Love of Wisdom

The word 'philosophy' derives from the Greek for 'love' and 'wisdom'. Philosophers throughout the ages may have loved–and sought after–wisdom, but most did not attain it. In other words, since philosophers first tinkered with conceptualization there have been some ridiculous theories out there.

Nevertheless, philosophy tackles metaphysical and value-laden questions in a systematic manner that is well worth study by any who value reason.

å René Descartes, cogito argument å David Hume å Gottfried Wilhelm Leibniz, monadology å Leibnizian Principle of Sufficient Reason å Locke å Occam's Razor ɷ William of Ockham å Pascal's Wager å Jean Piaget å Karl Popper å Bertrand Russell å Baruch Spinoza

å On Further Thought
å What's in a Naturalism?
å Seeker after the truth

å No Illusion Necessary

å Apologetic Failures
å Aquinas' cosmological argument
å Cosmological Arguments
å Kalām cosmological argument
å Leibnizian Principle of Sufficient Reason
å Plato Aristotle First Mover

abduction : a priori : a posteriori : Aquinas' Third Way : Cartesian dualism : categorical logic : causation : ceteris paribus : Cogito argument : contingency, contingent : correlation : correlation vs. causation : critical thinking : deduction : disproof, impossibility of disproving nonexistence : dual-attribute monism : empiricism : epistemology : induction : inference : informal logic : Humean skepticism : logic : metaphysical naturalism : methodological naturalism : mind-body : modal logic : naturalism : necessary cause : necessary vs sufficient : necessity, necessary : Occam's razor : Pascal's Wager : polemics : possible worlds : possibility : proof : propositional logic : scientific method : skepticism : sufficient cause : symbolic logic : tabula rasa : validity :

a priori vs a posteriori

A priori propositions merely require looking in one's own brain for justification, whereas a posteriori propositions require reflection upon experience of the world at large.In epistemology, a priori propositions can be known* independent of (prior to) experience, whereas a posteriori propositions can be known only on the basis of experience (after experience). Thus, the distinction between a priori and a posteriori corresponds roughly to the distinction between nonempirical and empirical knowledge.

The a priori/a posteriori distinction is applied to ways of knowing, propositions, arguments, and concepts. Because of its dependence upon verification by experience, the foundation for classifying a proposition as a posteriori is more easily grasped. An a priori concept can be acquired independently of experience, which may include, but is not necessarily confined to innate concepts.

The term 'justification' signifies that the person who believes something has an epistemic reason to thinking that the belief is true. So, a priori justification for believing a given proposition involves having a reason independent of experience for regarding that the proposition as true. Such propositions include simple perceptual, numerical, and logical relations – ice water is cooler than boiling water, blue is a colour, three plus two is five, when comparing two men the taller man is not shorter than the shorter man. One is a priori justified in believing a given proposition if, on the basis of pure thought or reason, one has a reason to consider the proposition to be true. Thus, propositions for which a priori justification obtains are necessarily confined—exclusive of mathematics and logic—to trivial situations.

* Knowledge is best defined as justified true belief. Belief signifies no more than possession of a mental state, and belief alone cannot be taken to represent knowledge.

ceteris paribus

Cēterīs paribus is derived from the Latin, and is literally translated as "with other things [being] the same." This is usually expressed in English as "all other things being equal."

A ceteris paribus assumption concerns causal or logical connections, and acknowledges – so as to rule out – the possibility of extraneous, confounding factors that could override the causal relationship between the antecedent and the consequent.

Ceteris paribus assumptions are often fundamental to the predictive purpose of scientific inquiry, where formulation of scientific laws requires the elimination of confounding factors that could interfere with examining a specific causal relationship.

Experimentally, the ceteris paribus assumption is realized when a scientist controls for all of the independent variables other than the one under study. This isolates the impact on the dependent variable under investigation to the operation of a single independent variable. By holding other relevant factors constant, a scientist hopes to focus on the unique effects of a specific factor in a complex causal situation. (Obviously, any as yet unrecognized independent variables could continue to confound results.)

For the same reasons, simplifying assumptions are also relevant to the descriptive purpose of modeling theories within analytical frameworks that describe fundamental concepts within fields such as economics, physics, and behavioral psychology.

contingent vs necessary

St. Thomas Aquinas, also called the Angelic Doctor. Demidoff Altarpiece by Carlo CrivelliA contingent truth, or falsehood, concerns something that could have been otherwise. A proposition that expresses a contingent truth can be rationally denied without resulting in any self-contradiction. A contingent event is one that does not necessarily take place.

A necessary truth could not have been otherwise, and to deny a necessary truth involves a contradiction. A proposition is said to be necessary if it holds (is true) in all logically possible circumstances or conditions, and denying that proposition would result in a self-contradiction.

It is not clear that there are any necessary propositions and, if there are, they are restricted to analytic propositions or other propositions that are true by virtue of their logical form.

If there are necessary events, then natural rather than logical necessity is involved.

The concept of possible worlds is used semantically to explicate contingency versus necessity. Contingent propositions or sentences are supposed to have truth values that depend upon the how the world actually is, and they could have differed in different possible worlds. Necessary propositions are conceptualized as the special limiting case in which the value turns out to be true for every possible world. The logical status of abstract entities (contingent) is quite different to that of concrete entities. Recognition of this leads to more complex ideas of what possible worlds are, with consequences for what statements turn out to be necessary.

The concept of contingent versus necessary is employed in cosmological arguments, for example in St. Thomas Aquinas' Five Ways: Third Way: Contingent and Neccessary Objects:

Aquinas' Third Way defines two types of objects in the universe: contingent beings and necessary beings. A contingent being is an object that cannot exist without a necessary being causing its existence. Aquinas believed that the existence of contingent beings would ultimately neccesitate a being which must exist for all of the contingent beings to exist. This being, called a necessary being, is what we call God. The argument runs:
1) Contingent beings are caused.
2) Not every being can be contingent.
3) There must exist a being which is necessary to cause contingent beings.
4) This necessary being is God.

The distinction between necessary and contingent objects is fatal to Aquinas’ argument because he acknowledges that some objects simply exist without causation. The question then becomes which object/s is/are in actuality the necessary being/s.

