Does modern logic miss "the point" of logic?
pyrrho
There is a position in 20-century philosophy which holds that modern
formal logic misses "the point" of logic, because it is supposedly
grounded in an inadequate analysis of the notion of "logical
proposition". The philosopher who advances this position is Martin
Heidegger (1889-1976). I give an overview in the form of opposing
thesis's between modern logic [ML] and Heidegger [MH].
[ML](1) Modern formal logic attempts to do the same as Aristotelian
logic, only that it is more precise. In short: ``predicate calculus
is to syllogism what a precision tool is to a blunt knife.'' E.J.
Lemmon, "Beginning Logic", 1983, p.169.
[MH](1) The difference between modern and traditional logic does not
lie in a "more and less" but in hitting the point and not hitting the
point of the nature of the proposition. (M.H. "Die Frage nach dem
Ding", chapter 5.b)
[ML](2) Modern logic aim at the formalization of "facts". Here an
account from Frege's "Begriffsschrift" (p.3-4): ``One can imagine a
language in which the sentence: `Archimedes died in the sack of
Syracuse' is expressed in the following way: `the violent death of
Archimedes in the sack of Syracuse is a fact. If you like, you can
distinguish here subject and predicate. But the subject contains the
complete content and the predicate has only one purpose, to present
this content as asserted. Such a language is our Begriffsschrift and
the sign |- is the common predicate for all propositions.'' Modern
propositions have only one predicate. "is the case" (=true) or "not
the case" (=false).
[MH](2) Propositions in the sense above are derived from a more basic
notion of proposition (M.H. "Sein und Zeit", paragraph 44). The
primary "logical" purpose of a proposition is to make something
manifest, to give tidings (Auskunft), eg. "Theaitetos flies." (M.H.
"Platon: Sophistes", paragraph 80). Because propositions make
something manifest, that what is made manifest can be compared to
"reality". Now the stage is set and "factual truth" can appear.
At the end a thesis of my own. If a proposition is true, then the
tidings expressed by it turn into information. On the other hand if a
proposition is false, then the tidings turn into disinformation.
Propositions as carriers of tidings come with their own formal logic,
categorical Aristotelian syllogistic (at least). Thus "old European"
logic is based on a completely different approach than that of modern
formal logic.
Thanks,
Claus
waveletter
Your post raises a number of issues, some of which are outside my area
of philosophical competence. I'll insert my comments [rla] below, and
if I can find some of the requisite resources, perhaps I can comment
further on the weekend. Thanks! --Ron
On Mar 6, 11:04 pm, pyrrho <c.brillow...@googlemail.com> wrote:
> Hi everybody!
>
> There is a position in 20-century philosophy which holds that modern
> formal logic misses "the point" of logic, because it is supposedly
> grounded in an inadequate analysis of the notion of "logical
> proposition". The philosopher who advances this position is Martin
> Heidegger (1889-1976). I give an overview in the form of opposing
> thesis's between modern logic [ML] and Heidegger [MH].
[rla] OK, I'm not well-versed in Heidegger. My thought is that logic
has to do with the validity of argumentation, not with "logical
propositions". A logical system comprises a syntax, a semantics, a
deductive system, and an associated theory of its decidability, so to
say that "the point" of logic is to analyze the notion of a "logical
proposition" seems very, very narrow to me. Logic has to do with
validity, mainly, the formalization of what constitutes a valid
argument. The original Greek word "logos" certainly had meanings that
overlapped with Heidegger's assertion here, and philosophical logic as
we take it today does embrace a theory of reference and meaning, but
to omit the deductive component seems to me to miss the point of
"logic"--be it ancient or modern--entirely.
>
> [ML](1) Modern formal logic attempts to do the same as Aristotelian
> logic, only that it is more precise. In short: ``predicate calculus
> is to syllogism what a precision tool is to a blunt knife.'' E.J.
> Lemmon, "Beginning Logic", 1983, p.169.
[rla] Well, OK, I have a hard time agreeing with Lemmon as well! I
must be in a "mood"! I think that syllogistic is precise for what it
was intended for: a logic of finite collections of objects.
Propositional calculus covers different things: the logic of
statements. Predicate calculus covers quantization in a more general
way than does syllogistic, and propositional calculus does not even
cover quantization, but even 1st order logic does not adequately
capture the logic implicit in natural language.
>
> [MH](1) The difference between modern and traditional logic does not
> lie in a "more and less" but in hitting the point and not hitting the
> point of the nature of the proposition. (M.H. "Die Frage nach dem
> Ding", chapter 5.b)
[rla] Strong and interesting remark, but it seems like he's talking
about meaning and reference rather than deduction and logical systems
per se.
>
> [ML](2) Modern logic aim at the formalization of "facts". Here an
> account from Frege's "Begriffsschrift" (p.3-4): ``One can imagine a
> language in which the sentence: `Archimedes died in the sack of
> Syracuse' is expressed in the following way: `the violent death of
> Archimedes in the sack of Syracuse is a fact. If you like, you can
> distinguish here subject and predicate. But the subject contains the
> complete content and the predicate has only one purpose, to present
> this content as asserted. Such a language is our Begriffsschrift and
> the sign |- is the common predicate for all propositions.'' Modern
> propositions have only one predicate. "is the case" (=true) or "not
> the case" (=false).
[rla] Frege is expressing a deflationary theory of truth here, but
it's based on statements that are not even granted factual
status...such as "Archimedes died in the sack of Syracuse". That is
generally assumed, but not known, and so it may be in fact the case,
but we don't know if it was violent or whether he choked while eating
a carrot about the time of the battle with the Romans. So, to say it's
a fact is to say something more, and it is not the same as "I assert
that Archimedes died in the sack of Syracuse."
