CLAS 196/PHIL 196
These notes are from the chapter in Sellars (on reserve in
Bailey-Howe), S. Bobzien's article in The Cambridge Companion to The Stoics, and the
Stanford Encyclopedia of Philosophy articles on ancient logic and
- Philosophy, according to Stoics, is divided into three areas:
- We've spent most of our time on ethics, because it's the most
immediately interesting and the part that has a lot to offer us.
- 'Logic' (Greek logike),
a great deal: almost everything to do with language, in fact.
- The two major divisions of 'logic'
- Some Stoics added two further divisions
- Canonic (= epistemology)
- Within Dialectic is found what we would call 'logic' (from now
on, 'logic' will be used in the modern sense, not the Stoic
- OUR sources for Stoic logic are primarily Diogenes Laertius,
Sextus Empiricus, and Galen
- Zeno, the founder of Stoicisim, studied with Stilpo, a
- The Megarians are much more lost to us than the Stoics: we
have scraps and pieces, but there were some famous ones:
- Diodorus Cronus, who came up with the "Master Argument":
- The Master Argument sets out to show the
incompatibility of (i) ‘every past truth is necessary’,
(ii) ‘the impossible does not follow from the possible’,
and (iii) ‘something is possible which neither is nor
will be true’ (Epict. Diss. II.19)
- Eubulides (creator of the paradoxes of the heap and the
- Chrysippus inherited his logical background from this
Megarian-derived stream of thought.
- "Chrysippus wrote over 300 books on logic, on virtually
any topic logic today concerns itself with, including speech
act theory, sentence analysis, singular and plural
expressions, types of predicates, indexicals, existential
propositions, sentential connectives, negations,
disjunctions, conditionals, logical consequence, valid
argument forms, theory of deduction, propositional logic,
modal logic, tense logic, epistemic logic, logic of
suppositions, logic of imperatives, ambiguity and logical
paradoxes, in particular the Liar and the Sorites (D. L.
7.189–199)." From Stanford Encycl. of Philosophy online.
- But before we explore that, it makes sense to briefly cover
Aristotelian logic, which is the other major stream of logic in
- An example of an Aristotelian syllogism:
- All humans are animals
- All animals are mortal
- Therefore, all humans are mortal
- The first two parts are the premises, and the third is the conclusion
- Together they make up a syllogism.
- If the premises are true, you MUST accept the conclusion of
- That is because it is a valid
- Now, consider that syllogism in the following form:
- All A's are B
- All B's are C
- Therefore all A's are C
- This is one of many valid Aristotelian forms of syllogism.
- The form is valid:
it does not matter what you put in there for A, B, and C: the
form is still valid.
- Now consider this:
- All humans are purple
- All purple things are eggplants
- Therefore, all humans are eggplants
- That form is still
- The syllogism is not sound,
because the premises are not true.
- Being sound is not the same as being valid.
- Consider that syllogism form again:
- All A's are B
- All B's are C
- Therefore all A's are C
- Note that the only things that can take the place of A, B,
or C are things
- A, B, and C are called the terms of the syllogism.
- Now consider the following different form:
- All bananas are fruit
- Some bananas are green
- Therefore, some green things are fruit
- and this one:
- No fruit are black
- All coals are black
- Therefore, no coals are fruit
- Those are two further valid forms of syllogism
- Note that all Aristotelian syllogisms have three terms and
make use of "all," "some," "no," and "is/are"
- They speak of universals,
not particular human beings such as "Socrates" or "this man"
- Stoic Propositional Logic
- Consider the following:
- If it is raining this afternoon, then I shall not go out
for a walk
- It is raining this afternoon
- Therefore, I shall not go out for a walk
- Note that this argument CANNOT be put in the form of an
Aristotelian syllogism (it mentions a particular)
- But an Aristotelian premise can be put into Stoic
propositional form: ‘Every A is B’ becomes the conditional
‘If something is A, it is B’ (Sextus Empiricus Against the Mathematicians
- It is of the form:
- If p, then q;
- Therefore, q.
