Philosophy of Language Notes
LOGICOMIX
Logicomix: an Epic Search for Truth.
OVERTURE. [Search for the foundations of mathematics: why is it true and how do we know it is.]
1) This is a dramatic story, which starts in September 1939, at Bertrand Russell’s lecture.
2) Themes
are: quest, superheroes, logic and madness,
[Doxiadis is not mathematically oblivious.]
PEMBROKE LODGE child Russell, in abounding secrets, fixes on his origins and, eventually,
Mathematical
truth. The basis of science.
a) Mystery of the moan.
b) The Library. Dante
c) Mystery of the parents. (John Russell, Katherine Russell.)
d) Tutors. German. Mathematics. Proof.
e) The family plot. Family mystery sort of solved. (Old Parker, WWI vet.)
f) Parallel postulate.
SORCERER’S
APPRENTICE,
“c to be an infinitesimal.”
Turgenyev Fathers and Sons
Ibsen’s Ghosts.
Alys Pearsall Smith.
Real Issues: Nature of Mathematical Truth (Why an issue)
The epistemological status of mathematical (logical) truth.
Tour of Philosophy. Plato & Aristotle
Innate ideas KANT, acquired HUME
Descartes, Spinoza (mind/body)
G. E. Moore. Logic and Leibniz (Boole).
Lewis Carroll and Alice in Wonderland. Maze. OR gates.
Science rests on mathematics but mathematics is a mess. Need powerful logic.
WHITEHEAD
WANDERJAHRE.
Gottlob Frege. Reduction of arithmetic to logic. Why? How? Formalization.
Add variables. (“x is a man”) and Sets.
INFINITY!!!!
The song playing in
the logicomix workplace
Machine Translation:
Lovers Of Public Banks Lyrics
People who see through the green benches think
Seen on the sidewalks
Are made for the helpless or the Belly
But it is absurd because in truth they are just notoriously
To accommodate some time loves beginners
The lovers on park benches s'bécottent
Benches, park benches
In s'fouttant lot of sidelong passers honest
The lovers on park benches s'bécottent
Benches, park benches
In s'disant of "I love you" pathetic
Have many mouths p'tites sympatic
They hold hands, talk the next day, the azure blue paper
What will be of the walls of their bedroom
They already see themselves gently, she sewed her smoking
In a welfare course
And choose the name of their first baby
The lovers on park benches s'bécottent
Benches, park benches
In s'fouttant lot of sidelong passers honest
The lovers on park benches s'bécottent
Benches, park benches
In s'disant of "I love you" pathetic
Have many mouths p'tites sympatic
When the holy family thing crosses his path
Two of these ill-mannered
She shoots them boldly about poisonous
Nevertheless, the whole family, father, mother, daughter
The son, the Holy Spirit
Would like that from time to time as they s'conduire
The lovers on park benches s'bécottent
Benches, park benches
In s'fouttant lot of sidelong passers honest
The lovers on park benches s'bécottent
Benches, park benches
In s'disant of "I love you" pathetic
Have many mouths p'tites sympatic
As the months have passed, when will appeased
Their dreams flaming
When their sky was heavy cloud cover large
They will find qu'c'est moved randomly Street
On one of those famous benches
They have lived the best part of their love
The lovers on park benches s'bécottent
Benches, park benches
In s'fouttant lot of sidelong passers honest
The lovers on park benches s'bécottent
Benches, park benches
In s'disant of "I love you" pathetic
Have many mouths p'tites sympatic
Human Translator:
People who give funny looks
Think that the green benches
That you see on the pavement
Are made for crippled people or pot-bellies,
But that’s an absurdity.
For in truth
They are there, it’s common knowledge,
To welcome for a little while couples whose love is
new.
{chorus}
Lovers who smooch on public benches
Public benches, public benches
Not caring one bit about the sidelong glances
Of the proper folk passing by
Lovers who smooch on public benches
Public benches, public benches
Moved by saying to each other "I love you"
Have such nice appealing faces.
They hold each other by the hand
Speak about the future
Of the sky blue paper
Which the walls of their bedroom will assume.
Sweetly, they see each other already
She sewing, he smoking his pipe,
Comfortably secure,
And choosing the names of their first baby.
{chorus}
When the holy family what’s-their-names
Pass on their way
Two of these badly brought up people
They let fly at them, full force, with hurtful remarks
as they walk by.
No matter that, all the family
Father, mother, daughter
Son, Holy Spirit
Would very much like to be able to behave like them
from time to time.
{chorus}
When the months have gone by,
When they have cooled down
The fires of their beautiful dreams;
When their sky is covered with big heavy clouds;
Deeply moved, they will become aware
That it was through a random choice of streets
On one of those famous benches,
That they lived out the best piece of their love.
ii
A language has a vocabulary, formation rules (syntax), and transformation rules (deductive syntax) – e.g., “merde” is not in the English lexicon but “daisy” is; e.g., “1=” “&p” and "we is going" are ill formed (violate grammar or formation rules); e.g. “O. J. has hair follows from O. J. is not bald,”, “Jill hit John” means the same as “John was hit by Jill,” and “From the fact that If the dog barked, then a stranger stole the horse and that The dog barked, it follows that A stranger stole the horse.” (transformational or deductive rule). The second example is “immediate inference,” the third “mediated inference” or syllogism (Aristotle). Logical languages, such as propositional logic, predicate logic, and set theory, have small vocabularies, a few syntactical (or formation) rules; and a small number of axioms or deduction rules.
