31 Mar 2009

Stoic Logic, Mates, Chapter 1, §6 Comparison with Modern Theories (§2)

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Stoics, Stoic Logic, Stoic Semantics, Entry Directory]

Benson Mates

Stoic Logic

Chapter II: Signs, Sense, and Denotation

§6 Comparison with Modern Theories (§2)

We will compare Stoic semantics with Frege's and Carnap's.

Mates provides a table that classifies each one's semantic distinctions. [Click on image for enlargement]

He explains that the Stoic theory bears two serious deficiencies compared with Frege's and Carnap's theories.
1) there is no principle of interchangeability or a discussion of problems related to it, and
2) there are no Stoic discussions of 'oblique' or 'not purely disignative' expressions.

The Stoics make three fundamental semantic distinctions.
a) το σημαίνον (to semainon)
b) το λεκτόν (to lekton), and
c) το τυγχάνον (to tugchanon)

These correspond in many ways to Frege's
a) Zeichen
b) Sinn, and
c) Bedeutung

And to Carnap's
a) designator
b) intension
c) extension.

The Lekton is what the sign designates or means. It is also what we grasp as existing in close connection with our intellect. As we noted before, the Lekton is what the Barbarians do not understand when they hear Greek words spoken. (22a.b)

According to Carnap, Sinn and intension "refer to meaning in a strict sense, as that which is grasped when we understand an expression without knowing the facts." (Carnap qt in Mates 22b)

For Frege, the sense (Sinn) of a sign is "the manner in which that which is denoted by the sign is given." (qt 22b) For example, we let A, B, C be the medians of a triangle. [Image credits provided below]

We see that lines A, B, and C meet at a point in the triangle's center. So we could refer to the "intersection of A and B." And that would denote the same point as if we referred-to "the intersection of B and C." Nonetheless, the two expressions do not have the same sense.

Or also consider how for long stretches of time, Venus appears at night before dawn. While during the other stretch of time, it appears after dusk.

For long, human cultures thought they were two different 'stars.' So the 'evening star' was called Hesperus or Vesper. And the "morning star' was called Phosphorus or Lucifer. Yet both Hesperus and Phosphorus denoted the same planet.

It is interesting to see why this phenomenon occurs.

Venus' orbit is closer to the sun.

And let's say from our cosmic perspective, the earth is rotating this direction.

And we mark our position on the earth with an 'x.' As the earth rotates through the night, the sun comes closer to the horizon. Just before dawn, Venus rises into the sky.

But every 584 days, Venus will cross in front of us, and pass-over to the sun's other side. Then, it will no longer show before dawn. However, right after dusk, it will be one of the first and brightest heavenly bodies in the early night sky.

Whole mythologies were developed around the distinct characters of Vesper and Lucifer. As Vesper bells ring, some make Vesper prayers, calling for God's assistance, as the evening star rises to be seen. And Lucifer was once the prince of light. To punish his heavenly rebellion, God casts him to hell. At dawn we see Lucifer's light be overcome by the sun.

Clearly the terms "morning star" and "evening star" have full rich meanings that can be distinguished from each other. But they both refer-to just one planet. The extensional meaning (Bedeutung) is Venus. Both expressions "morning star" and "evening star" extend out to Venus, the object in extended space. Yet, each one has a meaning internal to it. Their sense (Sinn) does not extend outward to extended objects. Rather it is an inner tendency to call upon unextended images, notions, emotions, and so forth. There are warring inner tensions of meaning. This is an intension, that is, an intense sense.

Frege also distinguishes the idea (Vorstellung) from the sense (Sinn). The idea is subjective and private. However, the sense is objective and public. Likewise, the Stoics distinguish the Lekton from the presentation (φαντασία phantasia). The Lekton is the content of a rational presentation. In this presentation, discourse may present the φαντασθέν (phantasthen). Hence, we may call the Lekton the presentation's "objective content" (το φαντασθέν). However, Frege considers sense to be the "objective content" of the Vorstellung. For Frege, sense is 'between' the subjective idea and the denoted object, much like Ammonius claim that the Lekton is between the thought and the thing. '(22c)

To make our comparisons more precise, we need to know if the Lekton of every expression is the same as its sense. So we turn to the further distinctions in rows b to e of our table.

'Signs' B: Individual Name
Consider the name "Aristotle." The Lekton corresponding to such an individual name is its characteristic properties. So for the name 'Aristotle,' the Lekton is the property of being Plato's student and Alexander the Great's teacher. Frege's understanding of sense is very similar, but he does not specify that the properties need to be peculiar to the individual. For him, the sense of 'Aristotle' is 'the student of Plato and the teacher of Alexander.' (23a.b)

'Sense' B: Individual Concept
For Carnap, an individual expression's intension is its 'individual concept.' This corresponds to Frege's Sinn. So like Frege, he does not agree with the Stoics that the intension must be peculiar to the individual. However, the Stoics, Carnap, and Frege all regard the intension as being properties.

Denotation B: Extension
Carnap uses the term 'individual' for the extension of an individual expression. However, neither Frege nor the Stoics specify such a category. Note a superiority of the modern view over the ancient.
The Stoics asserted flatly, in accordance with their materialism, that the objects denoted by all expressions are bodies, just as the signs are bodies. (23c, emphasis mine)
However, Frege and Carnap do not articulate such a metaphysics. Yet, Frege resists the skeptics and idealists who claim that no expression has a denotation. For, we
1) "usually intend to talk about something more than our own ideas"
2) assume that our expressions have denotations, and
3) presume that "our intention is justification enough for introducing the concept of denotation." (24a)

However, this is not a metaphysical argument.

'Signs' C: Class Names
For both Carnap and the Stoics, the intensions of class names are properties of its members. Yet, the only Stoic examples we have for class names are "man, "horse," "goddess," and "wrath." These seem more to be species, because "manhood" for example might more properly be considered a genus. And Frege does not refer to class names specifically.

D: Predicates
The Stoic's ρήμα (rema) corresponds well to Carnap's "predicate." In Stoic semantics, a predicate combines with a subject to form a proposition. Frege could have used the term Prädikat. Hence, the intension of a predicate is the property corresponding to the class name.

E: Sentences
The Stoics, Frege, and Carnap all agree that the intension of a sentence is a proposition. But unlike Frege and Carnap, the Stoics never say that a sentence's extension is its truth value.

We see then that there is remarkable similarity between the Stoic and modern semantical views in regard to the intension of various linguistic expressions. All three theories
1) agree-on the sorts of entities that serve as intentions for the different kinds of expressions, and
2) hold that "the intension of a part of a sentence is a part of the intension of the sentence." (26b)

[Entry directory for other entries in this series.]


Mates, Benson. Stoic Logic. Berkeley: University of California Press, 1973. [Originally published in 1953 as Volume 26 of the University of California Publications in Philosophy.]

Image of Venus in night sky:

Triangle image:

No comments:

Post a Comment