- Note that the letters here are not things, but whole
- Hence, this is called propositional
- This is the sort of Logic the Stoics explored.
- It's hard to say they invented it, because of course,
Aristotle and many before him used it.
- What they did was to explore this sort of logic formally,
which is a kind of invention.
- Each proposition is an assertible
(axioma, plural axiomata), which is
- a self-complete sayable
that can be stated as far as itself is concerned (Sextus
Against the Philosophers
- This means that they can be stated
- but they don't need to be: they still subsist as
sayables even when not said
- That is what "as far as itself is concerned"
- To understand this, we have to understand something
about Stoic philosophy of languages (see below).
- The basic point is that assertibles are not
statements: it takes a person to make a statement:
assertibles don't need people to subsist.
- Any proposition has the quality of being able to be true or
- The terms of Aristotelian syllogisms do not have that
- how can "all bananas" be true or false?
- Propositions can also be time-dependent for their truth: 'It
is night' is only true at night.
- They can be complex or simple:
- 'It is night' is simple, because it contains one
- 'If it is night, it is dark' is complex, because it
contains >1 simple assertible
- When you say a complex assertible, you are not actually
stating the simple assertibles within it: you are stating
one assertible, namely the complex one.
- Saying the simple ones would have to be a separate
- An assertible can be positive or negative:
- It is night
- It is not night
- An assertible can have different modalities
- Ancient Stoics preferred using "first" and "second" instead
of p and q.
- Thus the form above becomes:
- If the first, then the second
- The first
- Therefore, the second.
- They also used "antecedent" for "first" and "consequent"
- Where Aristotle discovered the form of many valid
syllogisms, so did the Stoics
- Most descriptions of Stoic logic say that they held that
there were 5 most basic unproveable modes that were valid:
If p, then q; not q; therefore not-p.
Not p and q; p; therefore, not-q.
Either p or q; p; therefore, not-q.
Either p or
q; not-p; therefore, q.
Each one has a complex assertible as first premise, a simple
assertible as second premise, and a simple assertible as
They use logical terms:
- If p, then q; p; therefore, q.
The assertibles can be negative or positive: "not" marks the
The Stoics thought that all valid arguments could be reduced
to one or more of those five valid forms
To see how this might be so, consider the following basic
- those containing an "if" are called conditionals
- those containing "or" are called disjunctions
- those containing "and" are called conjunctions
The Stoics devised guidelines to transform an argument into
one of the five basic forms.
BUT those modes are a convenient modern description:
- If p, then q;
- Therefore, q.
- The following are not the same as that basic form, but
could be re-formed into that basic form:
- If not-p, then
q; not-p; therefore, q.
- If p, then not-q; p; therefore, not-q.
The "five basic modes "were defined by five standardized
meta-linguistic descriptions of the forms of the arguments (S.
E. M 8.224–5; D. L. 7.80–1):
- A first indemonstrable is an argument composed of
a conditional and its antecedent as premises, having the
consequent of the conditional as conclusion.
- A second indemonstrable is an argument composed of a
conditional and the contradictory of its consequent as
premises, having the contradictory of its antecedent as
- A third indemonstrable is an argument composed of a
negated conjunction and one of its conjuncts as premises,
having the contradictory of the other conjunct as
- A fourth indemonstrable is an argument composed of a
disjunctive assertible and one of its disjuncts as premises,
having the contradictory of the remaining disjunct as
- A fifth indemonstrable, finally, is an argument composed
of a disjunctive assertible and the contradictory of one of
its disjuncts as premises, having the remaining disjunct as
- quoted from the Stanford Encyclopedia of Philosophy,
online entry on ancient logic
- Philosophy of Language
- The Stoics said that three
things are linked together, the thing signified and the
thing signifying and the thing existing; and of these the
thing signifying is the utterance ("Dion" for instance); and
the thing signified is the actual thing indicated thereby
and which we apprehend as subsisting in dependence on our
intellect, whereas foreigners although sharing the utterance
do not understand it; and the thing existing is the external
object, such as Dion himself. And of these, two are
bodies--that is, the utterance and the existing thing--and
one is incorporeal, namely the thing signified and sayable,
and this too is true or false. (Sextus Empiricus Against the Mathematicians
- So there is the voice, which is physical movement of air: a
body: that is the "utterance"
- It is a body and so it can be a cause
- It by itself has no meaning (see "sayable" below)
- There is also the thing signified: Dion.