Syntax; wellformedness. (“syntax” or
“grammar” for linguists; “wellformed” (WFF) for
logicians). Philosophical logicians often pay little attention to wellformedness because it is very simple; natural languages
have very complex grammars and very large vocabularies. But this could be said
to be a result of the fact that artificial languages ignore what might be
called non-logical or non-formal content words or content (predicate logic, for
example, uses the capital letters P, Q, R, etc. to stand for any predicates
whatsoever, while English has an almost endless set of adjectives such as
“red,” “small,” “oblong,”
“polysyllabic,” etc. However, natural language linguists distinguish form words from content words. Languages have a
stable and quite finite number of form words, of which many are clearly
“logical” words such as “and,” “the,” “some,” “is,” “all,” “did,” “never,”
“of,” etc.; while they also have scads and scads of nouns, adjectives, and
verbs (not however scads of auxiliary verbs (“have,” “might,” “should,” etc.)
or scads of pronouns (“I,” “he,” “they,” etc.) – linguists also consider these
to be form words.
For example, Lewis
Carroll’s poem “Jabberwocky”:
‘Twas brillig and the slithy toves
Did gyre
and gimbal in the wabe
All mimsy were the borogroves
And the momraths out grabe.
The poem is clearly has English syntax and English form words; only the
content words are strange (although they do conform to English phonology – they
could be English words.
Propositional logic.
For example, consider the nice, simple, formal language called "propositional logic" (or "sentence logic").
1) Its vocabulary consists of variables standing for sentences or statements: p, q, r, s, etc. These are T(rue) or F(alse); they may also be called atomic propositions because they aren’t broken down any further. The rest of its vocabulary, the operators, is: v, &, à, ~, and =. v means “or”; & means “and”; à means “if _then_”; ~ means “not”; = means “equivalent”; so, “p à q” means “If p, then q”; “~(p & q)” means “not (p and q)”; “p = q” means “p is equivalent to q.” Syntax can be given thus:
(a) an atomic proposition (i.e. p, q, r, etc. as long as you like) standing alone is a WFF;
(b) An operator (except ~) flanked by WFFs is a WFF;
(c) ~ preceding a WFF is a WFF.
2) Instances of its deductive rules are:
(1) ((p à q) & p) à q) Called Modus Ponens.
E.g., “If Paul is dead, then Mary is sad.
Paul is dead. So Mary is sad.”
(2)((p à q) & ~q) à ~p) Called “Modus Tollens.” E.g., “If a stranger was there, the dog
barked. The dog didn't bark. So a stranger was not there.” MP and MT are some of the most important
proof or argument forms; both are frequently employed in philosophical,
scientific, legal and everyday writing and talk.
Propositional logic is neat! The language, using just the ps and qs and operator vocabulary
indicated above, can be straightforwardly proved to be consistent,
complete, and decidable. And those parts of the English language
that can be translated into the propositional logic language (and ignoring
everything else about English) can be regarded in the same way.
In Ludwig Wittgenstein’s famous Tractatus Logico-Philosophicus,
he insists that this suffices to capture the fundamental logic underlying all
languages; in part, indeed, Wittgenstein developed the method – using truth
tables – that can decide, of any well-formed formula, whether it is
logically truth. All such formulae are tautologies: strictly, they are
shown to be true whatever the assignment of truth values to their atomic
propositions, namely, the ps, qs,
and rs, etc. that figure in the formulae, leaving
aside the logical operators (v, &, à, -, =).
A really neat feature is that these logical
operators are truth functional; their meaning is exhausted by the truth
table of their atomic propositions. E.g., the & in “p&q”
means that it is T IFF (if and only if) p is T and q is T; the v in “p v q”
simply means that it is T IFF either p is T or q is truth (or both); the - in
“-p” is T IFF p is F; the à in “pàq” simply means that it is T IFF p is F or q
is T (or both). Because this interpretation of à is not much like the meaning of “If p, then
q” in natural language the à is sometimes
called material implication. So, unfortunately, many English sentences don’t
map well into propositional logic (that is not so neat). Also, and even more
importantly, propositional logic doesn’t reflect many of the other apparently
logical features of natural languages such as English, features such predicates
(adjectives such as “red”, “heavy”, “long”, etc.), quantifiers such as any,
all, some, a, the, and so on.
At this point you may want to ask: What
do “consistency, completeness, and decidability” mean exactly? Briefly:
[Metamathematics: examine axiom systems (=languages) to determine:
1) Consistency. IFF you can't prove a contradiction (e.g. p & ~p 1=0).
2) Completeness. IFF you can prove all the true statements (or equations, etc.). Sometimes we can fix by adding axioms; sometimes we cannot fix this.
3) Decidability.
IFF there is a mechanical (no-brainer) procedure for deciding true or falsity in a finite number of steps. In
propositional logic just use truth tables: given all the possible assignments
of T or F to the atomic propositions, we get T for the whole formula we are
trying to decide.
Yes, proposition logical has these neat features. But, unfortunately, arithmetic and some other mathematical or logical languages provably do not, so far as (2) and (3) goes; and (1) is sort of a wash since, while our language may be consistent, we cannot actually prove this within the language (since we can do arithmetic in English, it also follows that English has all of these features as well). A bit of a surprise Godel & Turing showed us.]
