Today’s logic is usually understood to be “the formal analysis of arguments.”
For the Stoics, logic was divided into two principal divisions: rhetoric and dialectic.
Rhetoric is defined as: “the art of speaking or writing effectively” (Merriam-Webster).
Dialectic is defined as: “discussion and reasoning by dialogue as a method of intellectual investigation” (Merriam-Webster).
The central them of Stoic logic is “the acquisition of knowledge” (p. 79, Sellars).
Epistemology is the theory of knowledge – “the process by which the individual gains knowledge” (p. 64-65, Sellars)
Birth of Cognition
At birth, human infants possess little to no knowledge. Jean Piaget’s knowledge experimentations on babies conclude infants are born not knowing much. To quote a Time magazine article, “Piaget's work led him to conclude that infants younger than 9 months have no innate knowledge of how the world works or any sense of "object permanence" (that people and things still exist even when they're not seen). Instead, babies must gradually construct this knowledge from experience” (The Brain: What Do Babies Know? Time, Monday, Jan. 29, 2007). The article later notes modern experimentation have drawn the same conclusions as Piaget.
Humans gain information about our world, largely through impressions and sensations – through experience, as stated in the previous point.
Empiricism is defined as: “a theory that all knowledge originates in experience” (Merriam-Webster).
Regarding the epistemology of the Stoics, Sellars notes, “Whereas most impressions are assumed to come from sensation, and so the Stoics might broadly be characterized as empiricists in epistemology, they do also acknowledge impressions received from the mind that are the product reasoning” (p. 65, Sellars).
An example of an inadequate impression might be light coming into a room and someone thinking it is day, when in fact, they’ve not gone outside to check that it is night, and it was a fire or street light causing the light to enter the window.
An example of an adequate impression would be someone thinking it is day while they are standing outside at noon, with the bright sun over their head.
The Stoic response to the Skeptics’ claim that we can never know if an impression is adequate, would be to “reply by saying that over time it will become possible to develop a certain ability to recognize adequate impressions. One might not be infallible at first, but one might eventually be able to become highly accurate with certain sorts of impressions” (p. 70, Sellars). Therefore, a Stoic can point to the sun directly above our heads and be absolutely certain that it is day; while at the same time, the Stoic can accept the possibility of mistakes by suspending judgement when uncertain (see p. 73, Sellars).
When we give assent to an impression, the impression is called an adequate impression (p. 73-73, Sellars).
When we withhold assent to an impression, we are suspending judgment (p. 73, Sellars).
The Greek word for cognition is katalepsis (p. 70, 164, Sellars).
An instance of cognition is “an assent to an adequate impression; a building block for knowledge” (p. 70, 164, Sellars). It is the mental process of knowing (by experience or through reasoning) by giving assent to an adequate impression.
For the Stoics, knowledge (episteme) is more substantial than cognition. To me, it represents putting experience from cognition together into a system or structure. Cognition provides the basis and building blocks to make something – knowledge – which is to see a wider, bigger picture as it were – something greater than the individual part.
Sellars states “An adequate impression is an impression that is so clear, vivid and distinct that it is its own guarantee of its accuracy” (p. 69). We can also guarantee the accuracy of an empirical impression by observing the “causal history” and ensuring that nothing has interfered with “one’s sense organs, the object in question, and all the other variables involved are not obstructed or in an abnormal state” (p. 69).
“The impressions we receive that present external objects to us are not within our control. We do not have the power to choose them; instead they force themselves on us. However, we do have the power to choose whether to assent to these impressions or not” (p. 66, Sellars). Stoics will often be forced to confront these external circumstances and will at least have the choice to behave virtuously and serenely, but this does not mean they will choose to do so every time. Because “first movement” emotions come to all humans, many people do not question or analyze these emotions and propositions before assenting to them. The Stoic will try to pause and reflect on the emotions and proposition from the “first movement” before fully assenting to or rejecting an external object. Assuming a Stoic consistently practices this pause before assent, then over time, the Stoic will act correctly (virtuously) and serenely more often than not.