Aquinas attributes the qualities of the Christian “God” to this necessary object. However, Aquinas has failed to make the case that the ultimate, necessary existence could not in fact be that which Aquinas is taking to be caused by “God”. In other words, Aquinas has invented an extra, regression step in order to conform to received religious belief. His argument is fatally circular .

Thomasian Five Ways


conjunction vs disjunction

Formally, within mathematics or logic, the conjunction "and" is a two-place logical operator that yields true whenever both of its operands are true, or false whenever both of its operands are false.

In the vernacular, we use "and" to indicate conjunction. A grammatical conjunction is employed to connect two words, phrases, or clauses. Coordinating conjunctions include "and" and "or".

Formally, within mathematics or logic, the disjunction "or" is a logical operator that yields true whenever one or more of its operands is true.

In the vernacular, we use the coordinating conjuction "or" to indicate disjunction. When presented with two, or more, propositions, only one of which can be true, or when presenting alternates, opinions, or ideas of equal importance, we say either this or that/those. In other words, it could be this or it could be that/those or (often implied) it could be something else.

A disjunctive syllogism revolve around "not". The modus tollendo ponens, or MTP, is a classically valid, simple argument form:
P or Q
Not P
Therefore, Q

A is B or C or D
A is not C or D
Therefore, A is B

A fallacious disjunctive syllogism is found in the typical creationist fallacy:
Either God or Darwinian-evolution. (a false dichotomy)
Not-Darwinian-evolution. (a false premise)
Therefore, God. (a false conclusion)

The Cogito argument

René Descartes contrived his famous Cogito argument as a stage within his ontological argument for the existence of God.

Descartes claimed that he had cast all that he had previously believed into doubt before examining what remained. The argument runs that even if God has deceived him by placing thoughts in his mind, the mere fact of his being deceived means that something capable of being deceived must necesserily exist.

"But how do I know that there is not something different altogether from the objects I have now enumerated, of which it is impossible to entertain the slightest doubt? Is there not a God, or some being, by whatever name I may designate him, who causes these thoughts to arise in my mind ? But why suppose such a being, for it may be I myself am capable of producing them? Am I, then, at least not something? But I before denied that I possessed senses or a body; I hesitate, however, for what follows from that? Am I so dependent on the body and the senses that without these I cannot exist? But I had the persuasion that there was absolutely nothing in the world, that there was no sky and no earth, neither minds nor bodies; was I not, therefore, at the same time, persuaded that I did not exist? Far from it; I assuredly existed, since I was persuaded. But there is I know not what being, who is possessed at once of the highest power and the deepest cunning, who is constantly employing all his ingenuity in deceiving me. Doubtless, then, I exist, since I am deceived; and, let him deceive me as he may, he can never bring it about that I am nothing, so long as I shall be conscious that I am something. So that it must, in fine, be maintained, all things being maturely and carefully considered, that this proposition (pronunciatum) I am, I exist, is necessarily true each time it is expressed by me, or conceived in my mind."[L][ F][M2]

The Discourse on Method was written in French, and there Descartes used the phrase, "Je pense, donc je suis." Descartes decided that this phrase could be misleading because it implied that he was appealing to an inference, so he changed the phrase to "I am, I exist" ("the first certainty") so as to avoid the term "cogito" in the later Meditations.

There have been a number of criticisms of the Cogito argument.
This video is the argument itself, and not one of the many criticisms:

Link .

correlation vs. causation

Correlation indicates the direction (+/-) and degree of relationship between two random variables, and does not necessarily indicate a cause-effect relationship (causation). That is, correlation does not imply causation.

For example, if a group of people are wearing lightweight clothing and perspiring, this positive correlation does not indicate that lightweight clothing causes people to perspire. On the other hand, a correlation between strenuous exercise and perspiration is associated with causation.

Critical Thinking

Critical thinking is not necessarily negative thinking, rather it involves shedding light on an issue.We shed light on any subject by thinking analytically, or critically, about available information. Critical thinking can be defined as, “Reasonable reflective thinking that is focused on deciding what to believe or do. More precisely, critical thinking involves assessing the authenticity, accuracy, and/or worth of knowledge claims and arguments. This process requires careful, precise, persistent and objective analysis of any knowledge claim or belief to judge its validity and/or worth.” Source: definition of critical thinking

The practice of critical thinking sets out to assess the validity of premises, logic of arguments, and reliability of conclusions. In practice, discerning the truth of an argument is not always a simple task. Core Concepts in Critical Thinking Introduction to Statements or Claims

An argument is a set of statements. The premisesfacts or propositions – are intended to provide support for the conclusion. The conclusion is asserted to be true on the basis of the premises. If an argument is cogent, then a true conclusion follows logically from true premises.

Critical thinking is not equivalent to that vernacular meaning of skepticism that refers to a habitual, cynical attitude of incredulity. However, where philosophical skepticism equates to a methodology for obtaining knowledge through systematic doubt and continual testing, then skepticism is a phase of critical thinking.

Scientific method is akin to formalized skepticism in that it proceeds by rigorous scrutiny of falsifiable hypotheses. Any hypotheses that are demonstrated to be faulty will be discarded, and alternated explanations for empirical observations will be formulated and tested. Eventually, any reasonable hypotheses that are not disproven will be regarded as so acceptable as to be elevated to the level of scientific theory.


René Descartes (1596-1650) was a French rationalist philosopher, mathematician, physicist, and physiologist who is regarded as the father of modern philosophy. Decartes is best known for the phrase "cogito ergo sum", for his argument for mind-body dualism, and for Cartesian geometry.

Descartes revitalized philosophy by his rejection of the Aristotelian and Scholastic traditions of the "schoolmen".

Descartes, in Discourse on Method and Meditation, claimed to have proved the existence of God.

In brief, Descartes’ argument runs as follows. Descartes first claimed* to have discarded all received information:

• My senses may mislead me, and I may have been deceived by a malignant demon.

So, I can only be certain of the content of my consciousness, and thus know that I exist as a thinking being – cogito ergo sum.