Predicate
Logic. Adds to propositional logic variables that
range over individuals (x, y, z, etc.), predicates (P, Q, R, etc.), and
universal and existential quantification (For any….; there exists at least
one…). So we have “(x)[Px à Qx]” (if anything is a P-er,
then it is a Q-er). E.g., “All men are moral,” “If
anything is a cobra, then it is deadly,” and so on. Notice, in passing, that
this formula does not promise that there actually is a P-er;
it just says that if there exists a P-er, then it is a Q-er. For
example, “If someone jumps out this window, they will fall” doesn’t claim that
anyone is actually jumping or going to, it just says
that they will fall if they do. So we need the existential quantifier, which is
normally written as a backward capital E (I will use the normal E because it is
convenient). So we have “Ex [Px & Qx]. E.g., “Some men are moral.” Sometimes we may add a, b,
c, etc. to stand for particular named individuals. A restricted version of
predicate logic can have the neat features of consistency, completeness, and
decidability.
Set
Theory. Introduces
the notion of set (or class), which is given by specifying the individuals that
belong to the set (e.g., the set of all objects in my left pocket, which is
one, my wallet, the set of all planets in the solar system, which is Mercury,
Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune (and used to be nine,
rather than eight), and so on).
Sets are defined extensionally: just
by listing or pointing out the members; so the set containing George W. Bush is
the same set as the one containing the current president of the US; the set of
all creatures with a kidney is the same as the set of all creatures with a
heart (because every kidney-ed creature is a heart-ed creature and vice versa).
To sets we also add, naturally, the notion of membership so that we can say a
is a member of set B and we also add equality (=), so that we can now say a=b
(or A=B, meaning two sets are equal or one and the same set); distinguish
equality from “equivalence” (=) which just means that two propositions
have the same truth value (equal valence). If you add set theory to predicate
logic (and propositional logic), you do get a language that is adequate to
express the truths of arithmetic; the catch is that you lose completeness and
decidability and get a wash on consistency.
How did philosophy become logic-minded. Consider the sad fate of Gottlob Frege (1848-1925).
Frege decided to reduce arithmetic to logic. (Why do this? - any inconsistency in logic would show, so we could be sure numbers would be all right: there would be no inconsistencies) Here's a first try at defining away numbers logically:
1 = the set of all sets with only one member.
2 = the set of all sets with only two members.
3 = the set of all sets with only three members.
............................. and so on
But there's a problem: the number one (1) occurs on both sides of the "=". So you haven't got rid of one. Let's try again:
0= the set of all sets with no members.
1= the set of all sets such that some x is in the set and, if any y is a member, then x = y.
2= the set of all sets such that some x and some y are in the set, x does not equal y, and if
z is a member, then z = x or z = y.
3= the set of all sets such that some x, some y, and some z are in the set, and x does not
equal y or z and y does not equal z ................................... and so on.
[So 1 is the set of all the unit sets, 2 is the set of all the pair sets, 3 is the set of all the trio sets, and so on. So, e.g., 2 + 2 = 4 means that if you join each pair set with all the pair sets, then you will have the set of all four membered sets. 0 is the set of all sets that have no members. Etc. What else could numbers be? We have triumphed in reducing numbers to purely logical notions.]
However, a problem developed for Frege:
Russell's Paradox (Bertrand Russell (1872-1970)).
Divide all sets into:
1) non-self-membering (oranges, apples, atoms... these are all not members of their sets;
an orange is not a set of oranges; an atom is not a set of atoms; and so on)
2) self-membering (set of all sets, set of all sets of nonapples. the set of all sets is surely a
set; and so on)
Russell's BIG QUESTION:
Is the set of all non-self-membering sets a member of itself???? (If it isn't, then it is; but
if it is, then it isn't).
[Russell sent Frege a postcard that destroyed Frege's life-project. Russell, however, thought he could really solve the problem]
Russell's solution in Principia Mathematica: a hierarchy of languages (in which no language can refer to itself):
1) the object
language (only refer to objects).
etc., allowed.
2) 2nd level
language (refer to objects & 1-type language).
objects but no sets of sets.
3) 3rd level (refer to objects & 1&2). Etc. And so on, and so on.
[NOTE: Since Principia comprehends all of our logico-mathematical (formal) knowledge it is like a mind minus empirical (or sensory) data. Like a programmed computer with no data. Could math (or us) have hidden contradictions? Recall Descartes’ argument that while God, in giving humans free will and senses, made it possible for incautious humans to fall in error, God would not have given humans defective reasoning powers (defective clear and distinct ideas), for that would make human error unavoidable, so that God would indeed be a deceiver.]
The Revenge of the Numbers: 1929. (Courtesy Kurt Godel 1903-1978 and Alan Turing). So you thought you could be sure of mathematics!:
1) Godel assigned a unique number to each possible symbol, expression, proposition, and proof in
Principia Mathematica. All the structure and logical relationships of PM would be
mirrored in Godel’s numerical equations
2) He showed how to construct a true equation that pictured an enormously long true
proposition in Principia that said in effect "I am not provable." But this proposition
would, however, be true. [We now call such propositions "Godel propositions"].
3) Hence, Principia
is incomplete. You cannot prove all the
true propositions. Godel
credited Turing with making this argument general: any formal language
that can
express the truths of arithmetic will be incomplete.
