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Single Idea 13002
[filed under theme 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
]
Full Idea
To reduce the number of axioms is always something gained.
Gist of Idea
It is always good to reduce the number of axioms
Source
Gottfried Leibniz (New Essays on Human Understanding [1704], 4.06)
Book Ref
Leibniz,Gottfried: 'New Essays on Human Understanding', ed/tr. Remnant/Bennett [CUP 1996], p.407
A Reaction
This is rather revealing about the nature of axioms. They don't have any huge metaphysical status - in fact one might say that their status is epistemological, or even pedagogic. They enable us to get out minds round things.
The
476 ideas
from Gottfried Leibniz
19392
|
I don't recommend universal doubt; we constantly seek reasons for things which are indubitable
[Leibniz]
|
12735
|
Everything has a fixed power, as required by God, and by the possibility of reasoning
[Leibniz]
|
16709
|
Some people return to scholastic mysterious qualities, disguising them as 'forces'
[Leibniz]
|
13192
|
Power is passive force, which is mass, and active force, which is entelechy or form
[Leibniz]
|
13193
|
Active force is not just potential for action, since it involves a real effort or striving
[Leibniz]
|
13194
|
God's laws would be meaningless without internal powers for following them
[Leibniz]
|
13195
|
To explain a house we must describe its use, as well as its parts
[Leibniz]
|
13196
|
All qualities of bodies reduce to forces
[Leibniz]
|
12742
|
A whole is just its parts, but there are no smallest parts, so only minds and perceptions exist
[Leibniz]
|
12693
|
A body is that which exists in space
[Leibniz]
|
12700
|
Form or soul gives unity and duration; matter gives multiplicity and change
[Leibniz]
|
12699
|
A body would be endless disunited parts, if it did not have a unifying form or soul
[Leibniz]
|
12736
|
If we understand God and his choices, we have a priori knowledge of contingent truths
[Leibniz, by Garber]
|
12698
|
Every body contains a kind of sense and appetite, or a soul
[Leibniz]
|
12734
|
Every necessary proposition is demonstrable to someone who understands
[Leibniz]
|
12733
|
Because of the definitions of cause, effect and power, cause and effect have the same power
[Leibniz]
|
12743
|
A true being must (unlike a chain) have united parts, with a substantial form as its subject
[Leibniz]
|
12714
|
The substantial form is the principle of action or the primitive force of acting
[Leibniz]
|
12710
|
As well as extension, bodies contain powers
[Leibniz]
|
12702
|
Causes can be inferred from perfect knowledge of their effects
[Leibniz]
|
12712
|
Substance is that which can act
[Leibniz]
|
12737
|
Nature can be fully explained by final causes alone, or by efficient causes alone
[Leibniz]
|
19389
|
Truth is a characteristic of possible thoughts
[Leibniz]
|
19388
|
True and false seem to pertain to thoughts, yet unthought propositions seem to be true or false
[Leibniz]
|
7558
|
Substances mirror God or the universe, each from its own viewpoint
[Leibniz]
|
2119
|
People argue for God's free will, but it isn't needed if God acts in perfection following supreme reason
[Leibniz]
|
5023
|
Future contingent events are certain, because God foresees them, but that doesn't make them necessary
[Leibniz]
|
12711
|
The immediate cause of movements is more real [than geometry]
[Leibniz]
|
5024
|
Knowledge doesn't just come from the senses; we know the self, substance, identity, being etc.
[Leibniz]
|
5025
|
Mind and body can't influence one another, but God wouldn't intervene in the daily routine
[Leibniz]
|
5026
|
Animals lack morality because they lack self-reflection
[Leibniz]
|
5027
|
If a person's memories became totally those of the King of China, he would be the King of China
[Leibniz]
|
13085
|
Leibniz is some form of haecceitist
[Leibniz, by Cover/O'Leary-Hawthorne]
|
19349
|
The complete notion of a substance implies all of its predicates or attributes
[Leibniz]
|
13088
|
Subjects include predicates, so full understanding of subjects reveals all the predicates
[Leibniz]
|
16761
|
Forms are of no value in physics, but are indispensable in metaphysics
[Leibniz]
|
19342
|
Reason avoids multiplying hypotheses or principles
[Leibniz]
|
5035
|
The two basics of reasoning are contradiction and sufficient reason
[Leibniz]
|
5037
|
God doesn't decide that Adam will sin, but that sinful Adam's existence is to be preferred
[Leibniz]
|
5038
|
Assume that mind and body follow their own laws, but God has harmonised them
[Leibniz]
|
12741
|
If experience is just a dream, it is still real enough if critical reason is never deceived
[Leibniz]
|
12740
|
The strongest criterion that phenomena show reality is success in prediction
[Leibniz]
|
12721
|
Light, heat and colour are apparent qualities, and so are motion, figure and extension
[Leibniz]
|
19387
|
Hypotheses come from induction, which is comparison of experiences
[Leibniz]
|
19400
|
Possibles demand existence, so as many of them as possible must actually exist
[Leibniz]
|
19401
|
God's sufficient reason for choosing reality is in the fitness or perfection of possibilities
[Leibniz]
|
19402
|
The actual universe is the richest composite of what is possible
[Leibniz]
|
5039
|
If non-existents are possible, their existence would replace what now exists, which cannot therefore be necessary
[Leibniz]
|
5040
|
Necessary truths can be analysed into original truths; contingent truths are infinitely analysable
[Leibniz]
|
5041
|
God does everything in a perfect way, and never acts contrary to reason
[Leibniz]
|
13159
|
Only God sees contingent truths a priori
[Leibniz]
|
13162
|
Sloth's Syllogism: either it can't happen, or it is inevitable without my effort
[Leibniz]
|
19339
|
Evil is a negation of good, which arises from non-being
[Leibniz]
|
13163
|
Circles must be bounded, so cannot be infinite
[Leibniz]
|
13164
|
God only made sin possible because a much greater good can be derived from it
[Leibniz]
|
13083
|
The essence is the necessary properties, and the concept includes what is contingent
[Leibniz]
|
19398
|
Minds are best explained by their ends, and bodies by efficient causes
[Leibniz]
|
19376
|
A machine is best defined by its final cause, which explains the roles of the parts
[Leibniz]
|
19405
|
Substances are in harmony, because they each express the one reality in themselves
[Leibniz]
|
2116
|
The concept of an existing thing must contain more than the concept of a non-existing thing
[Leibniz]
|
13082
|
The complete concept of an individual includes contingent properties, as well as necessary ones
[Leibniz]
|
19399
|
Prime matter is nothing when it is at rest
[Leibniz]
|
22908
|
When one element contains the grounds of the other, the first one is prior in time
[Leibniz]
|
7931
|
If a substance is just a thing that has properties, it seems to be a characterless non-entity
[Leibniz, by Macdonald,C]
|
7644
|
The monad idea incomprehensibly spiritualises matter, instead of materialising soul
[La Mettrie on Leibniz]
|
11857
|
He replaced Aristotelian continuants with monads
[Leibniz, by Wiggins]
|
7843
|
Is a drop of urine really an infinity of thinking monads?