The four stages of assent are (p. 67, Sellars, emphasis added):
- “a perception of an external event or state of affairs”
- “an almost involuntary and seemingly unconscious value judgement that is made about the content of the perception”
- “the presentation to the conscious mind of an impression in the form of a proposition that is composed of both the perceptual data received from the outside and the unconscious value judgement”
- the act of assent to an adequate impression or we suspend judgement of the impression
- The corporeal aspect would be physical utterance or written word of the proposition.
- The incorporeal aspect would be the meaning of the physical element presented.
- Incorporeal propositions subsist, if they are never spoken or written and remain as a cognition in our mind.
Sellars notes, “What is perhaps unique to the Stoic position is their rejection of meaning as something that exists. As incorporeals, sayables only subsist” (p. 63). How does this explain how the meaning of words can cause action? The key aspect would be in the assent of the person comprehending the sayable. A man shouts a warning to a woman that a ball is being thrown her way. She hears the words the man shouts, she comprehends the sayable, she assents to the meaning and therefore chooses to act, either to catch the ball or move out of the way to avoid being hit by the ball.
There are two kinds of sayables – complete and incomplete (p. 62, Sellars).
- A complete sayable would be: Rocky is typing on his computer.
- An incomplete sayable would be: is typing.
“An assertible is a complete sayable” (p. 58, Sellars).
The four important characteristics of assertibles are (p. 58-59, Sellars):
- Simple assertibles can be
- Complex which include logical connectives
- conditional ... if
- conjunction ... and
- dis-junction ... either/or
- pseudo-conditional ... since
- causal ... because
- comparative ... more/less-likely
- possible - an assertible which can become true and is not hindered by external things from becoming true
- impossible - an assertible which cannot become true or which can become true but is hindered by external things from becoming true
- necessary - an assertible which (when true) cannot become false or which can become false but is hindered by external things from becoming false
- non-necessary - an assertible which can become false and is not hindered by external things from becoming false
The four kinds of assertibles listed above are the propositions that can be combined to form Stoic arguments for systematic scientific knowledge of the world. These arguments are called syllogisms (p. 59, Sellars).
Summary of Stoic Logic (p. 79, Sellars)
- “the mind at birth is like a blank sheet of paper”
- “via sensory experiences or impressions … we gain information” of an external event or state of affairs.
- we experience "first movements" which are almost involuntary and unconscious value judgements
- “the impressions we [initially] assent to are presented to the mind in the form of propositions” which are composed of the perceptual data and the unconscious value judgement.
- we either assent or reject the impression as either adequate or inadequate.
- "a proposition is a physical entity” or corporeal [spoken or written] which carries meaning/sense, which subsists and incorporeal.
- Sayables are the subsistence of the meaning of the proposition.
- Sayables are either complete or incomplete.
- Complete sayables are called assertibles used in Stoic dialectic.
- Four kinds of assertibles (true/false/simple/complex) can be combined with other assertibles to form syllogistic arguments.
Aristotelian syllogisms used universals with letters, whereas Stoic syllogisms could use either universal or particular assertibles for their propositions. In Stoic formal logic, ordinal numbers replace propositions, not individual terms. (p. 57-59, Sellars).
An argument may be valid “in its logical form” but if we doubt the premise, the conclusion may not be true. So, we can just say, "no." :)
An example of a logically valid argument that is untrue would be:
All Texans are human;
All humans are male;
Therefore, all Texans are male.
An example of the 3rd Stoic argument using ordinal numbers:
Not the seventh and the eighth;
Therefore, not the eighth.
The above example would contain a complex negative conjunction assertible as one premise and a simple assertible as the second premise.
An example from the physical world of the 3rd argument would be:
The temperature is not both hot and cold;
It is hot;
Therefore, it is not cold.
Examples of the other four arguments (1, 2, 4, 5):
If the man is in Texas, then he is in the United States;
The man is in Texas;
Therefore, the man is in the United States.
If the boat is sailing, then it is on the water;
The boat is not on the water;
Therefore, the boat is not sailing.
Either is it night or it is day;
It is night;
Therefore, it is not day.
The animal is either a mammal or a reptile;
It is not a reptile;
Therefore, it is a mammal.
More on Stoic Logic: https://en.wikipedia.org/wiki/Stoic_logic