>
> [MH](2) Propositions in the sense above are derived from a more basic
> notion of proposition (M.H. "Sein und Zeit", paragraph 44). The
> primary "logical" purpose of a proposition is to make something
> manifest, to give tidings (Auskunft), eg. "Theaitetos flies." (M.H.
> "Platon: Sophistes", paragraph 80). Because propositions make
> something manifest, that what is made manifest can be compared to
> "reality". Now the stage is set and "factual truth" can appear.
[rla] Well, now, this is pretty interesting as an analysis of how a
natural language proposition works. The proposition gives "tidings" in
that it is tied contextually to some aspect of reality. I'm thinking
of Austin's distinction between descriptive conventions and
demonstrative conventions in discourse...the descriptive conventions
giving a statement that something is the case and the demonstrative
conventions gesturing at external objects and establishing the
reference from descriptive language elements to extra-linguistic
objects and render the statement or sentence as truthful or not.
>
> At the end a thesis of my own. If a proposition is true, then the
> tidings expressed by it turn into information. On the other hand if a
> proposition is false, then the tidings turn into disinformation.
> Propositions as carriers of tidings come with their own formal logic,
> categorical Aristotelian syllogistic (at least). Thus "old European"
> logic is based on a completely different approach than that of modern
> formal logic.
>
> Thanks,
> Claus
[rla] I'm inclined to disagree for the moment. A proposition does not
bring forth a deductive apparatus. For example, "All Greeks are men"
does not bring forth any deduction with it. If we are working with
Aristotelian syllogistic, though, and we are give also that "All men
are mortal", then we may conclude under the Barbara syllogism that
"all Greeks are mortal". But, this comes from the natural deduction
system supplied by the syllogistic, not from the incidental
proposition about Greeks and men and inclusion.
Thanks!
--Ron
pyrrho
nice to hear from you! You make the following point:
>My thought is that logic has to do with the validity of argumentation,
>not with "logical propositions". ... To say that "the point" of logic
>is to analyze the notion of a "logical proposition" seems very, very
>narrow to me. .. To omit the deductive component seems to me to miss
>the point of "logic"--be it ancient or modern--entirely.
OK. "A deduction is a logos, which results from an assertion, if
something different follows from the assertion by necessity." [My
slightly liberal translation of AnaPr 24b18-20]
Whatever follows by necessity from an an assertion depends very much
on the nature of what is asserted. For example, if you assume the
asserted items to be proofs, you get the deductive rules of
constructive logic. Different kind of assertions give you different
logics. Formally there is an infinite universe of possible logics. It
all depends on how you define a "logical proposition". Now we come to
Aristotle. He discovered, that language (logos) comes in modes. There
is a logos which allows you to command, another one expresses
promises, and so on. But there is one kind of logos which is all
important for logic, the "logos apophantikos a `logos which shows' or
"makes visible".(De Int. 17a2) That mode is variously translated as
`assertion' and proposition. The Romans translated "apophansis" from
Cicero and Quintilian onwards as "enuntiatio", "propositio",
"iudicium". In turn, the German "Aussage" is derived from
"enuntiatio", "Urteil" from "iudicum".
This `showing' capacity of "propositions" is independent of the
propositions being true or false. The sentence "Kant is Chinese"
evokes a Chinese Kant. Together with the assertion, that all Chinese
are philosophers, it follows by necessity that Kant is a philosopher.
It follows because of the tidings asserted, not because the tidings
convey the truth. Here, from two false propositions, a conclusion is
drawn which happens to be true. Aristotle treats systematically
propositions as evocations together with deductions and the relations
to possible "facts" in AnaPr. Book B, chapter 2-4.
This dimension of tidings, which originated with the logical
proposition of Aristotle and which later was discussed as "realitas"
and intension is completely eliminated from the modern proposition.
That is why the deductive rules are different. Assertion of tidings
carry its own necessary deductions. Sets of truth values carry
others.
Thanks,
Claus
GEVA...@aol.com
Hi Claus:
Your post raises a number of issues, some of which are outside my area
of philosophical competence. I'll insert my comments [rla] below, and
if I can find some of the requisite resources, perhaps I can comment
further on the weekend. Thanks! --Ron
On Mar 6, 11:04 pm, pyrrho <c.brillow...@googlemail.com> wrote:
> Hi everybody!
>
> There is a position in 20-century philosophy which holds that modern
> formal logic misses "the point" of logic, because it is supposedly
> grounded in an inadequate analysis of the notion of "logical
> proposition". The philosopher who advances this position is Martin
> Heidegger (1889-1976). I give an overview in the form of opposing
> thesis's between modern logic [ML] and Heidegger [MH].
[rla] OK, I'm not well-versed in Heidegger. My thought is that logic
has to do with the validity of argumentation, not with "logical
propositions". A logical system comprises a syntax, a semantics, a
deductive system, and an associated theory of its decidability, so to
say that "the point" of logic is to analyze the notion of a "logical
proposition" seems very, very narrow to me. Logic has to do with
validity, mainly, the formalization of what constitutes a valid
argument. The original Greek word "logos" certainly had meanings that
overlapped with Heidegger's assertion here, and philosophical logic as
we take it today does embrace a theory of reference and meaning, but
to omit the deductive component seems to me to miss the point of
"logic"--be it ancient or modern--entirely.
>
Jud Evans
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Reifications (like biological entozoic infections of the gut) are
proto-socio-neurological enculturations, and as useful fictions
are not necessarily symbiotic with, nor necessarily benignly
adjuvant to the welfare of their unwitting and often naive hosts.
Jud Evans.
Freedom in humans consists of the ability to liberate
oneself from the tyranny of reificationalist imprinting.
Antonio Rossin.
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