[Voltaire on Leibniz]
|
12751
|
It is unclear in 'Monadology' how extended bodies relate to mind-like monads.
[Garber on Leibniz]
|
12707
|
The true elements are atomic monads
[Leibniz]
|
17554
|
There must be some internal difference between any two beings in nature
[Leibniz]
|
19363
|
Changes in a monad come from an internal principle, and the diversity within its substance
[Leibniz]
|
2109
|
Increase a conscious machine to the size of a mill - you still won't see perceptions in it
[Leibniz]
|
19352
|
A 'monad' has basic perception and appetite; a 'soul' has distinct perception and memory
[Leibniz]
|
2110
|
We all expect the sun to rise tomorrow by experience, but astronomers expect it by reason
[Leibniz]
|
19362
|
We know the 'I' and its contents by abstraction from awareness of necessary truths
[Leibniz]
|
2111
|
Falsehood involves a contradiction, and truth is contradictory of falsehood
[Leibniz]
|
4642
|
No fact can be real and no proposition true unless there is a Sufficient Reason (even if we can't know it)
[Leibniz]
|
2112
|
Truths of reason are known by analysis, and are necessary; facts are contingent, and their opposites possible
[Leibniz]
|
9344
|
Mathematical analysis ends in primitive principles, which cannot be and need not be demonstrated
[Leibniz]
|
2113
|
God alone (the Necessary Being) has the privilege that He must exist if He is possible
[Leibniz]
|
2114
|
This is the most perfect possible universe, in its combination of variety with order
[Leibniz]
|
2115
|
Everything in the universe is interconnected, so potentially a mind could know everything
[Leibniz]
|
2595
|
If the universe is a perfect agreement of uncommunicating substances, there must be a common source
[Leibniz]
|
2596
|
Maybe mind and body are parallel, like two good clocks
[Leibniz]
|
5063
|
Music charms, although its beauty is the harmony of numbers
[Leibniz]
|
19353
|
'Perception' is basic internal representation, and 'apperception' is reflective knowledge of perception
[Leibniz]
|
5061
|
Animals are semi-rational because they connect facts, but they don't see causes
[Leibniz]
|
5062
|
First: there must be reasons; Second: why anything at all?; Third: why this?
[Leibniz]
|
19377
|
A monad and its body are living, so life is everywhere, and comes in infinite degrees
[Leibniz]
|
12755
|
Final causes can help with explanations in physics
[Leibniz]
|
11854
|
If there is some trace of God in things, that would explain their natural force
[Leibniz]
|
12756
|
Substance is a force for acting and being acted upon
[Leibniz]
|
12758
|
It is plausible to think substances contain the same immanent force seen in our free will
[Leibniz]
|
12759
|
There are atoms of substance, but no atoms of bulk or extension
[Leibniz]
|
12718
|
Secondary matter is active and complete; primary matter is passive and incomplete
[Leibniz]
|
12760
|
Something rather like souls (though not intelligent) could be found everywhere
[Leibniz]
|
19408
|
To say that nature or the one universal substance is God is a pernicious doctrine
[Leibniz]
|
5058
|
Animals have thought and sensation, and indestructible immaterial souls
[Leibniz]
|
5054
|
Animal thought is a shadow of reasoning, connecting sequences of images by imagination
[Leibniz]
|
5057
|
If you fully understand a subject and its qualities, you see how the second derive from the first
[Leibniz]
|
5055
|
No two things are totally identical
[Leibniz]
|
5053
|
The instances confirming a general truth are never enough to establish its necessity
[Leibniz]
|
5056
|
Material or immaterial substances cannot be conceived without their essential activity
[Leibniz]
|
11855
|
Substances cannot be bare, but have activity as their essence
[Leibniz]
|
11856
|
Qualities should be predictable from the nature of the subject
[Leibniz]
|
12931
|
Particular truths are just instances of general truths
[Leibniz]
|
4302
|
You may experience a universal truth, but only reason can tell you that it is always true
[Leibniz]
|
12930
|
The senses are confused, and necessities come from distinct intellectual ideas
[Leibniz]
|
12929
|
All of our thoughts come from within the soul, and not from the senses
[Leibniz]
|
12933
|
Arithmetic and geometry are implicitly innate, awaiting revelation
[Leibniz]
|
17079
|
Proofs of necessity come from the understanding, where they have their source
[Leibniz]
|
12932
|
The idea of being must come from our own existence
[Leibniz]
|
19360
|
General principles, even if unconscious, are indispensable for thinking
[Leibniz]
|
12937
|
We shouldn't just accept Euclid's axioms, but try to demonstrate them
[Leibniz]
|
12935
|
Every feeling is the perception of a truth
[Leibniz]
|
12936
|
There are natural rewards and punishments, like illness after over-indulgence
[Leibniz]
|
12934
|
We can't want everyone to have more than their share, so a further standard is needed
[Leibniz]
|
12944
|
It is a serious mistake to think that we are aware of all of our perceptions
[Leibniz]
|
12942
|
Memory doesn't make identity; a man who relearned everything would still be the same man
[Leibniz]
|
12938
|
An idea is an independent inner object, which expresses the qualities of things
[Leibniz]
|
12945
|
Thoughts correspond to sensations, but ideas are independent of thoughts
[Leibniz]
|
12940
|
What is left of the 'blank page' if you remove the ideas?