- Also body: can be a cause
- Then there is the "sayable," the lekta, which is roughly the 'meaning.'
- There are other kinds of lekta, but we are concerned with
incomplete and complete lekta
that are assertibles (rather than questions, imperatives,
- They subsist: they don't actually exist: they subsist
- They always subsist, whether someone or some thing is
actually thinking or saying them
- Their primary function is to be uttered or thought
- They are the only sort of thing that can be uttered or
- From Seneca letter 117
- We of the Stoic school
believe that the Good is corporeal, because the Good is
active, and whatever is active is corporeal. That which is
good, is helpful. But, in order to be helpful, it
must be active; so, if it is active, it is
corporeal. They (the Stoics) declare that wisdom is
a Good; it therefore follows that one must also call
wisdom corporeal. But they do not think that being
wise can be rated on the same basis. For it is
incorporeal and accessory to something else, in other
words, wisdom; hence it is in no respect active or helpful.
- So, strictly speaking, "The state of being wise" is not
good according to Stoics, because it is not active: it is
- Meaning does not exist, for Stoics. It subsists. Only
bodies exist, and meaning is not a body.
- And since it is not a body, no meaning can cause anything.
- So when I say "Fire!", the meaning of that utterance
cannot cause anything!
- Why in the world did they come up with this?
- And how can language cause me to do things?
- Well, language always comes to us in a bodily
form: as utterances. Utterances are bodies: they are
physical movements of bodies. Thus they can cause things.
- When I say "Oh lord, a god just came in the door!", that
utterance presents an impression to you, and you assent to
it and are thereby caused to move.
- The meaning does not figure into the causal explanation.
- Thoughts are material too: they are arrangements of soul
- Any incorporeal sayable can only be said by a body: a
voice or thought.
- An important problem for logic arises:
- two utterances which use NONE of the same words might in
fact correspond to the same assertible.
- And on the other hand, one and the same utterance may in
fact be ambiguous between two quite different assertibles!
- The Stoics attempted to find a way around this by regimenting their use
of language to eliminate such situations: they do this to
analyze and understand: they are not saying everybody has to
think like this, but rather that everybody's logical
thoughts can be reduced to this unambiguous regimented
- for example, they require that any assertible start with
the logical particle characteristic of that type of
assertible (e.g. "Not:" for negations, "If ..." for
conditionals, "Both ... and ..." for conjunctions, "Either
... or ... or ... etc." for disjunctions.
- Let's look at some examples of assertibles:
- Definite Assertible: 'This person is dead.'
- Predicative Assertible: 'Dion is dead.'
- 'This person is dead' could be used infinite times
with altogether different meanings.
- 'This person is dead' (pointing at Dion), however,
seems more specific and even seems equivalent to "Dion
- NOT SO
- The Stoics thought that "Dion is dead." becomes true
the moment Dion dies, but "This person is dead"
(pointing at Dion) becomes nonsense at that moment,
because Dion no longer exists and so there is no "this
person" for "this person" to relate to.
- Also, remember that propositions can have different
truth values depending on when they are uttered. These
two propositions have different truth values at
different times, and thus they are separate
- When an assertible becomes nonsense, it is simply no
longer an assertible: it ceases to subsist.
- But there's a further problem:
- The indefinite assertible 'Someone is sitting' is only
- The definite assertible "This one is sitting"
- What happens when no one is sitting? Doesn't 'Someone
is sitting' become nonsense and so cease to subsist?