• I comprehend the nature of corporeal objects – a ball of wax – more fully with my intellect than with my senses. Concerning my clear and distinct ideas, I could have no assurance of the truth of my perceptions if any proved to be false.

So, as a general rule all that is clearly and distinctly apprehended (conceived) is true.

• I could be deceived about the truths of arithmetic and geometric objects, but my idea of God does not include His being a deceiver.

So, God is not a deceiver.

• Assuming that ideas conform to external things is the commonest error of judgment. Some such ideas are innate, others adventitious, and others factitious. Considering ideas as images, I note great degrees of diversity. Ideas that represent substances have more objective reality (content concerning finite substances) than those that represent modes or accidents. The idea by which I conceive a God has more objective reality than those ideas by which finite substances are represented.

Conclusion: God exists. God exists according to the preceding arguments, and because: It is manifest by the natural light [innate wisdom] that there must be as much reality in cause as effect, both for real objects and for ideas with objective reality. My imperfect, finite self could not have originated the idea of a perfect, infinite God, nor could the idea of God have come from nothing. My idea of the infinite is a true idea and not a negation of the finite.

And (sub-proof)

• I did not bring myself into existence because I am not God and do not possess God’s perfection. A different God could not have created me because only one such God can exist according to my concept of God. My parents did not produce me as a thinking being, they do not conserve me from one of an infinity of independent instants into the next. God did not create me in his own image (counter to atheist claims), and I cannot complain that God allows me to be mistaken.

Conclusion: I could not have come to exist, nor be conserved in that existence except by the agency of God.

The most obvious difficulty with Descartes’ argument lies in its fatal circularity. However, problems with unacceptability of premises strike the reader before Descartes begs the question in his conclusion.

One of the most glaring errors in Descartes' argument lies in the following premise, "My imperfect, finite self could not have originated the idea of a perfect, infinite God, nor could the idea of God have come from nothing. My idea of the infinite is a true idea and not a negation of the finite."

The idea of a perfect, infinite God predates Descartes by thousands of years since the Christian God is actually the Jehovah (Yahweh) of Judaism. So, pious, Jesuit-educated Descartes clearly must have obtained this idea through Christian teachings. He conveniently*, and dishonestly, ignored this obvious fact for the sake of his highly contrived and ultimately ineffectual argument.

Equally faulty is Descartes' claim that, "The idea by which I conceive a God has more objective reality than those ideas by which finite substances are represented." Unless Descartes had a highly distorted sense of reality, or he was lying again, he would have actually experienced his earliest, clearest, and most distinct “ideas” due to the existence of a substantial world outside his conscious self.

Descartes quickly and unknowingly refutes his own argument when he states, “But if I desire to think of a chiliagon, I indeed rightly conceive that it is a figure of a thousand sides, as easily as I conceive that a triangle is a figure composed of only three sides; but I cannot imagine the thousand sides of a chiliagon as I do the three sides of of a triangle, nor, so to speak, view them as present [with the eyes of my mind].”

When Descartes admits that he cannot as clearly imagine a thousand-sided figure as a triangle–hardly surprising!–he is inadvertantly admitting that he could not clearly imagine perfection, so could not possible conceive of God with more objective reality than finite substances.

In essence, Descartes tries–and fails–to prove that the subject of an idea has reality outside the idea.

* Descartes failed to discard the inculcated notion of God. To do so would obviously have defeated the purpose of his argument. Considering the religio-political climate in which Descartes lived, his bias is understandable.

Disprove the Nonexistence!

White swan with cygnet.It is possible to negate a categorical, contingent proposition by finding a counter example: Black swan with cygnets.

The proposition that "all swans are white" is easily disproven by even a single instance of a black swan.

However, given that some birds are blue, some overimaginative ornithologist might declare, "some swans are blue", or, even more difficult to disavow, "blue swans formerly existed."

To demonstrate – prove – this blue-swan proposition would require finding a blue swan. However, how could one disprove the existence of something that does not exist? Even though a survey of gazillions of swans would (almost certainly) only turn up white and black swans, it is remotely possible that there could have been a blue swan that left no trace of its existence. Vanishingly unlikely, of course, but remotely possible.

Altered photograph of a white mute swan feather.It is not logically possible to categorically demonstrate such a non-example. Such a failure of disproof would not indicate that the proposition had any validity, because it is even less likely that a blue swan has ever existed than that my hypothetical demented ornithologist should be correct.

When religionists taunt, "it is up to atheists to prove that God does not exist," they are making an illogical demand on several counts: a demand for the logically impossible, a shift in the burden of proof, a fallacious argument from ignorance, and ignoring or denying the counter-evidence (refutation of apologetics, scientific explanations).

Theistic claims fall into the "some swans are blue" category. Claims for the existence of some supernatural entity that purportedly once interfered with the cosmos (deism) fit into the "blue swans formerly existed" category. However, the claimed theistic supernatural supposedly interfered with the universe post-Bang and there ought to be some physical evidence that could be explained only by reference to this purported interference. Just like the case for blue swans, there ought to be some evidence of the purported existence. That is, there cannot be two contradictory explanations for one event.

Apologetic claims for God's existence fall into the same category as the swan feather that I altered to make it appear blue. The fact that I invented the blue-swan example purely for the sake of argument indicates that we can make assumptions about the possible truth (or untruth) value of a proposition by examining its source. The fact that creation myths and deities have been invented by almost every civilization yet examined, suggests that, like the blue-swan, we can dismiss claims for supernatural deities along with discarded mythologies and Russell's teapot.


Empiricist philosophers take the position that sense experience is the ultimate source of all our concepts and knowledge. By contrast, rationalist philosophers make the claim that there are significant ways in which our concepts and knowledge are gained independently of sense experience.[1]

David Hume : John Locke

Jean Piaget's research into the development of cognitive schemas provides empirical support for the empiricist position. Piaget's experiments demonstrated that children incorporate experience to generate a progressively more logical construct concerning the operation of reality. That is, during the development of cognitive rationality, experiential information is assimilated and accommodated in a progression through increasingly more accurate reality-representational stages.

1. Markie, Peter, "Rationalism vs. Empiricism", The Stanford Encyclopedia of Philosophy (Fall 2004 Edition), Edward N. Zalta (ed.), URL.