[Leibniz]
|
12943
|
Individuality is in the bond substance gives between past and future
[Leibniz]
|
12941
|
There cannot be power without action; the power is a disposition to act
[Leibniz]
|
12939
|
Wholly uniform things like space and numbers are mere abstractions
[Leibniz]
|
12946
|
The idea of the will includes the understanding
[Leibniz]
|
19357
|
The idea of green seems simple, but it must be compounded of the ideas of blue and yellow
[Leibniz]
|
12947
|
We only believe in sensible things when reason helps the senses
[Leibniz]
|
19358
|
Colour and pain must express the nature of their stimuli, without exact resemblance
[Leibniz]
|
12948
|
A pain doesn't resemble the movement of a pin, but it resembles the bodily movement pins cause
[Leibniz]
|
12949
|
Light takes time to reach us, so objects we see may now not exist
[Leibniz]
|
12950
|
We must distinguish images from exact defined ideas
[Leibniz]
|
12951
|
Abstraction attends to the general, not the particular, and involves universal truths
[Leibniz]
|
12952
|
Space is an order among actual and possible things
[Leibniz]
|
12953
|
Fluidity is basic, and we divide into bodies according to our needs
[Leibniz]
|
12956
|
Only whole numbers are multitudes of units
[Leibniz]
|
12955
|
If there were duration without change, we could never establish its length
[Leibniz]
|
12954
|
God's essence is the source of possibilities, and his will the source of existents
[Leibniz]
|
12957
|
The good is the virtuous, the pleasing, or the useful
[Leibniz]
|
12958
|
Love is pleasure in the perfection, well-being or happiness of its object
[Leibniz]
|
12964
|
If would be absurd not to disagree with someone's taste if it was a taste for poisons
[Leibniz]
|
19368
|
The will determines action, by what is seen as good, but it does not necessitate it
[Leibniz]
|
19364
|
Volition automatically endeavours to move towards what it sees as good (and away from bad)
[Leibniz]
|
12962
|
Pleasure is a sense of perfection
[Leibniz]
|
12963
|
Opposing reason is opposing truth, since reason is a chain of truths
[Leibniz]
|
12959
|
We discern active power from our minds, so mind must be involved in all active powers
[Leibniz]
|
12965
|
All occurrence in the depth of a substance is spontaneous 'action'
[Leibniz]
|
12960
|
We understand things when they are distinct, and we can derive necessities from them
[Leibniz]
|
19328
|
Without the principle of sufficient reason, God's existence could not be demonstrated
[Leibniz]
|
12967
|
I use the word 'entelechy' for a power, to include endeavour, as well as mere aptitude
[Leibniz]
|
12966
|
Objects of ideas can be divided into abstract and concrete, and then further subdivided
[Leibniz]
|
12969
|
The active powers which are not essential to the substance are the 'real qualities'
[Leibniz]
|
12968
|
A 'substratum' is just a metaphor for whatever supports several predicates
[Leibniz]
|
12972
|
Bodies, like Theseus's ship, are only the same in appearance, and never strictly the same
[Leibniz]
|
13098
|
We use things to distinguish places and times, not vice versa
[Leibniz]
|
12971
|
If two individuals could be indistinguishable, there could be no principle of individuation
[Leibniz]
|
12970
|
We can imagine two bodies interpenetrating, as two rays of light seem to
[Leibniz]
|
13075
|
No two things are quite the same, so there must be an internal principle of distinction
[Leibniz]
|
12973
|
We know our own identity by psychological continuity, even if there are some gaps
[Leibniz]
|
12884
|
The same whole ceases to exist if a part is lost
[Leibniz]
|
12974
|
People who can't apply names usually don't understand the thing to which it applies
[Leibniz]
|
12976
|
If our ideas of a thing are imperfect, the thing can have several unconnected definitions
[Leibniz]
|
12975
|
We have a distinct idea of gold, to define it, but not a perfect idea, to understand it
[Leibniz]
|
12978
|
A perfect idea of an object shows that the object is possible
[Leibniz]
|
12977
|
We will only connect our various definitions of gold when we understand it more deeply
[Leibniz]
|
12981
|
Essence is just the possibility of a thing
[Leibniz]
|
12979
|
The only way we can determine individuals is by keeping hold of them
[Leibniz]
|
12982
|
One essence can be expressed by several definitions
[Leibniz]
|
12984
|
Real definitions, unlike nominal definitions, display possibilities
[Leibniz]
|
12983
|
A nominal definition is of the qualities, but the real definition is of the essential inner structure
[Leibniz]
|
12980
|
Genus and differentia might be swapped, and 'rational animal' become 'animable rational'
[Leibniz]
|
12985
|
Maybe motion is definable as 'change of place'
[Leibniz]
|
12986
|
The essence of baldness is vague and imperfect
[Leibniz]
|
12987
|
For some sorts, a member of it is necessarily a member
[Leibniz]
|
12989
|
Our true divisions of nature match reality, but are probably incomplete
[Leibniz]
|
12988
|
The universe contains everything possible for its perfect harmony
[Leibniz]
|
12990
|
Real (non-logical) abstract terms are either essences or accidents
[Leibniz]
|
12991
|
Children learn language fast, with little instruction and few definitions
[Leibniz]
|
12993
|