- NOT AT ALL
- It simply becomes false: there is a difference between
being false and being nonsense.
- 'This person is dead' (pointing at Dion's corpse)
is nonsense once Dio dies, but false when he is
- 'Dio is dead' is false when he is alive, but true
when he is dead.
- Just so, 'Someone is sitting' does not become
nonsense when no one is sitting: it is false.
- That is why it makes sense to talk about
'Indefinite' versus 'Definite' assertibles: the two
have different conditions for being true, false, or
- Definite assertibles have some "pointing" word in
them that requires that there be something to point
at for them to have meaning: if the thing they are
trying to point at does not exist, then they have no
- But indefinite assertibles do not require some
specific thing to point at in order to subsist: the
whole point of being a"indefinite" is that they do
not point at any specific thing. Thus we can say
that "Some dinosaur is eating" is false, but not
nonsense, whereas "This dinosaur is eating" is
nonsense (because at this moment in time, there are
no dinosaurs that exist).
- Another case:
- To create an 'apophatic' negative, Stoics just
attached 'not' to an assertible:
- This is not the same as "Diotima is not walking."
- That is because "Diotima is not walking" has to be
analyzed as 'BOTH: Diotima exists AND not: Diotima
- But "Not: Diotima walks" does not assume that
- You have to understand that these assertibles have
those meanings not because of some innate quality of
the language: rather, the Stoics are creating a
- They have observed that sometimes in ordinary
language when we say "Diotima doesn't walk," we
mean two things:
- that Diotima exists and that she doesn't walk.
- other times, when we say "Diotima doesn't walk,"
we mean only one thing:
- Diotima doesn't walk (and I am not saying
anything at all about whether Diotima exists)
- Perhaps we can use this to say how "Unicorns
don't crawl" has a meaning even though unicorns
don't exist. It might be regimented as "Not:
- Adding "Not:" to true assertibles makes them false.
Adding "Not:" to false assertibles makes them true.
- Of these contradictory assertibles, one and only one
is true and the other one is false.
- Regimentation of complex assertibles
- Stoics required that complex assertibles start out with
a word that identifies what kind of complex assertible
each one is, and that they have connectors between the
simple assertibles within them:
- First, let's look at Chrysippus' three complex
- "If" starts a conditional, and English convention is
to put a comma and sometimes 'then' between the 'If'
part and the 'then' part
- "Either" starts a disjunction, and the connector is
- Disjunctions can contain many assertibles:
- "either p
or q or
r or s...
- Stoic disjunctives are both exclusive and
exhaustive: "either p or q" means
that p or q exhausts all
the possibilities as well as that either p
or q is correct, but excludes the
possibility that both are correct
- "Both" starts a conjunction and 'and' connects the
assertibles within the conjunction
- Now, let's note that later Stoics added several
further kinds of complex assertibles
- Such as pseudo-conditional, causal,
pseudo-disjunctions, comparative assertibles (e.g. 'It
is rather p
than q' and
'It's less p
- I am not currently prepared to fully accurately
explain each of these
- Why add those?
- Two possible reasons:
- They are required to accommodate further obviously
- Analyzing grammar in ordinary Greek or Latin lead
them to those.
- Complex assertibles can contain within themselves
- An illustration:
- First, here is the complex assertible in 'ordinary
language' that is not regimented:
- Either we will have pork and we will have beans
or we will have stew.
- Now here it is in several different possible
regimented logical forms:
- "Either both we will have pork and we
will have beans or we will have stew"
- Note that "either" starts the complex assertible
and so it is a disjunction
- Within it 'both' starts a conjunction
- both we will have pork and we will have beans
- "Both we will have pork and either we
will have beans or we will have stew"
- This one is a conjunction
- with a disjunction inside of it
- "Either we will have pork and beans or
we will have stew."