4) Further, Godel showed that to prove that Principia is consistent is to prove a Godel
proposition (one that cannot be proved without a contradiction).
5) So, Principia cannot prove its own consistency.
The same goes for any formalization of arithmetic. You cannot have
completeness or prove consistency. [You could prove the consistency of Principia in another language, call
it Beta (hierarchy again). But
the proof isn't conclusive unless you prove Beta to be consistent. You might prove Beta to be consistent in language Gamma. But this requires a proof in language Delta .... And do on ad infinitum.
Let's move on to:]
Alan Turing (1913-1954). Proved this general result, namely, that any language powerful enough to generate arithmetic must be incomplete & cannot prove its consistency. Further, Turing showed that all such languages contain undecidable propositions. I.e., there is no finite procedure for deciding the truth or falsity of every proposition; Turing also showed that there is nogeneral procedure for identifying undecidables. You cannot segregate them away. Here's the way Turing argued:
1) Every computation is equivalent to a particular "Turing machine"; each has a Turing
number. [Turing modestly just called them "theoretical machines"]
A machine that can do all such computations is a Universal Turing Machine (roughly,
you, me, and your IBM clone.
2) A "general procedure for identifying undecidables" would be a Universal Checker
Turing Machine; you feed it the number of a Turing machine and it decides whether it
computes (is decidable; halts).
3) Turing showed that if you feed a UCTM its own Turing number ("Am I decidable?"),
it would go into paradoxical oscillation (crash!). (The "I" would mean the
mathematical description of the UCTM)
4) Hence, a UCTM is impossible. Who would have thought the liar paradox could do so
much??
[Turing had another argument like
the one that mathematicians use to show that a list of all rational numbers
could not include the irrational numbers. (Rational numbers plus irrational
numbers compose the "real numbers.) Turing showed that any list of
Turing-machine-computable numbers would not include some "incomputable
numbers." Remember that our old friends, sentence logic and predicate,
don't have the problems that confront any language powerful enough to generate
the truths of arithmetic. Sentence logic is provably consistent, complete, and
has a decision procedure. Unfortunately, sentence and predicate logic do not
give you arithmetical truths. The problem comes in with sets and memberships in
sets. Once you introduce these notions, you can get arithmetical truths but you
also get incompleteness and undecidability. Once you
let numbers in, you’re out of
Another result is that once you show that provability and mathematical truth to be distinct, so that no formalization will make all mathematical truths provable, the (1) any formalization is somewhat arbitrary and (2) mathematical truth (or semantics) is more fundamental than provability. Consequently mathematicians are prone to find extensional formalization, or e-language, more fundamental. On the other hand, of course, i-language seems more fundamental psychologically: the natural linguist describing mind/brain states (devices) that are the fundamental natural phenomena. One possible move is to distinguish the language of natural science from the language of everyday life. An end to the logico-linguistic era?]
Notes on Chomsky’s Knowledge of Language:
1) Traditional views of language: aspect of mind, Cartesian linguistics; latterly, “modern linguistics” concerned with noise, infinite variety of conventions (structural linguistics).
2) Knowledge without grounds (not “consciously true and justified”).
3) The common sense view of language has crucial sociopolitical (a language is a dialect with an army and a navy); “learning rules.”)
4) Externalized languages: The notion of E-language is familiar from the study of formal systems: in the case of the “language of arithmetic,” for example, there is no objective sense to the idea that one set of rules that generates the well-formed formulas is correct and another is wrong.
5) Internalized language is the grammar (generative device). “The statements of grammar are statements of the theory of mind about the I-language, hence statements about structure of the brain formulated at a certain level of abstraction from mechanisms.” (comparison to “valence” in 19th century chemistry). (Saussure). “Quine and Lewis have the story backwards”
[Since the Middle Ages, philosophers have wanted to distinguish what is certain (a priori, analytic) from what is merely
factual (a posteriori, synthetic).
1) The central distinction if 17th and 18th Centuries: NECESSARY Statements (2+2=4, A thing is equal to itself) and CONTINGENT Statements (Earth is a spheroid, Leiber is bald)
The necessity was conceived as being out there, in the world (de re in Latin), not relative to human mental faculties or to language.
You could also say that Necessary Truths are “true in all possible worlds, all possible versions of this world),
While Possible Truths are true in at least one possible world, in at least one possible version of this world.
2) The central
distinction of the 19th Century: A PRIORI
Statements (giving the rule to experience, to any possible experience)
and A POSTERIORI Statements (actual experience).
So-called “necessary truths” were really just a priori, built into our mental faculties and determining what are possible experiences for us.
The world is Euclidean not because
it is in itself but because that’s the only way we can
experience the phenomenal world.
3)The central distinction of the 20th
Century: ANALYTIC Statements (true of anything that can be meaningfully said,
of logic) and SYNTHETIC Statements.
So-called “necessary truths” or “a priori truths” are really just analytic. “Contingent truths” and “a posteriori truths” are synthetic (verifiable).
(A
Synthetic Statement stitched together by logical particles (and, or, not,
if-then, etc.) are truth functional.
That means that their truth is determined by the truth or falsity of the synthetic propositions composing it. Tautologies. Ludwig Wittgenstein.