Epistemology is a branch of philosophy that deals with the nature, origin and scope of knowledge.

The term 'epistemology' derives from the Greek words episteme (knowledge) and logos (word/speech). Epistemic is an adjective that signifies being of or relating to epistemology.

Epistemologists are primarily interested in propositional or theoretical knowledge rather than in skill sets.

A belief is some proposition that the individual holds to be true. For a belief to count as knowledge, no matter how strongly the individual feels the belief to be true, the belief must actually be true. That is, to count as knowledge, a belief must be justified, and, according to Gettier, must be justified for the correct reasons (justified true belief that depends on no false premises, also termed 'no false lemmas'). The term 'justification' signifies that the person who believes something has an epistemic reason to thinking that the belief is true. A belief that consists of accidentally stumbling upon the truth does not constitute knowledge.

Relevant, empiric evidence can never provide inductive proof for a principle, because inductive proof is logically impossible. This means that failure to provide inductive proof is not necessarily failure of a theory given the facts upon which the induction is based. This also does not mean that there is not an underlying principle (mechanism) that is in reality responsible for the observed phenomena. Thus, some inferred principles are much more likely to reflect the actual underlying mechanism than are others, though a principle can never be proved by induction from the observations.

Scientific method can lead only to disproof (falsification) or to experimental corroboration that a scientific hypothesis or theory is the most probable explanation for observed phenomena. Similarly, correlation may result from causation, but it may also reflect some other relationship other than cause and effect, so correlation alone cannot be taken to indicate causation.

Epistemic probability refers to degree of belief in judgement-requiring propositions, uncertain events, or problems. Bayes' theorem (rule, law) derives from probability theory, a branch of mathematics that deals with the analysis of random phenomena. Bayes' theorem relates the conditional and marginal probability distributions of random variables.

Bayesianism is the philosophical tenet that the mathematical theory of probability can be taken to apply to the degree of plausibility of a statement, or to the degree of believability contained within the rational agents of a truth statement. When a statement is employed within the Bayes' theorem, the statement becomes a Bayesian inference.

Conditional probability is the probability of some event A, given the occurrence of some other event B – P(A│B) – the conditional probability of A, given B. P(A│B) is also called the posterior probability because it depends upon the specified value of B. P(B│A) is the conditional probability of B given A.

Marginal probability is the probability of one event, P(A), regardless of the other event, P(B). P(A) is termed the prior probability or marginal probability of A. P(B) is the prior or marginal probability of B, and acts as a normalizing constant. The marginal probability is derived by integrating the joint probability over the unrequired event (marginalization).

The joint probability is the probability of the two events in conjunction (both events together), where the joint probability of A and B is written P(A∩B) or P(A,B).

Bayes' Theorem: the conditional probability of event A given event B = the likelihood of event B given event A x the prior likelihood of event A, divided by a normalizing constant (the prior probability of event B) .

................................... likelihood x prior
......... posterior =... _______________

................................. normalizing constant

......... posterior = standardized likelihood x prior

In some interpretations of probability, Bayes' theorem is taken as a guide of how to update or revise beliefs in light of new a posteriori evidence. Here, Bayesian probability is an interpretation of Bayesian theory, which holds that the concept of probability can be defined as the degree to which a person believes a proposition.


David Hume (1711-1776) was a Scottish empiricist philosopher, economist, essayist, and historian. Hume is best remembered for "Humean skepticism". Hume considered philosophy to be the inductive, experimental science of human nature and considered himself chiefly as a moralist philosopher.

Hume built upon John Locke's epistemology and adapted the scientific method of Sir Isaac Newton as his model. He attempted to describe the operation of the mind in acquiring knowledge and concluded that there can be no knowledge of anything beyond experience. Hume raised the skeptical philosophical objection that inductive reasoning might fail whenever the past cannot be taken to be a reliable guide to the future.

"Does a man of sense run after every silly tale of hobgoblins or fairies, and canvass particularly the evidence? I never knew anyone, that examined and deliberated about nonsense who did not believe it before the end of his enquiries." ~ David Hume, Letters

Websites : Hume: Empiricist Naturalism : Hume texts online : David Hume: Writings on Religion : Hume on Religion : quotes from Hume's writings : EpistemeLinks - Hume quotations : philosophical skepticism : Skepticism :

inductive vs deductive

Inductive reasoning moves from the specific to the general, that is, from data to a principle.

Deductive reasoning moves from the general to the specific, that is, from the principle to particulars.

Abductive reasoning moves from relevant evidence (specific) to the best possible explanation (principle). Abduction is inference to the best explanation – beginning from a set of accepted facts, inference proceeds to the most likely explanation for those facts. Inference is the process of deriving a conclusion that is based solely on what is already known (a posteriori).

Inductive reasoning involves coming to a conclusion that is inferred from multiple observations. Repeated testing will help to ascertain whether first inference (conclusion derived) is correct or incorrect. In contrast, valid deductive reasoning is based in formal logic and will yield a true conclusion if the premises on which it is based are themselves true. That is, the inferred conclusion of a valid deductive inference is necessarily true when the premises are true, so a formally valid deductive inference cannot be false.

The Scottish empiricist, David Hume raised the skeptical philosophical objection that inductive reasoning might fail whenever the past cannot be taken to be a reliable guide to the future. In essence, if we have just seen 43 white swans, are we justified in assuming that all swans are white or even that the next swan that we see will be white?

The philosopher of science, Karl Popper expanded Hume's ideas of the 'problem of induction' and argued that there can be no solution to the problem of induction in that empirical observations cannot provide proof for a scientific hypothesis, theory, or law. Popper argued that, since only disproof is a certainty, science should proceed by a 'deductivist' method of conjecture and refutation, employing deductively valid reasoning that does not resort to inductive confirmation.

In practice, modern scientific method employs inductive, deductive, and abductive reasoning to move from empirical data to elucidation of principles. Ideally, hypotheses are couched so that they could be falsified should they fail to correctly predict experimental observations. However, since the hard sciences involve empirical observations of natural phenomena that can reasonably be expected to operate consistently, relevant positive results are taken to provide practical support for the likelihood that a theory is accurate.