- This one looks just the same as the ordinary
- It is NOT a complex assertible
- Interpreting it as a regimented assertible, it is
a simple disjunction:
- here, "pork and beand" is one dish rather than
two, "pork" and a separate dish called "beans"
- This use of regimented language is obviously a lot
like the parentheses used in mathematics
- Truth and complex assertibles:
- truth-condition for conjunctions: a conjunction is
true if every assertible in it is true
- Philo's truth-condition for conditionals: 'it must not
be the case that the antecedent is true and the
consequent false' (Bobzien Cambridge Companion P94)
- Chrysippus' truth-condition for conditionals: 'a
conditional is true precisely if its antecedent and the
contradictory of its consequent conflict'
- The reason why Chrysippus wanted it that way was to
deal with problematic cases such as:
- "If the earth has 7 continents, Axiothea
- You should know that Axiothea is just a regular
person, the earth is the earth, and having 7
continents and philosophising are just what you
think they are. Axiothea and the earth's having 7
continents have NOTHING to do with each other.
- Why is that a problem?
- Because Philo's truth-condition says that that
kind of conditional assertible is true: both
assertibles are true, and so it is not the case that
the antecedent is true and the consequent false.
- but Chrysippus' version makes it false: "Not:
Axiothea philosophizes" does not conflict with "The
earth has 7 continents" and so the conditional is
- at least if we think that 'conflict' means "is
- Modern logic makes further distinctions amongst
- for instance (examples from Bobzien P. 95):
- formal logical condition: "If it is daytime, it is
- what is "formally logical" about this is that the
only reason why such a conditional would be
interesting would be because it is formally logical,
even if trivial, I guess.
- Stoics thought this sort of conditional was true,
and so they at least recognized formal logical
- analytical condition: "If Plato walks, Plato moves"
- Called "analytical" because ana-lysis 'takes
apart' the concept of walking as "moving in a
certain way" and so it is "analytical" that if
someone walks, that person moves.
- Examples of this kind of conditional are found in
Stoic logic, so they knew of them implicitly even if
they didn't identify them explicitly as such
- empirical condition: "If Theognis is wounded in the
heart in this way, Theognis will die"
- every observed instance of such a wound has lead
to death has been true
- apparently Stoics recognized this sort too
- For each of these types of conditionals, Bobzien
adduces Stoic examples of that type of conditional.
- But remember, the Stoics did not formally recognize
these distinctions in the way that some modern logics
- So they used such conditionals, but we have no
reason to believe that they did in fact know about
those types of conditionals as distinct types of
- that's a very important distinction: they didn't
do the meta here.
- disjunctions: "Either ... or ... (or... ...)
- Chrysippus concentrated on exclusive and
- Exclusive: 'either p or q' means that one or the other is
the case, but not both: each excludes the other
- Exhaustive: 'either p or q' means that there are two
possibilities and only two, p or q: that exhausts the possibilities
- Gellius XVI
8.13 gives the following as the truth-conditions for
- ... (i) all the
disjuncts must be in conflict with each other and
(ii) their contradictories ... must be contrary to
each other. (iii) Of all the disjuncts one must be
true, the remaining ones false.
- i and ii can be the case even if none of the simple
assertibles are true
- but i and ii also entail that at most one of the
simple assertibles is true
- iii can only be true if one and only one of the
assertibles is true
- for "contradictories" and "contraries," see this
- in classical logic, a logical contradiction is a
logical incompatibility between two or more
- "all S are P" VERSUS "at least one S is not P"
- "no S is P" VERSUS "at least one S is P"
- in classical logic, a logical contrary is
different from a contradictory:
- all S are P IS CONTRARY TO no S are P
- some S is P IS SUBCONTRARY TO at least one S is
- in the end, I am not exactly sure what Gellius means
by "contrary" here. I would need some examples, etc.
- Stoic logical principles
- Stoics clearly recognized:
- The principle of bivalence:
- Any statement is either true or false.
- Not both
- There is no third option other than true or false
- the principle of Double negation:
- A "double negation" is of the form:
- the two negatives add up to a positive:
- to claim "not: not: p" is the same as
- all disjunctions which include p and not:p are true.