Have five categories - substance, quantity, quality, action/passion, relation - and their combinations
[Leibniz]
|
12992
|
Logic teaches us how to order and connect our thoughts
[Leibniz]
|
12994
|
Gold has a real essence, unknown to us, which produces its properties
[Leibniz]
|
12995
|
The name 'gold' means what we know of gold, and also further facts about it which only others know
[Leibniz]
|
12811
|
We can't know individuals, or determine their exact individuality
[Leibniz]
|
12996
|
I know more than I think, since I know I think A then B then C
[Leibniz]
|
12998
|
Understanding grasps the agreements and disagreements of ideas
[Leibniz]
|
12997
|
Analysis is the art of finding the middle term
[Leibniz]
|
12999
|
Substances are primary powers; their ways of being are the derivative powers
[Leibniz]
|
13000
|
Truth is correspondence between mental propositions and what they are about
[Leibniz]
|
13002
|
It is always good to reduce the number of axioms
[Leibniz]
|
13001
|
Our sensation of green is a confused idea, like objects blurred by movement
[Leibniz]
|
13003
|
The Cogito doesn't prove existence, because 'I am thinking' already includes 'I am'
[Leibniz]
|
13005
|
Truth arises among sensations from grounding reasons and from regularities
[Leibniz]
|
13006
|
Certainty is where practical doubt is insane, or at least blameworthy
[Leibniz]
|
10056
|
At bottom eternal truths are all conditional
[Leibniz]
|
13008
|
Geometry, unlike sensation, lets us glimpse eternal truths and their necessity
[Leibniz]
|
13009
|
A reason is a known truth which leads to assent to some further truth
[Leibniz]
|
12805
|
If two people apply a single term to different resemblances, they refer to two different things
[Leibniz]
|
12806
|
Locke needs many instances to show a natural kind, but why not a single instance?
[Leibniz, by Jolley]
|
12808
|
Part of our idea of gold is its real essence, which is not known to us in detail
[Leibniz]
|
12807
|
The word 'gold' means a hidden constitution known to experts, and not just its appearances
[Leibniz]
|
21252
|
Perfections must have overlapping parts if their incompatibility is to be proved
[Leibniz]
|
1414
|
A perfection is a simple quality, which is positive and absolute, and has no limit
[Leibniz]
|
21253
|
Descartes needs to demonstrate how other people can attain his clear and distinct conceptions
[Leibniz]
|
5044
|
Reality must be made of basic unities, which will be animated, substantial points
[Leibniz]
|
5043
|
To regard animals as mere machines may be possible, but seems improbable
[Leibniz]
|
5045
|
No machine or mere organised matter could have a unified self
[Leibniz]
|
13167
|
We need the metaphysical notion of force to explain mechanics, and not just extended mass
[Leibniz]
|
13168
|
My formal unifying atoms are substantial forms, which are forces like appetites
[Leibniz]
|
13169
|
I call Aristotle's entelechies 'primitive forces', which originate activity
[Leibniz]
|
13170
|
The analysis of things leads to atoms of substance, which found both composition and action
[Leibniz]
|
13171
|
Substance must necessarily involve progress and change
[Leibniz]
|
5046
|
The soul does know bodies, although they do not influence one another
[Leibniz]
|
12694
|
Essence is the distinct thinkability of anything
[Leibniz]
|
5020
|
Our thoughts are either dependent, or self-evident. All thoughts seem to end in the self-evident
[Leibniz]
|
5019
|
Supreme human happiness is the greatest possible increase of his perfection
[Leibniz]
|
5021
|
An idea is analysed perfectly when it is shown a priori that it is possible
[Leibniz]
|
19350
|
We should say that body is mechanism and soul is immaterial, asserting their independence
[Leibniz]
|
19355
|
The soul doesn't understand many of its own actions, if perceptions are confused and desires buried
[Leibniz]
|
19356
|
Minds unconsciously count vibration beats in music, and enjoy it when they coincide
[Leibniz]
|
13161
|
Substances are everywhere in matter, like points in a line
[Leibniz]
|
13160
|
To exist and be understood, a multitude must first be reduced to a unity
[Leibniz]
|
5042
|
For every event it is possible for an omniscient being to give a reason for its occurrence
[Leibniz]
|
19424
|
Knowledge needs clarity, distinctness, and adequacy, and it should be intuitive
[Leibniz]
|
19425
|
In the schools the Four Causes are just lumped together in a very obscure way
[Leibniz]
|
19426
|
'Nominal' definitions just list distinguishing characteristics
[Leibniz]
|
19427
|
True ideas represent what is possible; false ideas represent contradictions
[Leibniz]
|
12709
|
Motion is not absolute, but consists in relation
[Leibniz]
|
12738
|
Successful prediction shows proficiency in nature
[Leibniz]
|
12739
|
If we are dreaming, it is sufficient that the events are coherent, and obey laws
[Leibniz]
|
19404
|
Necessities rest on contradiction, and contingencies on sufficient reason
[Leibniz]
|
19403
|
Each of the infinite possible worlds has its own laws, and the individuals contain those laws
[Leibniz]
|
19396
|
Wisdom is knowing all of the sciences, and their application
[Leibniz]
|
19397
|
Perfect knowledge implies complete explanations and perfect prediction
[Leibniz]
|
7696
|
Leibniz first asked 'why is there something rather than nothing?'