Unlike the case for swans, would we not be fully justified in believing that all apples that fall from an apple tree will fall toward Earth rather than floating toward the moon? To stipulate that the apple tree is situated on Mars would appear to put a worm in this theory, but that problem can be avoided by asking instead, 'would we not be fully justified in believing that all apples will fall toward the planet?' Whether we talk of the force of gravity, or the more modern understanding of warping of space-time, natural laws dictate that objects are most 'attracted' to the largest nearby mass.

external links : Search the Stanford Encyclopedia of Philosophy :

Leibniz on Monads

Gottfried Wilhelm Leibniz (1646-1716) was a German rationalist philosopher and polymath. (Polymaths, are those who excel in a wide variety of subjects or fields – Leonardo da Vinci, and Hildegarde of Bingen are also regarded as polymaths. Polymaths are also called Renaissance men or Homo Universalis.)

Leibniz invented the calculus independently of Newton, and we owe present day notations within differential and integral calculus to Leibniz. and Leibniz's philosophy is best remembered for his monadology. Leibniz wrote, “These Monads are the real atoms of nature and, in a word, the elements of things.” [M, #4, p.455; #4]

Leibniz’s monads exist on three levels: bare monads capable of unconscious perception; soul monads with conscious awareness and memory; and spirit, or rational soul monads capable of self-awareness and reason.

Modern thinkers could agree with Leibniz that, “there must be simple substances, since there are compounds; for a compound is nothing but a collection or aggregatum of simple things.” [M, #2, p. 455; #2] Monads are defined as indivisible, simple substances that cannot be altered by external influences. [M, #s 1-7, p.455; #1]

Leibniz proposes that each of the infinite number of monads is different from every other because no two things can be perfectly alike. While this is our general experience, we do have the everyday experience that some substances are almost identical to other examples of the substance – glasses of water drawn from the same tap on different days, for example. Unfortunately, Leibniz is not always clear which forms of substance interest him, animal certainly, vegetable occasionally, but what about mineral? He seems to believe that even mineral substances possess perception in so far as they cannot, by his definition, be destroyed except by annihilation.

Leibniz asserts that monads exhibit continuous change, and he makes this proposal because he owns that ‘every created thing’ does change. [#10; #10] While common sense experience does indicate that assemblages of substance change with time, it seems equally reasonable to postulate that the aggregates change, rather than insisting that the elements themselves change, and Leibniz does acknowledge change in aggregates.

In The Monadology, Leibniz expands upon the theme of monads introduced in the Discourse on Metaphysics when he asserts that, “The passing condition which involves and represents a multiplicity in the unity, or in the simple substance, is nothing else than what is called Perception.” [M, #14, p. 456; #14] Leibniz makes this proposal counter to Descartes’ problematic dualist explanation for the mind-body problem, which does not allow for perceptions not immediately before consciousness. Leibniz states that, “[Cartesians] treat as nonexistent those perceptions of which we are not conscious . . . confusion between a protracted period of consciousness and actual death . . . and have even confirmed ill-balanced minds in the opinion that souls are mortal.” [M, #14, p. 456; #14]

Leibniz clarifies the distinction between the changes that comprise perception and the qualities that he regards inherent to souls, “I think it right that the general name of Monads or Entelechies should suffice for simple substances which have perception only, and that the name of Souls should be given only to those in which perception is more distinct, and is accompanied by memory.” [M, # 19, p. 456; #19] This obvious reference to his beliefs concerning those criteria that distinguish human cognition is an important point because Leibniz believes that mental experience after death will include awareness of the self prior to bodily death, and “they will always be conscious of their being.” [D, p. 452]

Descartes had written of the indivisibility of the mind without postulating a working hypothesis for its function, and Leibniz confesses that, “perception and that which depends upon it are inexplicable on mechanical grounds.” Having failed to explain how the inner workings of perception, he concludes, “Thus it is in a simple substance, and not in a compound or in a machine, that perception must be sought for.” [M, # 17, p. 457; #17] Now it becomes clear why Leibniz proposes that the units, rather than the assemblages change, emphasizing that “all those who admit that the soul is a simple substance should admit this multiplicity in the Monad.” [M, # 16, p. 457; #16] The perplexing difficulty of explaining the mechanism by which mental processes occur – how matter produces mind – has forced Leibniz into the position of postulating that monads themselves are the basis for perception, and ‘appetition’, or desire. “It is also in this alone that all the internal activities of simple substances can consist.” [M, # 17, p. 457; #17]

Of the mind-body connection that Descartes depicted as a dualist unity, Leibniz says, “The body belonging to a monad, which is its entelechy or soul, constitutes together with the entelechy what may be called a living being, and along with a soul what is called an animal.” [M, # 63, p. 465; #63] Leibniz is equating mind to body, but he makes the distinction that, “since feeling is something more than a mere perception, I think that the general name of Monads or Entelechies should suffice for simple substances which have only perception, while we may reserve the term Soul for those whose perception is more distinct and is accompanied by memory. [M, # 19, p. 458; #19]

Each Leibnizian monad is a more, or less clear mirror of every other of the infinity of monads, and of the universe as a whole, yet monads do not have windows through which externals may effect internal change. Another difficulty arises here because Leibniz must explain how experience of the external world – other monads – could bring about not only simple, conscious perception, but induce memory, and elicit rational thought when the change in monads is not brought about by interaction with other monads. Leibniz has two solutions to this problem – he views ideas as innate, part of the personal history of each individual in the world that God has chosen, and he resorts to God. He claims that each monad is affected only through the mediation of God, “But in simple substances the influence of one Monad upon another is only ideal. It can have its effect only through the mediation of God . . . For since one created Monad cannot have any physical influence upon the inner being of another, it is only through the primal regulation that the one can have dependence upon the other.” [M, # 51, p. 463; #51]

Thus, all individual substance comprises mental process in the Leibnizian analysis. This does not fit with common sense experience in that we experience a distinction between the content of mental processes and the perception of our bodies. We are aware that we are able to will our bodies to move, and that such action requires the operation of our mind, although alertness is not essential in so far as others move in their sleep. We certainly see no evidence of unconscious perception in plants even though they do respond to light. In other substances such as rocks, and water, and wine, we see absolutely no evidence of unconscious perception.