- Just for FUN:
- Modern logic does some utterly crazy things:
- Look up fuzzy logic (degrees of truth), ternary logic
(not just true and false, but also "possible"),
intuitionist logic, etc.
- From Stanford Encyclopedia Of Philosophy, online article on
- "Chrysippus may have tried to solve the Liar as follows:
there is an uneliminable ambiguity in the Liar sentence (‘I am
speaking falsely’, uttered in isolation) between the
assertibles (i) ‘I falsely say I speak falsely’ and (ii) ‘I am
speaking falsely’ (i.e. I am doing what I'm saying, viz.
speaking falsely), of which, at any time the Liar sentence is
uttered, precisely one is true, but it is arbitrary which one.
(i) entails (iii) ‘I am speaking truly’ and is incompatible
with (ii) and with (iv) ‘I truly say I speak falsely’. (ii)
entails (iv) and is incompatible with (i) and (iii). Thus
bivalence is preserved (cf. Cavini 1993). Chrysippus' stand on
the Sorites seems to have been that vague borderline sentences
uttered in the context of a Sorites series have no assertibles
corresponding to them, and that it is obscure to us where the
borderline cases start, so that it is rational for us to stop
answering while still on safe ground (i.e. before we might
begin to make utterances with no assertible corresponding to
them). The latter remark suggests Chrysippus was aware of the
problem of higher order vagueness. Again, bivalence of
assertibles is preserved (cf. Bobzien 2002)."
- Modal Logic
- (D. L. 7.75): An
assertible is possible when it is both capable of being true
and not hindered by external things from being true. An
assertible is impossible when it is [either] not capable of
being true [or is capable of being true, but hindered by
external things from being true]. An assertible is necessary
when, being true, it either is not capable of being false or
is capable of being false, but hindered by external things
from being false. An assertible is non-necessary when it is
both capable of being false and not hindered by external
things [from being false]. (transl. taken from
Stanford Encycl. of Phil. online entry on ancient logic)
- Epistemology reviewed
- The impression (phantasia)
is impressed upon the soul.
- It comes from the senses or the mind itself
- the mind at birth is a blank sheet of paper, says Aetius
(4.11.1-2), and so we are not born with knowledge.
- The impression 'causes' a proposition (an "assertible" or
- It is not always clear how this happens, or what it is
- Does our soul have any input, or is this rather a sort of
- and in what sense does it "cause" it: does it cause it to
exist? no, it can only subsist. does it cause it to subsist?
- can't only bodies cause bodies to X? Maybe bodies can
cause non-bodies, but only other bodies can cause other
bodies to X?
- It's not clear to me exactly what relation obtains between
an impression and its proposition.
- The mind then accepts or rejects the propositional content
of the impression
- But that's not the end of the story
- Many times, assenting to one proposition causes further
impressions to arise
For example, this dog snarling at me: I assent that the dog
is snarling at me
- But that causes further impressions about whether it's a
good or bad thing, and what I should do
- the chain of assents and impressions is often very very
fast indeed. Most of us don't even notice that they are
separate events, apparently.
- Any action we take has to have been caused by an impulsive
impression: one that had to come in addition to external
impressions and to have had a good deal of input from the
agent herself: Marcus Aurelius 8.49
- 49. Say nothing more
to thyself than what the first appearances report.
Suppose that it has been reported to thee that a certain
person speaks ill of thee. This has been reported; but
that thou hast been injured, that has not been reported.
I see that my child is sick. I do see; but that he is in
danger, I do not see. Thus then always abide by the
first appearances, and add nothing thyself from within,
and then nothing happens to thee. Or rather add
something, like a man who knows everything that happens
in the world.
- Remember that in order to be kataleptic, an impression has
to fulfill three criteria:
- It comes from what is real
- It corresponds to what is real
- It cannot have come from what is not real
- And even assenting to only kataleptic impressions is not
sufficient to create knowledge
- knowledge is organized and systematic: much more like
modern scientific knowledge