[Leibniz, by Jacquette]
|
5047
|
The world is physically necessary, as its contrary would imply imperfection or moral absurdity
[Leibniz]
|
19341
|
There must be a straining towards existence in the essence of all possible things
[Leibniz]
|
19343
|
We follow the practical rule which always seeks maximum effect for minimum cost
[Leibniz]
|
19336
|
Wisdom involves the desire to achieve perfection
[Leibniz]
|
19428
|
Because something does exist, there must be a drive in possible things towards existence
[Leibniz]
|
19429
|
The principle of determination in things obtains the greatest effect with the least effort
[Leibniz]
|
12697
|
Indivisibles are not parts, but the extrema of parts
[Leibniz]
|
12727
|
It's impossible, but imagine a body carrying on normally, but with no mind
[Leibniz]
|
9155
|
An a priori proof is independent of experience
[Leibniz]
|
12716
|
The concept of forces or powers best reveals the true concept of substance
[Leibniz]
|
19416
|
Not all of matter is animated, any more than a pond full of living fish is animated
[Leibniz]
|
19417
|
All substances are in harmony, even though separate, so they must have one divine cause
[Leibniz]
|
19418
|
Mechanics shows that all motion originates in other motion, so there is a Prime Mover
[Leibniz]
|
19420
|
Death and generation are just transformations of an animal, augmented or diminished
[Leibniz]
|
19419
|
Not all of perception is accompanied by consciousness
[Leibniz]
|
19421
|
Souls act as if there were no bodies, and bodies act as if there were no souls
[Leibniz]
|
19422
|
Every particle of matter contains organic bodies
[Leibniz]
|
5059
|
Power rules in efficient causes, but wisdom rules in connecting them to final causes
[Leibniz]
|
5060
|
All substances analyse down to simple substances, which are souls, or 'monads'
[Leibniz]
|
19394
|
Inequality can be brought infinitely close to equality
[Leibniz]
|
19395
|
Philosophy is sanctified, because it flows from God
[Leibniz]
|
19382
|
Abstracta are abbreviated ways of talking; there are just substances, and truths about them
[Leibniz]
|
13157
|
Choose the true hypothesis, which is the most intelligible one
[Leibniz]
|
13158
|
The Copernican theory is right because it is the only one offering a good explanation
[Leibniz]
|
19384
|
Space and time are the order of all possibilities, and don't just relate to what is actual
[Leibniz]
|
19406
|
I strongly believe in the actual infinite, which indicates the perfections of its author
[Leibniz]
|
5048
|
Perfection is simply quantity of reality
[Leibniz]
|
5049
|
Intelligent pleasure is the perception of beauty, order and perfection
[Leibniz]
|
5050
|
Evil serves a greater good, and pain is necessary for higher pleasure
[Leibniz]
|
13099
|
Analysing right down to primitive concepts seems beyond our powers
[Leibniz]
|
5022
|
We hold a proposition true if we are ready to follow it, and can't see any objections
[Leibniz]
|
12729
|
The cause of a change is not the real influence, but whatever gives a reason for the change
[Leibniz]
|
19437
|
Prayers are useful, because God foresaw them in his great plan
[Leibniz]
|
19337
|
How can an all-good, wise and powerful being allow evil, sin and apparent injustice?
[Leibniz]
|
19345
|
Being confident of God's goodness, we disregard the apparent local evils in the visible world
[Leibniz]
|
19326
|
God must be intelligible, to select the actual world from the possibilities
[Leibniz]
|
19325
|
God is the first reason of things; our experiences are contingent, and contain no necessity
[Leibniz]
|
19327
|
The intelligent cause must be unique and all-perfect, to handle all the interconnected possibilities
[Leibniz]
|
19346
|
Most people facing death would happily re-live a similar life, with just a bit of variety
[Leibniz]
|
19340
|
Metaphysical evil is imperfection; physical evil is suffering; moral evil is sin
[Leibniz]
|
19331
|
Will is an inclination to pursue something good
[Leibniz]
|
19367
|
Saying we must will whatever we decide to will leads to an infinite regress
[Leibniz]
|
19351
|
Perfections of soul subordinate the body, but imperfections of soul submit to the body
[Leibniz]
|
19344
|
God prefers men to lions, but might not exterminate lions to save one man
[Leibniz]
|
19335
|
Reasonings have a natural ordering in God's understanding, but only a temporal order in ours
[Leibniz]
|
19330
|
If justice is arbitrary, or fixed but not observed, or not human justice, this undermines God
[Leibniz]
|
19329
|
The laws of physics are wonderful evidence of an intelligent and free being
[Leibniz]
|
19366
|
You can't assess moral actions without referring to the qualities of character that produce them
[Leibniz]
|
15955
|
I think the corpuscular theory, rather than forms or qualities, best explains particular phenomena
[Leibniz]
|
12903
|
Wise people have fewer acts of will, because such acts are linked together
[Leibniz]
|
5031
|
Everything which happens is not necessary, but is certain after God chooses this universe
[Leibniz]
|
5030
|
Miracles are extraordinary operations by God, but are nevertheless part of his design
[Leibniz]
|
12905
|
I cannot think my non-existence, nor exist without being myself
[Leibniz]
|
12904
|
If varieties of myself can be conceived of as distinct from me, then they are not me
[Leibniz]
|
12906
|
Truths about species are eternal or necessary, but individual truths concern what exists
[Leibniz]
|
13077
|
Basic predicates give the complete concept, which then predicts all of the actions
[Leibniz]
|
13089
|
To fully conceive the subject is to explain the resulting predicates and events
[Leibniz]
|
12907
|
Each possible world contains its own laws, reflected in the possible individuals of that world
[Leibniz]
|
11981
|
If someone's life went differently, then that would be another individual