Some attributes of Leibniz’s monads, as noted, do correspond to matter as we understand it through science, and this seems more the result of a logical construction of how matter must behave than of pure observation of the common sense world. However, many of Leibniz’s constructs seem exactly that – concepts conveniently constructed to serve his purposes of explication when all conceptualizing necessarily leads from and to God.

Like Descartes and Spinoza before him, Leibniz begins his examination of metaphysics with the assumption of God’s existence, and he must adapt his explanations of the substantial and phenomenal world to this assumption. “In the strictly metaphysical sense no external cause acts upon us excepting God alone, and he is in immediate relation with us only by virtue of our continual dependence upon him.” [D, p. 441] Descartes, Spinoza, and Leibniz each depict a slightly different God, despite employing similar terms such as ‘perfect’ and ‘infinite’, and each makes God, in one way or another, the ultimate explanation for nature. Leibniz’s “God produces different substances according to the different views which he has of the world.” [D, p. 424] “God in co-operating with ordinary actions only follows the laws which he has established.” [D, p. 443] Spirit, rather than substance, constitutes the essence of Leibniz’s God. “God who in all things has the greatest perfection will have the greatest care for spirits . . . it is because he is a spirit that God is the originator of existences . . . spirits alone are made in his image.” [D, pp. 451-2] “God alone is the ultimate unity or the original simple substance, of which all created or derivative monads are the products” [M, # 47, p. 462; #47]

Leibniz claims that existence is a property of God. Yet, our earliest and clearest experience is of the existence of a substantial world of dimensional objects outside ourselves. For instance, the concept of object permanence, the understanding that objects persist when out of sight, is amongst the earliest cognitive schemas attained by infants. Thus, we come to equate existence with the existence of physical objects, though we make a special category of existence for the products of mental processes (concepts). We are also aware that an invisible force termed gravity (warping of space-time) binds us to the surface of the earth. In the modern age, we take for granted the existence of an invisible force of nature, the electromagnetic force, every time that we flick a switch, or listen to a radio. However, because we are aware that this force is generated by machinery, we do not attribute it to God, though Leibniz undoubtedly would attribute it to God if he were unaware of the physical laws behind the phenomenon.

Leibniz recognizes two forms of truth. He terms these truths of fact and truths of fact reasoning, and states that the facts could have been otherwise, but that the reasoning, the hypothesis, could not. Leibniz proposes two principles by which to recognize truth. Leibniz terms these the principles of contradiction and sufficient reason.

31. Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false; (Theod. 44, 169.)

32. And that of sufficient reason, in virtue of which we hold that there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us. (Theod. 44, 196.)

Within the sciences, or the physical as opposed to the metaphysical, we generally reserve the term ‘proof’ for reasoning within mathematics and for a specific class of syllogism. The principle of contradiction is akin to the method of falsification by which scientific hypotheses are experimentally rejected when their predictions are demonstrated inaccurate, or retained when not yet falsified. Thus, we employ facts, experimental empirical demonstrations, to assess the probability that the scientific reasoning is probably true. Ultimately, when a hypothesis has withstood repeated experimental tests for contradiction, it is judged to have show sufficient reason, and is elevated to the status of scientific theory. However, we recognize limitations to the physical sciences in that the metaphysical, what could be termed the supernatural, is not accessible to experimental verification

D. Leibniz: Discourse on Metaphysics. Translated by G. Montgomery, revisions A.R. Chandler. New York: Anchor Books, 1974

M. Leibniz: The Monadology. Translated by G. Montgomery, revisions A.R. Chandler. New York: Anchor Books, 1974

Online version: THE MONADOLOGY by Gottfried Wilhelm Leibniz translated by Robert Latta

Links : Gottfried Wilhelm Leibniz : Leibniz's Ethics : Gottfried Wilhelm Leibniz : Leibniz


John Locke (1632-1704) was a British empiricist philosopher, Oxford academic and medical researcher.

Locke is probably best known for his anti-authoritarian, humanist political philosophy, which inspired the American revolutionary ideology.

Locke's epistemology was partly a response to Descartes' insistence upon the rationalist supremacy of innate ideas. Locke countered with the concept of the tabula rasa – the mind as a blank slate that is writ upon by experience.


Logic can be symbolic or informal.

Symbolic logic examines the precise symbolic representation of logical concepts, the abstract relationships between these concepts, and the systematization of these relationships. Informal logic involves the application of logical principles to assessment the types of informal arguments and claims that we encounter in daily life.

Propositional logic is a branch of symbolic logic dealing with propositions as units and with their combinations and the connectives that relate them – if, then compound statements. Propositional Logic Terms and Symbols Proposition evaluator.

Categorical logic and categorical syllogisms are more concrete than is propositional logic – some, all, and/not. Venn diagram evaluator.

An understanding of Fallacies of Logic – recognized structural errors in argumentation – provides a shortcut to assessing the cogency of an argument. We most often encounter propositional arguments in daily life, while the logic of science, and of mathematics in particular, is more often categorical.

Test your Logic Skills : An Introduction to Philosophical Logic : The London Philosophy Study Guide, Logic and Metaphysics : forall x: an introduction to formal logic : Translation Tips : Logic Self-Taught: A Workbook : A Brief Introductory Guide to Formal Logic


From Cartesian dualism to Spinoza’s dual-attribute monism, Descartes’ and Spinoza’s arguments share some concepts while differing in significant ways concerning the relationship between mind and body. Descartes conceived of mind and body as separate, while Spinoza viewed mind and body as two attributes (aspects) of a single essence.

Descartes’ primary objectives in Meditations were to argue for the existence of God and for the possibility of the soul’s immortality. In The Ethics, Spinoza intended that his arguments correct what he perceived as the main difficulties in Descartes’ philosophy – the potential paradox of infinite division of finite dimension, the conceptualization of God, the mind-body problem, and the question of free will.

