Self Evident Truths
Self evident truths are thought to be evidently true taken by themselves - without the need for supporting evidence.
Example: The spruce is taller than the maple therefore the maple is shorter than the spruce.
Example: Mathematically A>B therefore B<A.
Example: The vixen is female. [Vixen is a female fox]
The self evident proposition can be broken down as follows:
- If one understands them, then by virtue of that understanding one is justified in believing them. Justifies Belief
- If one believes them on the basis of understanding them, then one thereby knows them. Grounds Belief
With the example of the spruce and maple you don’t have to consult experience. The concept of being taller than means something, the maple is shorter than the spruce.
The comparison of heights, our belief is immediate in both. There are two types of immediacy:
- Temporal sene of “instant formed” and
- Epistemic sense - the sense entailing that we see the truth without inferring them from anything else.
The point is that our belief exhibit its epistemic immediacy: The belief is not based on inference or on further evidential belief. If it is not epistemic immediate, it is epistemic mediate: mediated by the set of premises from which we infer the proposition.
Example: Socrates is mortal. We mediate that Socrates is a human and all humans are mortal.
The Socrates proposition is different than the spruce and maple proposition - it’s not self evident. First, Socrates and mortality are not intrinsically connected, as one being taller and second being shorter. Second, Socrates is mortal requires more reflection - a temporarily extended use of reason - on this proposition. One needs additional information not contained in the proposition itself.
Due to these differences, philosophers consider the spruce and maple proposition as a truth of reason - essentially knowable through using reason, as opposed to reliance on sense experience. This kind of knowability has philosophers calling it necessarily true, simply because falsehood is absolutely precluded. There’s no circumstance where it is false.
Example: A>B therefore B<A. It simply can’t be false.
Contingent is if a proposition is not necessarily true and its negation is not necessarily true. Why? Because whether it is true is contingent on circumstances.
Example: There are more than 2 trees in my yard. It’s contingent because my yard has more than 2, but it doesn’t have to be.
Analytic & Necessary Propositions
Take the sentence “all vixens are female”. I can grasp the truth and believe. No premises or evidence is required. There was a time when I didn’t know the term “vixen”, but I can easily look it up. Once I comprehend the sentence, I know the truth. It means that encountering a sentence which expresses a truth does not mean one considers that truth unless one understands the sentence.
In this particular example, truth isn’t derived from the structure of the sentence. The grounding comes from the concept of a vixen, which can be analyzed as female and being a fox. So we can say that the concept of being female is in the concept of being a vixen - being female is thus an element of being a vixen.
This makes all vixens are female is an analytic proposition. This type of proposition is considered self-evident. Simply put, provided one adequately understands the proposition, one can frame an analysis in which the containment relation is clearly evident.
The proposition all vixens are female cannot be false and is a necessary truth. How? Well can you conceive of a non-female vixen. Since vixen is analyzable as a female fox, one is conceiving a non-female female fox. There’s a contradiction in this statement. Hence there cannot be such a thing, on pain of contradiction. It’s just absolutely not possible.
Another example is the single bachelor. It’s just a necessary truth. You just can’t have a married bachelor. Bachelor is analyzed as a single person and married is not single. So we end up with a not single single guy.
On the pain of contradiction, when taking an analytic proposition, the falsity of it contains a contradiction. Falsity entails contradiction and it can only be false if contradiction is true.
Consider non-analytic truth - nothing can be red and green all over at the same time. This is self-evident and a truth of reason. Can one analyze the concept of non-red out of the concept of being green or the other way around? Doubtful.
There is a contingency objection to this example. It is possible that there is a scientific explanation of why nothing is red and green all over at once. If it does exist this proposition would be empirical and not self-evident. The classical view is the science can help understand the facts about red, but it does not indicated what is essential to the concept of a red thing - such as being non-green at the same time as red. It seems the scientific objection fails.
Another objection is that the proposition is analytic. If the concept of being red is equivalent to the concept of having a color other than green, blue, yellow and all other colors. The claim seems to have merit because it seems self evidently true, but the claim is doubtful. Could one really get a list of all possible colors. Another important point is it ever possible that the concept of being red is not simply to be a color other than green, blue, yellow, etc?
It’s also possible for one to have a concept of being red (and understand) without having all these other color concepts.
The analysis of a concept must meet two conditions:
- It must exhibit a suitable subset of the elements that constitute the concept.
- It must do so in such a way that one’s seeing that they constitute can yield some significant degree of understanding the concept.
This means that one couldn’t understand being red by a near infinite list of non-red colors.
Another way of thinking about analytic is that one needs to understanding: understanding of, not understanding that. The word “that” is the big part. Understanding that citizenship requires being politically informed, is different than understanding of - which has a connection to an explanation. The point is that analysis requires an explanation of.
The concept of a vixen as a female fox has a simple explanation. The concept of being red is equivalent to being non-green, non-blue, etc would not provide an explanation of what it is to be red.
The proposition that nothing is red and green all over at once is non-analytic. Though we are capable of grasping the truth of the proposition. Truths that are roughly knowable through conceptual understanding condition have been called a priori proposition (proposition knowable from the first) - known not on the basis of experience, but simply through reason as direct toward them and toward the concepts occurring in them. Non-analytic propositions are also known as synthetic propositions.
A Priori and A Posteriori
A Priori is a form of knowing something that comes from reason and not through observation or experience. For example, if you know that A=B and B=C, you therefore know that A=C.
Analytic propositions are characterized roughly in terms of how they are true - by virtue of conceptual containment, a priori propositions are characterized in terms of how they are known or can be known (through the operation of reason).