Notes on Sense and Reference:
1) Ueber Sinn und Bedeutung (and Frege’s earlier Begriffschrift) cut new ground and tried to put together new and more exact analyses of language. Some of his distinctions we now express with different words. For example, Frege’s “mode of presentation” would now be called “intension.” The extension (or denotation) of a term is the actual object or objects that happen to fall under a term (like the definition of “set” in logic, which is given by listing or otherwise specifying the objects that constitute the set), while intension means, or includes, the psychological criterion through which the speaker specifies this or these object(s). For Frege, proper names are treated as implicit definite descriptions. So, for him, “Hesperus” means “the evening star,” while “Phosphorus” means “the morning star” and all four have Venus (not “Venus”) as their referent (denotation). Frege also tries to extend his sense/reference distinction to whole sentences. A complete sentence has the thought as its sense and The True as its reference. The claim that the word only has meaning in the context of a sentence is often attributed to Frege. Certainly Frege initiated a strong distinction between a word and a sentence that characterized the logico-linguistic era and which was missing in prior talk of ideas and impressions. Be careful to remember that Frege strongly distinguishes the sign (type or token) from the “associated idea” (individual mind tone), the sense, and referent.
2) Leibniz’s Law(s). The Latin quote that Frege makes – Things are identical when one may be substituted for the other while preserving truth (salva veritate) – can be read as
Identity. Leibniz’s law (Frege’s version). (x) (y) [ x=y -> (Px -> Py)] “For any x and any y, if x=y, then if P is true of x, P is true of y”
If two things are actually one, then whatever is true of one, then is true of the other; the indiscernability of identicals) See page 93.
[But it can also be read as ). (x) (y) [(Px -> Py) e x=y]
(If whatever is true of one is also true of another, then the one and the other are identical; the identity of indiscernables.)]
The first formulation is the more important for Frege, etc., and it does not hold when the sentence considered (explicitly or implicitly) introduces an intentional context by quotation or by introducing a belief, desire, suspicion, etc., that something or other. Thus if “I (or you, etc.) believe (say, know, desire, wonder whether, etc.) that the morning star is Venus,” it does not follow that “I (or you, etc.) believe (say, know, desire, wonder whether, etc.) that the evening star is Venus.”
Note also that intentional context sentences are not truth functional. The truth of “Napoleon believed that he would win the battle of Waterloo” is not a function of the truth or falsity of “Napoleon won the battle of Waterloo,” while “Napoleon marched to Waterloo and he lost the battle of Waterloo” is a function of the truth or falsity of “Napoleon marched to Waterloo” and “Napoleon lost the battle of Waterloo.” Similarly, “Napoleon, who recognized the danger to his right flank, himself led his guards against the enemy position” contains two separate thoughts and is another truth functional conjunction. While in “Whoever discovered the elliptical form of the planetary orbits died in misery” the subordinate clause “whoever discovered the elliptical form of the planets” has Kepler as its reference and only acquires a truth value in the context of the full sentence.
Truth functionally = The
world is the totality of the atomic facts. Ludwig Wittgenstein
Truth functionally applies only when
propositions are extensional (and not intentional); functionality belongs to the
object language (avoids paradoxes).
NEWLY ADDED MATERIAL ABOUT FREGE AND
INTENTIONAL CONTEXTS OR PROPOSITIONAL ATTITUDES:
What follows is a draft answer a student ran by
me. The comments in brackets are mine. The unbracketed
parts are the student, who is doing quite well until he gets to
giving examples of the
self-referential, propositional attitude statements and how they violate
Leibniz’ law.
We understand the problem Leibnizs
law faces when it is applied to what is called a propositional attitude which
is the relation between a person a proposition. A
person has many psychological relationships with propositions by hoping,
desiring, knowing, believing, etc. A propositional attitude can be expressed as
so:
I believe that god exists.
.............................
Or put differently:
X believes that P
X hopes P
X wants P, etc.
But as Frege points out a problem arises when you
apply Leibnizs Law concerning identity to a
propositional attitude. Take the following argument:
Loves a Bitch is a movie.
Loves a Bitch=Amores Perros
Therefore, Amores Perros is
a movie. But to say;
I watched the movie Loves a Bitch. [This sentence does not have a
propositional attitude part -- you need 1) a subject (I), 2) an attitude, 3) a
proposition. Your sentence is just a single prosition]
Loves a Bitch = Amores Perros
Therefore, I watched the movie Amores Perros. [this is not a
propositional attitude sentence.]
However, the argument is invalid; despite its premises being true its
conclusion is false. Frege from there develops what
he calls sense and denotation which clears up some problems I suppose but I
have not really read too much into it so as of yet cant comment..[ No, the argument is valid because I watched Amores Perros even though I
didn't know that was one of its names]
[On further reading I really don't think you get the point. Consider the
parallel:
1) I watched Love's a
Bitch................................................................................................1)
I watched the Morning Star
2) Love's a Bitch = Amores Perros...................................................................................2)
The Morning Star is the Evening Star.
3) I watched Amores Perros
(Whether I knew it was Amores Perros
or not).......... 3) I watched the Evening
Star (Whether I knew it was the Evening Star or not, I still watched it.)
Both of these are valid arguments and if the premisses
then the conclusion has to as well.