[Leibniz]
|
19334
|
I can't just know myself to be a substance; I must distinguish myself from others, which is hard
[Leibniz]
|
19333
|
A truth is just a proposition in which the predicate is contained within the subject
[Leibniz]
|
12910
|
The predicate is in the subject of a true proposition
[Leibniz]
|
12913
|
Nature is explained by mathematics and mechanism, but the laws rest on metaphysics
[Leibniz]
|
12908
|
Essences exist in the divine understanding
[Leibniz]
|
12911
|
Concepts are what unite a proposition
[Leibniz]
|
12909
|
Everything, even miracles, belongs to order
[Leibniz]
|
12912
|
Immortality without memory is useless
[Leibniz]
|
12914
|
Metaphysics is geometrical, resting on non-contradiction and sufficient reason
[Leibniz]
|
12915
|
Definitions can only be real if the item is possible
[Leibniz]
|
12916
|
A body is a unified aggregate, unless it has an indivisible substance
[Leibniz]
|
12917
|
The soul is indestructible and always self-aware
[Leibniz]
|
12918
|
Animals have souls, but lack consciousness
[Leibniz]
|
12919
|
Unity needs an indestructible substance, to contain everything which will happen to it
[Leibniz]
|
5032
|
It seems probable that animals have souls, but not consciousness
[Leibniz]
|
12319
|
What is not truly one being is not truly a being either
[Leibniz]
|
12920
|
There is no multiplicity without true units
[Leibniz]
|
12704
|
Aggregates dont reduce to points, or atoms, or illusion, so must reduce to substance
[Leibniz]
|
12921
|
Accidental unity has degrees, from a mob to a society to a machine or organism
[Leibniz]
|
12746
|
We find unity in reason, and unity in perception, but these are not true unity
[Leibniz]
|
12745
|
Philosophy needs the precision of the unity given by substances
[Leibniz]
|
5033
|
Nothing should be taken as certain without foundations
[Leibniz]
|
12923
|
Every bodily substance must have a soul, or something analogous to a soul
[Leibniz]
|
12922
|
A thing 'expresses' another if they have a constant and fixed relationship
[Leibniz]
|
5034
|
Mind is a thinking substance which can know God and eternal truths
[Leibniz]
|
12924
|
Motion alone is relative, but force is real, and establishes its subject
[Leibniz]
|
13079
|
A substance contains the laws of its operations, and its actions come from its own depth
[Leibniz]
|
12925
|
Beauty increases with familiarity
[Leibniz]
|
12926
|
Wisdom is the science of happiness
[Leibniz]
|
12927
|
Happiness is advancement towards perfection
[Leibniz]
|
12706
|
Bodies need a soul (or something like it) to avoid being mere phenomena
[Leibniz]
|
19413
|
If we know what is good or rational, our knowledge is extended, and our free will restricted
[Leibniz]
|
13173
|
Death is just the contraction of an animal
[Leibniz]
|
13172
|
What we cannot imagine may still exist
[Leibniz]
|
13174
|
A piece of flint contains something resembling perceptions and appetites
[Leibniz]
|
13175
|
Entelechies are analogous to souls, as other minds are analogous to our own minds
[Leibniz]
|
19407
|
We want good education and sociability, rather than lots of moral precepts
[Leibniz]
|
13198
|
Gravity is within matter because of its structure, and it can be explained.
[Leibniz]
|
13197
|
The notion of substance is one of the keys to true philosophy
[Leibniz]
|
13189
|
A necessary feature (such as air for humans) is not therefore part of the essence
[Leibniz]
|
19432
|
Intelligible truth is independent of any external things or experiences
[Leibniz]
|
19430
|
We know objects by perceptions, but their qualities don't reveal what it is we are perceiving
[Leibniz]
|
19431
|
There is nothing in the understanding but experiences, plus the understanding itself, and the understander
[Leibniz]
|
23026
|
We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light
[Leibniz]
|
22894
|
If time were absolute that would make God's existence dependent on it
[Leibniz, by Bardon]
|
2099
|
The existence of God, and all metaphysics, follows from the Principle of Sufficient Reason
[Leibniz]
|
2098
|
The principle of sufficient reason is needed if we are to proceed from maths to physics
[Leibniz]
|
3646
|
There is always a reason why things are thus rather than otherwise
[Leibniz]
|
2100
|
Space and time are purely relative
[Leibniz]
|
2101
|
If everything in the universe happened a year earlier, there would be no discernible difference
[Leibniz]
|
2102
|
Atomism is irrational because it suggests that two atoms can be indistinguishable
[Leibniz]
|
2103
|
The idea that the universe could be moved forward with no other change is just a fantasy
[Leibniz]
|
2104
|
No reason could limit the quantity of matter, so there is no limit
[Leibniz]
|
2105
|
Things are infinitely subdivisible and contain new worlds, which atoms would make impossible
[Leibniz]
|
2106
|
The only simple things are monads, with no parts or extension
[Leibniz]
|
2107
|
No time exists except instants, and instants are not even a part of time, so time does not exist
[Leibniz]
|
20965
|
Leibniz upheld conservations of momentum and energy
[Leibniz, by Papineau]
|
21346
|
The ratio between two lines can't be a feature of one, and cannot be in both
[Leibniz]
|
19385
|
All simply substances are in harmony, because they all represent the one universe
[Leibniz]
|
19433
|
The universe is infinitely varied, so the Buridan's Ass dilemma could never happen
[Leibniz]
|
19434
|
There may be a world where dogs smell their game at a thousand leagues
[Leibniz]
|
13096
|
The force behind motion is like a soul, with its own laws of continual change
[Leibniz]
|
13177
|
An entelechy is a law of the series of its event within some entity
[Leibniz]
|
19409
|
Soul represents body, but soul remains unchanged, while body continuously changes
[Leibniz]
|
19410
|