It is worth first noting that Descartes and Spinoza held different views of God. For Descartes, God is both his creator and the creator of his supposedly innate idea of God. For Spinoza, God is not his creator, but instead equates to the totality of Nature. Spinoza views God/Nature’s essence as existence, and God/Nature as a single substance with two basic attributes – substance and thought. Spinoza proposes that God/Nature’s attributes generate an infinite number of existent or potentially existent components, including human minds and bodies.

Descartes expanded on the Cogito argument, “Thinking is another attribute of the soul; and here I discover what properly belongs to myself. This alone is inseparable from me. I am—I exist: this is certain.” Descartes claims that the essence of his individuality lies in his soul, his conscious mind, and not in his body, “I am not the assemblage of members called the human body.”

Descartes invested in two distortions for the sake of his argument–that ideas are more clear than sensations, and that the mind and body are distinct. Descartes identifies the pineal gland as the site of the inexplicable interaction between mind and body–he probably chose the pineal because it sits at the base of the brain.

Descartes’ mind-body dualism enabled him to claim both that God (author of Descartes’ innate idea of God) exists and that the soul persists after the death of the body. He claimed that mind and body could exist separately, but that the mind was tethered to the body during the body’s lifetime—convenient!

Spinoza responded to Cartesian mind-body dualism by countering that the mind knows of its own existence only through the body, “The human mind has no knowledge of the body, and does not know it to exist, save through the ideas of the modifications whereby the body is affected.” That is, the mind perceives the body through sensations that originate in the body. In essence, Spinoza is claiming that the mind perceives the body only through changes in the body, and we perceive external objects through their impacts upon our sensory organs – sight, sound, touch, taste, smell, and motion.

To Spinoza then, thought is simply a modification of the body. In a sense, he was sufficiently correct for a reawakening of interest in his ideas amongst those currently ‘meditating’ on how the brain constructs consciousness through its physiological processes. (Neurologist Antonio Damasio is author of Looking for Spinoza: Joy, Sorrow, and the Feeling Brain)

Other : Princess Elisabeth and the Problem of Mind-Body Interaction .

...section index...

Modal Logic

Philosopher, Saul Kripke.Modal logic is a branch of formal logic that deals with possibility (◊, L), necessity (□, M), and existence. The most familiar logics in the modal family are constructed from a weak logic named K, for Saul Kripke.

This narrow reading confines modal logic to concerns with necessity and possibility. Modal logic was first developed to deal with these special, alethic modality concepts (possibily true and necessarily true), and was later extended to other concepts. Using K as a foundation, a variety of different logical systems have been developed.

Alethic modality indicates the speaker’s estimation of the logical necessity or possibility of the content of a proposition. Alethic logic deals with factual, or "truth", issues.

A proposition is said to be:
possible if it is not necessarily false (regardless of whether it actually is true or false);
necessary if it is not possibly false;
contingent if it is not necessarily false yet not necessarily true either (a limited case of possibility).

◊ P ↔ ¬ □ ¬ P
P is possible if and only if it is not necessary that not P.

□ P ↔ ¬ ◊ ¬ P
P is necessary if and only if it is not possible that not P.

Because anything is possible that is not necessarily false, almost anything is possible and almost nothing is logically impossible. Thus, possibility is a very weak condition in that much that is logically possible is not necessarily true. In a real sense, logical possibility signifies very little because it inheres so much while explaining so litttle.

It is not clear that there are any necessary propositions and, if there are, they are restricted to analytic propositions or other propositions that are true by virtue of their logical form. If there are necessary events, then natural rather than logical necessity is involved.

Metaphysical possibility is generally considered to be stronger than bare logical possibility in the sense that fewer things are metaphysically possible than are logically possible. A thing is physically possible if it is permitted by the laws of nature, which themselves have been established by the empirical observation of physical entities and phenomena.

Apologetic arguments rely on the fact that almost anything is logically possible, in order to make claims that God 'necessarily exists' according to definitions specially contrived to inhere supernatural existence. Such arguments have been repeatedly refuted, though it is the nature of religious belief to deny inconvenient refutation.

Whereas alethic logic deals with "truth" issues, epistemic logic deals with logical issues stemming from such epistemological concepts as knowledge, belief, assertion, and doubt. Epistemology is a branch of philosophy that deals with the nature, origin and scope of knowledge.

Deontic logic, by contrast, is concerned with obligation, permission, and related concepts (licitum, illicitum, debitum, indifferens). Deontic logic is a formal system that attempts to capture the essential logical features of concepts such as are expressed in "ought", "could", "permissible", "requires", "forbidden", and "obligatory".

Modality and Possible Worlds

In much more detail, videos and text: The Modal Ontological Argument.

McNamara, Paul, "Deontic Logic", The Stanford Encyclopedia of Philosophy (Spring 2006 Edition), Edward N. Zalta (ed.), url.
Lokhorst, Gert-Jan, "Mally's Deontic Logic", The Stanford Encyclopedia of Philosophy (Winter 2004 Edition), Edward N. Zalta (ed.), url.
Hendricks, Vincent and John Symons, "Epistemic Logic", The Stanford Encyclopedia of Philosophy (Spring 2006 Edition), Edward N. Zalta (ed.), url.
Garson, James, "Modal Logic", The Stanford Encyclopedia of Philosophy (Summer 2007 Edition), Edward N. Zalta (ed.), url.
Carnielli, Walter and Marcelo Esteban Coniglio, "Combining Logics", The Stanford Encyclopedia of Philosophy (Fall 2007 Edition), Edward N. Zalta (ed.), url.

necessary vs sufficient

A necessary condition, is that condition without which an event could not take place. So, the presence of a necessary condition renders an event possible but does not guarantee its occurrence.

More formally: A condition A is said to be necessary for a condition B, if (and only if) the falsity (/nonexistence /non-occurrence) [as the case may be] of A guarantees (or brings about) the falsity (/nonexistence /non-occurrence) of B.


If X is a necessary cause of Y, then the presence of Y necessarily implies the presence of X. The presence of X, however, does not imply that Y will occur.

In logic, the terms necessity and sufficiency refer to the implicational relationships between statements or propositions.