These are valid because all of the sentences are object language sentences (no
reference to words or phrases)
On the other hand, we have a propositional attitude (1), and the argument is
invalid :
1) I (or You) believe that Love's a Bitch is a great movie....................................................................................1)
I (or You) think that the Morning Star is Venus
2) Love's a Bitch is another name for Amores Perros. [whether or not I (or You) knows or believes
this].2) It happens that the Morning Star is the Evening Star (whether or not I
(or You) know or believethis)
3) I (or You) believe that Amores Perros
is a great movie. [but I don't; I've never heard of it].....................3)
I (or You) think that the Evening Star is Venus [but I don't; I've never hear
of the Evening Star.
Perhaps the problem is that you didn't have a clear enough idea of what a
propositional attitude statement is. Also it confuses matters if you use
"I" rather than "You," "He," or even better
"Joe." The contrast Frege is getting at is
MOST OBVIOUS when the proposition part is literally quoted. For example
1) Joe said "The Morning Star is Venus";
2) in fact
the The Morning Star is The Evening Star;
3) Joe said "The Evening Star is Venus" (Oh no he didn't!)]
3) Note Frege’s yearning for an ideal language which strips away associated ideas and other imperfections of natural language.
Similarly, Russell held that the verb to-be (is, was, etc.) can stand for three entirely different notions: Identity (A is A, Scarface is Al Capone), Existence (there is an even prime, God is), Predication (John is bald, The cougar is asleep). (The ontological proof.)
Logical positivism and the Vienna Circle. Moritz Schlick, Otto Neurath, Friedrich Waismann, Herbert Feigel, Rudolph Carnap (Kurt Godel); Karl Popper and Ludwig Wittgenstein as outliers; Russell and Ernst Mach as elder statesmen; W. V. O. Quine and A. J. Ayer as junior visitors. Strong distinction between analytic (logical) truths and synthetic (empirical) truths. (“wherever possible substitute logical constructions for inferred entities. Emphasis on the hard sciences. Real language as the vehicle of truth. Ayer: analytic, synthetic, and emotive use of language.
Russell on Definite Descriptions (phrases of the form “the so-and-so”).
The
present king of
1) Someone
is presently king of
2) At
most one person is king of
3) That someone is bald.
The apparent subject-predicate proposition is actually:
(Ex), (y) [Presently king of
Distinguish
definite descriptions from proper names.
Notes on our author’s use of foreign words,
phrases, sentences.
Frege. Begriffsschrift = Concept-writing.
Eadem sunt, quae sibi mutuo substitui possunt, slava veritate. = Things are identical when one may be substituted for another while preserving truth. (51)
Kripke. de re = in reality. de dicto = in a proposition or rule. When Kripke writes “of modality de re and an object necessarily having certain properties as such”
he is harking back to a distinction, made by medieval logicians, between saying something had a necessary property and saying that the statement
that it had the property was a necessary proposition. Kripke also introduced the term “rigid designator” for names that designate one and the same thing
in all “possible worlds.” “Our world” means our actual universe past present and future. Another possible world might be one exactly like ours except that
in it Nixon lost the election to Hubert Humphrey, another might be like ours except you got up at 7:15 AM rather than 7:16 AM. To say that proposition
is necessary is to say it is true in all possible worlds; to say that a proposition is possible is to say that it is true in at least one possible world.
“(p)” means “Necessarily, p is true.” “◊(p)” means “Possibly, p is true.”
Contingent “Identity.” “The morning star is the evening
star” “The inventor of bifocals is the first Post Master General of the
Type Identity. “Pain is the stimulation of C-fibers,” “Heat is the mean motion of molecular particles”
Token Identity. “This particular mental state in this individual at this time is one and the same as this particular neurological state in
this particular individual at this particular time.”
Grice. Mutatis mutandis = With suitable adjustments made.
Fodor. Tout court = only that and nothing more.
Saul Kripke “Identity and necessity”
Leibniz’s law (Frege’s version). (x) (y) [ x=y -> (Px -> Py)]
“For any x and any y, if x=y, then if P is true of x, P is true of y”
“For any x and y, if x is one and the same as y, any predicate that is true of x has to also be true of y”
Kripke reintroduces modal logic (necessary, possible), claiming necessity of Leibniz’s law (Frege’s version). (x) (y) [ x=y -> (Px -> Py)]
“For any x and any y, if x=y, then if P is true of x, P is true of y”
“For any x and y, if x is one and the same as y, the any predicate that is true of x has to also be true of y”
So Kripke claims that there aren’t any contingent identities.
So-called “contingent” identities that are true (such “heat is (=) the mean motion of molecular particles”) are actually natural necessities
But they are not analytic in the same way as logical truths (which
are also analytic). They are discovered (not a priori).
Like proper names, “heat” and “the mean motion of molecular” are RIGID DESIGNATORS (they have no descriptive content).
But here “heat” means an objective natural phenomena (out there) and NOT the subjective, psychological experience of heat.
MARTIANS
MIGHT HAVE AN ENTIRELY DIFFERENT PSYCHOLOGIAL EXPERIENCE WHEN THEY RUN INTO
PHYSICAL HEAT.
Having explained all legitimate so-called “contingent” identities are really natural necessities, Kripke insists that proposed “identities”
between physical and mental phenomena are bogus. DESCARTES WAS RIGHT!
H. P. Grice.
meaning = xxx means that p establishes p. causal “A means (meant) to do so-and-so (by x)”
meaningnn = xxx means that p does not necessarily establish p. conventional “A means something by x.”
Natural science vrs. conventional/intentional
Informational and descriptive uses.
