Frege's tringle

Semantics (Sense, reference, Referent, Dennotation)

1. Frege’s triangle
real object, concept,
symbol: sense and reference
By: LonerangersBy: Lonerangers
Suhail Jamali 120Suhail Jamali 120
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2. Ferge’s triangle
It is a model of how linguistic symbol
are related to the object they represent.
Aspect of sementics
How lexeme make sense
Distinguish between real object,
concept and symbol.

3. Tree, love, Dinosaur.
Physically:
Abstract:
Extinct:

4. Triangle:

5. Symbol : Sense and
Reference
Sense: for legged animal makes mau sound.
abstract and decontexualized and it referes to the
inherent meaning of the linguistics form, sense is
concerned only with intera linguistics relations.
Collection of all the sementic features of the
linguistics form.
Reference: a linguistics form points to in the real
world
Deals with the linguistic element and the metalinguistic
world of experience.
I have a furry cat.

6. Sense vs reference
Sense and reference are both parts of meaning yet.
What relation is there between them.
A proper name( worf or sign) expresses its sense and
designates its references.
1. A linguistic form with unique sense may have
different referents in different situations.
2. The same referent might be pointed to by
numerous linguistic forms having different senses
3. All linguistic forms have senses, but not
necessarily reference.

7. Every expression has both a sense and
a reference: actually, it denotes its
reference, and expresses its sense.
A sense many references
Our president is giving speech
*Mamnoon
*Trump
*Roohani

8. Reference many senses
1.Bill’s wife
2. The winner of ohio election
3.The Minister of Foreign Affairs
4. Hillary Clinton

9. Sense no reference
A white unicorn is in my garden.
But unicorn doesn’t exist!

10. Denotation vs connotation
Denotation: The exact, literal meaning of a
word.
The family sat togather in front of a warm fire.
The denotative interperetion of warm= hot
Connotation: The unspoken, hidden meaning
that gives a word more emotional impact
The family sat togather in front of a warm fire.
Connotative interpretation of warm= friendly

11. symbolsymbol
Symbol: sense and reference
Friedrich Ludwig Gottlob Frege
(1848-1925)
Über Sinn und Bedeutung (On sense and ), 1892denotation
reference
Sign /name: Any designation representing a proper name. It can consist of a
name, combination of words, letters or other signs.
Sense: The mode of presentation
of that which is designated
Denotation (the « object » the sign refers to)
« A sign expresses its sense,
stands for or designates its
denotation. »
Driving force : cognitive value of a statement

12. Frege’s examplesFrege’s examples
The statement contains actual knowledge
signs
sensedenotatio
n
« Let a, b, c the lines connecting the vertices of a triangle with the midpoints of
the opposite sides. The point of intersection of a and b is then the same as the
point of intersection of b and c. So we have different designations for the same
point, and these names (‘point of intersection of a and b’, ‘point of intersection
of b and c’) likewise indicate the mode of presentation. »
1.
« The denotation of ‘evening star’ would be the same as that of ‘morning star’,
but not the sense. »
2.
To the sign there corresponds a definite sense and to that in turn a
definite denotation, while to a given denotation (an object) there does
not belong only a single sign.
A sign might have a sense but no denotation
c o
n
t r o
v
e r s e d
« The expression ‘the least rapidly convergent series’ has a sense;
but it is known to have no denotation, since for every given
convergent series, another convergent, but less rapidly convergent
series can be found. »
3.

13. Extending Frege’s ideasExtending Frege’s ideas
(1901) The expressions ‘Melbourne’ and ‘the australian capital’ have
different senses but denote the same city.
4.
4’ and ‘8/2’ have the same denotation but express different ways of
conceiving the same number.
5.
More examples…
SenseSense and and denotationdenotation in mathematics educational research in mathematics educational research
Denotation « within a universe »
I - Duval Treatment / conversion
II - DrouhardInterpretation / connotation
III - ArzarelloAlgebraic sense/ contextualised sense

14. Meaning and reference, ed. A. W. Moore, Oxford University
Press, 1993.
Translations from the Philosophical Writings of Gottlob Frege,
ed. P. Geach and M. Black, Oxford: Blackwell, 1952.
Frege’s theory of Sense and Reference. Its Origns and Scope.
W. Carl, Cambridge University Press, 1994.

15. Connotation and Denotation
Connotation:
Denotation:

16. Treatment Treatment and and Conversion Conversion (Duval)(Duval)
Treatment
Changing representations of an object within the same
semiotic system. Internal transformation.
Eg.: Calculating = substituting new expressions to given
expressions within the same s.system (i.e. writing numbers).
Conversion
Transpose the representation of an information/ object/
situation into a different system. External transformation.
Eg.: Formulating a problem given in natural language into equations.
Sense, denotation and Sense, denotation and TreatmentTreatmentSense, denotation and Sense, denotation and ConversionConversion
Students know how to add decimal and
fractions (= treatments), can’t shift from
one representation to another (=conversion)
Decimals and fractions: two different
representation systems.
0,25+0,25 = 0,5
¼ + ¼ = ½
Different senses,
different treatment
procedures
Distinguishing sense from denotation is
essential to conversion.

17. Interpretation Interpretation andand connotation connotation (Drouhard)(Drouhard)
Interpretation
of an algebraic expression X within a given framework is every object
that ‘corresponds’ to the denotation of X within this framework.
3x +7
Graphical framework : line y = 3x+7
Arithmetical: the writing of a number congru
to 7 modulo 3
Math/
Extra-math
Connotation is the subjective perception someone has of an algebraic expression
Representation
Many algebraic difficulties described as deficiences in the way students master the
invariance of denotation with respect to the sense.
A symbolic expression denotes itself as a collection of signs
One-to-one correspondance between sense, denotation and
expression
Pupils don’t see that algebraic transformation must preserve denotation, that
is the « value » of the square must remain the same throughout the operation.
Then proposing numerical values won’t help convincing them.
(a+b)
2
Frege

18. Representation (Frege)
« Somedody observes the Moon through a telescope. I compare the moon
itself to the reference; it is the object of the observation, mediated by the real
image projected by the object glass in the interior of the telescope, and by the
retinal image of the observer. »
sense
« The optical image in the telescope is indeed one-sided and dependent upon
the standpoint of observation; but it is still objective, inasmuch as it can be
used by several observers. But each one would have his own retinal image. On
account on the different shapes of the observers’s eyes, even a geometrical
congruence could hardly be achieved, and an actual coincidence would be out
of the question. »
representatio
n
representationsense denotation
objectivity