Scientific truths are supported by mutual agreement, as well as agreement with the phenomena
[Leibniz]
|
11873
|
Our notions may be formed from concepts, but concepts are formed from things
[Leibniz]
|
13180
|
Space is the order of coexisting possibles
[Leibniz]
|
13181
|
Time is the order of inconsistent possibilities
[Leibniz]
|
13178
|
Things in different locations are different because they 'express' those locations
[Leibniz]
|
19411
|
In nature there aren't even two identical straight lines, so no two bodies are alike
[Leibniz]
|
19412
|
If two bodies only seem to differ in their position, those different environments will matter
[Leibniz]
|
12747
|
Monads are not extended, but have a kind of situation in extension
[Leibniz]
|
13179
|
A complete monad is a substance with primitive active and passive power
[Leibniz]
|
19379
|
The law of the series, which determines future states of a substance, is what individuates it
[Leibniz]
|
13093
|
The only permanence in things, constituting their substance, is a law of continuity
[Leibniz]
|
13185
|
Even if extension is impenetrable, this still offers no explanation for motion and its laws
[Leibniz]
|
13186
|
Universals are just abstractions by concealing some of the circumstances
[Leibniz]
|
13183
|
Primitive forces are internal strivings of substances, acting according to their internal laws
[Leibniz]
|
13184
|
The division of nature into matter makes distinct appearances, and that presupposes substances
[Leibniz]
|
12748
|
Only monads are substances, and bodies are collections of them
[Leibniz]
|
12752
|
Only unities have any reality
[Leibniz]
|
13182
|
Changeable accidents are modifications of unchanging essences
[Leibniz]
|
12749
|
Derivate forces are in phenomena, but primitive forces are in the internal strivings of substances
[Leibniz]
|
13188
|
The only indications of reality are agreement among phenomena, and their agreement with necessities
[Leibniz]
|
13187
|
In actual things nothing is indefinite
[Leibniz]
|
12722
|
Thought terminates in force, rather than extension
[Leibniz]
|
19383
|
A man's distant wife dying is a real change in him
[Leibniz]
|
12774
|
Without a substantial chain to link monads, they would just be coordinated dreams
[Leibniz]
|
12775
|
Things seem to be unified if we see duration, position, interaction and connection
[Leibniz]
|
12776
|
Every substance is alive
[Leibniz]
|
12777
|
Monads do not make a unity unless a substantial chain is added to them
[Leibniz]
|
12753
|
A substantial bond of powers is needed to unite composites, in addition to monads
[Leibniz]
|
12781
|
A composite substance is a mere aggregate if its essence is just its parts
[Leibniz]
|
12785
|
Truth is mutually agreed perception
[Leibniz]
|
12779
|
There is a reason why not every possible thing exists
[Leibniz]
|
12782
|
Monads control nothing outside of themselves
[Leibniz]
|
12778
|
There is active and passive power in the substantial chain and in the essence of a composite
[Leibniz]
|
12783
|
Primitive force is what gives a composite its reality
[Leibniz]
|
12780
|
We can grasp the wisdom of God a priori
[Leibniz]
|
12784
|
Allow no more miracles than are necessary
[Leibniz]
|
12708
|
The soul is not a substance but a substantial form, the first active faculty
[Leibniz]
|
2117
|
The connection in events enables us to successfully predict the future, so there must be a constant cause
[Leibniz]
|
13095
|
Essence is primitive force, or a law of change
[Leibniz]
|
13097
|
Force in substance makes state follow state, and ensures the very existence of substance
[Leibniz]
|
12723
|
The most primitive thing in substances is force, which leads to their actions and dispositions
[Leibniz]
|
13190
|
I don't admit infinite numbers, and consider infinitesimals to be useful fictions
[Leibniz]
|
12720
|
Time doesn't exist, since its parts don't coexist
[Leibniz]
|
12719
|
Clearly, force is that from which action follows, when unimpeded
[Leibniz]
|
19415
|
Passions reside in confused perceptions
[Leibniz]
|
19438
|
Our large perceptions and appetites are made up tiny unconscious fragments
[Leibniz]
|
19439
|
God produces possibilities, and thus ideas
[Leibniz]
|
12732
|
Some necessary truths are brute, and others derive from final causes
[Leibniz]
|
19348
|
All that is real in motion is the force or power which produces change
[Leibniz]
|
11945
|
In addition to laws, God must also create appropriate natures for things
[Leibniz]
|
13432
|
The essence of a circle is the equality of its radii
[Leibniz]
|
12696
|
Bodies are recreated in motion, and don't exist in intervening instants
[Leibniz]
|
19414
|
Men are related to animals, which are related to plants, then to fossils, and then to the apparently inert
[Leibniz]
|
19436
|
Bare or primary matter is passive; it is clothed or secondary matter which contains action
[Leibniz]
|
13191
|
The properties of a thing flow from its essence
[Leibniz]
|
19370
|
'Blind thought' is reasoning without recognition of the ingredients of the reasoning
[Leibniz, by Arthur,R]
|
19390
|
Everything is subsumed under number, which is a metaphysical statics of the universe, revealing powers
[Leibniz]
|
19391
|
We can assign a characteristic number to every single object
[Leibniz]
|
19393
|
What is not active is nothing
[Leibniz]
|
2118
|
All other human gifts can harm us, but not correct reasoning
[Leibniz]
|
19423
|
By an 'idea' I mean not an actual thought, but the resources we can draw on to think
[Leibniz]
|
7564
|
Occasionalism give a false view of natural laws, miracles, and substances
[Leibniz, by Jolley]
|
5510
|
Leibniz has a panpsychist view that physical points are spiritual
[Leibniz, by Martin/Barresi]
|
13467
|
Leibniz was the first modern to focus on sentence-sized units (where empiricists preferred word-size)
[Leibniz, by Hart,WD]