1) “x meantnn something” is true if x was intended by utterer to induce a belief in y.
2) By getting y to recognize the intention behind the utterance.
3) Telling as opposed to showing or getting someone to think. “A uttered x with the intention of inducing a belief by means of the recognition of this intention.”
4) Interest in communicative action generally (not confined to natural language). Semiotics.
Imperatives, etc. A policeman who stops a car by standing in its way as opposed to waving.
Photograph vrs drawing.
[Characteristics
of ordinary language/Oxford philosophy.
1) Interest in non-descriptive
non-scientific language.
2) Speech acts, not propositions.
3) Ordinary language not artificial
or logical language.
4) Philosophers prone to misunderstanding ordinary language. Return to everyday usage; not reification.6) Interest in communicative action generally (not confined to natural language). Semiotics.
5) Task of philosophy is not to improve or “sublimere” or deep structure ordinary language. C. P. Snow
J. L. Austin. Performatives = First person present tense utterances where the main verb specifies the
speech act (or action) achieved by utterance. “I promise to come to your party.” (doing through saying)
But the performative doesn’t require such a narrow specification. “Shot him!” is an order.
“Other Minds” --- “There’s a bittern at the bottom of your garden”; “I know there’s a bittern there.”
Every utterance has a performatory aspect. Hence:
Locution. Saying. Sense and reference.
Illocution. Doing. Force. Felicitous/infelicitous.
Perlocution. Causal effect achieved.
In saying “Shoot him” utterer meant “shoot” and “him.” Sense/reference/truth value. Locution.
In saying “Shoot him” utterer ordered utteree to shoot him. Illocution.
In saying “Shoot him” utterer caused (urged) utteree to shoot him.
Felicitous/infelicitous
1) Qualification. Having the right authority, office, background, experience, credential, etc./ not
2) Sincerity. Intending to follow through, not joking, not being deceptive, etc. [rite of baptism]
3) Circumstances appropriate..
H P Grice. Logic and Conversation. Formalists (logic gives the correct account of the meaning). Informalists (no, it doesn’t)
But both are compatible and correct. The logic of conversation.
Implicatures. (as to implication).
a) Quantity. Provide adequate information and no more than needed.
b)Quality. Do not say what you believe is false or for which you don’t have proper evidence.
c) Relation. BE RELEVANT.
d) Manner. Avoid obscurity and ambiguity. Be brief and orderly
Looking ahead:
Jerry Fodor. Language of Thought. Modularity of Mind.
1) Proposition attitude psychology (PA). Characterizations of the form
“Agent (proper name, personal pronoun) + action verb (belief/desire) + that (proposition).” Intentional belief/desire psychology.
2) Irreducibility to purely neurological talk. Every mental state is token identical to a neurological state but no type-type identities to be expected.
3) The union of philosophy of mind and cognitive psychology.
4) Understanding PA characterizations require mental concepts, not “fusions.” Language of Thought.
[Jerry
Fodor can be hard to read.]
I.
PAs should be
analyzed as relations. “John [believes [it’s
raining]]”
I.a Intuitively plausible.
“no way of translating sentences nominally
about beliefs into sentences of reduced ontological load.
I.b Existential
Generalization. “John believes it’s raining” -> “John believes
something.”
I.c Only alternative is “fusion.” But it is no good
because:
1. Then how could languages be learned?
2. John (PA verb) proposition.
“proposition” the same whether believed, desired, etc.
But not on fusion view.
3. “John thinks Sam is nice”
and “Mary thinks Sam is nasty.” In disagreement. But
not on fusion view.
4. “John believes it’s
raining” has only accident relation to “It’s raining.”
II. PAs explain the parallelism between PA verbs and saying
verbs. “He can either doubt or demand
that the crew should douse the Jenny.” Vendler’s condition.
II.
A PA theory can account
for opacity. “Sentences containing verbs of PA are not, normally, truth
functions of their complements. All right forfusion.
III.
The objects of
propositional attitudes have logical form. Aristotle’s condition. The practical
syllogism.
“John
believes that it will rain if he washes his car. John wants it to rain. So John
washes his car.” Contrary
to fact conditionals. Counter factuals.
“Flying
planes can be dangerous.”
The
Martians might have the same propositional attitudes we do but not share our
system of internal representations.
Dennett. Three stances. Hard science. Design stance. Intentional stance (straightened out Folk Psychology; instrumental but effective). Chess.
The example of chemistry. 19th century chemistry and possible reduction to physics). Magnet – “attracts iron” – has thus-and-so field.
(Chomsky makes quite another use of the chemistry example. Reductions and upliftings.)
“The final reductive task would be to show not how the terms of intentional system theory are eliminable in favor of physiological terms via sub-personal cognitive psychology, but almost the reverse: to show how a system described in physiological terms could warrant an interpretation as a realized intentional system.”
Student of Gilbert Ryle (Concept of Mind; analytic behaviorism, ghost in the machine, Aristotle). Consciousness Explained.
Cartesian Theater demolished. Folk psychology, intentional system theory, subpersonal cognitive psychology. Physical reality, design stance, intentional stance.
Turing machine functionalism. Turing machine: Indefinitely long tape divided into cells, read head, write head, instruction tables limited to machine state, symbols (/, \, ), move forward, move back, stay, erase, print symbol.