Three Types of A Priori
A Priori in the broad sense
Most clearly those propositions not themselves knowable simply through reason as directed toward them and toward the concepts occurring within them, but self-evidently following from such propositions.
Consider nothing is red and green all over at once or I’m flying to the moon. As discussed before the red and green all over is self-evident, therefore it self-evidently follows that it is self-evident that if nothing is red and green all over at once, then either that is true or I am flying to the moon.
This disjunctive (either-or) proposition is self-evident, but it isn’t self-evident based on the proposition itself, but in virtue of its self-evidently following from something that is self-evident.
Ultimately A Priori
A proposition that is neither self-evident nor self-evidently entailed by a self-evident proposition, but is provable by self-evident steps (perhaps many steps) from a self-evident proposition.
It is not a priori in the broad sense because (1) it’s not linked to the self-evident by a simple step and - more importantly - (2) it is not necessarily self-evidently linked to it.
Example: A concept entails t and t entails ti. It’s self-evident that A entails t, but it is not self-evident that A entails ti. Steps need to be taken.
Analytic, Necessary & Synthetic A Priori
Analytic propositions are characterized roughly in terms of how they are true - by virtue of the conceptual containment. Synthetic propositions are characterized in terms of how they are known or can be known (by reason).
Analytic truths, as well as synthetic truths, are a priori because analytic truths are knowable through reason. But it seems that analytic truths are knowable through a different use of reason when compared to synthetic a priori truths.
When looking at the example of nothing is red and green all over at once, there is no containment relation between being red (or green) and anything else. This obviously differs from the analytic example of all vixens being female, as vixen contains the concept of female.
When thinking of a priori, it isn’t necessarily to acquire the concepts in question - such as the concept of color or the concept of a fox. Once one has the concepts, its the grasp of the relations - not experience - which is the basis of ones knowledge of analytic and other a priori truths.
In the classical view necessary propositions are a priori. Why? Necessity is grounded in relations of concepts and these are the same in all possible situations.
Summing up the classical view, all necessary propositions are a priori and vice versa. Analytic propositions are a subclass of a priori one. Since some a priori propositions are synthetic rather than analytic. The view conceives that truth of all priori propositions are grounded in relations of concepts.
A Posteriori (Empirical)
Truth that are not self evident are not a priori. They’re known as empirical truths or a posteriori truths. The spruce is taller than the maple can only be known by experience - as opposed to reason. Saying a simple a posteriori proposition leaves open whether it is true. The proposition can be false. The spruce might not be taller than the maple. A classical view sees the a posteriori proposition open to disconfirmation through experience - which a priori propositions are not.
John Stuart Mill held the view that there is ultimately only empirical truths and that our knowledge of them is based on experience (like perception). A name for this view is empiricism about the (apparent) truth of reason. the name is accurate as the view is that a priori truths as empirical, though it does not deny that reason as a capacity distinct from perception has some role in giving justification of knowledge.
Reason may be used in extended knowledge to move geometrical theorems from axioms. We’ll explore the view that denies reason grounds justification or knowledge in the non-empirical way (classical theory). Rationalism in epistemology takes reason as far more important in grounding our knowledge than empiricism allows and rationalists assert in addition to knowledge of analytic truths, there is knowledge of synthetic a priori truths.
Empiricism in epistemology takes experience, most notably sensory experience, to be the basis of all our knowledge, except possibly that of analytic propositions - understood as including logical truths (all whales are mammals and no fish are mammals then no whales are fish).
Both rationalists and empiricists - analytic propositions are typically taken to include logical truths. Not all empiricists hold this view of the analytic proposition as a priori. A radical empiricist (like Mill) takes all knowledge as ground in experience. A radical rationalist (not Kant) would take all knowledge to be grounded in reason.
Empircism and Arithmetic Beliefs
Empiricism truths of reason are most plausible for synthetic a priori ones. Mathematic truths - particularly simple arithmetic, are often regarded as synthetic a priori. Consider the proposition 7 + 5 = 12. It’s easy to say that one just knows this, just as one knows nothing is red and green all over at once. But how does now know?
It’s possible that it comes from our experience of counting apples or fingers. As we learn this simple combining of objects, we learn arithmetic truths and use reason to formulate general rules. To be sure, one cannot imagine how 7 added to 5 could fail to equal 12.
The classical view has some critical ideas regarding this. One concerns the distinction between two different things: the genesis of one’s beliefs (what produces them) and their justification. A second point concerns whether arithmetical propositions can be tested observationally. Third, focused on the possibility of taking account of what looks like evidence against arithmetical truths, so even if one’s final epistemological standard for judging a proposition is its serving the demands of the best overall account of experience, these truths can be preserved in any adequate account.
- The genesis of a belief - what products it - is often different from what justifies it. Once someone learns arithmetic, 7 + 5 = 12, experience doesn’t appear to be what justifies.
- It is doubtful that the proposition 7 + 5 = 12 can be empirically testable. By combining objects would be ‘exemplifiable in that way. Let’s say we did combine 5 objects with 7 objects and had a total of 11 objects, we look to point 3.
- How does one deal with systematic counter evidence? It is possible that the world could alter and work differently. A classical view would just say the world no long works for this arithmetic. It is hard to see how a simple arithmetical principle could be wrong. We could add 5 apples to 7 apples to see 12, but that’s not the same as numbers. Another point about gathering counter evidence is that one would have to rely on simple arithmetic to count up a significant sample size of this evidence. The concepts of arithmetic would need to be used to invalidate arithmetic. How would you even count it?