|
19365
|
Limited awareness leads to bad choices, and unconscious awareness makes us choose the bad
[Leibniz, by Perkins]
|
8110
|
Leibniz identified beauty with intellectual perfection
[Leibniz, by Gardner]
|
7569
|
Humans are moral, and capable of reward and punishment, because of memory and self-consciousness
[Leibniz, by Jolley]
|
19354
|
Leibniz introduced the idea of degrees of consciousness, essential for his monads
[Leibniz, by Perkins]
|
7841
|
We think we are free because the causes of the will are unknown; determinism is a false problem
[Leibniz]
|
16683
|
Leibniz eventually said resistance, rather than extension, was the essence of body
[Leibniz, by Pasnau]
|
7560
|
Leibniz struggled to reconcile bodies with a reality of purely soul-like entities
[Jolley on Leibniz]
|
12728
|
Leibniz rejected atoms, because they must be elastic, and hence have parts
[Leibniz, by Garber]
|
7574
|
Natural law theory is found in Aquinas, in Leibniz, and at the Nuremberg trials
[Leibniz, by Jolley]
|
7859
|
Leibniz had an unusual commitment to the causal completeness of physics
[Leibniz, by Papineau]
|
12725
|
Leibniz wanted to explain motion and its laws by the nature of body
[Leibniz, by Garber]
|
3889
|
God's existence is either necessary or impossible
[Leibniz, by Scruton]
|
7842
|
Leibniz was closer than Spinoza to atheism
[Leibniz, by Stewart,M]
|
3347
|
Leibniz said the principle of sufficient reason is synthetic a priori, since its denial is not illogical
[Leibniz, by Benardete,JA]
|
3346
|
For Leibniz rationality is based on non-contradiction and the principle of sufficient reason
[Leibniz, by Benardete,JA]
|
19359
|
Leibniz aims to give coherent rational support for empiricism
[Leibniz, by Perkins]
|
13086
|
Metaphysics is a science of the intelligible nature of being
[Leibniz, by Cover/O'Leary-Hawthorne]
|
16897
|
Reason is the faculty for grasping apriori necessary truths
[Leibniz, by Burge]
|
16710
|
Leibniz tried to combine mechanistic physics with scholastic metaphysics
[Leibniz, by Pasnau]
|
9147
|
Number cannot be defined as addition of ones, since that needs the number; it is a single act of abstraction
[Fine,K on Leibniz]
|
8627
|
Leibniz is inclined to regard all truths as provable
[Leibniz, by Frege]
|
18080
|
A tangent is a line connecting two points on a curve that are infinitely close together
[Leibniz]
|
18081
|
Nature uses the infinite everywhere
[Leibniz]
|
7561
|
Substances are essentially active
[Leibniz, by Jolley]
|
10419
|
If relations can be reduced to, or supervene on, monadic properties of relata, they are not real
[Leibniz, by Swoyer]
|
7565
|
Leibniz proposes monads, since there must be basic things, which are immaterial in order to have unity
[Leibniz, by Jolley]
|
12713
|
Forms have sensation and appetite, the latter being the ability to act on other bodies
[Leibniz, by Garber]
|
13087
|
The essence of a thing is its real possibilities
[Leibniz, by Cover/O'Leary-Hawthorne]
|
12701
|
Leibniz moved from individuation by whole entity to individuation by substantial form
[Leibniz, by Garber]
|
13105
|
The laws-of-the-series plays a haecceitist role
[Leibniz, by Cover/O'Leary-Hawthorne]
|
11862
|
Leibniz was not an essentialist
[Leibniz, by Wiggins]
|
16504
|
Two eggs can't be identical, because the same truths can't apply to both of them
[Leibniz]
|
11878
|
Leibniz's view (that all properties are essential) is extreme essentialism, not its denial
[Leibniz, by Mackie,P]
|
12035
|
Leibniz bases pure primitive entities on conjunctions of qualitative properties
[Leibniz, by Adams,RM]
|
13091
|
Leibnizian substances add concept, law, force, form and soul
[Leibniz, by Cover/O'Leary-Hawthorne]
|
12715
|
Leibniz strengthened hylomorphism by connecting it to force in physics
[Leibniz, by Garber]
|
4307
|
A reason must be given why contingent beings should exist rather than not exist
[Leibniz]
|
8650
|
Things are the same if one can be substituted for the other without loss of truth
[Leibniz]
|
13828
|
Necessary truths are those provable from identities by pure logic in finite steps
[Leibniz, by Hacking]
|
13080
|
Leibniz has a counterpart view of de re counterfactuals
[Leibniz, by Cover/O'Leary-Hawthorne]
|
15883
|
Leibniz narrows down God's options to one, by non-contradiction, sufficient reason, indiscernibles, compossibility
[Leibniz, by Harré]
|
18822
|
Each monad expresses all its compatible monads; a possible world is the resulting equivalence class
[Leibniz, by Rumfitt]
|
7837
|
Leibniz proposed possible worlds, because they might be evil, where God would not create evil things
[Leibniz, by Stewart,M]
|
19332
|
For Leibniz, divine understanding grasps every conceivable possibility
[Leibniz, by Perkins]
|
5509
|
Leibniz said dualism of mind and body is illusion, and there is only mind
[Leibniz, by Martin/Barresi]
|
7568
|
Leibniz is an idealist insofar as the basic components of his universe are all mental
[Leibniz, by Jolley]
|
19372
|
Concepts are ordered, and show eternal possibilities, deriving from God
[Leibniz, by Arthur,R]
|
15307
|
Leibniz uses 'force' to mean both activity and potential
[Leibniz]
|
13092
|
The essence of substance is the law of its changes, as in the series of numbers
[Leibniz]
|
19374
|
Microscopes and the continuum suggest that matter is endlessly divisible
[Leibniz]
|
19375
|
The continuum is not divided like sand, but folded like paper
[Leibniz, by Arthur,R]
|
16507
|
The law within something fixes its persistence, and accords with general laws of nature
[Leibniz]
|
16513
|
Identity of a substance is the law of its persistence
[Leibniz]
|
13078
|
Relations aren't in any monad, so they are distributed, so they are not real
[Leibniz]
|
13084
|
How can things be incompatible, if all positive terms seem to be compatible?
[Leibniz]
|