Quine. Two dogmas: 1) Analytic/synthetic distinction; 2) “Reductionism”; logical constructions out of sense data. “at root identical”
“The unit of empirical significance is the whole of science.” Wholism.
“As an empiricist I continue to think of the conceptual scheme of science as a tool for predicting future experience. Physical objects are conceptually imported as convenient intermediaries – not by definition in terms of experience but simply as irreducible posits comparable to the gods of Homer… The myth of physical objects is epistemologically superior…”
WHY WORRY ABOUT
INFINITY?????????
1) How could we know that there is an infinity (empirically?; logically?)?
2) What’s this about different orders of infinity? ---
3) Natural numbers: 1,2,3….. (Odd numbers?, Even numbers?---NO. All countable one-to-one correspondence.
4) Real numbers. Uncountable
5) Goldbach’s Conjecture. Every even number is the sum to two primes.
Tractatus.
1. The World is everything that is the case
1.1 The world is the totality of facts, not of things.
1.2 The world can be broken down into facts.
1.21 Each one can be the case or not be the case while all else remains the same.
2. What is the case – a fact – is the existence of atomic facts.
2.1 We make pictures of facts to ourselves.
3. A thought is the logical picture of a fact.
3.3 Only sentences make sense; only in the context of a sentence does a name signify anything.
4. A sentence that makes sense is a thought.
4.01 A sentence is a picture of reality. A sentence is a model of reality as we think it is.
4.1 A sentence presents the existence or nonexistence of elementary facts.
4.11 The totality of true sentences is the whole of natural science.
4.111 Philosophy is not one of the natural sciences.
5. A sentence is a truth function of atomic sentences.
6.1 The sentences of logic are tautologies.
6.11 The sentences of logic therefore say nothing (They are analytic sentences.)
6.1262 Proof in logic is nothing more than a mechanical procedure for facilitating
the recognition of it as a tautology.
6.4 All sentences are of equal value.
6.41 The meaning of the world must lie outside of the world.
7. Whereof one cannot speak, thereof one must be silent.
Wittgenstein’s Investigations:
Philosophy 255ff; pain 244-46, 303; rule following 185ff, 201, 202,; privacy 202, 246-268; private language 202, 258ff, 270; Fly Bottle 309.
Wittgenstein quotes to think about:
255. The philosopher’s treatment of a question is like the treatment of an illness.. 309. What is your aim in philosophy? – To shew the fly the way out of the fly-bottle.
202. And hence also ‘obeying a rule’ is a practice. And to think that one is obeying a rule is not to obey a rule. Hence it is not possible to obey a rule ‘privately’: otherwise thinking one was obeying a rule would be the same as obeying it… When I obey a rule, I do not choose. I obey the rule blindly.
244-46. Here there is one possibility: words are connected with the primitive, the natural, expressions of the sensation and used in their place. A child has hurt himself and he cries; and then the parents teach him exclamations and, later, sentences. They teach the child new pain-behavior. … It can’t be said of me at all (except as a joke) that I know I am in pain.
What is it supposed to mean except perhaps that I am in pain.
258. I want to keep a diary about the recurrence of a certain sensation. To this end I associate it with the sign “S” and write this sign in a calendar for e very day on which I have the sensation.
…. In the present case I have no criterion of correctness… whatever is going to seem right to me is right. And that only means that here we can’t talk about ‘right.’….270. Let us now imagine a use for the entry of the sign “S” in my diary. I discover that whenever I have a particular sensation a manometer shews that my blood pressure rise. This is a useful result. And now it seems quite indifferent whether I have recognized the sensation right or not. Let us suppose I regularly identify it wrong, it does not matter in the least. That alone shews that the hypothesis that I make a mistake is mere show.
[Chomsky on reductionism: “physical”
not well-defined; a real problem for Descartes evaporates because “physical” is
no longer defined. 19th century physicists thought chemistry would
reduce to physics but it went the other way – physics “rose up” to chemistry.
H P Grice Logic and Conversation
Cooperative principle
Quantity – enough needed; no more
Quality – 1) speak truth. 2) adequate evidence.
Relation. Be relevant.
Manner. Avoid obscurity, ambiguity; be brief and orderly
Peter Strawson On Referring. (As opposed to “On Denoting”; regular logical form (syntax); sentences have meaning by themselves.)
“We very commonly use expressions of certain kinds to mention or refer to some individual person, person, event, or process. I shall call this way of using the expressions the “uniquely referring use.”
The “grammatical form is subject/predicate”
; the presupposition is that the subject exists.
Keith Donnellan Reference and Definite Descriptions.
Attributive use is Russellian. “Smith’s murderer is insane.” (Whoever killed Smith is insane)
Referential use is Strawsonian. “Smith’s murderer is insane” (That man is insane)
“Who is the man drinking a martini?” (Who is that man?)
“Who is the man drinking a martini?” (Who is drinking a martini?)
“The Republican candidate for president will be a conservative.” [Note that we are back to the thought of the speaker; not what he said.]
Daniel Everett (2005), “Cultural constraints on grammar and cognition in Piraha,” Current Anthropology, 46: 621-646
http://www.icsi.berkeley.edu/~kay/Everett.CA.Piraha.pdf
New Yorker magazine article:
http://www.newyorker.com/reporting/2007/04/16/070416fa_fact_colapinto
LingBuzz Piraha Exceptionality ReVisited, Nevins, et al.