For a statment to be true, any necessary condition of that statement must be satisfied. Formally, a statement P is a necessary condition of a statement Q if Q implies P.

The logical relation is expressed as "If Q then P" is denoted "Q P" (Q implies P).

Modal logic deals with alethic modality concepts (possibily true and necessarily true):
A proposition is said to be:
possible if it is not necessarily false (regardless of whether it actually is true or false);
necessary if it is not possibly false;
contingent if it is not necessarily false yet not necessarily true either (a limited case of possibility).

Because anything is possible that is not necessarily false, almost anything is possible and almost nothing is logically impossible. Thus, possibility is a very weak condition in that much that is logically possible is not necessarily true. In a real sense, logical possibility signifies very little because it inheres so much while explaining so litttle.

Disjunctions of sufficient conditions may achieve necessity, while conjunctions of necessary conditions may achieve sufficiency.

A sufficient condition is that condition which guarantees the occurence of an event.

More formally: A condition C is said to be sufficient for a condition D, if (and only if) the truth (/existence /occurrence) [as the case may be] of C guarantees (or brings about) the truth (/existence /occurrence) of D.


If S is a sufficient cause of T, then the presence of S necessarily implies the presence of T. However, another cause U may alternatively cause T. Thus the presence of T does not imply the presence of S.

A statement is true if a sufficient condition for its truth is satisfied. Formally, a statement P is a sufficient condition of a statement Q if P implies Q. The logical relation is expressed as "If P then Q" or "P Q," and may also be expressed as "P implies Q."

A condition that is both necessary and sufficient can produce the effect when acting alone.

The assertion that one statement is a necessary and sufficient condition of another indicates that one statement is true if and only if (iff) the latter is true. That is, either both statements are true, or both statements are false. The logical relation can be alternately expressed as "P is sufficient for Q" or as "Q is necessary for P", since both statements mean that P implies Q.

Brennan, Andrew, "Necessary and Sufficient Conditions", The Stanford Encyclopedia of Philosophy (Fall 2003 Edition), Edward N. Zalta (ed.), url.

Necessary and sufficient conditions (wikipedia)

Occam's Razor

Occam's razor.It's January in the northern hemisphere and you are suffering elevated body temperature, muscle aches, a cough, and a runny nose. Would it be more likely that you are suffering from the common cold or that you are simultaneously suffering from heat stroke, fibromyalgia, pneumonia, and hay fever? Obviously, the single unifying, parsimonious explanation is a far more acceptable answer.

William of Ockham (~1285–1349) was a Franciscan friar best remembered for the heuristic maxim that translates as "entities should not be multiplied beyond necessity" (entia non sunt multiplicanda praeter necessitatem).

Occam's razor (or Ockham's razor) holds that one should always accept as most-likely the most economical explanation that accounts for all the facts. However, Occam's razor is not to be interpreted as suggesting that the simplest or most easily conceived mechanism is explanatory.

(Semiotician Umberto Eco alludes to William of Ockham in his protagonist in "The Name of the Rose".)

Bookcover for Umberto Eco's The Name of the RoseWhile the common cold would be a better explanation for those diverse symptoms, as many as 200 different "common cold" viruses could cause these symptoms, as could influenza. So, applying the razor does not provide the specific answer, but rather eliminates cumbersome alternative hypotheses.

Why should we prefer the common cold/influenza explanation? In January in the northern hemisphere, the incidence of the common cold might reach one in ten, whereas the incidence of heat stroke might be near zero, the prevalence of fibromyalgia one in fifty, the incidence of pneumonia one in a thousand, and the incidence of hay fever zero.

(1/10 is greater than 0 x 1/100,000 x 1/50 x 0, in other words, 1/10 is greater than 0)

For primitive man, a God of the Gaps strategy invented an oversimplified explanation of phenomena ranging from weather to illness. However, much to the chagrin of creationists, we now know that natural laws provide more accurate, though more complex, explanations for observed phenomena. In this reverse of Occam's razor–let's call it Shaving Miracles–such oversimplified, miraculous, supernatural explanations for physical phenomena do not provide any explanation at all. In other words, the probability of God is 0.

How did it happen?

It was a miracle.

How did the miracle operate?

That's for God to know.

How do we know that there is a God?

How else could the miracles have happened?

. . . no explanation at all.

Sites Elsewhere: Why The Simplest Theory Is Never The Right One: Occam's Razor Has A Double Edge : Against parsimony, again : Failures of Reductionism? Level of Analysis Problems in Cognitive Neuroscience :


Jean Piaget (1996-1980) was an enormously influential Swiss child psychologist. His structuralist philosophy held that “In all fields of life (organic, mental, social) there exist ‘totalities’ qualitatively distinct from their parts and imposing on them an organization.”

In 1919, Piaget conducted intelligence tests under the direction of Alfred Binet. Piaget became fascinated not so much with measuring IQ as with determining why children made logical errors. Piaget subsequently devoted his life's work to determining how children passed through stages of cognitive development–via assimilation and accommodation –to construct cognitive schemas.

Piaget conducted empirical research on "genetic epistemology" – the sequential development of logic throughout childhood. He concluded that, "the growth of knowledge is a progressive construction of logically embedded structures superseding one another by a process of inclusion of lower less powerful logical means into higher and more powerful ones up to adulthood."

Piaget used the term assimilation to refer to the process in which an individual adjusts mentally to the environment. This process might require a reinterpretation of the evidence of their senses. Accommodation involves the internal modification of mental concepts that accompanies assimilation.

Piaget's research followed children's cognitive development from birth through to the stage of formal operations (~ age 11). Children pass through substages and stages in a set sequence, building each cognitive schema upon that preceding. However, beyond the logical schema acquired in childhood, not all individuals attain the full repetoir of logical operations necessary for critical thinking. The worldviews of many adults exhibit considerable philosophical tension, and many adults display internally inconsistent, illogical, emotional reasoning fraught with many of the errors found in fallacious arguments. Religious beliefs, particularly those of YECs and other creationists, force illogical inconsistencies into the thinking process.

Websites: Jean Piaget Society, About Piaget, Resources for Students : Piaget's Theory of Cognitive Development :