Must distinguish our experienced world from other possible worlds
3 means has been subjected to tests
positivists say that science must be verifiable and falsifiable
no such thing as induction in Popper's view
falsifiable means testable, refutable by experience
universal statements not derivable from singular statements, but falsifiable by them
it is logically possible to avoid falsification by rejecting apparent falsifications
Popper says his empirical method shall be defined as not doing that, i.e. by being rigorous about testing theories
survival of the fittest (meme!)
objective, empirical theories must be intersubjectively testable, reproducible
subjective experience is only psychological
intersubjective testability means from any statement that is to be tested, other testable statements can be derived
this means infinite regress, and no ultimate statements
Popper says "need not have been tested", need only be logically testable
tests must be finite, obviously
positivists see empirical science as a system of statements that meet certain logical criteria, such as meaningfulness or verifiability
Popper sees the distinguishing characteristic as their being subject to revision, supersession by better ones
upholding a theory until it has been conclusively disproved is bad science, confirmation bias
no strict disproof (as already seen) or proof possible
methodology is not an empirical science
methodological rules are conventions for defining the "game of science"
when you declare no further need for testing, you stop playing
don't reject theories that have proved their mettle without good reason (a better hypothesis, or falsification of one of the conclusions)
causation means universal laws plus initial conditions
the notion that everything has a cause is not falsifiable
but Popper says as a convention that you can't stop looking
existential statements can't be falsified by the absence of singular statements
universal statements that prohibit can be falsified by a singular statement
theoretical system is axiomatized if
1) non contradictory
2) independent (no axiom deducible from the remaining)
3) sufficient for the deduction of all the conclusions to be drawn from it
4) necessary (no superfluous axioms)
implicit definitions
higher-level universal theories
lower-level universal statements can be deduced from them
we decide that we will test our theories rigorously and not try to save them by resorting to stratagems
this is a decision that we make because it's useful to us
introduce new hypotheses only those that do not diminish the testability of the system, but increases it (not sure if it stays the same, guessing doesn't add anything)
We define a theory as empirical if it allows us to deduce more empirical singular statements than we can deduce from the initial conditions alone
It's falsifiable if it divides the set of all possible basic statements into those that are incompatible with it (non-empty set) and those that are compatible with it (but not verified by it).
Falsifiability means the set of potential falsifiers is not empty.
Falsified means we have accepted a basic statement that is incompatible with the theory.
We reject inconsistent theories not merely because they're false (because approximations are sometimes useful) but because any statement can be derived from a logically contradictory (not merely false) system, and thus they're not falsifiable and don't rule anything about about the universe.
The problem of the empirical basis.
In some ways, yes, math & logic are thought and hard sciences proceed through sense-experience.
But our feelings of conviction are not the point.
Intersubjectively reproducible steps are the point.
You can't say "I deduced X because it made a strong impression on my senses and I was convinced." You have to say, "If you do A, B, and C, you will observe X."
equivalent to saying "known by experience"
induction = proceed from singular statements to universals
singular statements known by experience
principle of induction is a universal statement
can we know its truth from experience? leads to infinite regress
or a priori true
inductive logic insurmountable
rejects probability on the same grounds as truth
psychology of knowledge deals with empirical facts
logic of knowledge deals with logical relation
belief in inductive logic due largely to confusion of psychology with epistemology
4 different ways in which the testing of a theory could be carried out
1. internal consistency (logical comparison of statements)
2. decide if it's empirical or tautological
3. compare with other theories to see if it's an advance in knowledge
4. testing theory by way of empirical applications of the conclusions that can be drawn from it
singular conclusions can be verified
temporarily support theory, but can always be overthrown
corroborated but not verified if withstands detailed and severe tests
demarcation between metaphysics and empirical sciences
older positivists wanted to accept only the concepts which were derived from experience
positivists, instead of proposing a suitable convention, are trying to discover a natural difference in which metaphysics is meaningless
Wittgenstein says every meaningful proposition must be reduced to elementary/atomic propositions
but this means no natural laws either, so empirical, natural science is left hurting
Popper's criterion of demarcation is a convention
he thinks the only way to defend it is by a value judgment: how useful is it?
Criteria for empirical systems:
1. Synthetic, non-contradictory
2. Must be not tautological/metaphysical, but describe a possible world of experience
3. Must distinguish our experienced world from other possible worlds
3 means has been subjected to tests
positivists say that science must be verifiable and falsifiable
no such thing as induction in Popper's view
falsifiable means testable, refutable by experience
universal statements not derivable from singular statements, but falsifiable by them
it is logically possible to avoid falsification by rejecting apparent falsifications
Popper says his empirical method shall be defined as not doing that, i.e. by being rigorous about testing theories
survival of the fittest (meme!)
objective, empirical theories must be intersubjectively testable, reproducible
subjective experience is only psychological
intersubjective testability means from any statement that is to be tested, other testable statements can be derived
this means infinite regress, and no ultimate statements
Popper says "need not have been tested", need only be logically testable
tests must be finite, obviously
positivists see empirical science as a system of statements that meet certain logical criteria, such as meaningfulness or verifiability
Popper sees the distinguishing characteristic as their being subject to revision, supersession by better ones
upholding a theory until it has been conclusively disproved is bad science, confirmation bias
no strict disproof (as already seen) or proof possible
methodology is not an empirical science
methodological rules are conventions for defining the "game of science"
when you declare no further need for testing, you stop playing
don't reject theories that have proved their mettle without good reason (a better hypothesis, or falsification of one of the conclusions)
causation means universal laws plus initial conditions
the notion that everything has a cause is not falsifiable
but Popper says as a convention that you can't stop looking
existential statements can't be falsified by the absence of singular statements
universal statements that prohibit can be falsified by a singular statement
theoretical system is axiomatized if
1) non contradictory
2) independent (no axiom deducible from the remaining)
3) sufficient for the deduction of all the conclusions to be drawn from it
4) necessary (no superfluous axioms)
implicit definitions
higher-level universal theories
lower-level universal statements can be deduced from them
we decide that we will test our theories rigorously and not try to save them by resorting to stratagems
this is a decision that we make because it's useful to us
introduce new hypotheses only those that do not diminish the testability of the system, but increases it (not sure if it stays the same, guessing doesn't add anything)
We define a theory as empirical if it allows us to deduce more empirical singular statements than we can deduce from the initial conditions alone
It's falsifiable if it divides the set of all possible basic statements into those that are incompatible with it (non-empty set) and those that are compatible with it (but not verified by it).
Falsifiability means the set of potential falsifiers is not empty.
Falsified means we have accepted a basic statement that is incompatible with the theory.
We reject inconsistent theories not merely because they're false (because approximations are sometimes useful) but because any statement can be derived from a logically contradictory (not merely false) system, and thus they're not falsifiable and don't rule anything about about the universe.
The problem of the empirical basis.
In some ways, yes, math & logic are thought and hard sciences proceed through sense-experience.
But our feelings of conviction are not the point.
Intersubjectively reproducible steps are the point.
You can't say "I deduced X because it made a strong impression on my senses and I was convinced." You have to say, "If you do A, B, and C, you will observe X."
